Trade and Divergence in Education Systems

Transcription

1 Trade and Divergence in Education Systems Pao-Li Chang & Fali Huang December 2010 Paer No ANY OPINIONS EXPRESSED ARE THOSE OF THE AUTHOR(S) AND NOT NECESSARILY THOSE OF THE SCHOOL OF ECONOMICS, SMU

2 Trade and Divergence in Education Systems Pao-Li Chang School of Economics Singaore Management University Fali Huang y School of Economics Singaore Management University November 16, 2010 Abstract This aer resents a theory on the endogenous choice of a country s education olicy and the two-way causal relationshi between trade and education systems. The setting of a country s education system determines its talent distribution and comarative advantage in trade; the ossibility of trade by raising the returns to the sector of comarative advantage in turn induces countries to further di erentiate their education systems and reinforces the initial attern of comarative advantage. Seci cally, the Nash equilibrium choice of education systems by two countries interacting strategically are necessarily more divergent than their autarky choices, although the di erence is still less than what is socially otimal for the world. We rovide some reliminary emirical evidence on the relationshi between education, talent distribution, and trade. JEL Classi cation: F16, I20, J24. Key Words: Education System, Talent Distribution, Comarative Advantage, Trade Pattern. School of Economics, Singaore Management University, 90 Stamford Road, Singaore lchang@smu.edu.sg. Tel.: Fax: School of Economics, Singaore Management University, 90 Stamford Road, Singaore huang@smu.edu.sg. Tel.: Fax: Huang gratefully acknowledges the suort of SMU research grant C244/MSS6E019. 1

3 1 Introduction In this era of globalized knowledge economy, the education system, by shaing a country s human caital, may exert signi cant in uences on its comarative advantages in international trade. And conversely, a country s trade attern and intensity may a ect how its education system is run. Such interactions between education and trade could be seen in recurrent reviews of education olicies by nations across the world. In the US, for examle, the National Commission on Excellence in Education (1983) claimed in an in uential reort that America is at risk: The risk is not only that the Jaanese make automobiles more e ciently than Americans..., or that American machine tools... are being dislaced by German roducts. It is also that these develoments signify a redistribution of trained caability throughout the globe.... If only to kee and imrove on the slim cometitive edge we still retain in world markets, we must dedicate ourselves to the reform of our educational system... 1 In site of the clear imortance and urgency of educational reform in its role of a ecting countries comarative advantages, we are not aware of any formal analysis in the economics literature to shed light on this matter. This aer makes a rst attemt at roviding a theory on the two-way interactions between education olicies and trade. In articular, we show that any initial di erence in education olicies across countries that contributes to countries comarative advantages will be further enlarged when countries move from autarky to trade. The intuition is that international trade increases the returns to the sector of comarative advantage, and thus induces countries to further di erentiate their education systems in order to maximize gains from secialization. As a result, a small di erence in initial education systems across countries, ossibly due to historical or cultural variation, will be further amli ed by the increase in international trade. In this aer, we focus on an imortant characterization of a country s education system, which is the degree of centralization or homogenization imosed on the curriculum, and its e ect on a country s talent distribution. A more homogeneous structure of curricula across schools imroves 1 For related discussions on the US education, see Schaub and Baker (1991), Westbury (1992), Bracey (1996), Hanushek (2002), and Dillon (2007), among others. For recent educational reforms in other countries, see for examle Takayama (2007) on Jaan, Mok (2005) on East Asia, and Green (1999) for general discussions on the e ects of globalization on education across countries. 2

4 the likelihood that the same set of subjects are taught, and delivered in similar manners to the students; as a result, students are more likely to acquire a common set of skills. This tye of education system is often associated with a centralized curriculum council that sets and enforces a uniform curriculum via textbooks, instructional guide to teachers, curriculum evaluation, or national standardized tests, as is evident in Jaan and some East Asian countries. The resulting ressures to conform with the uniform standards in terms of education oututs, however, leave relatively little room for individual exlorations and hence could ush the more-talented students toward the mean as well as the lower-ability students. In contrast, if schools/teachers do not need to follow a standardized set of curricula or erformance targets, this tends to introduce more variation in student erformance, as students have more freedom to ursue their individual interests and realize their otentials under a exible curriculum; without the necessary disciline, however, the less-talented students may fail to acquire the basic set of skills. This aroach is often carried out in a decentralized education system as is exemli ed by the US system. Thus, relatively seaking, the Jaanese style of education system romotes homogeneity in the distribution of skills, while the US education system leads to more diversity. The education systems in other countries, di erent in their orientation toward these two aroaches, generally fall in between these two extremes (Cummings 1999). We show in theory that by altering the resulting talent distribution, di erent educational aroaches will lead to di erences in comarative advantage and trade structure in countries with otherwise identical economic constraints. Seci cally, the decentralized education system in the US tends to romote talent diversity in its work force, which enhances the roductivity of industries that bene t from worker skill heterogeneity, e.g., software and movie; in contrast, with a centralized education system, Jaanese work force tends to be more homogenous in their skills, which increases the roductivity of industries characterized by long and comlex roduction rocesses, e.g., automobile and machinery. It then follows that countries with more decentralized education systems will have a comarative advantage in the software-tye industries and countries with more centralized education systems a comarative advantage in the automobile-tye industries. Given the e ects of education system on roduction and a country s comarative advantage, we 3

5 show that the endogenous choice of education system across countries will exhibit more divergence under trade than under autarky. This is because the equilibrium rice with trade will fall in between autarky rices and thus strengthen the incentives of a country to secialize more in the sector of its comarative advantage, not only via automatic resource reallocation across sectors with a given work force, but also through active adjustment in education olicies to reshae the comosition of its work force and the osition of its roduction ossibility frontier. In articular, we identify the choice of education system under autarky by individual countries who may di er in their costs of imlementing homogeneous curricula, but are otherwise identical in economic constraints and initial talent distributions. We then characterize the choice of education system under trade that is socially otimal for the world as a whole. This is comared with the noncooerative choice in the Nash equilibrium where each country maximizes its own welfare taking into account the terms-of-trade e ect of its education olicies. It is shown that the di erence in education systems across countries under trade is larger than under autarky. However, the crosscountry di erence in education systems under the Nash equilibrium is less than what is socially otimal for the world. The intuition is that the incentive to secialize through more divergent education systems is weakened in each country by the accomanying terms-of-trade loss, which on the other hand cancels out for all countries in the world welfare s calculation. We conduct some reliminary emirical analysis to demonstrate our theory s emirical relevance. Based on the Trends in International Mathematics and Science Study (TIMSS) dataset, which contains information on student erformance and curriculum structure, we roose some measures of curriculum centralization to cature the theory s characterization of national education systems in terms of the degree of homogenization imosed on students skill formation. We show that in the samle of OECD countries, a more centralized curriculum structure is indeed associated with a lower skill diversity, and the relationshi is statistically signi cant and consistent across di erent years of study. Furthermore, as the trade intensity between a air of countries increases, their di erence in curriculum centralization also tends to increase. This is consistent with our theoretical rediction that trade tends to reinforce countries initial di erences in education systems. However, given the caveats that will be noted in the emirical section, more research into 4

6 the emirical measures of education systems is needed to rovide more ersuasive conclusions. Viewed from a broader ersective, this aer contributes to the literature in two ways: First, it demonstrates the ossibility of education olicy as a new source of comarative advantage in trade, and second, it emhasizes how trade can in turn a ect a country s institutions such as education systems. To our knowledge, this endogenous determination of both education system and trade attern as an equilibrium outcome has not been examined in the literature. This aer is closely related to the literature on human caital (talent) and trade. This literature generally falls into two branches: The rst branch takes talent distribution as given and analyzes its e ect on comarative advantage and trade attern (see Grossman and Maggi 2000 for examle), while the second branch studies the e ect of trade on the stock of human caital using xed human caital roduction functions (see Findlay and Kierzkowski 1983, and Bond et al for examle). Our aer integrates these two strands of literature by exlicitly modeling the triangular relationshi between education olicy, human caital and trade. The introduction of education olicy in our model in uences the human caital formation rocess and determines the comosition of human caital in a country. The resulting talent distribution then a ects a country s comarative advantage and trade attern (as in the rst literature). When countries endogenously choose their education olicies relative to their trading artners to maximize social welfare, there are feedback e ects of trade on human caital (as in the second literature). This aer thus rovides new insights into the imortant role of education olicy in a ecting the relationshi between human caital and trade. 2 2 The rst branch of the literature starts with the ioneering work by Grossman and Maggi (2000), who show that between two trading countries, the one with a more diverse (alternatively, homogeneous) talent ool tends to exhibit a comarative advantage in roducing goods or services with a submodular (alternatively, suermodular) technology. This may account for the trade attern between the US and Jaan, where the US has more diverse talents and exorts software, while Jaan has more homogeneous talents and exorts cars. The e ect of talent distribution on trade is also examined by other studies based on alternative mechanisms including the role of costly monitoring of workers (Grossman 2004), the imlications of two-dimensional skill heterogeneity (Ohnsorge and Tre er 2007), the trade of high-tech versus rimary roduct (Bougheas and Riezman 2007), and the emirical evidence about the e ect of skill disersion on trade atterns (Bombardini et al. 2009). The second branch of the literature includes Findlay and Kierzkowski (1983) and Bond et al. (2003) among others. In Findlay and Kierzkowski (1983), it is observed that trade will accentuate the autarky di erence between countries in skilled-unskilled labor roortions. This is similar in sirit to our result that the initial attern of comarative advantage is sustained and the di erence in the human caital comosition between countries is augmented by trade. By allowing endogenous formation of both hysical and human caital, Bond et al. (2003) show that the ranking of countries relative factor abundance and trade attern may actually ersist or reverse over time. Such indeterminacy is thus in contrast with the above result. 5

7 In another strand of literature, several aers also exlicitly link education with trade but di er from us in the issues and the seci c education olicies studied. Kim and Kim (2000) assume that school education enhances general human caital versus industry-seci c skills, which together with international trade allows workers to move easily to the fastest-growing industry and hence facilitates economic growth. In an oligarchy society where landed elites have more olitical ower, Falkinger and Grossmann (2005) show that ublic education investment conducive to industrialization is tyically lower in an oen economy than in autarky; this is similar in sirit to our result that an oen economy may adot a more extreme education aroach than in autarky. Bougheas et al. (2009) also analyze the ossible e ect of trade on a country s education olicy. They formulate the education olicy, however, as a choice by a small oen economy of whether to move u or down the skill chain, taking the terms of trade as given; this is in contrast with our focus on the education olicy s role in a ecting the diversity of human caital and the otimal allocation of talent across sectors. More imortantly, our analysis takes into account the consequence of education olicies on the equilibrium trade rices and atterns, which enables us to study the interactions of education olicies across countries and their endogenous divergence. The current aer also connects with the economics literature on education that examines how di erent education regimes (ublic versus rivate, ability tracking versus ability ooling) a ect the disersion of skills and aggregate outut in closed economies (see for examle Bénabou 1996, Ele and Romano 1998, Fernández and Rogerson 1998, Takii and Tanaka 2009). An innovative feature of the current aer in comarison to this literature is that the education regimes are endogenously determined across countries and inherently linked with international trade. The aer s focus on the degree of curriculum centralization in an education system also highlights an imortant dimension distinct from the above literature s tyical emhasis on school nancing methods. The education literature has only recently begun to assess the imlications of globalization on education olicies (Green 1997, Burbules and Torres 2000, Mok 2005). Though there is considerable convergence at the level of olicy rhetoric and general olicy objectives, there is less evidence of any systematic convergence at the level of structures and rocesses in di erent countries (Green 1999). This is consistent with our nding in this aer that di erences in education systems across 6

8 countries may be a ersistent attern reinforced by trade. To our knowledge, this result is new to the education-related literature and may rovide a fresh ersective on how education olicies are formed. This aer is organized as follows. The elements of the model are described in Section 2. The endogenous choice of education system is analyzed in Section 3. We take our model to data and resent some reliminary emirical evidence in Section 4. Section 5 discusses modeling choices and ossible extensions. Section 6 concludes. 2 The Basic Model 2.1 The Education System Suose there is a unit measure of a continuum of uils indexed by i, whose innate abilities a i0 are not individually observable, but follow a distribution G() with suort [a l0 ; a h0 ] (0; +1). All uils have to go through an education system that may ossibly change their initial skills. The education system is characterized by a arameter 2 [0; 1], which indicates the degree of curriculum centralization/homogeneity imosed on each student. Seci cally, a uil with an innate ability a i0 will acquire a skill level a i at graduation such that (1) a i = (1 )a i0 + a m ; where a m = R a h0 a l0 a i0 dg(a i0 ) is the average ability of the cohort. Thus, an education system with a high will ush all students skills to the middle and reduce the skill diversity, while keeing the mean ability unchanged. Each uil s adulthood skill a i is ublicly observed with a suort [a l ; a h ] [a l0 ; a h0 ], where a h a l = (1 )(a h0 a l0 ), and its corresonding distribution function is G( a i a m 1 ) F (a i ; ). We will often write the adulthood distribution as F (a i ) to simlify resentations, bearing in mind that it deends on. The adults are ranked according to their abilities such that a i a j for i < j. We can generalize (1) to allow an additional bene t e > 0 of education that is indeendent of 7

9 the curriculum centralization, that is, a i = (1 )a i0 + a m + e. It is straightforward to verify that the subsequent results will not be a ected. We take the functional form (1) henceforth to focus on the education system s imact on talent diversity and abstract from its otentially ositive e ect on human caital accumulation. This simle model of education attemts to cature the necessary tension between equiing all students with a common set of knowledge versus romoting talent diversity. The former goal is usually better achieved with a more standardized set of curricula, where students have to go through the same subjects, and numerous exercises and exams that test whether they have met required standards before they can go to the next level of study. The time and e orts committed to following the same curriculum and activities, however, often discourage students from exloring and acquiring new knowledge in their own ways, and hence may reduce the creativity comonent of human caital (Mayer et al. 1991). The oosite is true for ursuing the second goal, where exible curricula and lenient standards are set to leave more freedom for individual exloration and hence may reserve more talent diversity. Education systems may vary across countries in their orientation toward these two goals. Among industrial countries, Jaan and the US are arguably the two rominent examles at the oosite ends of the sectrum in terms of curriculum centralization. The innate or initial abilities a i0 are taken to be unobservable to educators or even to the student herself/himself. This is to underlie the di culty of the education system to correctly evaluate each student s true talent and to tailor the teaching method according to each individual s ability. For examle, if the initial abilities were fully observable, the education resources would be best utilized to raise the skills of the less-talented students with a more discilined education method but those of the more-talented students with a more exible curriculum. Alternatively, if the innate abilities a i0 were known to the students, a menu of education methods could be o ered such that students self select into di erent schemes. The assumtion of unobservability of initial abilities highlights the inevitable trade-o of ositive and negative e ects of choosing a articular education style on the human caital of a country. 8

10 2.2 The Economy Technology. We lay out the structure of the economy below and demonstrate the imlications of given education systems on roduction and trade atterns. The results are consistent with the existing work in the literature with exogenous talent distributions. 3 Our main dearture from the literature starts in Section 3 where we exlicitly analyze the choice of education system. There are two industries in the economy. In the automobile industry, the roduction technology is suermodular with decreasing returns to overall talent, 4 y A = [a(1) + a(2) + + a(n) ] = ; 0 < < < 1 where n is the number of tasks required. The suermodularity of the auto roduction is re ected by the fact 2 y A =@a(j)@a(j 0 ) > 0, for all j 6= j 0 2 f1; 2; : : : ng and the decreasing returns to overall talent by the fact that < 1. In the other industry, the software industry, the outut is comletely re ective of individual talent, y S = a ; > 1 and exhibits increasing returns to the talent. Let = S = A denote the relative rice of software. As shown in Grossman and Maggi (2000) or similarly argued in Kremer (1993), the outut of an industry characterized by suermodular technology is maximized when workers of the same ability work in the same team ( rm). Thus, in a cometitive equilibrium, where each rm earns no ositive ro t, the wage structure of the auto industry satis es (2) w A (a) = (na ) = n a ; 3 Comarison between our setu and that of Grossman and Maggi (2000) and the reasons for the modi cations are rovided in Section 5. 4 The seci c roduction functional form for the auto industry is adoted for illustrative uroses. The same results can be achieved with the following general functional form: y A H(a(1); a(2); ; a(n)) with symmetric tasks such 2 H=@a(j)@a(j 0 ) > 0, for all j 6= j 0 2 f1; 2; : : : ng and that H(a(1); a(2); ; a(n)) = H(a(1); a(2); ; a(n)), with 0 < and 0 < < 1. 9

11 where n 1 corresonds to the benchmark wage when each task is erformed by workers of a unit talent. Thus, in each auto rm, the workers sharing the same talent level divide evenly and exhaust the revenue of the auto outut. Firms are indi erent between hiring a lower-talent team and a higher-talent team, as the wage ayment is re ective of the outut resonse to the talent level. On the other hand, the software industry s wage structure in a cometitive equilibrium is simly (3) w S (a) = a where each software worker receives the whole value of his/her outut. Preferences. Individuals have identical references, which are reresented by the utility function u(c Ai ; c Si ) = c Ai c1 where 0 < < 1, and c Ai and c Si denote individual i s consumtion of cars and software, resectively. The budget constraint is c Ai +c Si = w i, where w i is the individual s income that is equal to either w A (a i ) or w S (a i ) deending on the worker s occuation. The otimal consumtion choices are thus Si ; (4) (5) c Ai (; w i ) = w i ; c Si (; w i ) = (1 )w i ; which lead to the indirect utility function (6) (; w i ) = (1 ) 1 (1 ) w i : Talent Allocation Across Industries. Each worker takes as given the relative rice of 10

12 software. A worker joins the auto industry if and only if w A (a i ) w S (a i ), which imlies (7) a i 1 ea(). As a worker s wage income increases in his own ability at a decreasing rate if he works in the auto industry but at an increasing rate if he works in the software industry, a worker will choose to work in the software industry if his own ability is su ciently high. In (7), ea() denotes the highest ability of workers to join the auto industry, which coincides with the ability of the marginal worker who is indi erent between joining either one of the two industries. This cuto obviously hinges uon the relative goods rice. < 0. Proof. Based on the de nition ea() in (7), = 1 ea < 0: The intuition is that, as the relative rice of software falls, a worker s income in the software industry dros; as a result, the cuto talent level ea increases. When the rice falls to l a even the most talented worker a h will become indi erent between working in either one of the industries. On the other hand, when the rice of software rises above h a l h,, even the least talented worker a l will be attracted to work in the software industry. When the cuto ability is equal to the mean a m, the corresonding rice is m a m, where l m h holds due to a h a m a l. For 2 ( l ; h ), there is incomlete secialization. Our following analyses focus on the scenarios where there is incomlete secialization unless otherwise noted. Given the talent allocation, the total oututs in the auto and software industry are, resectively, Y A (; ) = Y S (; ) = Z ea a Z l ah ea df (a) y A (a) = n a df (a): Z ea a l a df (a); Note that an auto rm consists of n workers of the same ability; thus, the density of auto rms is 1 n times the density of the auto workers abilities df (a) in the above calculation of auto outut. 11

13 Production Possibility Frontier (PPF). The PPFs corresonding to two di erent education systems with J > U are illustrated in Figure 1. The maximum otential outut of software Y max S = R a h a l a df (a) is lower with a higher, as a higher decreases the talent diversity and the software outut is convex in talent. On the contrary, the maximum otential outut of cars Y max A = R a h a l a df (a) is higher with a higher, as the auto outut is concave in overall talent. Thus, a country with a higher degree of curriculum centralization in the education system will have a PPF that is relatively skewed toward the auto outut axis and vice versa for a country with a lower level of. Note that the corresonding rices at the end oints of the PPF are l at Y max A and h at YS max. With a higher, l increases and h decreases; thus, the curvature of PPF also reduces with a higher. 5 Note that for given and PPF, an increase in the cuto ability ea corresonds to a migration of workers toward the auto sector from the software sector, which has a ositive e ect on the auto outut and a negative e ect on the software: (8) A = ea f(ea) > 0; = ea f(ea) < 0: These two conditions imly that MRT the otimality of the cometitive = ea, which is equal to by (7), verifying As indicated in Figure 1, for a large range of otential rices, the country with a higher level of will roduce relatively more auto while the country with a lower level of relatively more software, given the same relative rice. Only when the rice is extremely high, near the rice level at T 0 J, will we see a reversal of the ositive relationshi between the relative auto outut and the education olicy. The following lemma seci es a su cient condition on the rice level for the ositive relationshi to hold. Lemma > 0 S < 0 for m, where j denotes holding 5 The range for incomlete secialization ( l ; h ) is smaller, the higher the education olicy. In the extreme case when = 1, the PPF becomes a straight line (not shown) with a constant sloe m, and there is incomlete secialization only when the rice is exactly equal to m. 12

14 Automobile ( A S / ) ( Y AJ / YSJ ) T J δ J > δ U T U δ J δu ( Y AU / YSU ) 0 T J ' Figure 1: E ects of Education System on PPF ' T U Software Proof. See the Aendix. Lemma 2 shows that an education system with a higher degree of curriculum centralization increases the outut of the auto industry but decreases the outut of the software industry when the relative rice of software is not too high. The intuition is as follows. With the rice level (and hence the cuto talent level ea) held constant, an increase in reduces the diversity of worker abilities in both industries. Because the auto industry s outut is concave in each rm s worker ability while the software industry s outut is convex in each worker s ability, a reduced diversity in worker abilities in the above manner has a ositive e ect on the aggregate auto outut and a negative e ect on the aggregate software outut. Furthermore, an increase in also changes the identity (ea 0 = ea am 1 ) of the marginal workers and hence the density of workers in each industry. Within the rice range m, however, the mean ability workers always work in the auto sector (since a m ea), and thus an increase in will increase the density of auto workers, reinforcing the rst e ect. The condition m is su cient but not necessary for the results in Lemma 2 to hold. 6 6 In the rice range > m such that the mean ability workers work in the software sector (ea < a m), a higher will reduce the worker density in the auto sector and raise that in the software sector. This density e ect may more than o set the average e ect and alter the result. In articular, the reversal is more likely, the further the relative rice increases above m and the closer the cuto level ea aroaches a l. 13

15 2.3 Equilibrium Analysis Autarky Equilibrium. In the autarky equilibrium, the domestic markets of both auto and software are clear so that the ratio of total sulies for cars and software is equal to the ratio of their total demands. That is, (10) by A b b Y S = R ca (b; w(a))df (a) b R c S (b; w(a))df (a) = 1 ; where the second equality is derived from (4) and (5), and a decoration bx over a variable x indicates the autarky equilibrium value of the corresonding variable x. This leads to the autarky equilibrium rice (11) b = 1 by A by S ; which is unique because the LHS is strictly increasing in, while the RHS of the equation strictly decreases @ea < 0 due > 0 S by (8) and (9), < 0 by Lemma 1. Lemma 3 A su cient condition for m (or equivalently, a m ea) to hold is (A1) 1 2 and G(a m) 1 2. Proof. See the Aendix. This lemma shows that under condition (A1), the equilibrium rice will not be larger than m, or equivalently, workers with the mean talent level will work in the auto sector. The same outcome that the mean talent workers work in the suermodular (auto) sector is achieved in Grossman and Maggi (2000) under the assumtion of symmetric talent distributions; in comarison, condition (A1) covers more grounds by allowing asymmetric talent distributions as long as the mean talent level is not above the median. The assumtion 1 2 on the references imlies that a larger roortion of consumtion is on manufacturing goods characterized by roduction chains (e.g., cars, electronics, food, clothing) than on creative roducts characterized by individual erformance 14

16 (e.g., software, movies, books, concerts), which seems consistent with reality. In what follows, we assume condition (A1) holds. 7 Lemma 4 The autarky equilibrium rice increases with the degree of curriculum centralization in the education > 0. Proof. De ne V (; ) (1 )Y A (; ) Y S (; ). Condition (11) can be rewritten as V (b; ) = 0, based on which we (; (; )=@ = =b (1 (1 A S > 0 Y S =b Lemma 1. > 0 S by Lemma 2 S > 0 by (8), (9), and Lemma 4 shows that the more centralized the education system, the higher the relative autarky rice for software in equilibrium. The intuition is obvious; as the relative suly of software is lower when is higher and as the reference is homothetic, a closed economy with a higher will have a higher relative rice for software. Free Trade Equilibrium. Suose that a world consists of two reresentative countries, Jaan (J) and the US (U). They have the same economic structure as described above, but di erent education systems ( J > U ). That is, Jaan s education system is more centralized than the US s, and as a result, the adult talent distribution a i is more homogenous in Jaan than in the US, though the talent distribution among children (a i0 ) is identical in the two countries. Rationales for such a di erence in education systems across countries even though they are the same in economic structure to begin with will be discussed in Section 3. Given the di erent education systems ( J > U ), Lemma 4 suggests that Jaan will have a higher relative autarky rice for software than the US (b J > b U ). Thus, with the ossibility of 7 Note that condition (A1) is a su cient but not necessary condition for m, which is in turn a su cient but not necessary condition for Lemma 2. Thus, there is amle room for violations of condition (A1) without invalidating the ositive relationshi between the relative auto outut and the education olicy. 15

17 trade, Jaan (the US) will have a comarative advantage in cars (software) and will exort cars (software). By similar arguments as in the case for the autarky rice b, we know that the free trade equilibrium rice is uniquely determined by (13) = 1 Y AJ + Y AU Y SJ + Y SU ; where Y AJ and Y AU are the auto oututs in Jaan and the US, resectively, and Y SJ and Y SU are the software oututs in the two countries. A decoration x over a variable x indicates the free trade equilibrium value of the corresonding variable x. It follows that b J > > b U holds for any given education systems in the two countries with J > U. The free trade equilibrium rice is higher when either J or U is higher, as either change will increase the relative suly of cars in the world market. The following lemma shows this formally. Lemma 5 The free trade equilibrium rice increases with either country s curriculum centralization in the education system, i.e., Proof. See J > U > 0: 3 Endogenous Education System In the revious section, we take education systems as given and analyze its in uence on the formation of talent distributions. The redictions on the trade attern are similar to the existing literature taking talent distributions across countries as given. We now exlore the endogenous choice of education systems. 8 We begin the analysis by characterizing the socially otimal education system under autarky. Given the di erent choices of education systems under autarky, we then analyze how countries 8 We have generalized some asects of the existing models at the cost of restricting other asects to arrive at a structure that embeds inherent trade-o s in setting education olicies. Most existing models do not exhibit such trade-o s; instead, there exists some strictly dominating PPF in these models if PPFs (talent distributions) are allowed to change by olicies. 16

18 will react to the ossibility of trade and how their otimal choice of education system will change comared to autarky. A higher degree of curriculum centralization in the education system usually corresonds to more rules and regulations imosed on the curriculum, the textbooks, the allocation of school hours, the frequency of tests, and the monitoring of student erformance. Requirements such as these entail administrative costs, e.g., to communicate, imlement, enforce, and evaluate the rules and regulations. They may also translate into disutility for each student undergoing the system. For examle, the disutility could be the lack of exibility to ursue one s own subjects of interest at di erent ace or deth, the stress endured during each test, the leisure time sacri ced for study, and so on. The more centralized the education system, the more stringent the rules and regulations, and the more administrative cost and disutility it may entail. For a given degree of curriculum centralization, some country may nd it easier to imlement than others. For examle, if a country is more homogeneous in terms of ethnic comosition, the country may nd it less costly to set and imlement a common set of curriculum and standards, as educators/uils in the system share similar cultural, linguistic, behavioral or religious traits. In a country where the national/federal government has a stronger administrative caacity relative to the local/state government, the cost of imlementing a centralized curriculum may also be lower. To cature these observations, we assume that imosing curriculum centralization entails a disutility of K j () k j in country j, where j = J; U, and 0 < k J < k U. That is, one society attaches a lower disutility to a given level of curriculum centralization than the other society, ossibly due to di erences in their ethnic comositions or olitical systems as discussed above. In articular, we assume that the Jaanese society nd it less costly than the American society in making e orts to conform to homogeneity in education standards (Section 5 rovides more discussions on why this seems to be the case). 17

19 3.1 Education Systems under Autarky Given the indirect utility function in (6), the net aggregate welfare of a country imlementing a degree of curriculum centralization is (14) U() = Z ah a l (; w(a)) f(a)da k Z ah = (1 ) 1 (1 ) w(a)f(a)da k a l = (1 ) 1 (1 ) (Y A + Y S ) k; where we have suressed the deendence of most variables on the education olicy to simlify resentations. The last equality holds since the total wage income of the oulation is equal to the total value of roduction of the economy by erfect cometition. In autarky, the rice observes the autarky equilibrium condition (11). Let a denote the otimal education choice under autarky that maximizes U() and b a the corresonding autarky equilibrium rice. The following rst order condition (FOC) must hold at (; ) = ( a ; b a = (1 ) 1 ( (Y S (1 ) 1 Y A = (1 ) 1 (1 k = 0; where the second equality follows, rst MRT = 0 by the fact that =, and second, by lugging in the autarky equilibrium condition (11). At the otimal choice, the second order condition 2 (;)=( a ;b a ) < 0 must also hold. Thus, with k J < k U, it follows that the otimal degree of curriculum centralization under autarky will be higher in Jaan than in the US, i.e., a J > a U. 18

20 3.2 Education Systems under Trade Small Oen Economy. We rst characterize the unilateral otimal choice of education system that would be made by a small oen economy. That is, the country takes the world rice as given and does not take into account the e ect of its choice of education system on the world rice. The analysis here thus assumes away the terms-of-trade consideration by a large country when setting the education olicy. We will analyze the terms-of-trade e ect shortly. As will become clear, many useful insights can be drawn from comaring this simle scenario against the other more comrehensive scenarios. Proosition 1 The otimal education system of a small oen economy, s, decreases with the given trade rice,. Proof. The FOC to maximize the aggregate welfare of a small oen economy taking the trade rice as given is " = = s (1 ) 1 (1 k = 0: = s Note = (1 ) 1 = (1 ) 1 (1 ) [ (1 ) 1 Y A + Y S ]; (1 ) 1 Y A + Y S where the second equality obtains because MRT =. Based on the above condition, we 2 U(; = (1 ) 1 (1 ) " (1 ) # S < since < 1 > 0 S by Lemma 2. = U(; 2 U(; 2 ) < 0; = s 19

21 h i 2 < 0 holds by the SOC for 2 = s. s Proosition 1 states that an increase in the relative rice of software,, will induce a small oen economy to adjust downward the the degree of curriculum centralization in its education system, while the oosite is true when goes down. Note that the autarky otimal education system of country j, a j, in (15) coincides with its small-oen-economy otimal education system in (16) if the given trade rice haens to be the same as its autarky rice, = b a j, where j = J; U. That is, a J = s J (ba J ) and a U = s U (ba U ). Recall that as countries move from autarky to trade, the free trade rice falls relative to the autarky rice of the country with an initially more centralized education system and rises relative to the autarky rice of the country with an initially more decentralized education system (b a J > a > b a U ), where a indicates the free trade equilibrium rice when a J and a U are adoted. Given this, an imortant imlication of Proosition 1 is that as countries move from autarky to trade, a small oen economy initially having a more centralized education system will further raise its degree of curriculum centralization (as the relative rice of software falls after trade comared to its autarky level) and a small oen economy initially having a more decentralized education system will further lower its degree of curriculum centralization (as the relative rice of software rises after trade comared to its autarky level). World Otimal Choice. We now analyze the otimal choice of education systems for the two countries by a world social lanner who takes into account the e ects of education systems on equilibrium trade volumes and rice. The world social lanner chooses the education systems that maximize the joint welfare of the two countries: (17) U w ( J ; U ) = (1 ) 1 (1 ) (Y AJ + Y SJ + Y AU + Y SU ) k J J k U U ; 20

22 where the rice observes the free trade equilibrium condition (13). Given (17), we obtain the following FOC for J : w ( J ; U ) = (1 ) 1 (1 J @ + Y J @ + Y J J (1 ) 1 (Y AJ + Y SJ + Y AU + Y SU = (1 ) 1 (1 J J k J k J = 0; where the second equality follows by the fact that MRT = in both countries and by lugging in the free trade equilibrium condition (13). Similarly, we can obtain the following FOC for U : w ( J ; U ) = (1 ) 1 (1 U U k U = 0: Let w J ( U) denote the solution of J to (18) given any U, and similarly let w U ( J) denote the solution of U to (19) given any J. It is straightforward to verify U w( J ; U U it follows J ( U U < 0 U ( J J otimal choice of education systems by the world social lanner, w J < 0; thus, < 0. These two FOC s are illustrated in Figure 2. The and w U, for Jaan and the US, corresonds to the intersection W of the two schedules w J ( U) and w U ( J). The fact that k J < k U is re ected by the fact that the schedule w J ( U) is further away from the origin than the schedule w U ( J), and as a result, the otimal degree of curriculum centralization for Jaan, w J, is higher than that for the US, w U. Let w indicate the free trade equilibrium rice when ( w J ; w U ) are adoted. Note that these two FOC s, (18) and (19), coincide with the FOC (16) for small oen economies taking the trade rice as given. The intuition for this result is that the terms-of-trade considerations in setting when countries erceive their market owers are neutralized in a world social lanner s roblem since one country s terms-of-trade gain is the other country s terms-of-trade loss. This 21

23 can be seen in the derivations of (18), where the e ects of J on and the e ects of on the joint income and welfare of the two countries are eliminated in the nal exression. The only things that matter are the direct e ect of J on Jaan s own roduction choice and that of U on the US s own roduction choice. Thus, the otimal choice of education systems by a world social lanner turns out to be the same as the noncooerative equilibrium choice of education systems by individual countries if they behave as rice takers. Proosition 2 The otimal choice of education systems ( w J ; w U ) by a world social lanner that maximizes the world welfare under trade coincides with the noncooerative equilibrium choice of education systems by individual countries behaving as rice takers in the world market. Relative to autarky, the di erence in education styles is further enlarged after trade in the world socially otimal outcome: w J > a J > a U > w U. Proof. If Jaan behaves as a rice taker, its FOC to maximize its aggregate welfare is (16) with k = k J, which is identical to the world social lanner s FOC (18). Thus, w J ( U) can also be regarded as Jaan s best resonse function, when Jaan behaves as a rice taker, where the rice taken as given by Jaan follows the trade equilibrium condition (13) for given U and J. Similarly, w U ( J) can also be regarded as the US s best resonse function, when the US behaves as a rice taker. The noncooerative equilibrium outcome, when each of these two countries maximizes their individual welfare but behaves as rice takers, occurs at the intersection W of the two schedules w J ( U) and w U ( J), which is identical to the world social lanner s choice. This roves the rst art of the roosition. To show the second art of the roosition, note that if k U were to decrease to the level of k J, w U ( J) would shift out (not shown) in Figure 2 and intersect w J ( U) at oint W J on the 45 line. This is the hyothetical world social lanner s choice if both countries had identical disutility factors equal to k J. But if both countries were identical, the equilibrium trade rice would be equal to either country s autarky rice. In articular, this is Jaan s realized autarky rice with k J. Hence, the level of J corresonding to oint W J is Jaan s autarky otimal choice of education system, given that the FOC for Jaan s autarky decision (15) and the FOC for the world social 22

24 δ U 45 W J a δ U A W U N δ U δ ) n ( J W δ U δ ) w ( J 0 a δ J n δ J ( δ U ) w δ J ( δ U ) δ J Figure 2: Endogenous Choice of Education System lanner s decision of Jaan s education system (18) are identical if evaluated at the same rice level. Analogously, if k J were to increase to the level of k U, w J ( U) would shift in (not shown) and intersect w U ( J) at oint W U on the 45 line in Figure 2. This is the hyothetical world social lanner s choice if both countries had identical disutility factors equal to k U. But then the equilibrium trade rice would be equal to either country s autarky rice. In articular, this is the US s realized autarky rice with k U. Hence, the level of U corresonding to oint W U is the US s autarky otimal choice of education system, given that the FOC for the US s autarky decision (15) and the FOC for the world social lanner s decision of the US s education system (19) are identical if evaluated at the same rice. Thus, the combination of the socially otimal education systems under autarky in the two countries corresonds to oint A in Figure 2. It lies to the northwest of the world social lanner s choice with trade W. The result w J > a J > a U > w U therefore follows. Thus, from the world s ersective, it is socially otimal to further enlarge the autarky di erence in the education systems between Jaan and the US to reinforce their initial attern of comarative 23

25 advantage and to maximize the gains from trade. With endogenous education olicies (and PPFs), the outut resonse to the ossibility of trade is more elastic and the otential gains from trade are bigger than classical trade theories with given PPFs would suggest. Not only does the world aggregate roduction increase as individual countries reallocate more roductive resources to their sector of comarative advantage (corresonding to a movement along the given PPF), but it is further enlarged as individual countries revise their education olicies (and restructure their PPFs) to be further skewed toward their sector of comarative advantage. Nash Equilibrium Choice. If countries choose education systems unilaterally (as is likely the case in reality) and take into consideration the terms-of-trade e ect of their education olicies, the resulting Nash equilibrium ( n J ; n U ; n ) tends to di er from the above socially otimal outcome ( w J ; w U ; w ). The intuition is that Jaan would not want to raise J in the Nash equilibrium as much as it would as a rice taker (or in the world otimal outcome), since a higher J increases the auto outut, deresses the world rice of cars which it exorts, and hurts its terms of trade; the reverse is true for the US, who would not want to lower U in the Nash equilibrium as much as it would as a rice taker. Such a terms-of-trade loss is ignored by a small oen economy, or is o set by the equivalent terms-of-trade gain of the other country in a world social lanner s calculation. Thus, by taking the terms-of-trade e ect into consideration, countries tend to secialize less than in the socially otimal outcome. This is formally roved in the following roosition. Proosition 3 In a free trade equilibrium where each country simultaneously chooses its education system taking as given the other country s choice, the education systems in Jaan and the US diverge more from their autarky levels but less than the socially otimal levels: w J > n J > a J > a U > n U > w U : Proof. The objective function of Jaan is (20) max J U J ( J ; U ) = (1 ) 1 (1 ) (Y AJ + Y SJ ) k J J 24

26 subject to the trade equilibrium condition (13). The FOC for a best resonse n J ( U) given U is J ( J ; U J = " (1 ) 1 (1 J AJ + Y J J (1 ) 1 (Y AJ + Y SJ k J " = (1 ) 1 (1 J J + Y SJY AU Y SU Y k J = 0: Y AJ + Y J The second equality follows again by the fact that MRT = and by lugging in the trade equilibrium condition (13). J > 0 by Lemma 5, it follows that Y SJ Y AU Y SU Y AJ Y AJ J Q 0 if and only if J R U. Comaring the FOC for n J ( U) in (21) with the FOC for w J ( U) in (18) imlies that n J ( U) Q w J ( U) if and only if J R U. The osition of n J ( U) relative to w J ( U) is illustrated in Figure 2. For examle, in the area below the 45 line we have J > U, which imlies Y AJ > Y AU and Y SU > Y SJ so that the term Y SJ Y AU Y SU Y Y AJ +Y J is negative; this in turn suggests that the best resonse function n J ( U) lies to the left of w J ( U) of the world social lanner. In addition, the divergence between the two is larger, the more asymmetric the two countries are in their education systems and hence in their roduction atterns (re ected as a larger term Y SJ Y AU Y SU Y AJ Y AJ +Y AU in absolute value). The oosite is true for the area above the 45 line, where J < U and thus n J ( U) lies to the right of w J ( U). Finally, the two lines n J ( U) and w J ( U) cross each other on the 45 line when J = U, as in this case, the two countries have the same roduction structures and the term Y SJ Y AU Y SU Y Y AJ +Y J is equal to zero. The objective function of the US is (22) max U U U ( U ; J ) = (1 ) 1 (1 ) (Y AU + Y SU ) k U U 25