آیا تنوع سرمایه انسانی ، تولید ناخالص داخلی را افزایش می دهد ؟ مقایسه سیستم های آموزش و پرورش

This paper examines how different education systems affect GDP by influencing the diversity of human capital. We construct an overlapping generation model in which agents are heterogeneous in income and innate ability, and the final goods are produced with differentiated intermediate goods. It is shown that under a realistic condition, the diversity of human capital induced by income inequality always lowers the GDP of the next period, while the diversity of human capital induced by heterogeneous ability can increase GDP, if the produced intermediate goods are sufficiently substitutable and firms have a large span of control. Hence, as public education equalizes education resources across households, it mitigates the negative effect of income inequality on GDP, while the effects of ability tracking crucially depend on the production structure of the economy.

Economists typically consider that education can improve the human capital of workers and raise GDP. Several researchers estimate the level of human capital from education attainment and examine the impact of human capital on GDP or economic growth (e.g., Mankiw, Romer and Weil, 1992). On the other hand, relatively little is known about the effect of the diversity of human capital on GDP. Apparently, the diversity of human capital differs across countries. Several recent international surveys reveal this variation. Although different surveys compare different abilities at different ages, some common tendencies can be found in the surveys.1Brown, Micklewright, Schnepf and Waldmann (2006) find that among 18 OECD countries, results from three surveys (Trends in International Mathematics and Science Study, Programme for International Student Assessment, and International Adult Literacy Survey) consistently indicate that Finland and the Netherlands have relatively small inequalities of achievements; the United Kingdom, New Zealand and the USA have relatively large inequalities of achievements.2 How does this diversity of human capital influence GDP? The importance of this question can be understood when we recognize that one of the central aims of an education policy is to provide students with equal education resources. For example, several reforms have been conducted to achieve equity in education outcomes in the United States. The 1971 landmark decision in Serrano vs Priest transformed the public education system in California, and other states (e.g., Michigan in 1994 and Washington in 1979) have also centralized their education systems in order to achieve equity in education resources. More recently, the “No Child Left Behind Act” by the George W. Bush administration aims to achieve equity in and a high quality of education by raising the performance of the lowest achieving students. Hence, the previous question leads us to ask a more important question: can an egalitarian education policy raise GDP? The answer is not obvious. On the one hand, if a government fails to provide everybody with enough literacy skills, it would be difficult for workers to communicate and cooperate with each other. On the other hand, as top managers' decisions are influential in a company, we want them to understand the varieties of opinions and to make sound decisions. Hence, some may insist that an education policy should target the bottom of ability distribution; others may advocate the importance of education for the elite. In order to evaluate the impact of an egalitarian education policy on GDP, we need a model to link education reform, the diversity of human capital and GDP in a unified framework. This paper aims to accomplish this task. It constructs an overlapping generation model in which education systems influence GDP by changing the variance in human capital and compares alternative education systems by their effects on GDP. This model is distinguished from the previous literature in two aspects. First, we tractably parameterize the structure of industries and firms and examine how an education system and the production structure of an economy have an interactive effect on GDP. In particular, this paper pays special attention to the span of control in a firm and the complementarity of goods in an industry. A large span of control gives an individual the authority to reallocate large amounts of resources. Without authority, an able person cannot fully utilize his/her unusual talents. Hence, a high level of control favors an education system that produces a few highly educated workers. If complementarity of goods exists, the value of a firm's product depends on other firms' product, and a good produced by incompetent persons may reduce the value of other firms' product. Hence, high complementarity of goods demands an education system that produces many reasonably well-trained workers.3 Secondly, different from the previous literature that analyzes education policies in a dynamic general equilibrium model, education systems are characterized not only by their financing systems, but also by their ability-tracking programs. Hence, education systems change the way the heterogeneities of both income and ability influence the diversity of human capital. A private education system yields more diverse human capital than a public education system because the rich spend more on education than the poor.4 On the other hand, ability tracking students into separate groups according to their ability restricts those with whom they can interact as schoolmates or classmates. Since advantaged students interact with advantaged students, ability-tracking benefits advantaged students more than disadvantaged students through the peer effects. Hence, a streamed program yields more diverse human capital than an untracked program by amplifying the benefits from high innate ability. This paper shows that when the intergenerational income elasticity (i.e., the elasticity of children's income to parents' income) is less than one, a public system with equal provision of resources to students yields higher GDP than a private system, regardless of industry and firm structure, while the effect of an ability-tracking program on GDP depends on the production structure. As far as the intergenerational income elasticity is less than one, it is shown that, given a current GDP and an ability distribution, a larger income difference reduces GDP at the next period. Since the public system always lowers income inequality more than the private system through the redistribution of income, it always attains a higher GDP than the private system. The required condition that the intergenerational income elasticity is less than one seems realistic. In fact, it is easy to find evidence that can support this condition. Solon (1992) finds that the intergenerational income elasticity is around 0.4 in the United States.5Charles and Hurst (2003) find that the intergenerational wealth elasticity is 0.37. Moreover, Solon (2002) shows that there is no cross-country evidence that the elasticity is greater than 0.6. With these pieces of empirical evidence, our theory unambiguously predicts that providing students with financially equal education resources raises GDP. A similar mechanism is emphasized in the previous literature when the human capital accumulation function is concave in expenditure on education and the production function is linear in human capital (e.g., Loury, 1981). Our result shows that their result still holds under a realistic condition, even if the diversity of human capital increases GDP on the production side. However, when the diversity of human capital is enhanced by ability tracking, the structure of the production side becomes important. Different from the dynamics of income distribution, it is shown that a rise in inequality in ability can increase GDP at the next period. It is also shown that an ability-tracking program attains higher GDP if and only if goods in an industry are fairly substitutable and the span of control in a firm is sufficiently large. This result highlights a distinctive role of ability tracking in macroeconomics. This paper is based on the literature that compares the performance of different education systems in a dynamic general equilibrium model (e.g., Glomm and Ravikumar, 1992, Bénabou, 1996 and Fernández and Rogerson, 1998). These papers compare different financing methods for education. Although it is considered that the redistribution of income through the public education system increases GDP in this strand of literature, Glomm and Ravikumar (1992) firstly identify the advantages of private education. They show that private education can increase GDP if a child can choose to exert effort in the accumulation of human capital. As parents must pay for tuition for their children in the private education system, when parents are young, they are provided with an incentive to make more effort in human capital accumulation to prepare income for their future children's education. In contrast to Glomm and Ravikumar (1992), we exclude effort choice and include ability tracking in the human capital accumulation function. This deviation allows us to focus on the productive impacts of sorting in human capital accumulation. In fact, this paper shows that if private schools are better able to screen students according to ability than the public system, there is a production structure through which the private system attains higher GDP. The importance of sorting is also analyzed by Bénabou (1996). Bénabou (1996) examines the effect of diversity of human capital on economic growth when the human capital of individual agents have interactive effects on GDP. His main focus is to examine the role of complementarity of human capital at the community level and at the production level. By contrast, we do not consider a local interaction at the community level and pay more attention to the interaction at a production level. In particular, we explicitly examine the role of complementarity of products and a manager's span of control to compare education systems. We also explicitly analyze the effect of ability tracking on GDP. Ability tracking has been examined by Epple, Newlon and Romano (2002) and Brunello, Giannini and Ariga (2007). Although these papers examine the benefits and costs of ability tracking, they do not examine the role of the production structure. The interaction between an education system and the structure of an industry and firm is the main focus of our paper. The rest of this paper is organized as follows. Section 2 describes the model, and Section 3 shows some results about the relationship between income inequality and GDP. Section 4 compares the two education systems, the public and the private. Section 5 considers the case with ability tracking in public schools. Section 6 discusses some extensions and concludes. All proofs are in the Appendix A.

In this paper, we examined how different education systems change GDP through their influence on the diversity of human capital. We analyze an economy in which an income distribution converges to a stationary distribution. We show that the diversity of human capital due to income inequality always lowers GDP, while diverse human capital induced by heterogeneous ability can increase GDP if produced goods are sufficiently substitutable and firms have a large span of control. Hence, we may conclude that tax financing of education always yields higher GDP than private financing, though the effect of ability tracking on GDP depends on the structure of industries and firms. We can consider several future studies. Firstly, although this paper focuses on the vertical diversity of human capital, it is also interesting to examine the impact of the horizontal variety on GDP. In fact, because each agent specializes in the production of a particular good, it would be possible to modify the model for the examination of horizontal diversity. In this case, a household can choose a particular variety of goods before making an investment decision about human capital and accumulating a specific skill. The advantages of this approach would be that a household might choose skills for the production of new goods. In this way, the expansion of the variety of goods can be endogenized as the result of education choice. This interesting extension is left for future research. Secondly, it may be interesting to examine a more general utility function. We assume that the utility function is log-separable. This simplifying assumption brings the result that the preferred tax rate does not depend on income. Therefore, we can ignore the effect of income distribution on tax choice. If the utility function is more general, the utility of a household with median income matters. This means that the skewness of income distribution influences the tax rate and therefore the amount of investment in human capital. Because a difference in education systems would influence the skewness of income distribution, this extension may add an additional mechanism. This interesting extension is also left for future research. Finally, although we examine the effect of ability tracking on GDP in this paper, we can extend our analysis to other policies that can change a mapping from ability to human capital. More specifically, we can extend our analysis to policies that influence the human capital accumulation function through the following path, ht + 1i = (ξt + 1i)ϕ(θ,p)((eti)θ(gt)1 − θ)α, where p is a policy parameter. For example, when policy allows individuals more flexibility in choosing how many credits they can take in a year, it is likely that talented students take more courses than ordinary students do.20 In this case, more able students accumulate a larger human capital not only because they are talented, but also because they study harder. Hence, the effect of ability on human capital is more than proportional and ϕ(θ, p) becomes larger by this policy. According to our analysis, the impact of this policy on GDP depends on the structure of production. In this way, our analysis suggests that we must evaluate the economic consequences of a liberal education policy with the knowledge of how industries and firms are organized. As indicated by this example, there will be more unexplored issues about the relationship between education policy and the structure of the production sector. We hope that this paper helps researchers in unraveling part of the complicated relationships.