The labour theory of value and the prices in China methodology and analysis

Everlam Elias Montibeler (Universidade Federal de Mato Grosso Do Sul) Ceacutesar Saacutenchez (Universidad

Nacional Autoacutenoma de Meacutexico Universidad Complutense de Madrid)

Resumo

Este trabalho examina a relaccedilatildeo entre valores e preccedilos para China Utilizando as matrizes insumo-produto chinesas de 2002 e a metodologia desenvolvida por Shaikh (1984) satildeo estimados os diferentes tipos de preccedilos Concluiu-se em primeiro lugar e em linha com o que foi obtido em outros estudos a existecircncia de desvios inferiores a 20 entre os diferentes tipos de preccedilos Em segundo lugar e em consonacircncia com resultados de trabalhos similares se detectou que o requerimento de trabalho comparado com os requerimentos (accedilo petroacuteleo etc) satildeo os que melhores explicam a determinaccedilatildeo de preccedilos Propotildee-se uma metodologia para ponderar o tamanho do sector na anaacutelise de regressatildeo Este teste determinou que os preccedilos satildeo proporcionais ao valor Aleacutem disso analisamos se uma maacute especificaccedilatildeo possiacutevel pode causar um vieacutes consideraacutevel no impacto de valores para os preccedilos do mercado Nosso estudo mostra que esse vieacutes eacute de pouca importacircncia Finalmente foi estimado os valores meacutedios da taxa de lucro mais-valia e composiccedilatildeo orgacircnica Eacute interessante notar que os niacuteveis das taxas de lucro na China satildeo maiores que as apresentadas em estudo similar para outros paiacuteses (Estados Unidos Greacutecia Espanha)

Abstract

This paper examines the relationship between values and prices in China From the information of input-output table from 2002 and using Shaikh`s methodology (1984) are counted the different types of prices We concluded first and in line with what was obtained in other studies a distance between the different types of prices less than 20 Secondly and briefly reviewing some criticisms of these kind of studies it appears that labor requirements confronted with the requirements of steel oil etc are the ones that explain better market prices Is proposed a way to weight the size of the sector in the regression analysis This test determines that prices proportional to the value In addition we analyze whether a possible misspecification may cause a considerable bias in the impact of values to market prices Our study shows that this bias is of little importance Finally we estimate the average values of the rate of profit capital gain rate and organic composition It is interesting to note that profit rate levels in China are higher than those shown in other studies for other countries (United States Greece Spain)

KEY WORDS China Economy Prices Deviation Labor Theory of Value

JEL B41 B50 P16

1 Introduction

In the classics there is developed the idea that prices of commodities are determined by the amount of work (Meek 1980) This idea is taking a gradual approach Since Smith we have the notions of labor commanded and on the other side the efforts that involves producing goods Ricardo is more accurate and develops the idea that the value of a commodity is determined by the direct and indirect labor incorporated in it Marx theory not only develops the idea of Ricardo but includes the total labor (direct and indirect) as social labor and work not only as the direct producer labor In addition Marx integrates his value-labor theory (LTV hereafter) his theory of the surplus value absent in the understanding of Ricardo (Carcanholo 2002)

Since the eighties the idea of calculating empirical values has emerged from the proposal of Shaikh (1984) The author uses for the US the input-output framework and Leontief data to estimate values and direct and indirect labor requirements These total requirements standardized and expressed in money are called direct prices and also calculated Sraffian production prices and regression analysis and of distance measures between the different prices finding in general values that approached quite well at current prices (market) Ochoa (1984 1989) again for US and based on Shaikh methodology calculates values direct prices marxist production prices and sraffianos production prices using input-output tables (IOT hereafter) for several years including measures of fixed capital in the estimations Chilcote (1997) updates the IOT for more recent years and OECD countries in addition to examining the so-called alternative valuesrdquo (inputs other than labor which for some authors could also be explanatory such as labor) Chilcote deepens as Ochoa in various ways of calculating the production prices gradually adding different aspects fixed capital capital turnover capacity utilization etc In this way producer prices are conceptually closer to market prices Both authors use different measures of distance and conclude that direct prices are quite close to production prices and even more to market prices Cockshott y Cotrell (1994) with IOT information from United Kingdom consider the different kinds of prices and confirm that the base values as electricity petroleum chemistry and agriculture do not explain better the current prices than the estimated by labor Guerrero (2000) following Chilcote applies the methodology for Spain finding that direct prices are closer to production ones if incorporating to the calculation fixed capital turnover etc Guerrero also makes a thorough theoretical analysis of the calculated and developed categories in this kind of studies and confirms that vertically integrates value capital compositions explain almost totally deviations between direct prices and production ones idea theorized by Marx in volume III On the other hand Tsoulfidis and Manitis (TampM hereafter) have applied this same methodology to Greece with information from IOT from 1970 Tsoulfidis along with other authors has extended this type of study to Korea Japan Canada and China In the case of China the central difference in our study with that of Mariolis and Tsoulfidis (2009 with IOT from 1997 with 38 sectors) is that incorporates data about fixed capital stock

The structure of the research is as follows After the introduction in the second section we will describe the data and methodology used in this research First sources data and adjustments made (21) and right away the mathematical formalization and details of the determination of the different prices (22) In the third section the empirical results are displayed showing the different distance indicators among direct prices production prices sraffianos ones and market ones (31) Immediately after comparing our results of China to the proximity between prices found in the US Greece and Spain We will find very similar results which reinforces the notion that current prices gravitate around the values raised by the LTV (32) The fourth section addresses some specific replicas of LTV Particularly that which suggests that human labor is not the only one to explain the current prices as other prices aroused from requirements of electricity and steel could supply the role of LTV (41) Another criticism that emerged recently in this kind of work argues that the sector size can create a false correlation in regressions between values and prices (42) In this section is shown how to create and incorporate a rank variable with vector size in regression analysis does not become statistically significant values to explain current prices On the other hand has also been raised that the regressions used may involve a bias in the estimates calculated since they omit the impact of vertically integrated compositions in the Shaikh prices model (43) It will be

exemplified empirically that this bias is minor in nature since the explanatory variables of this model imply a weak covariance In the fifth section will appear under the different prices levels of the key variables in China profit rate rate of surplus value and composition of capital Finally some conclusions will be drawn

2 Data and methodology

21 Sources and limits of statistics

IOT for China are available for the period 1987-2005 These Tables are not published for every year although it certainly has been increasing the level of disaggregation in which they are presented Choosing to work with the Table of 2002 has been for several reasons because it is a stable year in the growth of China because the data are deeply analyzed by other authors such as Holz (2006) and because it will serve to better compare the results with other papers on deviations between prices (Greece and Spain)

Most of the literature estimated the prices and productivity of Chinas economy has encountered problems getting a reliable source for estimating capital stock Beyond the statistical problems on the capital stock we also had to face the problem of information on the labor force employed by each production sector This is because the China official statistical department publishes a very little detailed methodology and unclear about how they are distributed and paid workers in the countryside and the city Much of this research was to estimate the statistics on labor and capital stock in China For data on capital stock and labor were used the outstanding papers of the econometrist Gregory C Chow (1993 2002 2006) as well as Carsten A Holzacutes (2006) who made pioneering estimates of the amounts of capital stock in China The IOT were obtained from the National Bureau of Statistics China (NBSC)

22 Methodology for calculating the different prices

Labor values are calculated according to expression one

(1)

Where A is the technical coefficients matrix (39 sectors)1 and D depreciation coefficients matrix I identity matrix and ao row vector of labor requirements2 Let`s explain how we can obtain ao Labor requirements represent direct labor required per production unit for j sector However the meaning of this concept is still more complicated as far as it includes reducing the concrete to abstract labor3 This theoretically should be done weighing in some way the preparation of the workforce (in study years experiencehellip) but due to the lack of this information for now we are forced to ldquoreduce itrdquo by wages rates Thus the abstract labor (Tai) is the product of three components the number of workers per sector (Tci) the annual working hours on (ii) and the relative salary rate (zi) more specifically this last measure is the ratio of average salaries for each sector among the lowest ones which are agricultural

(2)

For the calculation of (1) should be obtained before

Therefore

Where Tci and Tai are row vectors and T transactions matrix A technical coefficients matrix divided by the gross production column vector invested and diagonalized (pb) Similarly obtaining the depreciation of fixed capital matrix D can be done as followed

(3)

Depreciation matrix is the result of multiplying capital requirements square matrix (K) to produce one unit of i for j sector for the inverse of average life of capital goods column vector (IL) diagonalized This average was obtained following Holz estimation Holz (2006 162)

On the other side

(4) and (5)

Matrix (K) is the product of gross fixed capital formation participations row vector (f) y ratio capitalsector product row vector (ky) Following this argumentation the estimation of direct and indirect labor (values) from prices matrix and no quantities ones end in [λ

i] this is the quantity of total labor the monetary unit of sector i

Normalizing by the equation (6)

This is assuming that (7)

Where U is a unit column vector and therefore (UT pb) represents the sum of sales at sectors market prices Then direct prices are

d= λ middotα (8)

Production prices are defined following

(9)

Where p is production prices row vector B salary goods requirements for workers square matrix and r profit rate We can rename and simplify the equation (9)

where

Thus the preceding eigenvalue equation defines the relation

(10)

Following Perron-Frobenius we know the highest eigenvalue establishes the highest profit rate R (this is R=r) and the associates left eigenvector of H prices production without normalization p As the former

case we normalize using (11) and obtain price production normalized

(12)

Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary

column vector and consume one both obtained by IOT We can define

(13)Where x is clearly the proportion of consumption that is spent as salary Then we can define (14)

as row vector expressing consumption of salary goods for each sector If we also define the weight of employment in each sector as the following column vector (15) this

weighting can be used for (16) this is the consumption square matrix in salary goods The last step is as in the case of A D and K expressing it in terms of gross production unit production

(17)

Sraffian prices can be obtained (18)

This like Marxist production prices is an eigenvalue equation where

(19)

In which Similarly we must normalize but now with (20) thus

(21)

Where s is Sraffian prices row vector

3 Empirical results

It is often mistaken empirical studies as mere statistical cumulus devoid of theory However in scientific practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they are not supported by a theoretical model to contrast The central hypothesis of these studies is to verify the assertion that the values movements are determining prices movements The methodology to get the various prices involves the use of categories and concepts of the LTV that due to its complexity in some cases are necessarily simplified in order to be estimated (vrg reduction from complex to simple labor) This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very specific model like Shaikh prices model (detailed in section 42) This is the context of empirical support in this study

31 The close proximity between values and prices in China 2002

Next in table (1) we present the distance measures that are usually shown in the literature The Mean Absolute Weighted Deviation (MAWD) between direct and market prices is 1419 while the distance between direct and production ones is just 907 The proximity between production and Sraffian prices and market ones is even higher 1655 y 1813 respectively This is valid for the others distance indexes Mean Absolute Deviation (MAD) Normalized Vector Distance (NVD) and even with indexes ldquodrdquo Variation Coefficient CV y θ proposed by Steedman amp Tomkins (1998) who suggest to use these parameters (d CV θ) because they are independent of numeraire As shown these measures do not alter the previous conclusions direct prices and production are closer to market prices It is interesting to note that in China there is a greater proximity between (dp) regarding (dm) comparing with other studies such as Ochoa`s (1989) for United States and Cockshott amp Cotrell (1998) for United Kingdom4

Insert Table 1 Here

Guerrero (2000) points out that in deviations among prices there is a in which whether they are calculated by the method that uses only circulate capital such as the one that adds capital stock the results are not very different In exchange for profit estimates it is observed a significant difference Also when it comes to measuring the deviations between p m and d the initial hypothesis is that deviations between p and m are greater and this can be found for the case of China in this paper (see Table 1) as well as in Tsoulfides and Marioles (2009) In the same way the regression analysis (Table 2) between prices shows the following order of determination the direct price growth determines the movement of production ones (98) and the latter determine the market prices (95) However prices proportional to the value determine the movement of market prices very significantly (96) This is confirmed statistically by the

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

1 Introduction

In the classics there is developed the idea that prices of commodities are determined by the amount of work (Meek 1980) This idea is taking a gradual approach Since Smith we have the notions of labor commanded and on the other side the efforts that involves producing goods Ricardo is more accurate and develops the idea that the value of a commodity is determined by the direct and indirect labor incorporated in it Marx theory not only develops the idea of Ricardo but includes the total labor (direct and indirect) as social labor and work not only as the direct producer labor In addition Marx integrates his value-labor theory (LTV hereafter) his theory of the surplus value absent in the understanding of Ricardo (Carcanholo 2002)

Since the eighties the idea of calculating empirical values has emerged from the proposal of Shaikh (1984) The author uses for the US the input-output framework and Leontief data to estimate values and direct and indirect labor requirements These total requirements standardized and expressed in money are called direct prices and also calculated Sraffian production prices and regression analysis and of distance measures between the different prices finding in general values that approached quite well at current prices (market) Ochoa (1984 1989) again for US and based on Shaikh methodology calculates values direct prices marxist production prices and sraffianos production prices using input-output tables (IOT hereafter) for several years including measures of fixed capital in the estimations Chilcote (1997) updates the IOT for more recent years and OECD countries in addition to examining the so-called alternative valuesrdquo (inputs other than labor which for some authors could also be explanatory such as labor) Chilcote deepens as Ochoa in various ways of calculating the production prices gradually adding different aspects fixed capital capital turnover capacity utilization etc In this way producer prices are conceptually closer to market prices Both authors use different measures of distance and conclude that direct prices are quite close to production prices and even more to market prices Cockshott y Cotrell (1994) with IOT information from United Kingdom consider the different kinds of prices and confirm that the base values as electricity petroleum chemistry and agriculture do not explain better the current prices than the estimated by labor Guerrero (2000) following Chilcote applies the methodology for Spain finding that direct prices are closer to production ones if incorporating to the calculation fixed capital turnover etc Guerrero also makes a thorough theoretical analysis of the calculated and developed categories in this kind of studies and confirms that vertically integrates value capital compositions explain almost totally deviations between direct prices and production ones idea theorized by Marx in volume III On the other hand Tsoulfidis and Manitis (TampM hereafter) have applied this same methodology to Greece with information from IOT from 1970 Tsoulfidis along with other authors has extended this type of study to Korea Japan Canada and China In the case of China the central difference in our study with that of Mariolis and Tsoulfidis (2009 with IOT from 1997 with 38 sectors) is that incorporates data about fixed capital stock

The structure of the research is as follows After the introduction in the second section we will describe the data and methodology used in this research First sources data and adjustments made (21) and right away the mathematical formalization and details of the determination of the different prices (22) In the third section the empirical results are displayed showing the different distance indicators among direct prices production prices sraffianos ones and market ones (31) Immediately after comparing our results of China to the proximity between prices found in the US Greece and Spain We will find very similar results which reinforces the notion that current prices gravitate around the values raised by the LTV (32) The fourth section addresses some specific replicas of LTV Particularly that which suggests that human labor is not the only one to explain the current prices as other prices aroused from requirements of electricity and steel could supply the role of LTV (41) Another criticism that emerged recently in this kind of work argues that the sector size can create a false correlation in regressions between values and prices (42) In this section is shown how to create and incorporate a rank variable with vector size in regression analysis does not become statistically significant values to explain current prices On the other hand has also been raised that the regressions used may involve a bias in the estimates calculated since they omit the impact of vertically integrated compositions in the Shaikh prices model (43) It will be

exemplified empirically that this bias is minor in nature since the explanatory variables of this model imply a weak covariance In the fifth section will appear under the different prices levels of the key variables in China profit rate rate of surplus value and composition of capital Finally some conclusions will be drawn

2 Data and methodology

21 Sources and limits of statistics

IOT for China are available for the period 1987-2005 These Tables are not published for every year although it certainly has been increasing the level of disaggregation in which they are presented Choosing to work with the Table of 2002 has been for several reasons because it is a stable year in the growth of China because the data are deeply analyzed by other authors such as Holz (2006) and because it will serve to better compare the results with other papers on deviations between prices (Greece and Spain)

Most of the literature estimated the prices and productivity of Chinas economy has encountered problems getting a reliable source for estimating capital stock Beyond the statistical problems on the capital stock we also had to face the problem of information on the labor force employed by each production sector This is because the China official statistical department publishes a very little detailed methodology and unclear about how they are distributed and paid workers in the countryside and the city Much of this research was to estimate the statistics on labor and capital stock in China For data on capital stock and labor were used the outstanding papers of the econometrist Gregory C Chow (1993 2002 2006) as well as Carsten A Holzacutes (2006) who made pioneering estimates of the amounts of capital stock in China The IOT were obtained from the National Bureau of Statistics China (NBSC)

22 Methodology for calculating the different prices

Labor values are calculated according to expression one

(1)

Where A is the technical coefficients matrix (39 sectors)1 and D depreciation coefficients matrix I identity matrix and ao row vector of labor requirements2 Let`s explain how we can obtain ao Labor requirements represent direct labor required per production unit for j sector However the meaning of this concept is still more complicated as far as it includes reducing the concrete to abstract labor3 This theoretically should be done weighing in some way the preparation of the workforce (in study years experiencehellip) but due to the lack of this information for now we are forced to ldquoreduce itrdquo by wages rates Thus the abstract labor (Tai) is the product of three components the number of workers per sector (Tci) the annual working hours on (ii) and the relative salary rate (zi) more specifically this last measure is the ratio of average salaries for each sector among the lowest ones which are agricultural

(2)

For the calculation of (1) should be obtained before

Therefore

Where Tci and Tai are row vectors and T transactions matrix A technical coefficients matrix divided by the gross production column vector invested and diagonalized (pb) Similarly obtaining the depreciation of fixed capital matrix D can be done as followed

(3)

Depreciation matrix is the result of multiplying capital requirements square matrix (K) to produce one unit of i for j sector for the inverse of average life of capital goods column vector (IL) diagonalized This average was obtained following Holz estimation Holz (2006 162)

On the other side

(4) and (5)

Matrix (K) is the product of gross fixed capital formation participations row vector (f) y ratio capitalsector product row vector (ky) Following this argumentation the estimation of direct and indirect labor (values) from prices matrix and no quantities ones end in [λ

i] this is the quantity of total labor the monetary unit of sector i

Normalizing by the equation (6)

This is assuming that (7)

Where U is a unit column vector and therefore (UT pb) represents the sum of sales at sectors market prices Then direct prices are

d= λ middotα (8)

Production prices are defined following

(9)

Where p is production prices row vector B salary goods requirements for workers square matrix and r profit rate We can rename and simplify the equation (9)

where

Thus the preceding eigenvalue equation defines the relation

(10)

Following Perron-Frobenius we know the highest eigenvalue establishes the highest profit rate R (this is R=r) and the associates left eigenvector of H prices production without normalization p As the former

case we normalize using (11) and obtain price production normalized

(12)

Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary

column vector and consume one both obtained by IOT We can define

(13)Where x is clearly the proportion of consumption that is spent as salary Then we can define (14)

as row vector expressing consumption of salary goods for each sector If we also define the weight of employment in each sector as the following column vector (15) this

weighting can be used for (16) this is the consumption square matrix in salary goods The last step is as in the case of A D and K expressing it in terms of gross production unit production

(17)

Sraffian prices can be obtained (18)

This like Marxist production prices is an eigenvalue equation where

(19)

In which Similarly we must normalize but now with (20) thus

(21)

Where s is Sraffian prices row vector

3 Empirical results

It is often mistaken empirical studies as mere statistical cumulus devoid of theory However in scientific practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they are not supported by a theoretical model to contrast The central hypothesis of these studies is to verify the assertion that the values movements are determining prices movements The methodology to get the various prices involves the use of categories and concepts of the LTV that due to its complexity in some cases are necessarily simplified in order to be estimated (vrg reduction from complex to simple labor) This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very specific model like Shaikh prices model (detailed in section 42) This is the context of empirical support in this study

31 The close proximity between values and prices in China 2002

Next in table (1) we present the distance measures that are usually shown in the literature The Mean Absolute Weighted Deviation (MAWD) between direct and market prices is 1419 while the distance between direct and production ones is just 907 The proximity between production and Sraffian prices and market ones is even higher 1655 y 1813 respectively This is valid for the others distance indexes Mean Absolute Deviation (MAD) Normalized Vector Distance (NVD) and even with indexes ldquodrdquo Variation Coefficient CV y θ proposed by Steedman amp Tomkins (1998) who suggest to use these parameters (d CV θ) because they are independent of numeraire As shown these measures do not alter the previous conclusions direct prices and production are closer to market prices It is interesting to note that in China there is a greater proximity between (dp) regarding (dm) comparing with other studies such as Ochoa`s (1989) for United States and Cockshott amp Cotrell (1998) for United Kingdom4

Insert Table 1 Here

Guerrero (2000) points out that in deviations among prices there is a in which whether they are calculated by the method that uses only circulate capital such as the one that adds capital stock the results are not very different In exchange for profit estimates it is observed a significant difference Also when it comes to measuring the deviations between p m and d the initial hypothesis is that deviations between p and m are greater and this can be found for the case of China in this paper (see Table 1) as well as in Tsoulfides and Marioles (2009) In the same way the regression analysis (Table 2) between prices shows the following order of determination the direct price growth determines the movement of production ones (98) and the latter determine the market prices (95) However prices proportional to the value determine the movement of market prices very significantly (96) This is confirmed statistically by the

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

exemplified empirically that this bias is minor in nature since the explanatory variables of this model imply a weak covariance In the fifth section will appear under the different prices levels of the key variables in China profit rate rate of surplus value and composition of capital Finally some conclusions will be drawn

2 Data and methodology

21 Sources and limits of statistics

IOT for China are available for the period 1987-2005 These Tables are not published for every year although it certainly has been increasing the level of disaggregation in which they are presented Choosing to work with the Table of 2002 has been for several reasons because it is a stable year in the growth of China because the data are deeply analyzed by other authors such as Holz (2006) and because it will serve to better compare the results with other papers on deviations between prices (Greece and Spain)

Most of the literature estimated the prices and productivity of Chinas economy has encountered problems getting a reliable source for estimating capital stock Beyond the statistical problems on the capital stock we also had to face the problem of information on the labor force employed by each production sector This is because the China official statistical department publishes a very little detailed methodology and unclear about how they are distributed and paid workers in the countryside and the city Much of this research was to estimate the statistics on labor and capital stock in China For data on capital stock and labor were used the outstanding papers of the econometrist Gregory C Chow (1993 2002 2006) as well as Carsten A Holzacutes (2006) who made pioneering estimates of the amounts of capital stock in China The IOT were obtained from the National Bureau of Statistics China (NBSC)

22 Methodology for calculating the different prices

Labor values are calculated according to expression one

(1)

Where A is the technical coefficients matrix (39 sectors)1 and D depreciation coefficients matrix I identity matrix and ao row vector of labor requirements2 Let`s explain how we can obtain ao Labor requirements represent direct labor required per production unit for j sector However the meaning of this concept is still more complicated as far as it includes reducing the concrete to abstract labor3 This theoretically should be done weighing in some way the preparation of the workforce (in study years experiencehellip) but due to the lack of this information for now we are forced to ldquoreduce itrdquo by wages rates Thus the abstract labor (Tai) is the product of three components the number of workers per sector (Tci) the annual working hours on (ii) and the relative salary rate (zi) more specifically this last measure is the ratio of average salaries for each sector among the lowest ones which are agricultural

(2)

For the calculation of (1) should be obtained before

Therefore

Where Tci and Tai are row vectors and T transactions matrix A technical coefficients matrix divided by the gross production column vector invested and diagonalized (pb) Similarly obtaining the depreciation of fixed capital matrix D can be done as followed

(3)

Depreciation matrix is the result of multiplying capital requirements square matrix (K) to produce one unit of i for j sector for the inverse of average life of capital goods column vector (IL) diagonalized This average was obtained following Holz estimation Holz (2006 162)

On the other side

(4) and (5)

Matrix (K) is the product of gross fixed capital formation participations row vector (f) y ratio capitalsector product row vector (ky) Following this argumentation the estimation of direct and indirect labor (values) from prices matrix and no quantities ones end in [λ

i] this is the quantity of total labor the monetary unit of sector i

Normalizing by the equation (6)

This is assuming that (7)

Where U is a unit column vector and therefore (UT pb) represents the sum of sales at sectors market prices Then direct prices are

d= λ middotα (8)

Production prices are defined following

(9)

Where p is production prices row vector B salary goods requirements for workers square matrix and r profit rate We can rename and simplify the equation (9)

where

Thus the preceding eigenvalue equation defines the relation

(10)

Following Perron-Frobenius we know the highest eigenvalue establishes the highest profit rate R (this is R=r) and the associates left eigenvector of H prices production without normalization p As the former

case we normalize using (11) and obtain price production normalized

(12)

Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary

column vector and consume one both obtained by IOT We can define

(13)Where x is clearly the proportion of consumption that is spent as salary Then we can define (14)

as row vector expressing consumption of salary goods for each sector If we also define the weight of employment in each sector as the following column vector (15) this

weighting can be used for (16) this is the consumption square matrix in salary goods The last step is as in the case of A D and K expressing it in terms of gross production unit production

(17)

Sraffian prices can be obtained (18)

This like Marxist production prices is an eigenvalue equation where

(19)

In which Similarly we must normalize but now with (20) thus

(21)

Where s is Sraffian prices row vector

3 Empirical results

It is often mistaken empirical studies as mere statistical cumulus devoid of theory However in scientific practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they are not supported by a theoretical model to contrast The central hypothesis of these studies is to verify the assertion that the values movements are determining prices movements The methodology to get the various prices involves the use of categories and concepts of the LTV that due to its complexity in some cases are necessarily simplified in order to be estimated (vrg reduction from complex to simple labor) This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very specific model like Shaikh prices model (detailed in section 42) This is the context of empirical support in this study

31 The close proximity between values and prices in China 2002

Next in table (1) we present the distance measures that are usually shown in the literature The Mean Absolute Weighted Deviation (MAWD) between direct and market prices is 1419 while the distance between direct and production ones is just 907 The proximity between production and Sraffian prices and market ones is even higher 1655 y 1813 respectively This is valid for the others distance indexes Mean Absolute Deviation (MAD) Normalized Vector Distance (NVD) and even with indexes ldquodrdquo Variation Coefficient CV y θ proposed by Steedman amp Tomkins (1998) who suggest to use these parameters (d CV θ) because they are independent of numeraire As shown these measures do not alter the previous conclusions direct prices and production are closer to market prices It is interesting to note that in China there is a greater proximity between (dp) regarding (dm) comparing with other studies such as Ochoa`s (1989) for United States and Cockshott amp Cotrell (1998) for United Kingdom4

Insert Table 1 Here

Guerrero (2000) points out that in deviations among prices there is a in which whether they are calculated by the method that uses only circulate capital such as the one that adds capital stock the results are not very different In exchange for profit estimates it is observed a significant difference Also when it comes to measuring the deviations between p m and d the initial hypothesis is that deviations between p and m are greater and this can be found for the case of China in this paper (see Table 1) as well as in Tsoulfides and Marioles (2009) In the same way the regression analysis (Table 2) between prices shows the following order of determination the direct price growth determines the movement of production ones (98) and the latter determine the market prices (95) However prices proportional to the value determine the movement of market prices very significantly (96) This is confirmed statistically by the

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Depreciation matrix is the result of multiplying capital requirements square matrix (K) to produce one unit of i for j sector for the inverse of average life of capital goods column vector (IL) diagonalized This average was obtained following Holz estimation Holz (2006 162)

On the other side

(4) and (5)

Matrix (K) is the product of gross fixed capital formation participations row vector (f) y ratio capitalsector product row vector (ky) Following this argumentation the estimation of direct and indirect labor (values) from prices matrix and no quantities ones end in [λ

i] this is the quantity of total labor the monetary unit of sector i

Normalizing by the equation (6)

This is assuming that (7)

Where U is a unit column vector and therefore (UT pb) represents the sum of sales at sectors market prices Then direct prices are

d= λ middotα (8)

Production prices are defined following

(9)

Where p is production prices row vector B salary goods requirements for workers square matrix and r profit rate We can rename and simplify the equation (9)

where

Thus the preceding eigenvalue equation defines the relation

(10)

Following Perron-Frobenius we know the highest eigenvalue establishes the highest profit rate R (this is R=r) and the associates left eigenvector of H prices production without normalization p As the former

case we normalize using (11) and obtain price production normalized

(12)

Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary

column vector and consume one both obtained by IOT We can define

(13)Where x is clearly the proportion of consumption that is spent as salary Then we can define (14)

as row vector expressing consumption of salary goods for each sector If we also define the weight of employment in each sector as the following column vector (15) this

weighting can be used for (16) this is the consumption square matrix in salary goods The last step is as in the case of A D and K expressing it in terms of gross production unit production

(17)

Sraffian prices can be obtained (18)

This like Marxist production prices is an eigenvalue equation where

(19)

In which Similarly we must normalize but now with (20) thus

(21)

Where s is Sraffian prices row vector

3 Empirical results

It is often mistaken empirical studies as mere statistical cumulus devoid of theory However in scientific practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they are not supported by a theoretical model to contrast The central hypothesis of these studies is to verify the assertion that the values movements are determining prices movements The methodology to get the various prices involves the use of categories and concepts of the LTV that due to its complexity in some cases are necessarily simplified in order to be estimated (vrg reduction from complex to simple labor) This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very specific model like Shaikh prices model (detailed in section 42) This is the context of empirical support in this study

31 The close proximity between values and prices in China 2002

Next in table (1) we present the distance measures that are usually shown in the literature The Mean Absolute Weighted Deviation (MAWD) between direct and market prices is 1419 while the distance between direct and production ones is just 907 The proximity between production and Sraffian prices and market ones is even higher 1655 y 1813 respectively This is valid for the others distance indexes Mean Absolute Deviation (MAD) Normalized Vector Distance (NVD) and even with indexes ldquodrdquo Variation Coefficient CV y θ proposed by Steedman amp Tomkins (1998) who suggest to use these parameters (d CV θ) because they are independent of numeraire As shown these measures do not alter the previous conclusions direct prices and production are closer to market prices It is interesting to note that in China there is a greater proximity between (dp) regarding (dm) comparing with other studies such as Ochoa`s (1989) for United States and Cockshott amp Cotrell (1998) for United Kingdom4

Insert Table 1 Here

Guerrero (2000) points out that in deviations among prices there is a in which whether they are calculated by the method that uses only circulate capital such as the one that adds capital stock the results are not very different In exchange for profit estimates it is observed a significant difference Also when it comes to measuring the deviations between p m and d the initial hypothesis is that deviations between p and m are greater and this can be found for the case of China in this paper (see Table 1) as well as in Tsoulfides and Marioles (2009) In the same way the regression analysis (Table 2) between prices shows the following order of determination the direct price growth determines the movement of production ones (98) and the latter determine the market prices (95) However prices proportional to the value determine the movement of market prices very significantly (96) This is confirmed statistically by the

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

weighting can be used for (16) this is the consumption square matrix in salary goods The last step is as in the case of A D and K expressing it in terms of gross production unit production

(17)

Sraffian prices can be obtained (18)

This like Marxist production prices is an eigenvalue equation where

(19)

In which Similarly we must normalize but now with (20) thus

(21)

Where s is Sraffian prices row vector

3 Empirical results

It is often mistaken empirical studies as mere statistical cumulus devoid of theory However in scientific practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they are not supported by a theoretical model to contrast The central hypothesis of these studies is to verify the assertion that the values movements are determining prices movements The methodology to get the various prices involves the use of categories and concepts of the LTV that due to its complexity in some cases are necessarily simplified in order to be estimated (vrg reduction from complex to simple labor) This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very specific model like Shaikh prices model (detailed in section 42) This is the context of empirical support in this study

31 The close proximity between values and prices in China 2002

Next in table (1) we present the distance measures that are usually shown in the literature The Mean Absolute Weighted Deviation (MAWD) between direct and market prices is 1419 while the distance between direct and production ones is just 907 The proximity between production and Sraffian prices and market ones is even higher 1655 y 1813 respectively This is valid for the others distance indexes Mean Absolute Deviation (MAD) Normalized Vector Distance (NVD) and even with indexes ldquodrdquo Variation Coefficient CV y θ proposed by Steedman amp Tomkins (1998) who suggest to use these parameters (d CV θ) because they are independent of numeraire As shown these measures do not alter the previous conclusions direct prices and production are closer to market prices It is interesting to note that in China there is a greater proximity between (dp) regarding (dm) comparing with other studies such as Ochoa`s (1989) for United States and Cockshott amp Cotrell (1998) for United Kingdom4

Insert Table 1 Here

Guerrero (2000) points out that in deviations among prices there is a in which whether they are calculated by the method that uses only circulate capital such as the one that adds capital stock the results are not very different In exchange for profit estimates it is observed a significant difference Also when it comes to measuring the deviations between p m and d the initial hypothesis is that deviations between p and m are greater and this can be found for the case of China in this paper (see Table 1) as well as in Tsoulfides and Marioles (2009) In the same way the regression analysis (Table 2) between prices shows the following order of determination the direct price growth determines the movement of production ones (98) and the latter determine the market prices (95) However prices proportional to the value determine the movement of market prices very significantly (96) This is confirmed statistically by the

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test ndash note the greater robustness (dp) and (dm) in that order Sraffian prices explain satisfactory market prices however production prices and direct ones do better from the Marxist perspective

Insert Table 2 Here

Insert Figure 1 Here

Figure 1 shows the dispersion of the different prices expressed in neperian logarithms related to direct prices (45ordm line) Each point represents a sector of the 39 used in Chinas TIO It is slightly more dispersed the cluster of points of market prices than production prices But in general there is a good fit for different prices This means in other words the labor time direct plus indirect expressed in money is a useful variable to explain to the production prices (Marxist and Sraffian) and market prices

32 International Comparison China USA Greece and Spain

Given the empirical research in recent years can make international comparisons of the distances between these types of prices With this purpose we will use data from 1970 from Greece (TampM 2002) and USA (Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain In a general way can be seen in the Table 3 that although there is a time lag between the countries compared deviations in the indices used do not exceed 26 meaning that for Marxist prices theory the determination values rarr direct prices rarr production prices rarr market prices is a valid general scheme to explain the prices system in modern economies (Table 3)

Insert Table 3 Here

4 Some critics to the LTV

If empirical support based on a theory and a specific model requires continuously analyze the relationship between theory categories and results it is normal and necessary that contrast methods are also continually reviewed (such as usually happens in natural sciences) Regression analysis and correlation between prices have been the place of criticism of several authors Without attempting to analyze all these criticisms we will briefly discuss some of them

41 Comparing the labor values with other base values

Smith (1965 47) Ricardo (1954 22) and Marx (1990 129) argued that the relative prices of commodities are determined by the time of labor employed in production In particular for Marx the only value-creating factor is expressed as price is human labor But the view that the labor value theory determines the prices is and has been persistently attacked because drives into analyzing capitalism on the exploitation between social classes Such critics argue that prices of goods could be measured by other variables that refer to other theories of value for example wheat steel energy etc (see Guerrero 1997 61-66) In this direction Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally the only theory that could explain the prices However these approaches miss a crucial question What is the only factor of production that is present in every processes of direct and indirect production of all commodities

Insert Table 4 Here

In Table 4 the DAMP between direct prices estimated from the different productive factors is presented in ascending order of deviation so between the LTV direct prices and market prices the minimum deviation found is 1513 The maximum deviation is established when using the farm inputs vector (33345) On the other hand in correlation of the direct prices of each sector and alternative value and market prices we have that it is stronger with job requirements than with any other alternative productive factor The same findings throw the robustness of the t of the estimates of labor requirements and the joint F-test It should be noted that although estimates of alternative theories of value are statistically different

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

from zero most robust estimator is the labor one an elasticity of 0977 and greater individual significance (3355)

42 The relationship between prices and the size of each sector

Might be expected that there is a necessary partnership between sectorial prices analyzed Then direct prices and production ones would be correlated simply because small production sectors have small prices d and p and sectors with higher production would have d and p prices proportional to the size If true then the correlations obtained in regression analysis could hide a spurious component by the size of sector vgr Kliman (2002) and Diacuteaz and Osuna (2009) This is a second critique of the LTV To advance an answer we must remember that in econometrics temporal series it is customary to monitor the effect of the trend in the regression between two variables as in model (I) Then if both series grow over time it is possible to isolate this component by incorporating a trend variable (t) as in model (II) of this way it would be proves the relationship between Y and X excluding the underlying trend (as in well know keynesian regression of consumption function explained by income) Returning to this idea is similarly possible in the cross-sectional analysis (III between p and d vgr) approach to create a variable that identifies the order of sectors sizes This rank (R) orders each sector from lowest to highest according to their level of production and incorporates it shaping the cross-sectional model (IV)

Yt= 1+ 2 X2t + ut (I)

Yt= 1+ 2 X2t+ t + ursquot (II)

pi= 1+ 2 di + vi (III)

pi= 1+ 2 di+ 3 Ri +vrsquoi (IV)

Figure 2 shows the correlation between prices m p d and variable rank The dispersion between these variables in turn shows some unusual items that are modeled in the regressions of Table 5

Insert Figure 2 Here

Model 1 and 2 of Table 5 shows how the inclusion of the rank variable does not makes irrelevant the direct prices to explain market prices The models have a residue with homoskedastic and normal distribution Should be noted that all multiple models 2 4 y 6 (where they are present more than one explanatory variable) there appears not to be multicollinearity according to the determinant of the matrix of explanatory variables which does not approach zero and although are not reported of variance-inflating factor (VIF) they did not turn out to be high This way being models 1 and 2 significant according to F-test the direct price elasticity is also statistically significant individually Can be stated then for model 2 that with a 1 growth in direct prices market prices will grow by 0725 discounting the effect of the sector size A similar result is obtained with models 3 and 4 variable rank again is little significative for production prices explaining market prices It is interesting to note that the hierarchy of d on p is maintained since the elasticity in model 4 is 0625 In model 5 the explanation of p by d is not affected by rank in fact this variable is not significant Finally model 6 explains production prices by direct prices Vertically Integrated Composition and variable rank These variables are significant but the impact of proportional prices is also a unitary elasticity even weighing the impact of other variables

Insert Table 5 Here

In short it seems that by including a variable that controls the size of the sector the relationship between different prices remain significant This suggests that the critique of spurious correlation is either small or of no significant amount

43 The effect of an omitted variable in the relationship between values and prices

Another critique of LTV arises from the possibility of bias of the estimates in the regressions among prices To understand the problem let us consider the Shaikh production prices model (1984 y 1990 103-

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

112) Assuming any price (pc) they shall consist of the amount of wages wage workload (wL) plus profits (π) and material costs (M)

These material costs are in turn composed of the same items

Where the superscript (1) indicates another stage of production The other materials from other stages in turn used other wages profits and materials Thus the price of a commodity can be viewed as the sum of wages and earnings integrated

Where

Consequently above expression reduces to

Being Z the integrates quotient profit-wage w salary rate and Λ values

If we relate two prices i and j

Any kind of relative prices depends on the product of relative values and relative integrated quotients profit-wage This works for any kind of price But here Shaikh introduces a fundamental requirement in the formation of production prices He assumes that profits are equal to the product of profit rate (r) by the total advanced integrated capital (KT)

Then

That is why now

Simplifying with logarithms

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

By normalizing the production prices and direct ones and evaluating econometrically the previous model in general empirical studies contrast

(i)

However considering all the variables could be adjusted

(ii)

There arises the need to assess whether there is bias in that rsquo1 violates the LTV due to the exclusion of zi To this end we consider also estimates

(iii)

(iv)

Although the bias and consistency of an estimator should be evaluated by the expected value and the limit of the probability in an equation6 is possible to find a relationship between rsquo1 and 1 using models (i-iv) estimated by OLS Can be shown of (i-iv) and coefficient that7

Always for sample values if the coefficient of determination ( ) is null also will be coefficient δ1 and for this reason this is there is no bias however if there will be a difference established by the previous equation Coefficient as well as the estimated are of moderate size so the bias will be small After all at the sectorial level the huge direct prices in agriculture or services need not be associated with higher levels of vic (vertically integrated composition) At a theoretical level the values of different sectors should not have a relationship with their vic If the vector d is a vector proportional to the values then it should not be associated either with the vic In a log-log model the elasticity obtained in (i) and (ii) will be very close to unity however this is an empirical question For the previous models has the following variances and covariancersquos matrix of variables (Table 6)

Insert Table 6 Here

With this information we can calculate the elasticities of the models (i-iv) y and

Then the bias can easily be deduced

Therefore the important conclusion is that no matter the size of the effect of ln z in ln p if the association among ln z and ln d is weak the bias between will be small in that measure These observations on the regression analysis recognize the need to further development of improved econometric estimations However is shown that traditional empirical work based on a theoretical model such as Shaikhs (1984) is still useful to explain the relationships among them8

5 The level of fundamental variables in China

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

The calculations of the main Marxist variables rate of profit surplus value and composition of capital have specific behaviors when compared internationally with other researches However they follow the guidelines outlined by the Marx theory The rate of profit (r ) the rate of surplus value (s) and the capital composition are defined as

Where are the row vectors of the various unit prices ldquoirdquo which indicates the various prices d p s y m The other matrices and their orders have been defined above We estimated the simple organic composition (ccs) and a version of the vertically integrated composition (vic) with the aim to relate immediately rrsquo=srsquoccs and observe the levels of profitability rate based on the known s and ccs but also to compare the ccs and vic (which presents a better inter-sectorial homogeneity)

Insert Table 7 Here

The fundamental variables in direct prices and production ones are almost identical the differences are only slightly higher between market prices and direct ones as concluded above (column 5 and 6 of table 7) The rate of return (r ) in value appears to be higher than shown in current prices It should be remembered that in 2002 Chinas economy was expanding rapidly (in real terms grew by over 8 Holz 2006 113) Profitability levels are relatively high between 51 and 58 if considered only the fixed capital but past relationships are maintained by adding the variable capital where levels change between 31 and 37 With the limitations involved in comparing different IOT is interesting to note that with or without weighting fixed capital the profit rate of China is greater than that shown for other countries around the same year with the same methodology and measurement of r In Spain for example with of an IOT disaggregated to 65 sectors in 2000 the return is 1609 1729 and 1338 for market prices direct ones and production ones respectively (Saacutenchez and Nieto 2010) On the other hand in Korea with of an IOT disaggregated to 27 sectors in 2000 and for the same price returns are 116 136 and 133 (Tsoulfidis and Rieu 2006) In contrast when comparing rates of surplus value (s) whereas in China these are between 96 and 100 in Spain are between 66 and 76 and in Korea between 73 and 86 In short China has a higher profit rate based on a lower composition level (a measure of technical change) but with a higher level of exploitation This is interesting because following proposal of Emmanuel (1972) Carchede (1991) and Shaikh (1998)-for whom the law of value operates at international level - high profit rates are poles for attracting capital Reflection of the high mobility of international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher rates of profit Is not by chance that in recent years China has received a large amount of investment Investment in mainland China has already exceeded 100 billion dollars and the total investment amount (Hong Kong Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009

6 Conclusions

The results of the close proximity between prices in Chinarsquos case agree to other recent papers The weighted average absolute deviation between direct and market prices is 1513 while between direct prices and production ones is only 907 These results are not modified by changing the measure of deviation or distance The meaning and order in the vicinity is not significantly affected It seems that for one of the largest economies in the world the force of attraction that have values to different prices is quite strong in particular changes in values determine the variations in current prices by 97 The regression analysis between the different prices also shows this conclusion in line with what has been found in several countries like USA Greece Korea Spain etc

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Since Shaikh and Ochoa (1984) empirical studies some doubts have been raised about the use of correlation and regression analysis to assess the relationship between values and prices Without intending to answer to all approaches made so far this papers deals with three aspects the validity of other alternative theories of value the effect of the sector size in the regressions and the magnitude of bias involved in excluding a variable in the model Shaikh for prices As in the researchrsquos Cockshott and Cotrell (1995 1997 and 1998) assessing other direct requirements to explain market prices electricity requirements the chemical industry oil etc have no higher goodness of fit and increased robustness in their regressions In this direction the idea that the labor theory of value can be replaced by another theory of value steel empirically remains in doubt On the other hand has been argued that sector size could cause a false correlation since it would necessarily have a direct association between the different prices as those are related by the effect of physical production Analogous to the use made of the trend in the econometric analysis of time series we propose the use of a variable in ascending order of production levels this variable has been appointed rank The use of an instrument as the rank variable does not make the goodness of fit previously found significantly modified In the case of the relationship between direct and market different prices include the rank variable the estimator that measures the direct price effect on market prices does not become insignificant Even when evaluating the regression between prices of production explained by direct prices the variable rank is not significant as discussed above this study found greater closeness between these different prices Finally it could be argued that omitting a relevant variable in the model that explains the different prices of production like vertically integrated compositions there may be a bias in the estimated elasticity This is just true to the extent the direct prices are related to them Theoretically there is no relationship between the various sectorial values and vic in any case the correlation for a sample is very sparse which makes the bias to be small In the case of China this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12 A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this measured with different prices lies between 51 and 58 only fixed capital weighted But even taking into account circulating capital the range goes down between 33 and 37 In short profitability in China (2002) is well above profitability found with very similar methodologies in countries like Korea (2000) and Spain (2000) below 18 for different prices Again it appears that the LTV has the empirical explanatory power to assess the dynamism in an economy like China

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Apendix I

Deviation measures

If we deal for example with direct prices (d) and production ones (p) mean absolute deviation between them is

(1)

This measure assumes that a sector has the same weight as others so may be more useful to ponder the weight of each sector in the production (q) The weighted average absolute deviation is then defined as

(2)

The normalized vector distance is used by Ochoa (1989) and is defined as

(3)

A weighted measure (in addition to DAMP) is the Theil index of inequality although based on a price vector In d case

(4)

Gini coefficient

It is the most popular measure for inequality and therefore deviation but it should be noted here that it is just an indicative measure since the formulation is built for ungrouped data (Milanovic 1997) however is calculated as it conceptually involves variation and correlation coefficients

(5)

Vector is written in ascending order and is associated with a vector that indicates that order (η)

subsequently we obtain the correlation between them

Coefficient of variation is the quotient between of standard deviation and mean deviation

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

(6)

The distance Steedman y Tomkins (1998) is defined as

(7) showing that

Defined as a vector (see last Gini coefficient) and U unit vector the angle measured in degrees can be deduced as

(8)

Notessup1The IOT originally of 42 sectors was reduced to 39 eliminating those non-mercantile 2For simplicity reasons A is weightened as annual rotation Must be warned that even deviation between values and prices should not be notably altered levels of fundamental variables can suffer modification3A proposal of reduction to simple labor based in Brody (1970) is developed in Guerrero (2000) However such as raised by this latest study disaggregated information is needed on labor which is currently not yet available4It is interesting to note that in China there is a greater proximity between (dp) and (dm) when comparing with other studies like Ochoarsquos (1989) for US and Cockshott amp Cotrellrsquos (1998) for United Kigdom Further details in section 325The confidence interval for the estimated elasticity of 0724 is in fact [060 084]6When it comes to seeing the relationship of sample value to their population value the relations are simplified In fact the expected value ie the average value with infinite sampling of β1rsquo in (i) is E(β1rsquo)= β1+β2˙δ1 while the consistency of the same is the limit of the probability when the sample size grows indefinitely plim (β1rsquo)= β1+β2˙δ1 In both concepts the important aspect is the size of the Cov (ln z ln d) because the latter determines the value δ1 What is made with models (i-iv) is simply to find a relationship of OLS estimation of the coefficients β1 and β1rsquo It should also be noted that the standard deviation of β1 is greater and so the estimator is inefficient7The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables8For example Valle (2010) and Froumllich (2011) show the total validity of the measures correlation and distance between values and prices from the viewpoint of dimensional analysis (DA) This type analysis has unfortunately been neglected in economics still quite useful for checking the consistency of an equation an instrument used quite frequently in economic modeling and corroboration Discussion about correlation and measure distance between values and prices is undetermined and therefore the relation between these two variables was unverifiable empirically has been superseded (Diacuteaz y Osuna 2009) Valle and Froumllich show that correlation between two non-homogeneous vectors is an impossible operation Focusing just in the correlation coefficient the relationship between sectorial p and d must be value like Corr (puq duq) where prices vectors are ldquounitarianrdquo multiplied by its quantities this is Corr (p d) calculated in this paper While Corr(pu du) must be seen as an impossible operation more tan undetermined Of course when dealing with sector producing more than one good and with information in money and no in physical quantities discussion terms are a Little bit modified but not in conclusion and sense only homogeneous variables can be correlated Because of this correlation coefficient is not modified by the units measure change in unitarian prices such as is determined by (DA) This way continues being valid and precious for economic theory empirical corroboration between values and prices

Tables Pictures and Graphics

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Table 1 - Deviation measures among prices

Deviation

Measures(dm) (dp) (pm) (sm)

1 MAD 1419 1201 1654 18502 MAWD 1513 907 1655 18133 NVD 23 87 255 2294 Theil 203 076 294 3165 Gini 107 89 13 1416 CV 1925 1553 2325 24587 d 1899 1539 2279 24048 θ (degrees) 1089 882 1308 1381

Note Where d = direct prices p = production prices s = sraffian production prices y m = market prices Deviation measures are defined in the Appendix

Table 2 - Simple log-log regressions among prices

Models F R2

mi = f(di)ln mi = 064 + 097 ln di + ui

t (082) (3350)

112229 9681

pi = f(di) ln pi = -059 + 104 ln di + ui

t (-243) (5037)

253738 9856

mi = f(pi) ln mi = 099 + 091 ln pi + ui

t (254) (2734)

74749 9528

mi = f(si) ln mi = 124 + 089 ln si + ui

t (318) (2674)

71546 9508

Note Being n=39 sectors and k=2 number of estimator critical value t α2 with freedom degrees n-k=37asymp40 so t52=202 As we know in these models critical value of F 5 significance is F(k-1) (n-k) asympF140= t2

52 = 408 Thus to be larger t and F values calculated than critical values are statistically significant the explanatory variables used and the model in general

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Figure 1 - Dispersion of different prices related to direct prices

Table 3 - Deviation and correlation between values and prices China USA Greece and Spain

Direct pricesmarket prices

(dm)

Production pricesmarket prices

(pm)

Direct pricesproduction prices

(dp)

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

China

2002

USA

1970

Gr

1970

Sp

2000

DAM 141 103 231 122 165 125 143 188 1201 169 187 190

DAMP 151 111 216 110 165 131 154 189 907 178 181 190

DVN 230 127 251 132 255 153 204 206 87 183 230 205

R2 978 978 942 978 949 986 939 958 943 971 971 954

Note Data for USA are from Ochoarsquos (1989) with 71 sectors data for Greece are from TampMrsquos (2002) with 35 sectors and to Spain from Saacutenchez and Nietorsquo`s (2010) with 65 sectors

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Table 4 - Deviation and regression of the labor value and base values on market pricesIndependent

Variable

MAWD (dm)

Models F R2

Labor 1513

ln mi = 0280 + 0977 (ln di ) + ui

t (0825) (33500) 112229 9681

Electricity 3546

ln mi = 227 + 0706 (ln di ) + ui

t (2548) (8916) 7950 6883

Chemistry 3714

ln mi = 140 + 0806 (ln di ) + ui

t (1762) (10304) 106171 7468

Oil 6113

ln mi = 571 + 0256 (ln di ) + ui

t (4666) (3073) 9446 2079

Farm 33345

ln mi = 725 + 0067 (ln di ) + ui

t (7052) (3325) 11062 2351

Note For alternative bases values the first estimator is 109 RMB

Figure 2 - Dispersions between prices and la variable rank

24

25

26

27

28

291

23

45

67

89

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln m

24

25

26

27

28

29

30

1

2

345

67

8910

11

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

ln p

1

2

345

67

89

1011

12

13

14

15

1617

1819

2021

22

2324

25

26

27

28

29

303132

3334

35

363738

39

0

10

20

30

40

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln d

Rank

24 25 26 27 28 29

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln m

24 25 26 27 28 29 30

1

23

45

6

7

8

9

1011

12

13

14

15

1617

18

19

2021

22

2324

25

26

27

28

29

3031

32

3334

35

36

37

38

39

ln p

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Table 5 - Different price regressions including the variable rank and VIC

(below p values)

Mod1 Mod2 Mod3 Mod4 Mod5 Mod6

Dependent variable ln(m) ln(m) ln(m) ln(m) ln(p) ln(p)

Independent variable

Constant 0646 6849 1777 9408 0266 -213

0414 000005 00304 00001 08766 08154

ln (d) 0977 0724 0982 101

lt00001 lt00001 lt00001 lt00001

ln (p) 0936 0625

lt00001 lt00001

ln (vicr) 102

lt00001gt

Rank 0027 0033 0006 -0001

000004 00001 03196 00048

Dummy 0447 0808 0579 -003

lt00001 00007 lt00001 lt00001

R 2 0968 9884 09658 9802 09860 0999

Adjusted R2 0967 9874 09639 9785 09852 0999

F (k-1 n-k) F(137) F(335) F(236) F(335) F(236) F(434)

F-statistic 11222 10002 5087 4966 12698 217624

lt00001 lt00001 lt00001 lt00001 lt00001

Homoskedastic

White 08807 06862 07315 06475 01345 04469

Breusch-Pagan 06891 09032 07184 02750 04281 03253

Koenker 06891 09181 07837 02524 02902 02366

Normality

Chi-squared 018929 025521 0165189 07598 04756 09670

Multicollinearity

Determinant XrsquoX - 23385944 - 17818021 8617209306952755900672

Note The variable dummy controls outliers for model 2 in sectors 3 11 y 28 for model 3 just in sector 3 for model 4 3 and 11 and for model 6 the sector 11 All econometric estimates have been developed in Gretl free software designed and supported by Allin Cotrell

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Table 6 - Variances and covariances matrix of the variables p d and z (in logarithms)

Ln p Ln d Ln z

Ln p 1381137 1298231 0078864

Ln d 1298231 1238096 0056776

Ln z 0078864 0056776 0021520

Table 7 - Marxist Fundamental Variables

Market prices

(1)

Direct prices

(2)

Production prices

(3)

Sraffa production

prices

(4)

(2)(3) (2)(1)

Profit rate (rrsquo) 5124 5618 5602 5845 1002 1096

Surplus rate (srsquo) 10041 9682 9621 10224 1006 0964

Simple organic composition (ccs)

19593 17231 17173 174921005

0882

Vertically integrated composition (vic)

22609 19884 19817 20185 1003 0876

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Bibliography

Carcanholo R A 2002 Ricardo e o fracasso de uma teoria do valor Curitiba In VII Encontro Nacional de Economia Poliacutetica Anais do VII Encontro Nacional de Economia Poliacutetica

Chilcote E 1997 Interindustry structure relative prices and productivity an input-output study of the US and OECD countries theses doctoral no posted New York New School for Social Research

Cockshott P Cottrell A and Michaelson G 1995 ldquoTesting Marx some new results form UK datardquo Capital and Class vol 55 Spring pp 103-29

Cockshott P and Cottrell A 1997 ldquoLabour time versus alternative value bases a research noterdquo Cambridge Journal of Economics vol 21 pp 545-49

Cockshott P and Cottrell A 1998 ldquoDoes Marx need to transformrdquo in R Bellafiore (Ed) Marxian economics A Reapparasal vol 2 Basingstoke McMIllan st Martinacutes Press

Chow GC 1993 Capital Formation and Economic Growth in China Quarterly Journal of Economics vol 108 pp 809-42

_________ 2006 New Capital Estimates for China Comments China Economic Review 17 pp 186-92

Chow GC and Kui-Wai Li 2002 ldquoChinarsquos Economic Growth 1952-2010rdquo Economic Development and Cultural Change vol 51 247-56

Diacuteaz-Calleja E Osuna R 2009 ldquoFrom correlation to dispertion geometry of the prices- value deviationrdquo Empirical Economics vol 36(2) pp 427-440

Froumllich N 2010 ldquoDimensional analysis of price-value deviationrdquo Chemnitz University of Technology httpwwwboecklerdepdfv_2010_10_29_froehlichpdf

Guerrero D 2000 Teoriacutea del valor y anaacutelisis insumo-producto manuscrito 158 pp

Hogdson G Capitalism Value and Explotation Oxford Martin Robertson 1982

Holz CA 2006 ldquoMeasuring Chinese Productivity Growth 1952-2005rdquo disponible en SSRN httpssrncomabstract=928568

Kliman A 2002 ldquoThe law of value and laws of statistics sectoral values and prices in the US economy 1977-1997rdquo Cambridge Journal of Economics vol 26 pp 299-311

Mariolis T y Tsoulfidis L 2009 ldquoDecomposing the Changes in Production Prices into lsquoCapital-Intensityrsquo and lsquoPricersquo Effects Theory and Evidence from the Chinese Economyrdquo Contributions to Political Economy

Marx K 2002 El Capital Libros I II y III Madrid S XXI

Meek Ronald 1980 Smith Marx y despueacutes Diez ensayos sobre el desarrollo del pensamiento econoacutemico Madrid Ed Siglo XXI

Milanovic B ldquoA simple way to calculate the Gini coefficient and some implicationsrdquo Economics Letters vol 56 issue 1 1997 pp 45-49

Ochoa E 1984 ldquoLabor Values and Prices of Production An Interindustry Study of the U S Economy 1947-1972rdquo Ph D dissertation Department of Economics New School for Social Research New York

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Ochoa E 1989 ldquoValues prices and wage-profit curves in the US economyrdquo Cambridge Journal of Economics vol 13 pp 413-429

Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981

Shaikh A 1984 ldquoThe Transformation from Marx to Sraffa prelude to a critique of the neo-ricardiansrdquo in E Mandel and A Freeman (eds) Ricardo Marx Sraffa The Langston memorial volume London Verso pp 43-84

Shaikh A 1990 Valor acumulacioacuten y crisis Bogotaacute Tercer Mundo Editores

Tsoulfidis L 2008 ldquoPrice-Value Deviations Further Evidence from Input-Output Data of Japanrdquo International Review of Applied Economics

Tsoulfidis L and Paitaridis D 2008 ldquoOn the Labor Theory Value Statistical Artefacts or Regularitiesrdquo Research in Political Economy

Tsoulfidis L and Rieu D 2006 ldquoLabor Values Prices of Production and Wage-Profit Rate Frontiers of the Korean Economyrdquo Seoul Journal of Economics

Tsoulfidis L Maniatis T 2002 ldquoValues prices of production and market prices some more evidence form the Greek economyrdquo Cambridge Journal of Economics vol 26 pp 359-369

Steedman I and Tomkins J 1998 ldquoOn measuring the deviation of prices from valuesrdquo Cambridge Journal of Economics vol 22 no 3 pp 379-85

Valle A1994 ldquoCorrespondence between labour values and prices a new approachrdquo Review of Radical Political Economics vol 26 no 2 pp 57-66

Valle A 1991 Valor y precio una forma de regulacioacuten del trabajo social Facultad de Economiacutea UNAM Meacutexico

Valle A 2010 ldquoDimensional analysis of price-value correspondence a spurious case of spurious correlationrdquo Investigacioacuten Econoacutemica UNAM Meacutexico

• 2 Data and methodology
• 21 Sources and limits of statistics
• Where p is marxist production prices row vector We should highlight the two different ways of obtaining B following Chilcote (1997) and Guerrero (2000) or TampM (2002) If S and C are defined as salary column vector and consume one both obtained by IOT We can define (13)
• (17)
• Sraffian prices can be obtained (18)
• This like Marxist production prices is an eigenvalue equation where
• 31 The close proximity between values and prices in China 2002
• 32 International Comparison China USA Greece and Spain
• Figure 1 - Dispersion of different prices related to direct prices
• Roemer J Analytical Foundations of Marxian Economic Theory Cambridge University Press 1981