978-1-4244-2503-7/08/$20.00 © 2008 IEEE

Proceedings of the IEEE

International Conference on Automation and Logistics Qingdao, China September 2008

Thermal Power Enterprise's Total Factor Productivity Model and Its Application

HUANG Renhui Li Wei ZHANG Lizi School of Electrical and Electronic

EngineeringDepartment of Economy and Management School of Electrical and Electronic

EngineeringNorth China Electric Power University North China Electric Power University North China Electric Power University

Changping, Beijing 102206, China Baoding city, Hebei Province 071003,China Changping, Beijing 102206, Chinancepuhuangrenhui@163.com hd11111@126.com lizizhang@sina.com

Abstract- Total factor productivity theory has got widespread applications in macroeconomic research field, but few in microscopic enterprise economic activities, because it’s difficult to establish the total factor productivity model for microscopic enterprise and it’s complicated to calculate. From thermal power enterprise’s aspect, this paper, based on productivity theory and total factor productivity theory, analyzes interior and exterior influencing factors of our county’s thermal power enterprises and establishes the total factor productivity model fit for those enterprises. The established model is of simple calculation course and clarified result. Thermal power enterprises can easily calculate the total factor productivity by using this model, so as to pointedly improve the resource allocation productivity as well as offer feasible proposals to advance the comprehensive productivity of business and management.

Index Terms- Thermal power enterprise; Total factor productivity (TFP); Energy-saving generation dispatching; Production function; Technical progress

. INTRODUCTION

In order to create continuous growth of an economic system, it’s necessary to make great effort to realize the progressive increase of factor return. The total factor productivity (TFP) is the important index which assesses factor return on the whole. In our country or abroad, there are widespread and deep researches on total factor productivity. Documents [1-11] study the problem between total factor productivity and economic growth from macroscopic view; documents [12-15] research into the total factor productivity of electricity industry, which give some instruction to this industry. At present, there are few of documents on the total factor productivity of micro-enterprise especially thermal power enterprise. There are three reasons mainly: first, total factor productivity theory has developed from the research between economic growth and technical progress gradually; second, most of enterprises have not recognized the significance of total factor productivity; third, it’s difficult to establish the total factor productivity model for microscopic enterprise and it’s complicated to calculate.

For a system, it has to enable obtaining technical progress at the lowest cost in order to realize sustainable economic growth[9] [16]. On one hand, natural resources are scarce and being exhausted constantly, so the cost to acquire resource

becomes higher and higher. On the contrary, it’s necessary to obtain resource and technique at the lowest cost so as to achieve economic development. Presently, thermal power enterprises of our country are in the dilemma above. In our country’s electricity industry reform, the first step is “separation of grid and generation”, which forces the generation side into market competition and makes our thermal power enterprises’ market environment change greatly. Under the new situation of energy-saving and emission reduction, for gaining larger living and development space as well as realizing the real increase, thermal power enterprises should properly recognize the inside and outside environment they are situated, research into their production functions and growth factors seriously, focus on pursuing the increase of TFP, endeavor to improve the usage efficiency of unit input factor and organize production at the probable highest productivity[17].This is strongly of actual significance. On the basis of productivity theory as well as TFP theory and model, this paper utilizes theory on factors of production to analyze the interior and exterior influencing factors of thermal power enterprise and establishes the TFP model fit for it, which is applied to one thermal power enterprise’s economic activity analysis then.

. PRESENT STATE OF THERMAL POWER ENTERPRISES

A. Influence of Coal Market’s Change on Thermal Power Enterprises

In recent years, coal supply has been tense continuously; the price of coal rises suddenly and sharply. Meanwhile, generation enterprises also have entered into the high-speed development stage, the demand of electricity-coal has been raised because of putting new units into production, which further aggravates the tense degree of coal supply. The double-effect of electricity-coal’s inferior quality and ascending price has brought about obvious influence on thermal power enterprises’ production and business. Since from 2002, the supply quality of electricity-coal has taken on a descending trend overall, such as heat-value falls down while ash goes up, which causes the dramatic deterioration of those enterprises’ productive and technical indicator as well as business indicator. Coal is the most essential fuel for coal-fired power enterprise, the cost of which accounts for 60%-70% of

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the total cost generally. At present, the double-effect above makes coal-fired power enterprises’ business performance drop greatly, even causes the deficit of some old enterprises.

B. Influence of Energy-saving Generation Dispatching on Thermal Power Enterprises

Energy-saving and emission reduction is the tendency, in which thermal power enterprises should carry out foremost. Energy-saving Generation Dispatching is one of the major means for power industry and is extremely beneficial for the enterprises which generate electricity by renewable energy such as wind energy, solar energy, ocean energy, water energy, biomass energy and geothermal energy. It’s also extremely beneficial for the garbage power enterprises which satisfy the demand of environmental protection, as well as nuclear power enterprises. As to the generation enterprises of “fixing power based on heat” coal-fired combined heat and power units as well as those of resource comprehensive utilization generation units, it’s advantageous on the whole. But it’s very disadvantageous for the units of low installment capacity, high energy-consumption and large quantity discharge. Therefore, thermal power enterprises should regard the generation Energy-saving Generation Dispatching as an opportunity to adjust industrial structure and change development pattern based on analyzing the influence of energy-saving generation dispatching seriously. The real development can be realized by energetically innovating and improving backward equipment (including energy-saving reform, emission reduction reform and heating reform), cutting down pollution and energy-consumption to make its consumption lower than other same level units’ in province (or district), enhancing the TFP.

. TOTAL FACTOR PRODUCTIVITY THEORY AND MODEL OFTHERMAL POWER ENTERPRISES

A. Theoretic Basis of TFP1) Productivity TheoryProductivity is “the efficiency of production activity within

some time” . Therefore, in the market economic environment, productivity is defined as the efficiency and benefit of social production and reproduction activities within some time. Productivity is not an absolute total amount but a relative ratio , which can be indicated that productivity=input/output.

2) Analysis on Modern Enterprise’s Factors of Production Among traditional production factor theories, labor and

capital are the most important production factors. So in traditional production function models, production input factor refers to labor and capital, while other factors like technique are supposed invariable or processed as the margin of economic growth. Along with the development of society and economy, technique has become the third important source of modern knowledge economy growth besides labor and capital. Consequently, there exists dramatic limitation to apply traditional production functions to investigate the resource optimization collocation of modern enterprises. This paper makes a new analysis on production factor:

Production factor can be divided into labor, capital, technique and other production factors;

Just like labor and capital, technique and other production factors are independent that firms should pay to obtain from element market; Since technique and other factors are independent, the total cost of production should include the cost of technique and other factors, too.

3) Quantitative Measure of Technical ProgressSamuelson, the winner of Nobel economics prize, defined

that “production function is one kind of technological relation, which is used to illustrate the possible maximum yield produced by combining every kind of input (that is production factor) of concrete quantity”. It’s the theoretic basis of technical progress quantitative measure.

Select the form of production function ( ) ( )[ ]tLtKFQ ,= ,within the interval ( )21, tt , the technical progress rate can be defined:

( ) ( ) ( )[ ] ( ) ( )[ ]( ) ( )[ ]111

11122221 ,,

,,,,,

ttLtKFttLtKFttLtKF

tta−

= 1

If 12 tt → , t is called year-technical progress rate when its unit is year, which is recorded as ( )ta , then

( ) ( ) ( )FdttFta ⋅∂∂= 2In fact, being as the result of production process, output

quantity is also influenced by many technological and non-technological factors besides input factors (labor and capital). So many scholars call ( )ta TFP or comprehensive factor productivity. If the effect of non-technological factors can be excluded from the estimation of production function, or that effect can be fixed relatively, then technical factors will play an important part in the course of advancing labor productivity and promoting economic increase, which are the principal elements to restrict the variation of ( )ta . At this moment, the TFP is just equal to the technical progress rate, which is also the reason why ( )ta is called technical progress rate[17].

B. Establishment of Total Factor Productivity’s Mathematic Model

TFP is a synthetic indicator that reflects the effective utilization degree of input elements of one economic system (country, region, industry or enterprise). It’s a relative value

whose equation is inputsgross

outputstotal . From 3) above, when the

price of input element and the scale benefit are fixed, the growth rate of TFP, namely the growth rate of technical progress, amounts to the partial derivative of output function versus time, or the negative value of the partial derivative of cost function versus time. The mathematic model of TFP can be established according to its meaning.

In case the production function presents neutral technical change, being as an independent divisor, the technical progress can be separated. So the production function can be written as:

( ) ( )( ) ( ) ( )( )tXftAttXFtQ ⋅== , 3Then:

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( )( )

( )( ) ( ) ( )

( )−=n

n

nn tx

txtS

tQtQ

tAtA

1 4

Where ( )tSn refers to the proportion of n input factors’ value in the total input factors’ value.

The output growth rate ( )( )tQtQ

minus the contribution made

for it by total input factors leaves just the technical growth

rate ( )( )tAtA , namely the growth rate of TFP. If ( )

( ) 0=tAtA that

indicates enterprise has no technological progress, and then the TFP which measures enterprise’s economic benefit has no variation, that is 0=ΔTFP .

Make integral calculus to (4) within ( )T,0 , then ( )( )

( ) ( )( ) ( )

( )

=T n

n

nn dt

txtx

tS

QTQA

TA

01

exp

00

5

In [ ]T,0 , the Dirichlet exponent of the total input factors is ( ) ( )0XTX , then

( )( ) ( ) ( )

( )= T n

n

nn dt

txtxtS

XTX

01

exp0

6

Supposing that iC is the proportion of i kinds of output value in the total output value, the Dirichlet exponent of the total output can be written as:

( )( ) ( ) ( )

( )= T i

i

ii dt

tqtqtC

QTQ

01

exp0

7

Then the Dirichlet exponent of TFP can be defined as the ratio of (7) versus (6), that is

( ) ( )( )

( ) ( )( )

==T n

n

nn

T n

n

nn

TT

dttxtxtS

dttxtxtC

DD

TFPTFP

01

01

00 exp

exp8

C. The Total Factor Productivity Mathematic Model of Thermal Power Enterprise

The economic data used in actual application do not come out in the form of time-continuous function ( )tX or ( )tYbut in the discrete form. Therefore, transform the Dirichlet exponent model of (8) to discrete form in actual application, there will be:

( )0,,1

0 lnlnlnln iTii

iT qqCQQ −=− 9

( )0,,1

0 lnlnlnln nTnn

nT xxSXX −=− 10

Where

0lnln QQT − The growth rate of enterprise’s total output within the time-interval T

0lnln XXT − The growth rate of enterprise’s gross input within the time -interval T

0,, lnln iTi qq −The growth rate of enterprise’s No. i output quantity within the time-interval T

0,, lnln nTn xx −The growth rate of enterprise’s No. n input factor within the time-interval T

iC The proportion of No. i output value in the total output value

nS The proportion of No. n factor value in the gross input value

The subscript T and 0 can not only stand for two different times but also represent two different compared enterprises. If

iC and nS are the average value of time-interval between beginning and end, the TFP’s econometric model of Christensen and Jorgensen can be obtained according to the derivation course above, as follows:

+−

+=−

01

0

01

00 ln

2ln

2lnln

n

nTn nnT

i

iTi iiTT X

XSSQQCCTFPTFP 11

In many researches and applications, Christensen and Cavese found that the transitivity of this model can’t be guaranteed, which was caused by the weight. Through a lot of tests and calculation, economists like Christensen, Cavese and Dirichlet had put forward an econometric model that is of both transitivity and individuality. The expression is following:

+−

+=−

i

ii ii

i

iTi iiTT q

qCCq

qCCTFPTFP ~ln

2~ln2

lnln 0

1

0

10

++

+−

n

nn nn

n

nTn nnTxxSS

xxSS

~ln2~ln

20

1

0

112

Where

iCThe arithmetic average value of enterprise’s No. i output-income proportion

nSThe arithmetic average value of proportions of enterprise’s No. i input factor

iq~ The geometric average value of enterprise’s No. i output

nx~ The geometric average value of enterprise’s No. i input factor

Equation (12) is a general econometric model applicable to each independent economic system, which we transform into the model suited to thermal power enterprise. As to thermal power enterprise, there is only one kind of output namely the power generation Q , while input factors include the labor L ,the capital K and the fuel G , therefore:

+++−−=−KKkk

LLll

QQ

QQTFPTFP TTTTT

T ~ln2~ln

2~ln~lnlnln 00

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++++++KKkk

LLll

GGgg TT ~ln

2~ln2~ln

20000

++

G

Ggg~ln

200 13

Where Q (or

power sale quantity) l The proportion of labor cost in the total cost

L Labor input (the number of staff)

k The proportion of capital cost in the total cost

K Capital input g The proportion of fuel cost in the total cost

G Fuel input The arithmetic average value of this variable

Different time-intervals or different enterprises

The geometric average value of this variable

. APPLICATION

Taking a thermal power plant in North China for example and utilizing the TFP theory and model as analytic tools, an approximate analysis on this plant’s business performance from 1995 to 2005 is made.

A. Model Selection and Estimation This paper adopts the production function form which was

proposed by CHEN Si (2005) in document [20]. ( )

ttt

tlklkTTTiti

it

vu

xxttxY

+=

+++++=

ε

εβββββ lnlnlnln 20 14

Where ,2,1=t means the time, Y is the output, x is the input, v is the random factor that affects production activities, u (non-negative) means the efficiency of productivity or management which is generally supposed as half-normal random variable or exponential random variable of independence and the same distribution. u is independent to v .

The comprehensive efficiency indicator of one economic system is restricted by technical efficiency indicators of every subsystem. Therefore, TFP indicator of thermal power enterprise is the function for subsystems’ technical efficiency indicators. That is,

iN

iiCTFP αβ+=

=1 15

Where C is an invariable, β is the regression coefficient, α is the technical efficiency indicator [12] [17].

B. Result and Analysis Convert the original data into dimensionless data and carry

the dimensionless date in Eviews4.0. Then use Eviews4.0 to calculate such dimensionless data. The results are as follows:

The estimated production function is: 2

)97.0()27.0()34.3()42.0()45.0()31.0(*0014.0*006.0ln250.1ln129.0ln120.0948.2ln ttGLKQ

−−−−++−+−=

(16) That is

11,,2,1,2*0014.0*006.025.1129.012.0948.2 == −−− teGLKeQ tt

(17) TABLE 1

DATA PROCESSING RESULTS

R-squared Mean dependent var

S.D. dependent var

Akaike info criterion

Schwarz criterion

Durbin-Watson stat TABLE 2

PRODUCTIVITY RESULTS

Year Labour

Productivity %

Capital Productivity

%

Fuel Productivity

%

Total Factor Productivity

%

Fig. 1 Single-factor Productivity and Total Factor Productivity As shown in Table 1, R-squared and Adjusted R-squared are

close to 1, which manifests that this model is of good fitting effect. The T-Statistics of each parameter’s estimated value is also very significant, most of Prob. is close to zero and approximates being significant at 1% level. So the model can be used to analyze business state of thermal power enterprise.

It can be seen from Table 2 and Figure1 that, among

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single-factor productivity, the labor productivity has shown a declining trend between 1995 and 1999. A turning point appears in 2000. The labor productivity begins to ascend, which is kept up to 2004, but it declines slightly in 2005.

The fluctuation range of capital productivity is large. It has been declining from 1995 to 1999 and the annual declination rate is 14.5%. The capital productivity goes up slowly in 2000. Between 2000 and 2005, it takes on a growth trend on the whole, but there are slight fluctuations during that period.

The fluctuation of fuel productivity is little. However, since 2000, the fuel productivity has begun to show a slow downward trend.

Then analyze the TFP. As shown in Figure 1 and Table 2, the TFP of thermal power enterprise increases from 1995 to 1996. The reduction of input index is less than that of output index between 1996 and 2000. The TFP has always been declining, which presents a negative growth. The trend of technical progress is as same as total factor productivity’s. At the time of putting into production, the thermal power enterprise had the units that were more advanced than other units in our country, the technical parameters were relatively ideal, too. After a period of running-in, the skill of staff enhances gradually, also the production efficiency and benefit increases gradually. Meanwhile, the TFP raises and reaches a peak in 1997. Hereafter, those indicators start to decline along with the wear and aging of equipment.

. CONCLUSION

Based on the theory of total factor productivity, this paper, taking characteristics of thermal power enterprise into consideration, establishes the mathematic model of TFP fit for thermal power enterprise. Through this model, the entire process analysis of some thermal power enterprise’s TFP is made, the result of which is entirely consistent with the enterprise’s actual situation. The model established is not only of simple calculation course and clarified result, but also of distinct structure characteristic. It can be well applied to the economic activity analysis of thermal power enterprises, so as to provide quantitative basis for management decision and offer market-analysis means to those enterprises. Only considering four inputs and single output, the TFP model of enterprise is relatively easy to be established. However, there are more inputs and more outputs for most enterprises (such as coal-fired combined heat and power enterprise), the TFP model and theory of which need further research.

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