Education, Technical Change, and Openness

Education,Technical Change,and Openness∗Krishna B.KumarFebruary2001AbstractIn this paper,we develop a simple open economy growth model that allows for the possibility that productivity growth and education affect each other and use it to empirically address issuesof causality between the two.Technology adoption fostered by economic openness is modeled asthe primary determinant of productivity growth.Thus,this framework also allows us to evaluatewhether the much-documented effect of openness on growth carries over to a simultaneous systemthat features human capital accumulation.The model implies that an increase in openness willstimulate technical change,but,for empirically plausible values of the intertemporal elasticity ofsubstitution,it will cause a decrease in the level of education.The increase in the rate of costlytechnology adoption caused by the increased openness,induces an even greater increase in theequilibrium local interest rate,thereby increasing the discount factor that applies to the educationdecision.The theory motivates the speciÞcation of a simultaneous equation regression systemin which technical change,captured by total factor productivity growth rates,and educationalattainment are endogenous variables.The evidence is broadly consistent with the theory—opennessand the level of education stimulate productivity growth and there is a negative effect of this growthon schooling.∗Department of Finance and Business Economics,Marshall School of Business,University of Southern California,Los Angeles,CA90089-1427.e-mail address:kbkumar@.I am grateful to Ayse Imrohoroglu,Peter Klenow,Robert Lucas,Hans Mikkelsen,Thomas Sargent,and Nancy Stokey,for comments,criticisms,and suggestions.1IntroductionThree related strands can be identiÞed in the recent empirical literature on economic growth.One strand examines the correlation between growth and its determinants suggested by growth models. These studies typically examine the effect of human capital and investment on growth,and convergence effects in growth.The original inßuence is Barro(1991).A highly abbreviated list of other studies in this vein is Mankiw,Romer,and Weil(1992),Benhabib and Spiegel(1994),and Barro and Sala-i-Martin(1995).A second examines the effect that economic openness has on output and productivity growth by facilitating capital and technologyßow.Lee(1993),Lee(1995),Sachs and Warner(1995), Barro,Mankiw,and Sala-i-Martin(1995),Harrison(1996),Edwards(1998),and Borensztein,De Gregorio,and Lee(1998)are a few examples.1A more recent strand questions the empirical relevance of human capital as a causal factor in economic growth.While Bils and Klenow(2000)most directly address this question and go so far as to suggest that the causality might actually run from growth to schooling,the question of whether differences in human capital or productivity,a commonly suggested alternative,is responsible for economic growth and development has also been addressed in Klenow and Rodriguez(1997),Klenow(1998),Prescott(1998),and Temple(1999).This paper takes the position that these related ideas need to be addressed in a uniÞed framework. There is a compelling theoretical motivation to do so.Increased openness,by facilitating technology adoption,fosters productivity growth and this anticipated growth affects the incentives to acquire education.Similarly,an increase in the level of education affects the incentives to adopt complementary technologies.It will therefore be useful to construct a model that features education,productivity growth,and openness to identify the nature and strength of interactions among them.Given the simultaneity of inßuences,and the inherent difficulties in pinning down causalities,there is also a strong empirical motivation to have an integrated framework.2Explicitly allowing for the possibility that productivity growth and education simultaneously affect each other allows us to derive an empirical speciÞcation in which issues of causality between the two can be suitably addressed.Since technology adoption fostered by economic openness is modeled as the primary determinant of productivity growth, the framework allows us to evaluate if the much-documented effect of openness on growth carries over to a simultaneous system that features human capital accumulation.31See,however,the skepticism voiced by Rodriguez and Rodrick(1999).2Benhabib and Spiegel(1994)offer suggestive evidence that there is an interactive effect between technology gap and human capital,and Borensztein et.al.(1998)likewise argue there is an interactive effect between openness and human capital.Such evidence bolsters the case for an integrated framework that features human capital,technological change, and openness.3At least on a superÞcial level,the total factor productivity(TFP)growth rate and level of educational attainment are negatively correlated with measures of distortion such as the black market premium on exchange rates,and positivelyToward this end,this paper synthesizes ideas from two related strands of growth literature that have remained separate,the human capital literature(as exempliÞed by Lucas(1988)),and the technical change literature(as exempliÞed by Romer(1990)),to develop a simple model of growth in an open economy.4In particular,unlike most other papers in the growth literature,the paper goes on to model the schooling decision itself.The empirical contribution is a study of the causal nature of the above-mentioned correlations in a simultaneous regression framework that is motivated by the model.Most previous empirical studies in the growth literature have used single equation regressions where issues regarding causality have been hard to pin down,or instrumented regressions that focus on one aspect of the problem.The basic model uses the endogenous technical change setup in Romer(1990),suitably modiÞed to accommodate technology adoption.Technology is captured by an ever-increasing variety of inter-mediate goods which can be used to manufactureÞnal goods.Any new intermediate good can be used in the production process provided the technology to make it isÞrst adapted to the local environment by incurring aÞxed cost.It is assumed that all physical capital needed to manufacture intermediate goods has to be rented from advanced countries at a given world interest rate.The elimination of physical capital accumulation from the local agents’problem makes the analysis simpler.5At the same time it allows us to study the effect of tariffs,which is an index of openness in the model,on the incentive that localÞrms have to adopt technologies.Technology in this model is thus embodied in capital imported from advanced countries.To model education,the human capital accumulation model of Stokey(1991)is followed.Agents live for aÞnite amount of time and are situated in a dynasty with continuously overlapping generations. Each agent spends a certain period of time initially acquiring education,and later supplies the human capital acquired through education toÞnal goodÞcation has to beÞnanced locally.This assumption is motivated by incompleteness in human capital markets,especially global ones,that arise correlated with measures of international inßows such as the ratio of imports to GDP capital imports to GDP.The simple correlation coefficients,in a sample of64countries,between TFP growth rate in the1960-85period and(i)log(1+BMP) is−0.335,(ii)imports-to-GDP is0.179,and(iii)capital imports-to-GDP is0.248.The coefficients between the level of educational attainment and these three quantities are−0.502,0.419,and0.477respectively.The data is described in detail in section4.Only an empirical speciÞcation that is motivated by theory can disentagle the direction of causality in these simple correlations.4What is not modeled is the politico-economic interaction between policies of openness and the level of development of an economy.One would expect an increase in the level of education to increase the pressure on a closed economic regime to liberalize;the modeling of this interaction is left for future research.The empirical analysis,however,takes into account that openness is endogenous to the development process.5A less restrictive assumption used by Lee(1995),that domestic and imported investment are imperfect substitutes in the production of a composite investment good yields similar results.A brief discussion of the case with domestic capital accumulation is provided in the appendix.from moral hazard.The interest rate used in discounting is therefore the endogenously determined domestic rate.For similar reasons,it is also assumed that the adoption costs have to be borne locally. Hence the interest rate that the adoptionÞrms use in discounting their proÞts is also the domestic rate. The fact that these two rates are locally and endogenously determined is important to the paper’s main result.Thus,this model is most applicable to non-technology-producing countries that have the opportu-nity to acquire technologies available in advanced countries by importing capital from them,but would have to locally develop the educational and technological“infrastructure”to take advantage of these technologies.In the model,there is an interaction between the incentives to acquire education and to invest in new technologies.The level of human capital and the tariffrate affect the growth rate by affecting the proÞts from adopting new technologies,the former positively,and the latter negatively. The growth rate,in turn,inßuences the education decision of agents through the effective rate at which future earnings are discounted.The focus is on the stationary equilibrium that arises from this setup,where the growth rates of technology,output,and consumption,and the level of schooling are constant.The model implies that increased openness(a reduction in the tariffrate levied on imported capital)will stimulate technical change,but whether this causes an increase or a decrease in the level of education depends on the intertemporal elasticity of substitution.When this quantity is less than unity,the increase in the rate of costly technology adoption caused by the increased openness,induces an even greater increase in the equilibrium local borrowing and lending rates,thereby increasing the discount factor that applies to the education decision;this will cause the level of education to decrease.If the elasticity is greater than unity,the level of education will increase.An elasticity less than one seems to be the empirically plausible value,and therefore there is reason to believe that any increase in growth,ceteris paribus, is likely to cause a decrease in the level of education.We argue that this result is robust to adding human capital to the adoption speciÞcation.Even though the focus is on the unique equilibrium case where there is positive growth,another type of equilibrium that can also result is illustrated.Growth traps arise when the life expectancy or productivity of the education sector are low,or the tariffrate or cost of adoption are high.Low life expectancy negatively affects the return to education while a high tariffrate affects the return to technology adoption.Motivated by the theory,we specify a simple simultaneous equation regression system with TFP growth rates and the level of educational attainment as endogenous variables.The evidence is in favor of openness and the level of education stimulating technical change and a negative effect of growthon schooling.The positive effect of schooling and openness on growth that earlier studies have found are corroborated in this integrated framework.However,we do notÞnd the strength that Bils and Klenow(2000)Þnd in the positive“reverse”channel between growth and schooling.Toward the end of the paper we speculate on the reasons for this difference.The stationary version of the model analyzed here is silent on how opening up the economy might preferentially affect the returns to relatively more skilled labor.This is a limitation it shares with most representative agent models of human capital and growth.The negative coefficient on growth in the schooling regression need not be inconsistent with an increase in wages of the skilled,when an economy opens up.6In addition to the empirical studies cited above,on the theoretical front,this paper is related to some recent models that attempt to explore the complex ways in which the incentives to acquire new technology and accumulate human capital might interact.For instance,Ciccone(1996)argues that barriers to technology transfer can translate into less human and physical capital intensive production methods,thereby decreasing the incentive to accumulate both forms of capital.As in his model,we haveÞxed adoption costs.However,unlike the unbounded labor quality which he uses for human capital,we have schooling acquired byÞnite-lived agents.This allows us to focus on the effect of openness and growth on schooling and facilitates our empirical analysis.Eicher(1996)models technical change arising in a serendipitous fashion during the process of human capital accumulation.Since this change has to be“absorbed”by skilled labor in the subsequent period,it increases skilled wages and thus the cost of teachers in that period.In our model,the engine of growth,technology adoption, occurs in a sector different from the education sector,though the cost of adoption will affect the incentives to acquire education through the interest rate.Apparently,the type of education that Eicher focuses on is university education,which is capable of giving rise to technological change as a by-product,while the education envisioned here is general education that is a complementary to capital goods in production.His focus is on explaining episodes in which the skill premium and the supply of skilled labor move in opposite directions,while the aim here is to develop joint implications on openness,growth,and education that can be taken more directly to the data.While neither of the above studies features openness,the model in Stokey(1996)does.In a model of development with capital-skill complementarity,sheÞnds that inßows of physical capital alone causes rapid increase in the accumulation of human capital,while full integration with a larger neighbor causes little change in the accumulation.Only the small open economy case is studied here,and it is 6Caucutt,Imrohoroglu,and Kumar(2000),construct a heterogeneous-agent endogenous growth model which explores the relative rates of return of skilled and unskilled labor to anticipated growth.However,the present representative agent framework is more readily amenable to cross-country data.shown that increased capital imports can cause a greater level of education to be acquired but only if the intertemporal elasticity of substitution is greater than one.Unlike her model,the present one has growth in the long run.The rest of this paper is organized as follows.In section2,the model is developed.The stationary growth path is analyzed in section3;the effect of a decrease in tariffrate on the equilibrium rate of technical change and the level of education is studied and theoretical robustness is explored.The data is described and the regression results are presented in section4.In section5,we compare our results with those of other studies.Section6concludes.2The Model Economy2.1Technology Adoption and ProductionThe production sector is a variant of the now standard setup used in Romer(1990),and will be described as brießy as possible.The idea is to capture technological progress as the adoption of new intermediate goods,for which blueprints have been developed elsewhere,that are used in the production process.The production of the singleÞnal good uses a continuum of available and imperfectly substitutable intermediate goods,x(i),with i ranging from0to N.Here N is to be interpreted as the technological index of the economy.Intermediate goods which have not been adapted to the local environment cannot be produced or used in the production process.Human capital,which depends on the education level of agents,is the other factor of production.We will describe how education translates into human capital supplied later.For now,it suffices to note that theÞrm hires an aggregate quantity H of human capital at a rental rate w.The instantaneous production function(suppressing the time argument)is:Y=A·Z N0x(i)1−αdi¸Hα,(1) where A is a constant productivity parameter.There is no loss of generality in assuming a singleÞnal goodÞrm that solves:A·Z N0x(i)1−αdi¸Hα−Z N0p(i)x(i)di−wH.maxx,HTheÞrm takes as given the price function,p,human capital rental rate w.x is chosen from the space of piecewise continuous,bounded functions.TheÞnal good is chosen as the numeraire and its price is normalized to one.TheÞrst-order conditions imply the factor demands:x(i)=·p(i)¸−1/αH,∀i.(2)The price elasticity of demand is therefore(−1/α).The rental rate of human capital satisÞes:w=αANµx(i)H¶1−α,∀i.(3) It can be seen that the rental rate increases with the technology index,N.Each intermediate good is produced by a monopolistically competitiveÞrm.TheÞrm buys the blueprint for manufacturing the intermediate good from the adoption sector for a price P N.(TheÞrm raises this amount by issuing shares to the households in the economy.)In addition to giving theÞrm the know-how to make the good,this also grants it an inÞnitely-lived exclusive right to manufacture the good.Each unit of any intermediate good requiresηunits of(general)physical capital.Assumption1:All physical capital used in the production of intermediate goods has to be im-ported(presumably from more advanced countries).•The advantages of this assumption are threefold.First,it makes the domestic household’s accu-mulation problem simpler.(As an extension to the above assumption,it is assumed that the economic agents in the less developed economy cannot accumulate or export physical capital.)Second,it gives content to the notion of openness toward ideas and technologies by assuming that all technology is embodied in imported capital.Third,it allows us to index openness by tariffs that are imposed on imported capital.A less restrictive assumption used by Lee(1995),that domestic and imported invest-ment are imperfect substitutes in the production of a composite investment good would yield results similar to ours.A brief discussion of the case with domestic capital accumulation is provided in the appendix.TheÞrm faces the economywide demand given by equation(2)directly.Its revenues are therefore given by p(i)x(i)=A(1−α)x(i)1−αHα.We assume that theÞrm faces a(constant)worldwide rental rate of capital r w.7We also assume that the local government imposes a tariffrateτon imported capital,so the effective cost of capital faced by the intermediate goodÞrm is(1+τ)r w.8 7This assumption is equivalent to assuming that the advanced countries from which the small open LDC imports capital are on a balanced growth path.8As will be shown below,an increase in the tariffrate will negatively affect the incentive to adopt technologies and therefore the growth rate.The question then arises as to why a benevolent government would choose to harm its citizens by imposing import duties on capital goods.One possibility is that this is an effective way to raise government revenues in an environment where the collection of income taxes is very difficult.See for instance,Þgures3and4in Easterly and Rebelo(1993)which show that the share of customs taxes in government revenue is high(and the corresponding ratio of income taxes is low)for low income countries.If the government expenditure enters the household’s utility function separably,none of the marginal conditions wouldTherefore,Þrm i’s problem to choose x(i)(and therefore,p(i))can be written as:maxx(i)A(1−α)x(i)1−αHα−η(1+τ)r w x(i).TheÞrst-order condition implies:9p=η(1+τ)r w1−α(4)µx(i)¶α=A(1−α)2w.(5) Given the common rental rate and aggregate human capital in the economy,it is clear that the quantity of intermediate good produced is independent of the good index,which is henceforth suppressed. Equation(4)is the constant marked-up price of any intermediate good.10The use of(4)in theÞrm’s objective function implies that the instantaneous proÞts of any intermediate-goodÞrm is given by:π=Aα(1−α)x1−αHα.(6)If we use the fact K,the aggregate quantity of physical capital,isηNx,and the totalßow of factor income abroad is r wηNx,in the production function,it is easy to show that the capital-to-output ratio is directly proportional to the rentalßow-to-output ing imports-to-output as a proxy for the latter,weÞnd that in a cross section of79countries the growth rates of imports-to-output and growth rates of capital-to-output for the1960-1985period are positively correlated(the simple correlation coefficient is0.235).The level correlation across93countries is higher,at0.346.This lends some plausibility to Assumption1.As mentioned earlier,the technology index in this economy is the number of intermediate goods for which blueprints have been adapted to local conditions.We assume that there is aÞxed cost of F units of good,per worker,for each new blueprint that is adopted.Having the cost in per worker terms might seem a forced way of avoiding scale effects.However,if at least part of the costs of adoption is training workers who would not have had knowledge about this new technology embodied in school, the assumption is reasonable.With this assumption,one can also avoid dealing with a reduction in the be affected and the analysis presented below stays unaltered.For simplicity we will just assume that the tariffrevenues are returned,lumpsum,to the households.In any case,the presumption that all LDC governments are benevolent and follow enlightened policies seems unreasonable.A more complete answer to this issue will require the modeling of politico-economic considerations mentioned in the introduction.9Evidently,this model is isomorphic to a closed economy model with taxation of capital.However,the motivation of the study and its empirical implementation lead one to identifyτwith measures of openness.One would also anticipate the various measures of distortion to be correlated.10We could have directly assumed that all intermediate goods were imported at this effective cost.This is in contrast with models where it is assumed that intermediate goods represent nontradeable services that have to be produced domestically.labor force that accompanies increased schooling in a constant population setup,an issue that seems peripheral to present considerations.Relaxing the per worker assumption would not alter the results that are central to this paper.If we denote the number of workers by L,the zero-proÞt condition for the adoptionÞrm implies that the cost of blueprint P N is given by P N(t)=F L(t).Since these technologies have been developed elsewhere,not using human capital as a factor of production in their local adoption is not a serious omission and is done mainly for ter, we argue that adding human capital to the adoption speciÞcation does not qualitatively change the results.Assumption2:The adoption costs have to beÞnanced locally.•These projects are located in the LDC and are therefore not amenable to continuous monitoring by foreign investors.Therefore it is reasonable for foreignÞrms to expect equity participation by local partners.11Several LDCs also restrict the percentage of equity that can be owned by foreigners for reasons of sovereign control.All we really need is that part of the funds be raised locally.However, it is simpler to assume that all equity is raised locally.A possible objection to this assumption is that it contradicts the previous assumption,since some of the capitalßows can occur through foreign direct investment(FDI).While this might be true,in practice it is not clear that FDI plays a greater role than direct capital imports in growth.For instance,the IMF’s World Economic Outlook(1999) reports that FDI was0.4%of GDP as late as the80s for developing countries.In contrast for the poorer half of the countries we use for empirical analysis,capital imports were1.7%of GDP.Japan and Korea,for example,actually tended to discourage FDI.(see Krueger(1995)).Moreover,as Hausmann and Fernandez-Arias(2000)argue,FDI does not constitute physical assets of aÞrm,which are more relevant for our purposes,but only one way by which itÞnances itself.The price of the blueprint P N would be bid down by potential intermediate goodÞrms till there is no pure rent in a present value sense.That is:Z∞t e−R z t r(s)dsπ(z)dz≤P N(t)=F L(t),(7) which holds with equality if a positive number of blueprints are adapted.If instead the left side is lower,it means that the discounted present value of proÞts is not high enough to cover theÞxed costs 11Also,as Telesio(1979)notes in the context of licensing technologies in countries where the investment climate is unfavorable,“Expropriation is probably less likely to occur if there is only a minority foreign position or no foreign ownership at all in a local enterprise than if it is controlled by a foreign investor.”(pp.14).Also see Lessard(1986),who notes,“In the case of risks involving an element of choice,···,comparative advantage lies with the party most able to mitigate the risks in question.···given the degree of choice involved in national economic policies,national governments have a clear comparative advantage in bearing these risks—that is,the existence of such moral hazard risks severely limit internationalÞnancial exchanges.”(pp.167).of adoption and therefore no blueprint is adapted.Given Assumption2,it is r,the local interest rate, and not r w,the world interest rate that is used to discount proÞts.A simple example might help place the above-mentioned production processes in perspective.An adoptionÞrm in the LDC translates computer manuals written in a developed country into the local language.TheÞrm incurs aÞxed cost in doing this.The intermediate goodÞrm that buys these translated manuals(blueprints),imports computer equipment(general capital)and uses the two to produce software services.These services form one of the intermediate goods that theÞnal goodÞrm uses in its production process.12This completes the description of the production sector of the economy.2.2Education and the Household’s ProblemThe economy is populated by a continuum(of measure one)of identical inÞnitely lived households.13 Each household consists of an inÞnite stream of continuously overlapping generations.Each individual lives for T units of time.We will refer to this quantity as the life expectancy of an individual.Since each generation(or cohort)is the same size(one),the size(T)and the demographic composition of the population are constant over time.Consumption and time allocation decisions are made by the household,whose preferences over inÞnite consumption streams for each individual alive are given by the standard isoelastic intertemporal utility function:Z∞0e−ρt c(t)1−σ1−σdt(8) where c(t)is the per capita consumption,andσ>0.Whenσ=1,this is interpreted as R∞0e−ρt log(c(t))dt.At the beginning of her life,an individual can spend s units of time acquiring education(that is, accumulating human capital),and thereafter work from age s to age T.In this section we assume that the human capital of an individual who has acquired s units of schooling is:h(s)=F(s)=Be f(s),(9) where f:[0,T]→R+satisÞes f0(s)>0and f00(s)≤0.14The exponential form is motivated by Mincerian regressions in which the logarithm of wages,rather than its level,is better explained by12See Ciccone(1996)for more examples on these lines.13The formulation in this section is motivated by the setup in Stokey(1991).14The mapping of schooling to human capital is inspired by the speciÞcation in Bils and Klenow(2000).For purposesof comparison,their speciÞcation is,h(s)=¯hφe f(s)+g(a−s),where g captures on-the-job learning,¯h is the human capitalof a prior generation(“teachers”),and0≤φ≤1.For sake of simplicity,we have omitted on-the-job learning in the theoretical modeling;adding it would not signiÞcantly alter our conclusions.Moreover,it will be empirically accountedfor given our use of the human capital data in Klenow and Rodriguez(1997).More importantly,we setφ=0.That is,the human capital of previous generations do not enter the productivity of education of the current generation.Itis only necessary for our analysis thatφ<1,and settingφto zero is only a simpliÞcation.In Stokey’s(1991)model,。