the world income distribution - stanford …klenow/acemoglu and ventura.pdfthe world income...

THE WORLD INCOME DISTRIBUTION

DARON ACEMOGLU AND JAUME VENTURA

We show that even in the absence of diminishing returns in production andtechnological spillovers international trade leads to a stable world income distri-bution This is because specialization and trade introduce de facto diminishingreturns countries that accumulate capital faster than average experience declin-ing export prices depressing the rate of return to capital and discouraging furtheraccumulation Because of constant returns to capital accumulation from a globalperspective the world growth rate is determined by policies savings and tech-nologies as in endogenous growth models Because of diminishing returns tocapital accumulation at the country level the cross-sectional behavior of the worldeconomy is similar to that of existing exogenous growth models cross-countryvariation in economic policies savings and technology translate into cross-country variation in incomes The dispersion of the world income distribution isdetermined by the forces that shape the strength of the terms-of-trade effectsmdashthe degree of openness to international trade and the extent of specialization

I INTRODUCTION

Figure I plots income per worker relative to the world aver-age in 1990 against its 1960 value and draws the 45 degree linefor comparison This picture of the world income distributionraises two questions rst why are there such large differences inincome across countries For example some countries such asthe United States or Canada are more than 30 times as rich asothers such as Mali or Uganda Second why has the world incomedistribution been relatively stable since 1960 A number ofgrowth miracles and disasters notwithstanding the dispersion ofincome has not changed much over this period most observationsare around the 45 degree line and the standard deviation of incomeis similar in 1990 to what it was in 1960 (106 versus 096)1

We thank Pol Antras and Ruben Segura-Cayuela for excellent researchassistance We also thank three anonymous referees Alberto Alesina and semi-nar participants at the University of California at Berkeley Brown and DukeUniversities the Federal Reserve Bank of Minneapolis the Federal Reserve Bankof New York the Massachusetts Institute of Technology Stanford University andthe University of California Los Angeles for comments and suggestions

1 Among subsets of countries with similar institutional structures there issubstantial narrowing of differentials For example the standard deviation of logincome per worker among OECD economies was 053 in 1960 and fell to 030 in1990 In contrast there appears to be signicant widening of income differentialsduring the 100 years before 1960 See for example Durlauf [1995] and Quah[1997] on changes in the postwar world income distribution and Parente andPrescott [1994] and Jones [1997] on its relative stability Note also that therelative stability of the world income distribution is a postwar phenomenon see

copy 2002 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnologyThe Quarterly Journal of Economics May 2002

659

Existing frameworks for analyzing these questions arebuilt on two assumptions (1) ldquoshared technologyrdquo or techno-logical spillovers all countries share advances in world tech-nology albeit in certain cases with some delay (2) diminish-ing returns in production the rate of return to capital or otheraccumulable factors declines as they become more abundantThe most popular model incorporating these two assump-tions is the neoclassical (Solow-Ramsey) growth model Allcountries have access to a common technology which improvesexogenously Diminishing returns to capital in production pullall countries toward the growth rate of the world technologyDifferences in economic policies saving rates and technologydo not lead to differences in long-run growth rates but in levelsof capital per worker and income The strength of diminishingreturns determines how a given set of differences in these

Pritchett [1997] for the widening of the world income distribution since 1870 andAcemoglu Johnson and Robinson [2001b] for the reversal in relative economicrankings over the past 500 years and widening over the past 200 years

FIGURE ILog of Income per Worker in 1990 and 1960 Relative to World Average from

the Summers and Heston [1991] Data SetThe thick line is the 45 degree line

660 QUARTERLY JOURNAL OF ECONOMICS

country characteristics translate into differences in capital andincome per worker2

This paper offers an alternative framework for analyzing theworld income distribution We show that even in the absence ofdiminishing returns in production and technological spilloversinternational trademdash based on specializationmdashleads to a stableworld income distribution Countries that accumulate capitalfaster than average experience declining export prices reducingthe value of the marginal product of capital and discouragingfurther accumulation at home They also increase the demand forproducts and the value of the marginal product of capital in therest of the world encouraging accumulation there These terms-of-trade effects introduce de facto diminishing returns at thecountry level and ensure the stability of the world income distri-bution Consequently cross-country differences in economic poli-cies saving rates and technology lead to differences in relativeincomes not in long-run growth rates How dispersed the worldincome distribution will be for a given set of country character-istics is determined by the forces that shape the strength of theterms-of-trade effects namely the degree of openness to interna-tional trade and the extent of specialization

Some degree of specialization in production is essential forthe terms-of-trade effects we emphasize here if domestic andforeign products were perfect substitutes countries would befacing at export demands and capital accumulation would notaffect their terms of trade That countries specialize in differentsets of products appears plausible Moreover this assumption hasproved to be crucial in explaining some robust features of inter-national trade such as the substantial two-way trade in productsof similar factor intensities and the success of the gravity equa-tion in accounting for bilateral trade ows (see for exampleHelpman [1987] or Hummels and Levihnson [1995])

We model the world as a collection of economies a la Rebelo[1991] with growth resulting from accumulation of capital In theabsence of international trade countries grow at different rates

2 A different but related story recognizes technology differences across coun-tries Despite these differences backward countries share some of the techno-logical improvements of advanced economies through spillovers These spilloversensure the stability of the world income distribution and also determine howdifferences in country characteristics translate into income differences See forexample Grossman and Helpman [1991] Parente and Prescott [1994] Coe andHelpman [1995] Howitt [2000] Eaton and Kortum [1999] Barro and Sala-i-Martin [1997] and Acemoglu and Zilibotti [2001]

661THE WORLD INCOME DISTRIBUTION

determined by their economic policies saving rates and technol-ogy With international trade and specialization the world as awhole still behaves as the standard AK economy but now allcountries share the same long-run growth rate

To understand why countries tend to grow at the same rateand what factors determine their relative incomes consider thefamiliar steady-state condition equating the rate of return tosavings to the effective rate of time preference In our model thiscondition takes the form

rental rate (domestic capitalworld capital technology)

price of investment goods

5 effective rate of time preference

The rental rate depends negatively on the relative capital of thecountry because of terms-of-trade effects countries that producemore face lower export prices and a lower value of the marginalproduct of capital This condition also shows how different charac-teristics affect relative incomes In the steady state countries withlower rates of time preference and lower price of investment goods(those with fewer distortions affecting investment) will have lowerrental rates hence higher relative capital and income Countrieswith better technologies will be richer in turn because they havehigher rental rates for a given level of relative capital and income

Despite rich interactions across countries cross-country incomedifferences take a simple form analogous to the basic Solow-Ramseymodel We also show that cross-country income differences and therate of conditional convergence depend on the strength of the terms-of-trade effects not on the capital share in output as in the Solow-Ramsey model For plausible values of the elasticity of export de-mand and the share of exports in GDP the terms-of-trade effects arestrong enough to generate an elasticity of output to capital sufcientto account for observed differences in incomes

We also provide evidence of terms-of-trade effects We look atcross-country growth regressions to isolate differences in growthrates due to accumulation As emphasized by Barro [1991] andBarro and Sala-i-Martin [1995] countries that are poor relativeto their steady-state income level accumulate faster We showthat this faster accumulation is also associated with a worseningin the terms of trade Our estimates imply that holding technol-ogy and other determinants of steady-state income constant a 1percentage point faster growth is associated with a 06 percentage


point deterioration in the terms of trade With terms-of-tradeeffects of this magnitude our model explains a signicant frac-tion of cross-country income differences

Our main results are derived in Sections II and III in a modelwith capital as the only factor of production and with exogenousspecialization Section IV extends the model to include labor as anadditional factor of production This extended model generateshigher wages and costs of living in richer countries as is the casein the data Section V generalizes our results to the case wherecountries choose which goods and how many goods to produceDespite endogenous specialization the terms-of-trade effects con-tinue to operate and ensure a common long-run growth rateacross countries As a by-product of this analysis we also obtaina simple theory of cross-country technology differences countrieswith lower rates of time preference (higher saving rates) havebetter technologies contributing to their higher relative income

Our study is related to the endogenous growth literature3

and to papers on cross-country technological spillovers mentionedabove Howitt [2000] is most closely related He shows that in amodel of Schumpeterian endogenous growth if innovations buildon a worldwide ldquoleading-edge technologyrdquo all countries grow atthe same rate and policy and saving rate differences affect rela-tive incomes Howittrsquos results are therefore parallel to ours butrely on widespread technological spillovers We emphasize in-stead the role of commodity trade and show that even a smallamount of commodity trade is sufcient for all countries to sharethe same long-run growth rate

Our paper also relates to the literature on international tradeand growth A rst strand of the literature emphasizes learning-by-doing and studies how international trade changes the indus-trial structure of countries and affects their aggregate rate ofproductivity growth4 A second strand studies how internationaltrade affects the incentives to innovate5 A third strand studieshow international trade affects the process of capital accumula-

3 See for example Romer [1986 1990] Lucas [1988] Rebelo [1991] Gross-man and Helpman [1991] and Aghion and Howitt [1992] Although we use theformulation of Rebelo with capital accumulation as the engine of growth ourresults generalize to a model in which endogenous growth results from technicalchange as in some of the other papers

4 Krugman [1987] Stokey [1991] Young [1991] and Brezis Krugman andTsiddon [1993]

5 See among others Segerstrom Anant and Dinopoulos [1990] Grossmanand Helpman [1991] and Rivera Batiz and Romer [1991]


tion in the presence of some form of factor price equalization6

Our paper is closer to this third line of research since we alsoexamine the effects of international trade on the incentives toaccumulate capital We depart from earlier papers by focusing onthe case without factor price equalization With factor priceequalization the rental rate of capital is independent of domesticcapital and countries can accumulate without experiencing di-minishing returns Without factor price equalization the rentalrate of capital is determined by the domestic capital stock even inthe absence of technological diminishing returns

II A WORLD OF AK ECONOMIES

In this section we outline a world of AK economies with tradeand specialization The main purpose of this model is to demon-strate how terms-of-trade effects create a force toward a commongrowth rate across countries We establish that any amount ofinternational trade ensures that cross-country differences intechnology saving and economic policies translate into differ-ences in income levels not growth rates Countries that accumu-late capital faster than average experience declining exportprices reducing the rate of return to capital and discouragingfurther accumulation These terms-of-trade effects create dimin-ishing returns to capital at the country level and keep the worlddistribution stable

A Description

The world we consider contains a continuum of countrieswith mass 1 Capital is the only factor of production There is acontinuum of intermediate products indexed by z [ [0M] andtwo nal products that are used for consumption and investmentThere is free trade in intermediate goods and no trade in nalproducts or assets

Countries differ in their technology savings and economicpolicies In particular each country is dened by a triplet ( )where is an indicator of how advanced the technology of thecountry is is its rate of time preference and is a measure ofthe effect of policies and institutions on the incentives to invest

6 See for instance Stiglitz [1970] and Ventura [1997] See also Cunat andMaffezoli [2001] who analyze growth in a world economy that starts outside thecone of diversication but eventually reaches factor price equalization


We denote the joint distribution of these characteristics byG( ) and assume it is time invariant

All countries admit a representative consumer with utilityfunction

(1) E0

`

ln c(t) z e2 zt z dt

where c(t) is consumption at date t in the ( )-countryThroughout the paper we simplify the notation by suppressingtime and country indices when this causes no confusion Thebudget constraint facing the representative consumer is

(2) pI z kCcedil 1 pC z c 5 y ordm r z k

where pI and pC are the prices of the investment and consump-tion goods k is capital stock and r is the rental rate Forsimplicity we assume that capital does not depreciate Sincethere is no international trade in assets income y must be equalto consumption pC z c plus investment pI z kCcedil

To introduce specialization we adopt the Armington [1969]assumption that products are differentiated by origin7 Let bethe measure (number) of intermediates produced by the ( )-country with z dG = M A higher level of corresponds to theability to produce a larger variety of intermediates so we inter-pret as an indicator of how advanced the technology of thecountry is In all countries intermediates are produced by com-petitive rms using a technology that requires one unit of capitalto produce one intermediate

Each country also contains many competitive rms in theconsumption and investment goods sectors with unit costfunctions

(3) BC(rp( z)) 5 r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )

(4) BI(rp( z)) 5 2 1 z r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )

7 We make this crude assumption to simplify the analysis and highlight theimplications of specialization for growth patterns in the simplest way In SectionV we model how countries choose the set of intermediates that they produce andtherefore provide a microfoundation for this assumption


where p( z) is the price of the intermediate with index z Theseequations state that the production of consumption and invest-ment goods requires the services of domestic capital and inter-mediates The parameter is the share of intermediates in pro-duction and it will also turn out to be the ratio of exports toincome This ratio is usually interpreted as a measure of open-ness The parameter is the elasticity of substitution among theintermediates and also the price elasticity of foreign demand forthe countryrsquos products The inverse of this elasticity is ofteninterpreted as a measure of the degree of specialization Weassume that gt 1 This assumption rules out immiserizinggrowthmdashthe country becoming poorer by accumulating more (seeBhagwati [1958]) Note that the technologies for consumption andinvestment goods are identical except for the shift factor Weuse this parameter as a crude measure of the effect of policies andinstitutions on the incentives to invest Examples of the policiesand institutions we have in mind include the degree of enforce-ment of property rights or the distortions created by the tax code8

B World Equilibrium

A competitive equilibrium of the world economy consists of asequence of prices and quantities such that rms and consumersmaximize and markets clear Our assumptions ensure that suchan equilibrium exists and is unique We prove this byconstruction

Consumer maximization of (1) subject to (2) yields the follow-ing rst-order conditions

(5)r 1 pCcedil I

pI2

pCcedil C

pC5 1

cCcedilc

(6) limt reg `

pI z kpC z c

z e 2 zt 5 0

Equation (5) is the standard Euler equation and states that therate of return to capital (r + pCcedil I)pI 2 pCcedil CpC must equal the rateof time preference plus a correction factor that depends on the

8 Jones [1995] Chari Kehoe and McGrattan [1997] and Parente Rogersonand Wright [2000] have emphasized the importance of such policies in explainingcross-country differences in income levels and a range of empirical studies haveshown the importance of institutional differences in affecting investment andeconomic performance (eg Knack and Keefer [1995] Barro [1997] Hall andJones [1999] and Acemoglu Johnson and Robinson [2001a])


slope of the consumption path Equation (6) is the transversalitycondition Integrating the budget constraint and using the Eulerand transversality conditions we nd that the optimal rule is toconsume a xed fraction of wealth

(7) pC z c 5 z pI z k

Equation (7) implies that countries with more patient consum-ersmdashlow mdashwill have lower consumption to capital ratios

Next consider rm maximization The production functions(3) and (4) ensure that all intermediates are produced in equilib-rium Since rms in the intermediates sector are competitivethey set their price equal to marginal cost which is the rentalrate of capital So the price of any variety of intermediate pro-duced in the ( )-country is equal to

(8) p 5 r

where r is the rental rate of capital in the ( )-country We usethe ideal price index for intermediates as the numeraire ie

(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1

Since all countries export practically all of their production ofintermediates and import the ideal basket of intermediates thischoice of numeraire implies that p is also the terms of trade of thecountry ie the price of exports relative to imports9

Firms in the consumption and investment sectors take pricesas given and choose factor inputs to maximize prots The loga-rithmic preferences in (1) ensure that the demand for consump-tion goods is always strong enough to induce some production inequilibrium so price equals cost

(10) pC 5 r1 2

On the other hand if the country starts with a large capital stockconsumers may want to dissave and there may not be any pro-

9 Although each country is small relative to the world it has market powerbecause of complete specialization in the production of intermediates So eachcountry may want to act as a monopolist imposing an optimal tariff or an exporttax Whether they do so or not does not affect our results and we ignore thispossibility In any case a cooperative equilibrium with free trade policies issuperior to a noncooperative equilibrium in which all countries actively use tradepolicy so we may think that countries have solved this coordination problem andhave committed not to use trade policy


duction of investment goods We rule this possibility out by as-suming that the initial capital stock is not too large This ensuresthat price equals cost for the investment good as well

(11) pI 5 2 1 z r1 2

Finally we need to impose market clearing for capital ByWalrasrsquo law this is equivalent to imposing trade balance10 Eachcountry spends a fraction of its own income on foreign interme-diates while the rest of the world spends a fraction z z p1 2 oftheir income on this countryrsquos intermediates Therefore tradebalance requires

(12) y 5 z p1 2 z Y

where Y y z dG is world income Equation (12) implies thatwhen the measure of varieties is larger a given level of incomey is associated with better terms of trade p and higher rentalrate of capital since r = p Intuitively a greater implies thatfor a given aggregate capital stock there will be less capitalallocated to each variety of intermediate so each will command ahigher price in the world market Conversely for a given agreater relative income yY translates into lower terms of tradeand rental rate

C World Dynamics

The state of the world economy is fully described by a distri-bution of capital stocks A law of motion for the world economyconsists of a rule to determine the trajectory of this distributionfrom any starting position This law of motion is given by thefollowing pair of equations for each country11

(13) kCcedil k 5 z r 2

(14) r z k 5 z r1 2 z E r z k z dG

10 Market clearing for capital implies that k = kn + z ki where kn iscapital used in the nontraded sector and k i is capital used in the production ofeach intermediate Given the Cobb-Douglas assumption we have kn = (1 2 ) z yrAlso because demand for each intermediate is of the constant elasticity form anda fraction of world income Y is spent on intermediates we have ki = z p1 2 z YpUsing y = r z k the market clearing condition for capital is equivalent to (12)

11 To obtain (13) we substitute equations (7) and (11) into the budgetconstraint (2) To obtain (14) we simply rewrite equation (12) using (2) and (8)


For a given cross section of rental rates the set of equations in(13) determines the evolution of the distribution of capital stocksFor a given distribution of capital stocks the set of equations in(14) determine the cross section of rental rates

The world economy has a unique and stable steady state inwhich all countries grow at the same rate12 To describe thissteady state dene the world growth rate as x YCcedil Y and therelative income of a ( )-country as yR yY Then setting thesame growth rate for all countries ie kCcedil k = yCcedil y = x we obtainthe steady-state cross section of rental rates as

(15) r 5 S 1 x D 1

where an asterisk is used to denote the steady-state value of avariable for example x is the steady-state world growth rateSince p = r equation (15) also gives the steady-state terms oftrade of the country p It is important to note that in steadystate terms of trade and rental rates are constant This highlightsthat the world income distribution is stable not because of con-tinuously changing terms of trade but because countries thataccumulate more face lower terms of trade reducing the interestrate and the incentives for further accumulation In the steadystate both the distribution of capital stocks and relative pricesare stable

Using equations (9) (8) (12) and (15) we can provide acomplete characterization of the world distribution of income inthe steady state

(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1

Equation (16) describes the steady-state world income distribu-tion and states that rich countries are those that are patient (low) create incentives to invest (high ) and have access to better

technologies (high ) Equation (17) implicitly denes the steady-state world growth rate and shows that it is higher if countries

12 Stability follows immediately since there is a single differential equationdescribing the behavior of each country given by (13) and this differential equa-tion is stable because from equation (14) a greater k leads to a lower r


have ldquogoodrdquo characteristics ie low values for and high valuesfor and

International trade and specialization play an essential rolein shaping the world income distribution To see this use equa-tions (8) (10) (11) and (12) to write the terms of trade and therate of return to capital as follows

(18) terms of trade 5 p 5 S yRD 1( 2 1)

(19) rate of return 5r 1 pCcedil I

pI2

pCcedil C

pC5 z p

These are the two key relative prices in our economy Equa-tion (18) states that for a given measure of country technology the terms of trade of the country are decreasing in its relativeincome Intuitively a greater level of income translates intogreater production for each variety of intermediates in which thecountry specializes and this greater supply reduces the relativeprices of these intermediates Equation (19) states that for giveneconomic policies the rate of return to capital is increasing inthe terms of trade This is also intuitive a higher price for thecountryrsquos exports raises the value of the marginal product ofcapital and hence the rate of return to capital Equations (18) and(19) together explain why countries face diminishing returns tocapital

These equations also illustrate the sources of income differ-ences across countries To provide incentives for accumulationthe steady-state rate of return to capital must equal the effectiverate of time preference + x Equation (19) implies that forcountries with greater patience and better economic policieslower terms of trade are sufcient to ensure accumulation (ie toensure that the rate of return is equal to + x) Equation (18)on the other hand translates lower terms of trade and bettertechnology into a greater relative income level yR So countrieswith low values for and high values for and will be richer

Equations (18) and (19) also give the intuition for the stabil-ity of the world income distribution A country with a relativeincome level below its steady-state value has terms of trade aboveits steady state (equation (18)) Terms of trade above steady statein turn translate into a rate of return to capital that exceeds theeffective rate of time preference (equation (19)) This inducesfaster accumulation than the rest of the world increasing relative


income As this occurs the terms of trade worsen the rate ofreturn declines and the rate of capital accumulation convergestoward the world growth rate

As in most growth models both the shape of the steady-stateworld income distribution and the speed of convergence towardthis steady state depend on the strength of diminishing returnsWhile in standard models diminishing returns are postulated asa property of technology in our model it is derived from changesin relative prices resulting from international trade and special-ization Naturally the strength of diminishing returns dependson the volume of trade and the extent of specialization There arestronger diminishing returns when the volume of trade and theextent of specialization are greater (high and low ) When islow equation (19) shows that the rate of return to capital is lesssensitive to changes in the terms of trade In the limit as reg 0we converge to a closed economy the rate of return is indepen-dent of the terms of trade and there are no diminishing returnsIn this case as in the standard endogenous growth models verysmall differences in country characteristics are sufcient to cre-ate arbitrarily large differences in incomes Similarly when ishigh equation (18) shows that terms of trade are less sensitive todifferences in relative incomes In the limit as reg ` we are backto the endogenous growth world

III EMPIRICAL IMPLICATIONS AND EVIDENCE

World income has experienced secular growth during thepast 200 years And over the postwar era as suggested by FigureI most countries have grown at similar rates Our model providesa unied framework for interpreting these facts Since there areconstant returns to capital accumulation from a global perspec-tive the rate of growth of the world economy is endogenousHowever since there are diminishing returns to capital accumu-lation at the country level the cross-sectional behavior of theworld economy is similar to that of existing exogenous growthmodels cross-country variation in economic policies savings andtechnologies translate into cross-country variation in incomesWe now discuss how our model can be used to interpret cross-country income differences and patterns of conditional conver-gence and provide some evidence of terms-of-trade effects


A Quantitative Implications

Does our model imply cross-country income differences thatare quantitatively plausible To answer this question rst con-sider the Solow [1956] model countries save a fraction s of theirincome and have access to the Cobb-Douglas aggregate produc-tion function y = ( A z ex zt)1 2 z k where A is a country-specicefciency parameter x is the exogenous rate of technologicalprogress common across all countries and is the share of capitalin national product Since lt 1 this production function exhibitstechnological diminishing returns Dene income per effectiveworker as y = y z e 2 x zt Then steady-state income is

(20) y 5 A z S sx D (1 2 )

So countries that save more (high s) and are more efcient (highA) have higher per capita incomes although all countries sharethe same growth rate x The responsiveness of income to savingsdepends on the capital share Mankiw Romer and Weil [1992]estimated a version of equation (20) and found that it provides areasonable t to cross-country differences in income for 23Similarly Klenow and Rodriguez-Clare [1997] and Hall andJones [1999] show that given the range of variation in capital-output ratios and education across countries the Solow modelaccounts for the observed differences in income per capita withoutlarge differences in the productivity term A if 23 Thisimplies a qualied success for the Solow model given the share ofcapital in national product of approximately 13 as in OECDeconomies the framework accounts for cross-country income dif-ferences only if there are sizable differences in productivity orefciency (the A term)

To relate these empirical ndings to our model note that ourkey equation (16) is in effect identical to (20) in our model thesavings rate is s = pI z kCcedil y So the steady-state savings rate is s =x( + x) and substituting this into (16) we have13

13 In practice Mankiw Romer and Weil [1992] use the investment-to-output ratio i rather than the savings rate Summers and Heston [1991] constructi with a correction for differences in relative prices of investment goods acrosscountries so effectively i = spI Using this denition an alternative way of express-ing the empirical predictions of our model is yR = z (ix) 2 1 In this case theefciency parameter A is simply equal to and the equivalent of in equation (20)is ( 2 1) The quantitative predictions of our model are affected little by this change


yR 5 z ( 2 1) z S sx D

( 2 1)

Our model therefore implies the same cross-country relationship asthe Solow model with two exceptions (i) the efciency parameter Acaptures the effects of both the technology term and the inverseof the relative price of investment goods and (ii) the elasticity ofrelative income to savings depends not on the capital share but onthe degree of specialization and the volume of trade In par-ticular the equivalent of in equation (20) is ( 2 1)( + 2 1) inour model so the elasticity of output to savings is decoupled from thecapital share14

Does this implied elasticity of output to savings generateplausible quantitative predictions Given the Cobb-Douglas pref-erences the share of traded goods is the share of exports inGDP Since except for the United States and Japan this numberis around 30 percent or higher for rich economies (see WorldDevelopment Report [1997]) here we take it to be = 03 On theother hand corresponds to the elasticity of export demandEstimates of this elasticity in the literature are for specic indus-tries and vary between 2 and 10 although there are also esti-mates outside this range (see for example Feenstra [1994] or Laiand Treer [1999]) For our purposes we need the elasticity forthe whole economy not for a specic industry Below we usecross-country data on changes in terms of trade to estimate anelasticity of = 26 So here we use this as our baseline estimateWith = 26 our modelrsquos predictions for cross-country incomedifferences are identical to those of the Solow model with =085 Therefore in contrast to the simplest neoclassical growthmodel which yields a small elasticity of output to savings ourmodel implies a reasonably large elasticity and in fact generatescross-country income differences even larger than those observedin the data If there were in addition technological diminishingreturns as in the Solow model or technological catch-up asemphasized for example by Howitt [2000] the implied elasticityof output to savings would be lower This suggests that perhapsterms-of-trade effects emphasized here and technological dimin-ishing returns or technological catch-up are jointly important in

14 In this economy the capital share in national product is equal to 1 In thenext section when we introduce labor the capital share will no longer be 1 butthe elasticity of output to savings will remain unchanged


determining the effect of differences in saving rates and distor-tions on cross-country income differences

Does the model also generate plausible implications forgrowth dynamics Barro [1991] and Barro and Sala-i-Martin[1995] represent country-level growth dynamics by regressions ofthe form

(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut

where gt is the annual growth rate of income of the country betweensome dates t 2 1 and t and Zt is a set of covariates that determinesteady-state income The parameter = 2 dgtd ln yt 2 1 is inter-preted as the speed of (conditional) convergence toward steady stateThese regressions typically estimate a value of 002 correspond-ing to a rate of conditional convergence of about 2 percent a year Inour model the growth rate of output can be expressed as15

(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G

When a county is at its steady state value ie yR = yR it growsat the rate ( x + ( 2 1) z x) which is a weighted average of thesteady-state world growth rate x and the current world growthrate x When the world is also in steady state ie x = x thecountry grows at the world growth rate x If yR is below itssteady-state value it grows at a rate that depends on the distanceaway from this steady state the elasticity of export demand the share of traded goods and the rate of time preference

The implied speed of convergence is therefore = 2 dgd ln y =z ( + x) z (yRyR) 2 ( 2 1) As in the Solow-Ramsey model the

speed of convergence is not constant countries away from theirsteady states grow faster Near the steady state yR yR we havethat = z ( + x) The baseline values of parameters suggestedby Barro and Sala-i-Martin [1995] imply that the term in parenthe-ses is about 0116 With these values the Solow model with a capital

15 To obtain this equation we use the trade balance condition (12) and thebudget constraint (2) to get an expression for y in terms of world income Y andthe capital stock of the country k y = ( z Y)1 z k( 2 1) We rst time-differentiate this equation next substitute from (13) for kCcedil k and (12) for r toobtain an expression for yCcedil y and then substitute for the steady-state relativeincome level yR from (16)

16 The standard formula includes the rate of population growth n and therate of depreciation of capital which we have set to zero to simplify notation Itis easy to check that if we allow for positive population growth and depreciationthe speed of convergence would be = z ( + n + + x) Barro andSala-i-Martin suggest a parameterization with an annual discount factor of about


share of one-third predicts convergence at approximately 66 percenta year considerably faster than the actual speed of convergence Incontrast with an elasticity of export demand of = 26 and the shareof exports in GDP of = 03 our model implies that 0011mdashconvergence at approximately 11 percent a year which is slowerthan observed in the data The predicted speed of convergence wouldbe higher again with additional technological diminishing returns ortechnological catch-up

B Empirical Evidence on Terms-of-Trade Effects

At the center of our approach is the notion that as a countryaccumulates more capital its terms of trade deteriorate Is thereany evidence supporting this notion A natural place to start is tolook at the correlation between growth and changes in terms oftrade Consider equation (12) which links the terms of trade of acountry to its relative income Taking logs and time differenceswe obtain

(23) t 5 ( gt 2 xt)( 2 1) 1 ln t

where t is dened as the rate of change in the terms of tradebetween date t and some prior date t 2 1 gt is the rate of growthof the countryrsquos income xt is the rate of growth of world incomeand ln t is the change in technology More generally this lastterm stands for all changes that affect income and terms of tradepositively including changes in technology and the worldrsquos tastestoward the countryrsquos products

In theory we can estimate an equation of the form (23) usingcross-country data Unfortunately in practice we do not havedirect measures of the technology term ln t so the only optionis to estimate (23) without this term or with some proxies FigureII plots changes in terms of trade between 1965 and 1985 againstthe growth rate of income during the same period for the entireset of countries we have data on terms of trade and separately fornon-OPEC countries17 It shows that there is no relationshipbetween growth and changes in terms of trade

099 (ie = 002) a depreciation rate of 5 percent a world growth rate of 2percent and a population growth rate of 1 percent per annum This implies that

+ n + + x 0117 The terms-of-trade data are from Barro and Lee [1993] in turn con-

structed from the World Bank and United Nations sources Barro and Lee reportve-year averages of the changes in the prices of exports minus the prices ofimports The change in terms of trade 1965ndash1985 is the geometric average of thesechanges between 1965 and 1985


FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985


Does this imply that there are no terms-of-trade effects in thedata Not necessarily Since changes in technology as capturedby the ln t term are directly correlated with changes inincome estimates from an equation of the form (23) and therelationship shown in Figure II will be biased This is the stan-dard identication problem and to make progress we need toisolate changes in growth rates that are plausibly orthogonalto the omitted technology term ln t A plausible source ofvariation would come from countries growing at different ratesbecause they have started in different positions relative to theirsteady-state income level and are therefore accumulating at dif-ferent rates to approach their steady state

How can we isolate changes in income due to accumulationHere we make a preliminary attempt by using a convergenceequation like (21) Recall that these equations relate cross-coun-try differences in growth rates to two sets of factors (i) a set ofcovariates Zt which determine the relative steady-state positionof the country and (ii) the initial level of income which captureshow far the country is from its relative steady-state positionAccordingly differences in growth due to the second set of factorsapproximate changes in income due to accumulation and give usan opportunity to investigate whether faster accumulation leadsto worse terms of trade

The estimating equation is

(24) t 5 z gt 1 Z 9t z 1 t

where as before t is the rate of change in terms of trade and g t

is the growth rate of output We will estimate (24) using Two-Stage Least Squares (2SLS) instrumenting gt using equation(21) The vector Zt includes potential determinants of steady-state income in particular human capital and institutions vari-ables The coefcient of interest is which in our theory corre-sponds to 2 1( 2 1) as in (23) The excluded instrument in our2SLS estimation is the initial level of income ln yt 2 1 Intuitivelyconditional on income growth and other covariates the initiallevel of income should not affect the terms of trade18

18 In the presence of technological convergence countries below their steadystate may also be improving their technologies and ln yt 2 1 may be correlated with

ln t In this case our estimate of would be biased upwards stacking the cardsagainst nding a negative More generally this consideration suggests that wemay want to interpret our estimate of the strength of the terms-of-trade effects asa lower bound


Table I reports cross-sectional regressions of the rate ofchange of terms of trade between 1965 and 1985 on the growthrate of income over the same period and various sets of covariatesas in equation (24) (all data are from Barro and Lee [1993]) Thetop panel reports the 2SLS estimate of the coefcient on outputgrowth in equation (24) The middle panel gives the rst-stagecoefcient on ln yt 2 1 Finally the bottom panel reports theOLS estimate of Naturally in the rst stage and the OLS thesame covariates as the 2SLS are included but the coefcients arenot reported to save space Different columns correspond to dif-ferent sets of covariates In the rst-stage relationship the coef-cients are very similar to the convergence equations estimatedby Barro and Sala-i-Martin [1995] and we do not report themhere

In column (1) we start with a minimal set of covariates thatcontrol for human capital differences These are average years ofschooling in the population over age 25 in 1965 and the log of lifeexpectancy at birth in 1965 Both of these variables are typicallyfound to be important determinants of steady-state relative in-come levels (or country growth rates) so they are natural vari-ables to include in our Zt vector We also include a dummy forOPEC countries (in our sample these are Algeria IndonesiaIran Iraq and Venezuela) The coefcient on log GDP in 1965reported in Panel B shows the standard result of conditionalconvergence at the speed of approximately 2 percent a year Theestimate of the coefcient of interest in column (1) is 2 06 witha standard error of 027 This estimate implies that a countrygrowing 1 percentage point faster due to accumulation experi-ences a 06 percentage point decline in its terms of trade Thisestimate is statistically signicant at the 5 percent level Thecoefcient on years of schooling is insignicant while the coef-cients on life expectancy and the OPEC dummy are positive andstatistically signicant The coefcient on the OPEC dummy im-plies that all else equal the terms of trade of the OPEC countriesimproved at approximately 0091 percentage points a year duringthis period We return to the interpretation of the other covari-ates later Notice also that as suggested by Figure II the OLScoefcient reported in Panel C is insignicant and practicallyequal to 0 The contrast between the OLS and the 2SLS estimateslikely reects the fact that the 2SLS procedure is isolatingchanges in income that are due to accumulation and hence or-thogonal to ln t


TABLE IIV REGRESSIONS OF GROWTH RATE OF TERMS OF TRADE

Mainregression

Detailingschooling

Addingpoliticalindicat

Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)

Panel A Two-stage least squares

GDP Growth1965ndash1985

2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)

Years ofschooling 1965

2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)

Years ofprimaryschooling 1965

2 0002(0003)

Years ofsecondaryschooling 1965

2 0002(0006)

Years of higherschooling 1965

0019(0034)

Log of lifeexpectancy1965

0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)

Politicalinstability

0007(0023)

Log blackmarketpremium

2 0005(0012)

Change in yearsof schooling1965ndash1985

0008 0009(0004) (0003)

Change in log oflife expectancy1965ndash1985

2 0000 2 0042(0078) (0045)

Panel B First-stage for GDP growth

Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034

Panel C Ordinary least squares


0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74

ldquoGrowth Rate of Terms of Traderdquo is measured as the annual growth rate of export prices minus the growthrate of import prices The OPEC dummy takes value 1 for ve countries in our sample (Algeria Indonesia IranIraq and Venezuela) The political instability variable is the average of the number of assassinations per millioninhabitants per year and the number of revolutions per year the war variable is a dummy for countries thatfought at least one war over the period 1965ndash1985 and the log black market premium is the average of thelogarithm of the black market premium over the period 1965ndash1985 All the data are from the Barro-Lee data set

Excluded instrument is log of output in 1965 in columns (1) (2) (3) and (4) and (6) while in column (5)excluded instruments are log of output in 1965 years of schooling in 1965 and the log of life expectancy in 1965


In column (2) we enter years of primary secondary andtertiary schooling separately and this has little effect on theestimate of Column (3) adds a number of common controls usedby Barro and Sala-i-Martin [1995] to control for differences ininstitutions and property rights which are likely to be rst-orderdeterminants of productivity and technology and hence ofsteady-state income These institutional variables are an index ofpolitical instability a dummy for experiencing a war during thisperiod and the log of the black market premium The estimate isnow 2 046 (standard error = 021)19

The coefcients on the covariates in columns (1)ndash(4) are dif-cult to interpret because they refer to values at the beginning ofthe sample For example a 10 percent higher life expectancy in1965 is associated with 05 percentage point improvement interms of trade This may capture the fact that initial level oflife expectancy is correlated with subsequent changes in thesehuman capital variables and therefore possibly correlated with

ln t as well In columns (5) and (6) we add the changes inyears of schooling and life expectancy between 1965 and 1985to the basic regression of column (1) In column (5) thesechanges are entered as additional covariates In column (6) weinstead use the initial levels of years of schooling and lifeexpectancy as excluded instruments in addition to the initiallevel of income In both columns the estimate of is similar toour baseline estimate and statistically signicant at the 5percent level We nd that changes in the years of schooling arepositive and signicant in the second stage indicating thatcountries that increased their human capital over this periodexperienced improvements in their terms of trade This isreasonable since improvements in human capital are likely tobe correlated with ln t

20

Finally in column (7) we repeat the basic regression of col-

19 As in typical cross-country growth regression analyses these institu-tional variables are treated as exogenous We also experimented with a speci-cation instrumenting for a measure of institutions among the former coloniesusing the mortality rates of European colonizers following Acemoglu Johnsonand Robinson [2001a] Unfortunately the restriction to former colonies left uswith too small a sample and the results were insignicant

20 We experimented with different specications and various subsets ofcovariates with similar results We also estimated using decadal changes anda random-effect model as in Barro and Sala-i-Martin [1995] and Barro [1997]rsquosfavorite specication In this case the results are similar to those reported inTable I For example the equivalent of column (1) yields an estimate of of 2 088with a standard error of 042 while the equivalent of column (6) which excludesoil producers yields an estimate of 2 085 with a standard error of 051


umn (1) excluding the ve OPEC countries from the sample Theestimate of is 2 062 (standard error = 035) which is no longersignicant at the 5 percent level but signicant at the 10 percentlevel

Figure III gives a visual representation of the 2SLS estimatereported in columns (3) and (6) of Table I On the vertical axis wehave the component of the changes in the terms of trade that isorthogonal to the covariates included in the regression and onthe horizontal axis the projection of GDP growth on our instru-ment initial income again orthogonalized with respect to the setof covariates The OLS regression of the rst variable on thesecond will give precisely the corresponding 2SLS estimate Thegure shows that countries predicted to grow faster because ofrelatively low initial income (relative to their human capitalindicators) such as the Philippines Thailand Taiwan or Koreatypically experienced a worsening in their terms of trade com-pared with countries with relatively high initial income such asMexico Switzerland or France

Overall the results in Table I provide some preliminaryevidence that higher output growth due to accumulation is asso-ciated with a worsening in the terms of trade as implied by ourmechanism Nevertheless given the relatively low number ofobservations and the usual difculties in interpreting cross-coun-try regressions this result has to be interpreted with caution

We can also use the magnitudes of the coefcient estimates tocompute implied values for the export demand elasticity Forexample the estimate in column (1) 2 06 implies that 26This is a reasonable elasticity estimate within the range of theindustry estimates Returning to the discussion in the previoussubsection recall that with a value of around 26 our modelaccounts for much of the variability in income levels across coun-tries (in fact as noted above it somewhat ldquooverexplainsrdquo theobserved differences) Therefore this evidence suggests thatterms-of-trade effects may be quantitatively important in under-standing the observed patterns of cross-country income differ-ences and growth

IV LABOR WAGES AND PRODUCT PRICES

Capital is the only factor of production in the model of SectionII This limits the potential applications of the model It alsomakes our approach silent on two important features of the data


FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)


(1) that wages for comparable workers are higher in richer coun-tries and (2) that costs of living are higher in rich countries (seeSummers and Heston [1991]) Fortunately it is straightforwardto generalize our baseline model of Section II by adding labor asanother factor of production all of the implications we haveemphasized so far remain unchanged and in addition the modelgenerates higher wages and higher costs of living in richercountries

A The Model with Labor

Let us add two assumptions to our basic model First theproduction of the consumption good now requires labor In par-ticular we adopt the following unit cost function

(25) BC(wrp(z)) 5 w(1 2 ) z(1 2 ) z r z(1 2 ) z F S E0

M

p(z)1 2 z dzD (1 2 ) G

which is identical to equation (10) except for the presence ofdomestic labor services in production implying that the consump-tion goods sector uses labor in addition to capital and tradedintermediates

Second each consumer supplies one unit of labor inelasti-cally The budget constraint of the representative consumer thenbecomes

(26) pI z kCcedil 1 pC z c 5 y ordm r z k 1 w

where w is the wage rate The rest of the assumptions in subsec-tion A remain the same The model in this section is therefore thelimiting case in which reg 1 In this limit labor is not used inproduction and the wage is zero

Consumers now maximize the utility function (1) subject tothe new budget constraint (26) The solution to this problem stillinvolves the Euler equation (5) and the transversality condition(6) Once again integrating the budget constraint and using theEuler and transversality conditions we obtain the consumptionrule as

(27) pC z c 5 z S pI z k 1 E0

`

w z e 2 0t(r+ pCcedil I)pI z dv z dt D


The optimal rule is still to consume a xed fraction of wealthwhich now also includes the net present value of wages

The existence of labor income has no effect on rms in theintermediate and investment goods sectors So equations (8) and(11) still apply But the condition that price equals marginal costfor the rms in the consumption good sector is now given by

(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )

so prices of consumption goods depend on the wage rateSince we now have two factor markets the trade balance

condition (12) is not sufcient to ensure market clearing and weneed to add a labor market clearing condition to complete themodel Labor demand comes only from the consumption goodssector and given the Cobb-Douglas assumption this demand is(1 2 ) z (1 2 ) times consumption expenditure pC z c divided bythe wage rate w So the market clearing condition for labor is

(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)

It is useful to note that (29) implies labor income w isalways proportional to consumption expenditure Using this factwe can simplify the optimal consumption rule (27) to obtain

(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k

The law of motion of the world economy is again described bya distribution of capital stocks but now this distribution is givenby a triplet of equations for each country21


(32) r z k 1 w 5 z r1 2 z E (r z k 1 w) z dG

(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z

Equation (31) is the law of motion for capital It is identical to(13) and gives the evolution of the distribution of capital stocks for

21 To obtain (31) we start with (26) and substitute for w using (29) for pC zc using (30) and for pI using (11) Equation (32) is simply the trade balancecondition (12) rearranged with y = r z k + w Finally we use (11) (29) and (30)to express w as a function of k and r and then rearrange to obtain (33)


a given distribution of rental rates Equation (32) determinesthe cross section of rental rates for a given distribution ofcapital stocks and wage rates The third equation (33) de-nes the labor sharemdashwage income divided by total income Thisequation also shows that the behavior of the labor share simplydepends on the rental rate as the rental rate increases the laborshare falls

The steady-state world distribution of income follows fromequations (31) and (32) In steady state kCcedil k = x ie all coun-tries will grow at the same rate This immediately gives thesteady-state rental rate as in equation (15) from the previoussection More important for our purposes the steady-state distri-bution of income and the world growth rate are still given byequations (16) and (17) Therefore the intuition regarding thedeterminants of the cross-sectional distribution of income fromsubsection C applies exactly Moreover the empirical implica-tions and the t of the model to existing evidence discussed inSection III are also valid22 But there are now new implicationsfor the cross section of wages and some key relative prices

B Factor and Product Prices

Equations (31) (32) and (33) give the steady-state factorprices The steady-state rental rate of capital is still given by (14)from Section II In addition the steady-state wage rate is

(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y

In the cross section the rental rate of capital continues to belower in richer countries ie countries with low and high Incontrast wages tend to be higher in richer countries countrieswith better technology (high ) and with better economic policies(high ) will have higher wages Both of these follow becausericher countries generate a greater demand for consumptionincreasing the demand for labor and wages23

22 The equation describing convergence to steady state is also similar Inparticular equation (22) from the previous section still gives the rate of growth ofcapital income (relative to average capital income) say yR

k but now total incomealso includes labor income We can write relative income as yR yR

k Rk where R

k

is the share of capital income relative to the average value of this share in theworld So long as factor shares do not change much near the steady state equation(22) still describes the convergence properties of this more general model

23 Interestingly the effect of on wages is ambiguous Countries with lowwill accumulate more and tend to be richer and through the same mechanism


The contrast between the behavior of the rental rate and thewage rate in the time series is also interesting While the rentalrate of capital remains constant equation (34) shows that wagesin all countries grow at the rate of world income growth Thisprediction is consistent with the stylized facts on the long-runbehavior of factor prices

Finally recall that equation (33) gives the share of labor innational product so the capital share in national product is nolonger equal to 1 while relative income differences are exactly thesame as in the model of Sections II and IV This highlights thatas claimed before the result that the responsiveness of relativeincome to savings and economic policies depends on the share ofexports in GDP and export demand elasticity was not predicatedon a capital share of 124

What about product prices While in the model of Section IIboth consumption and investment goods were cheaper in richcountries now equation (28) implies that consumption goods tendto be more expensive in richer countries This is because wagesare higher in rich countries As a result the cost of living (thegeometric average of consumption and investment goods prices)could be higher in rich countries In fact since the share of incomespent on investment goods is small differences in consumptiongood prices are likely to dominate making the costs of livinghigher in richer countries

Next note that the relative price of investment goods is nowpIpC = 2 1 z (wr) 2 (1 2 ) z (1 2 ) This is different from the relativeprice expression in the previous model because of the secondterm which incorporates the fact that consumption goods aremore labor-intensive than investment goods Our model in Sec-tion II generated lower relative prices of investment goods in richcountries only because of differences in policies Now we have

they will have a greater demand for consumption and higher wages However asequation (30) shows everything else equal a country with low will consume lesswhich tends to reduce the demand for consumption and wages Differentiationgives that

w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

In other words as long as the elasticity of foreign demand is large enoughcountries with low will have higher wages

24 More generally although the responsiveness of output to saving ratesand policies does not depend on the capital share in national product it can beshown that it does depend on the capital share in the investment goods sector


an additional effect reinforcing this richer countries have higherwages reducing the relative prices of investment goods

V SPECIALIZATION AND TECHNOLOGY DIFFERENCES

The previous sections have shown how trade and specializa-tion shape the process of world growth and cross-country incomedifferences At the center stage of our framework are diminishingreturns due to terms-of-trade effects as countries accumulatemore capital they increase the production of the commodities inwhich they specialize and their terms of trade worsen There aretwo assumptions underlying this mechanism

1 Each country specializes in a different set of products2 The set of products a country produces is xed (or at least

it does not grow proportionally with its income)The importance of these two assumptions is highlighted in

equation (18) If countries were not specialized or if reg ` so thatdifferent goods were perfect substitutes they would face atexport demands In this case capital accumulation and greaterproduction of intermediates would not worsen the terms of tradeOn the other hand if the set of products in which a countryspecializes were proportional to its income the production of eachvariety would not change with income In this case even withdownward-sloping export demands capital accumulation wouldnot worsen the terms of trade

In this section we show that these assumptions can be justi-ed as the equilibrium of a model in which countries choose theset of goods they produce We use a model of specialization due toincreasing returns as in Helpman and Krugman [1985] to illus-trate our main point The working paper version [Acemoglu andVentura 2001] shows that our results also apply if specializa-tion is driven by costly product development for example as inGrossman and Helpman [1991]

We introduce two modications to the model of Section IVFirst we assume that there is an innite mass of intermediatesand all rms in all countries know how to produce them Henceall countries have access to the same technology frontier Thetotal number of goods produced M as well as its distributionamong countries is determined as part of the equilibrium

Second we assume that one worker is needed to run theproduction process for each intermediate So there is a xed costof production equal to the wage w In addition one unit of capital


is required to produce one unit of each intermediate so there isalso a variable cost in terms of the rental rate of capital r Therest of the assumptions from Section IV still apply

The consumer problem is still to maximize (1) subject to thebudget constraint (26) The solution continues to be given by theEuler equation (5) and the transversality condition (6) and theconsumption rule is still represented by (27) from the previoussection

Firms in the consumption and investment goods sectors facethe same problem as before and equations (11) and (25) stilldetermine their prices But rms in the intermediate goods sectorare now subject to economies of scale Since an innite number ofvarieties are available at no cost no two rms will ever choose toproduce the same good So each producer is a monopolist Withisoelastic demands all intermediate good monopolists in a coun-try will set the same price equal to a constant markup overmarginal cost (which is equal to the rental rate r)

(35) p 5 ( ( 2 1)) z r

Hence the terms of trade are no longer equal but simply propor-tional to the rental rate of capital Because of the markup overmarginal cost each producer makes variable prots equal to 2 1

times its revenue z p1 2 z Y As long as these variable protsexceed the cost of entry there will be entry So we have a free-entry equation equating variable prots to xed costs

(36) w 5 ( ) z p1 2 z Y

where w the wage rate is the xed cost of producing an inter-mediate since one worker is required to run the productionprocess

The trade balance equation (12) still applies The marketclearing condition for labor needs to be modied because nowworkers are employed in the intermediate sector

(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w

Notice that the consumption-to-capital ratio is no longer con-stant so we need to add this ratio z ( pC z c) ( pI z k) as acostate variable and include the transversality condition to de-termine the trajectory of the system In addition the number ofvarieties is now endogenous and will be determined from thefree-entry condition equation (36)


The laws of motion of the key variables is given by two blocksof equations for each country

1 Dynamics For a given distribution of factor prices r andw and varieties this block determines the evolution of thedistribution of capital stocks25

(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0

Equation (38) gives the evolution of the capital stock as a functionof the rental rate r the number of varieties and the consump-tion-to-capital ratio z It differs from (31) only because the con-sumption-to-capital ratio now varies over time Equation (39)gives the evolution of the consumption-to-capital ratio as a func-tion of the number of varieties Finally equation (40) is thetransversality condition

2 Factor prices and varieties Three equations give the crosssection of factor prices and the number of varieties of intermedi-ates as functions of the distribution of capital stocks and con-sumption to capital ratios26

(41) r z k 1 w 5 z S 2 1 D 1 2

z r1 2 z E (r z k 1 w) z dG

(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2


Equation (43) is the trade balance equation and differs from (32)

25 To obtain (38) we start with (26) and substitute for w using (37) for pC zc using the denition z ( pC z c)( pI z k) and for pI using (11) Equation (39)follows from substituting for w from the market clearing equation (37) into (26)and using the denition z ( pC z c)( pI z k)

26 Equation (41) follows from (12) combined with (35) The wage equation(42) follows from the market clearing condition for labor (37) and the denitionof z in a manner analogous to the derivation of equation (33) in footnote 21 Finallythe free-entry equation (43) is obtained by substituting for world income Y


because due to monopoly power the rental rate and the terms oftrade are not equal (see equation (35)) Equation (42) gives thelabor share Finally (43) is the free entry condition

The dynamics of the world economy are again stable andconverge to a unique steady state This steady state is describedby two equations similar to (16) and (17)

(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1

The reason why (44) and (45) differ from (16) and (17) is thepresence of monopoly markup Otherwise they are identical to(16) and (17) and imply the same cross-sectional relationshipbetween economic policies saving rates and technology

The key modication is that the number of varieties is nowendogenous and given by27

(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x

The only country-specic variable in this equation is So allcountries have similar rsquos but those with lower discount rates(and hence higher saving rates) endogenously specialize in theproduction of more goodsmdash or loosely speaking they will ldquochoosebetter technologiesrdquo Intuitively countries with low accumulatemore capital and have a larger capital stock relative to their wagerates For a given number of goods they therefore face worseterms of trade Consequently they nd it protable to incur thexed cost of production for more goods

Now that technology differences rsquos are endogenous thereare two determinants of cross-country income differences coun-tries with better economic policies (ie high ) will be richer forthe same reasons as before Countries with lower discount rates(ie high ) will be richer both because of the reasons highlightedin Sections II and IV and because they will choose to specialize inthe production of more intermediates

27 To obtain this equation we divide the free-entry condition (43) by thetrade balance condition (41) to get w(r z k + w) = ( z ) We equate this to thelabor share equation (42) and then substitute the steady-state value of z fromequation (39)


Notice that technology differences in this model simply trans-late into differences in relative incomes not long-run growthrates This appears plausible since there is evidence pointing tosignicant technology differences across countries (eg Klenowand Rodriguez-Clare [1997] and Hall and Jones [1999]) and asnoted in the Introduction these differences do not seem to lead topermanent differences in growth rates

To understand why the steady-state number of goods is in-dependent of the level of capital stock or income (cf equation(46)) denote the xed cost of production by f (in equation (36) wehad f = w) Then using (12) the free-entry condition can bewritten as = ( ) z ( yf ) This equation states that the numberof goods in which a country specializes is proportional to itsincome divided by the xed cost of production The reason whyis constant is that as y increases f increases also This is aconsequence of the assumption that xed costs are in terms of thescarce factor As the country becomes richer demand for laborincreases causing a proportional increase in the wage rate Soyf and remain constant28

VI CONCLUDING REMARKS

This paper has presented a model of the world income dis-tribution in which all countries share the same long-run growthrate because of terms-of-trade effects Countries that accumulatefaster supply more of the goods that they specialize in to the worldand experience worse terms of trade This reduces the return tofurther accumulation and creates a demand pull on other nationsWe view this model as an attractive alternative to the existingapproaches where common long-run growth rates result only if allcountries share the same technology

Naturally a theory of diminishing returns due to terms-of-trade effects does not preclude diminishing returns in productionor cross-country technological spillovers It is relatively straight-

28 It is also useful to contemplate what would happen if the xed cost fdepended on the wage rate but less than proportionately say f = w As long as

gt 0 would still increase with income but less than proportionately As aresult our key mechanism that an increase in production translates into worseterms of trade would continue to hold since from equation (18) terms of tradeare proportional to y and are decreasing in y Nevertheless in this case themodel would not be well behaved for another reason as increases with incomethe world growth rate would increase over time eventually becoming inniteThis explains our particular choice of f = w to preserve steady growth


forwardmdashalthough cumbersomemdashto write down a model with allof these factors present and complementing each other The moreimportant question is their relative contribution to explaining theactual world income distribution Here we made a preliminaryattempt at estimating the extent of terms-of-trade effects Ourresults show that a country accumulating faster than othersexperiences a worsening in its terms of trade and the estimatedstrength of the terms-of-trade effect suggests that our mechanismcould be important in understanding cross-country differences inincome levels

Naturally other factors could be driving the negative rela-tionship between faster accumulation and the decline in terms oftrade so future empirical work on this topic is necessary Never-theless to our knowledge ours is the rst investigation of whyfaster accumulation leads to a lower value of marginal product ofcapitalmdashit is typically assumed that this is due to technologicaldiminishing returns despite no direct evidence of this effect Incontrast we showed both theoretically and empirically thatfaster accumulation may lead to a lower value of marginal prod-uct of capital because of its effect on the terms of trade

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

REFERENCES

Acemoglu Daron Simon Johnson and James Robinson ldquoThe Colonial Origins ofComparative Development An Empirical Investigationrdquo American EconomicReview XCI (2001a) 329ndash401

Acemoglu Daron Simon Johnson and James A Robinson ldquoReversal of FortuneGeography and Institutions in the Making of the Modern World IncomeDistributionrdquo NBER Working Paper No 8460 2001b Quarterly Journal ofEconomics forthcoming

Acemoglu Daron and Jaume Ventura ldquoThe World Distribution of IncomerdquoNBER Working Paper No 8083 2001

Acemoglu Daron and Fabrizio Zilibotti ldquoProductivity Differencesrdquo QuarterlyJournal of Economics CXVI (2001) 563ndash 606

Aghion Philippe and Peter Howitt ldquoA Model of Growth through Creative De-structionrdquo Econometrica LX (1992) 323ndash351

Armington Paul S ldquoA Theory of Demand for Products Distinguished by Placeand Productionrdquo International Monetary Fund Stuff Papers XVI (1969)159ndash178

Barro Robert ldquoEconomic Growth in a Cross Section of Countriesrdquo QuarterlyJournal of Economics CVI (1991) 407ndash443

mdashmdash Determinants of Economic Growth A Cross-Country Empirical Study (Cam-bridge MA MIT Press 1997)

Barro Robert and Jong-Wha Lee ldquoInternational Comparisons of EducationalAttainmentrdquo Journal of Monetary Economics XXXII (1993) 363ndash394

Barro Robert and Xavier Sala-i-Martin Economic Growth (New York NYMcGraw-Hill 1995)

Barro Robert and Xavier Sala-i-Martin ldquoTechnological Diffusion Convergenceand Growthrdquo Journal of Economic Growth II (1997) 1ndash26


Bhagwati Jagdish ldquoImmiserizing Growth A Geometrical Noterdquo Review of Eco-nomic Studies XXV (1958) 201ndash205

Brezis Elise Paul Krugman and Daniel Tsiddon ldquoLeapfrogging in InternationalCompetitionrdquo American Economic Review LXXXIII (1993) 1211ndash1219

Chari V V Patrick Kehoe and Ellen McGrattan ldquoThe Poverty of Nations AQuantitative Investigationrdquo Working Paper Federal Reserve Bank of Min-neapolis MN 1997

Coe David and Elhanan Helpman ldquoInternational RampD Spilloversrdquo EuropeanEconomic Review XXXIX (1995) 859ndash887

Cunat Alejandro and Marco Maffezoli ldquoGrowth and Interdependence underComplete Specializationrdquo mimeo Universita Bocconi 2001

Durlauf Steven and P Johnson ldquoMultiple Regimes and Cross-Country GrowthBehaviorrdquo Journal of Applied Econometrics X (1995) 365ndash384

Eaton Jonathan and Samuel Kortum ldquoInternational Technology Diffusion The-ory and Measurementrdquo International Economic Review XL (1999) 537ndash570

Feenstra Robert ldquoNew Product Varieties and the Measurement of InternationalPricesrdquo American Economic Review LXXXIV (1994) 157ndash177

Grossman Gene and Elhanan Helpman Innovation and Growth in the GlobalEconomy (Cambridge MA MIT Press 1991)

Hall Robert and Charles I Jones ldquoWhy Do Some Countries Produce So MuchMore Output per Worker Than Othersrdquo Quarterly Journal of EconomicsCXIV (1999) 82ndash116

Helpman Elhanan ldquoImperfect Competition and International Trade Evidencefrom Fourteen Industrial Countriesrdquo Journal of the Japanese and Interna-tional Economics I (1987) 62ndash81

Helpman Elhanan and Paul Krugman Market Structure and Foreign Trade(Cambridge MA MIT Press 1985)

Howitt Peter ldquoEndogenous Growth and Cross-Country Income DifferencesrdquoAmerican Economic Review XC (2000) 829ndash846

Hummels David and James Levinsohn ldquoMonopolistic Competition and Interna-tional Trade Reconsidering the Evidencerdquo Quarterly Journal of EconomicsCX (1995) 799ndash836

Jones Charles I ldquoEconomic Growth and the Relative Price of Capitalrdquo Journalof Monetary Economics XXXIV (1995) 359ndash382

mdashmdash ldquoOn the Evolution of the World Income Distributionrdquo Journal of EconomicPerspectives XI (1997) 19ndash36

Klenow Peter J and Andres Rodriguez-Clare ldquoThe Neoclassical Revival inGrowth Economics Has It Gone Too Farrdquo NBER Macroeconomics Annual BBernanke and J Rotemberg eds (Cambridge MA MIT Press 1997)

Knack Steven and Philip Keefer ldquoInstitutions and Economic PerformanceCross-Country Tests Using Alternative Institutional Measuresrdquo Economicsand Politics VII (1995) 207ndash227

Krugman Paul ldquoThe Narrow Moving Band the Dutch Disease and the Competi-tive Consequences of Mrs Thatcher Notes on Trade in the Presence of ScaleDynamic Economiesrdquo Journal of Development Economics XXIV (1987)41ndash55

Lai Huiwen and Daniel Treer ldquoThe Gains from Trade Standard Errors withthe CES Monopolistic Competition Modelrdquo University of Toronto mimeo1999

Lucas Robert ldquoOn the Mechanics of Economic Developmentrdquo Journal of Mone-tary Economics XXII (1988) 3ndash42

Mankiw N Gregory David Romer and David N Weil ldquoA Contribution to theEmpirics of Economic Growthrdquo Quarterly Journal of Economics CVII (1992)407ndash 437

Parente Stephen L and Edward C Prescott ldquoBarriers to Technology Adoptionand Developmentrdquo Journal of Political Economy CII (1994) 298ndash321

Parente Stephen Richard Rogerson and Randall Wright ldquoHomework in Devel-opment Economicsrdquo Journal of Political Economy CVIII (2000) 680ndash687

Pritchett Lant ldquoDivergence Big Timerdquo Journal of Economic Perspectives XI(1997) 3ndash18

Quah Danny ldquoEmpirics for Growth and Distribution Stratication Polarizationand Convergence Clubsrdquo Journal of Economic Growth II (1997) 27ndash60


Rebelo Sergio ldquoLong-Run Policy Analysis and Long-Run Growthrdquo Journal ofPolitical Economy CXIX (1991) 500ndash521

Rivera-Batiz Luis A and Paul M Romer ldquoEconomic Integration and Endoge-nous Growthrdquo Quarterly Journal of Economics CVI (1991) 531ndash555

Romer Paul M ldquoIncreasing Returns and Long-Run Growthrdquo Journal of PoliticalEconomy XCIV (1986) 1002ndash1037

mdashmdash ldquoEndogenous Technological Changerdquo Journal of Political Economy XCVIII(1990) S71ndashS102

Segerstrom Paul S T Anant and Elias Dinopoulos ldquoA Schumpeterian Model ofthe Product Life Cyclerdquo American Economic Review LXXX (1990)1077ndash1092

Solow Robert ldquoA Contribution to the Theory of Economic Growthrdquo QuarterlyJournal of Economics LXX (1956) 65ndash94

Stiglitz Joseph E ldquoFactor Price Equalization in a Dynamic Economyrdquo Journal ofPolitical Economy LXXVIII (1970) 456ndash 488

Stokey Nancy ldquoHuman Capital Product Quality and Growthrdquo Quarterly Journalof Economics CVI (1991) 587ndash616

Summers Robert and Alan Heston ldquoThe Penn World Table (Mark 5) An Ex-panded Set of International Comparisons 1950ndash1988rdquo Quarterly Journal ofEconomics CVI (1991) 327ndash368

Ventura Jaume ldquoGrowth and Interdependencerdquo Quarterly Journal of EconomicsCXII (1997) 57ndash 84

World Bank World Development Report 1997 The State in a Changing World(Oxford and New York Oxford University Press for the World Bank 1997)

Young Alwyn ldquoLearning by Doing and the Dynamic Effects of InternationalTraderdquo Quarterly Journal of Economics CVI (1991) 369ndash405


Existing frameworks for analyzing these questions arebuilt on two assumptions (1) ldquoshared technologyrdquo or techno-logical spillovers all countries share advances in world tech-nology albeit in certain cases with some delay (2) diminish-ing returns in production the rate of return to capital or otheraccumulable factors declines as they become more abundantThe most popular model incorporating these two assump-tions is the neoclassical (Solow-Ramsey) growth model Allcountries have access to a common technology which improvesexogenously Diminishing returns to capital in production pullall countries toward the growth rate of the world technologyDifferences in economic policies saving rates and technologydo not lead to differences in long-run growth rates but in levelsof capital per worker and income The strength of diminishingreturns determines how a given set of differences in these

Pritchett [1997] for the widening of the world income distribution since 1870 andAcemoglu Johnson and Robinson [2001b] for the reversal in relative economicrankings over the past 500 years and widening over the past 200 years

FIGURE ILog of Income per Worker in 1990 and 1960 Relative to World Average from

the Summers and Heston [1991] Data SetThe thick line is the 45 degree line






























A Description







(1) E0

`







(3) BC(rp( z)) 5 r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )

(4) BI(rp( z)) 5 2 1 z r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )




B World Equilibrium



(5)r 1 pCcedil I

pI2

pCcedil C

pC5 1

cCcedilc

(6) limt reg `

pI z kpC z c

z e 2 zt 5 0








(8) p 5 r


(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1



(10) pC 5 r1 2





(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

















































































A Description







(1) E0

`







(3) BC(rp( z)) 5 r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )

(4) BI(rp( z)) 5 2 1 z r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )




B World Equilibrium



(5)r 1 pCcedil I

pI2

pCcedil C

pC5 1

cCcedilc

(6) limt reg `

pI z kpC z c

z e 2 zt 5 0








(8) p 5 r


(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1



(10) pC 5 r1 2





(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(1) E0

`







(3) BC(rp( z)) 5 r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )

(4) BI(rp( z)) 5 2 1 z r1 2 z S E0

M

p( z)1 2 z dz D (1 2 )




B World Equilibrium



(5)r 1 pCcedil I

pI2

pCcedil C

pC5 1

cCcedilc

(6) limt reg `

pI z kpC z c

z e 2 zt 5 0








(8) p 5 r


(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1



(10) pC 5 r1 2





(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES






















































B World Equilibrium



(5)r 1 pCcedil I

pI2

pCcedil C

pC5 1

cCcedilc

(6) limt reg `

pI z kpC z c

z e 2 zt 5 0








(8) p 5 r


(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1



(10) pC 5 r1 2





(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

























































(8) p 5 r


(9) E0

M

p( z)1 2 z dz 5 E z p1 2 z dG 5 1



(10) pC 5 r1 2





(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES






















































(11) pI 5 2 1 z r1 2


(12) y 5 z p1 2 z Y


C World Dynamics



(14) r z k 5 z r1 2 z E r z k z dG






(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(15) r 5 S 1 x D 1



(16) yR 5 z S 1 x D( 2 1)

(17) E z S 1 x D( 2 1)

z dG 5 1









pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

























































pI2

pCcedil C

pC5 z p












(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES




























































(20) y 5 A z S sx D (1 2 )





yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES





















































yR 5 z ( 2 1) z S sx D

( 2 1)







(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(21) g t 5 2 z ln yt 2 1 1 Z 9t z 1 ut


(22) g ordmyCcedily

5 x 12 1

z ( 1 x) z F S yR

yRD 2 ( 2 1)

21 x

1 x G










(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES
























































(23) t 5 ( gt 2 xt)( 2 1) 1 ln t







FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES





















































FIG

UR

EII

Ch

ange

sin

Ter

ms

ofT

rade

1965

ndash198

5ve

rsus

GD

PG

row

th19

65ndash1

985





(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES
























































(24) t 5 z gt 1 Z 9t z 1 t










Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

























































Mainregression

Detailingschooling


Addingchangein Sch

Addingchangein Sch

Nonoilsample

(1) (2) (3) (4) (5) (6)



2 0595 2 0578 2 0458 2 0561 2 0455 2 0620(0265) (0261) (0221) (0248) (0187) (0354)


2 0001 2 0002 2 0000 2 0001(0002) (0002) (0002) (0002)


2 0002(0003)


2 0002(0006)


0019(0034)


0043 0045 0034 0020 0046(0024) (0024) (0021) (0027) (0030)

OPEC dummy 0091 0090 0092 0086 0087(0009) (0009) (0009) (0010) (0009)

War dummy 2 0013(0005)


0007(0023)


2 0005(0012)


0008 0009(0004) (0003)


2 0000 2 0042(0078) (0045)


Log of GDP 1965 2 0019 2 0020 2 0024 2 0020 2 0020 2 0016(0004) (0004) (0004) (0004) (0004) (0004)

R2 035 036 054 047 047 034



0037 0037 0038 0041 2 0005 0116(0106) (0107) (0107) (0112) (0103) (0114)

N of obs 79 79 70 79 79 74







20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES
























































20












FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES




























































FIG

UR

EII

IT

heIn

stru

men

tal-

Var

iabl

esR

elat

ions

hip

betw

een

Cha

nges

inT

erm

sof

Tra

de19

65ndash1

985

and

GD

PG

row

th19

65ndash1

985

(Ins

tru

men

ted

bylo

gG

DP

1965

)






M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

























































M

p(z)1 2 z dzD (1 2 ) G






(27) pC z c 5 z S pI z k 1 E0

`





(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(28) pC 5 w(1 2 ) z (1 2 ) z r z (1 2 )



(29) 1 5 (1 2 ) z (1 2 ) z (( pC z c)w)


(30) pC z c 51 2 (1 2 ) z (1 2 )

z pI z k




(33)w

r z k 1 w5

(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z z r 1 (1 2 ) z (1 2 ) z








(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES

























































(34) w 5(1 2 ) z (1 2 ) z

[ 1 (1 2 ) z ] z x 1z z S 1 x D

( 2 1)

z Y




k Rk where R

k









w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES


























































w 0 N 1 1

[ 1 (1 2 ) z ] z x z z ( 1 x)2 1 [ 1 (1 2 ) z ] z z x

















(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES


































































(35) p 5 ( ( 2 1)) z r



(36) w 5 ( ) z p1 2 z Y



(37) 1 2 5 (1 2 ) z (1 2 ) z ( pC z c)w





(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(38)kCcedil

k5 z r 2 F 1 2

(1 2 ) z (1 2 )

1 2 G z z

(39)zCcedilz

5 F 1 2(1 2 ) z (1 2 )

1 2 G z z 2

(40) limt reg `

z z e 2 zt 5 0



(41) r z k 1 w 5 z S 2 1 D 1 2


(42)w

r z k 1 w 5(1 2 ) z (1 2 ) z z

(1 2 ) z z r 1 (1 2 ) z (1 2 ) z z

(43) w 5 z S 2 1 D 1 2








(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES























































(44) yR 5 z S 2 1 D1 2

z S 1 x D( 2 1)

(45) E z S 2 1 D 1 2

z S 1 x D( 2 1)

z dG 5 1



(46) 5 z1 x z [1 2 (1 2 ) z (1 2 )]

z [ 1 z (1 2 ) z (1 2 )] 1 z x
















REFERENCES
































































REFERENCES





















































the world income distribution - stanford …klenow/acemoglu and ventura.pdfthe world income...

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