انباشت سرمایه انسانی درون زا، مزیت نسبی و توزیع مجدد مستقیم در مقابل توزیع مجدد غیر مستقیم

Recently, several papers have reexamined the so-called production efficiency theorem and the Atkinson and Stiglitz theorem on commodity taxes in the optimal taxation literature. Naito [J. Public Econ. 71 (1999) 65] showed that indirect redistribution through production distortion or consumption distortion can Pareto-improve welfare and that the two theorems do not necessarily hold when different factors are imperfect substitutes and factor prices are endogenous. On the other hand, Saez J. Public Econ. (2002) forthcoming argued that in the long run, where human capital accumulation is endogenous, the two theorems are still valid. This paper develops reasonable alternative models where individuals accumulate human capital based on their comparative advantage. The present paper shows that the production efficiency theorem is not necessarily valid and that indirect redistribution from the able to the less able such as tariffs and production subsidies can increase efficiency even when skill accumulation is endogenous.

Whether efficient income redistribution should be done through income taxation alone or should be complemented with other measures such as production distortion or consumption distortion is one of the key issues whenever optimal public policies are discussed. With this regard, the production efficiency theorem (Diamond and Mirrlees, 1971), which states that production distortion is not optimal, and the Atkinson and Stiglitz theorem on optimal commodity taxation Atkinson and Stiglitz, 1976 and Atkinson and Stiglitz, 1980, which shows that commodity taxation is not necessary in the presence of an optimal income tax system, are the most important results in public finance literature. However, in public finance literature, researchers started examining those results. For example, Cremer et al. (2001) showed that the Atkinson and Stiglitz theorem does not hold when individuals are different in ability and endowment. Saez (2002) showed that the Atkinson and Stiglitz theorem does not hold when tastes are heterogenous. Naito (1999) showed that in a model similar to the model of Stiglitz (1982), if multiple goods are produced and factor prices are endogenous, the Atkinson and Stiglitz theorem does not necessarily hold, and the production efficiency result does not either. On the other hand, many of the previous studies on optimal income taxation have received criticism that they did not focus on long-term decisions such as human capital accumulation, but focused on the short-term choices such as labor supply. As a result, it is sometimes argued that the result obtained in the short-run model might not hold in the long run. In particular, Saez (2003) made skill accumulation endogenous in the model of optimal taxation and analyzed several issues of public policy. He showed that Naito's results are not valid and that the production efficiency theorem and the Atkinson and Stiglitz theorem on commodity taxation are valid when human capital accumulation is endogenous. Since accumulation of human capital has a strong effect on the economy in the long run, and since the implications of the production efficiency theorem and the Atkinson and the Stiglitz theorem are important, the contribution of Saez's paper is substantial. Despite such contributions, however, we believe that a further investigation would be needed. In many previous analyses involving asymmetric information not only in public finance literature but also in other literature, conclusions were not often robust in the sense that they critically depended on the structure of information and the timing of information revelation. Thus, it is worthwhile investigating the robustness of the result of Saez (2003) with another reasonable set of assumptions. In particular, in this paper, we will show that if higher ability persons have comparative advantage in the sense that the relative return from accumulating skilled human capital to unskilled human capital is higher than that of lower ability persons, the production efficiency theorem does not hold.1 To explain the intuition of the present paper, it would be useful to look at the differences between the assumptions in Saez (2003) and those in Naito (1999). In Naito (1999), there are two factors of production that are imperfect substitutes. In addition, from the beginning, each individual is attached to a particular labor market (the skilled labor market or the unskilled labor market), but the government cannot observe whether each individual is attached to the skilled or unskilled labor markets. The main idea in Naito (1999) is that when the government cannot observe an individual's type, the government can affect different individuals differently by using the response of the factor markets in the Stolper and Samuelson theorem (Stolper and Samuelson, 1941). Since the income tax policy cannot discriminate the different types of agents attached to different labor markets but a commodity tax and a tariff can, using a commodity tax (in a case of a closed economy) or a tariff (in a case of an open economy) with the response of factor markets can increase the efficiency. In Saez (2003), each job requires predetermined skill levels. As a result, the income level represents the amount of skill the individuals acquired. People have a heterogenous ability to acquire skill. However, since such heterogeneity of ability is incorporated in the utility function as a difference of disutility to acquire skill, there is not any room for such heterogenous ability to interact with the market reaction. Thus, the heterogeneity of abilities is intrinsically independent of the external environment of the economy. When the heterogeneity of abilities is independent of the response of the factor market, it is essentially equivalent to assuming that the dimension of factors used for production is one. In such a case, changes of factor prices due to government policy cannot increase the economic efficiency. The key idea of the present paper is that in the presence of comparative advantage in accumulating different types of human capital, individuals with different abilities will be affected differently by the responses of factor markets even when skill accumulation is endogenous. In such a case, a policy that introduces inefficient production but affects the factor prices differently for different factors can indirectly redistribute from the less able to the able. Although such a policy cause a distortion, it has only the second-order effect, but such an indirect redistribution has the first-order effect on welfare. Thus, it can increase the social welfare. For illustration, consider a situation where there are two types of human capital, skilled human capital and unskilled human capital, and where those who have higher ability have comparative advantage in accumulating skilled human capital. Comparative advantage in accumulating skilled human capital for the able means that the relative benefit from accumulating skilled human capital to unskilled human capital for individuals with high ability is higher than for the less able. We could think that training, knowledge, and experience in white-collar jobs are skilled human capital, and those in blue-collar jobs are unskilled human capital. In such a situation, a decrease of the return from skilled human capital and an increase of the return from unskilled human capital will hurt the able relatively more and give relatively more benefit to the less able. The intuition of this paper is that when individual ability is not observable to the social planner but the social planner is interested in redistribution from high-ability individuals to low-ability individuals, then a policy that will change the returns from skilled and unskilled human capital differently might be useful for an efficiency reason. The crucial assumption in the present paper is the presence of comparative advantage in human capital accumulation. Whether such an assumption is reasonable or not is an interesting empirical question. Earlier literature of the human capital theory assumed that earning could be explained completely once it is conditioned by human capital level. Earlier empirical evidences showed that there is a strong correlation between earnings and the level of human capital and indicated that ability does not matter for explaining earnings once they are conditioned by the human capital levels. On the other hand, recent literature of labor economics and self-selection emphasizes that ability can also increase earning and play a systematic role for explaining earnings even after it is conditioned by the human capital level. This literature points out that even in an extreme case when human capital does not increase the productivity at all, if ability can increase the productivity and if higher ability agents tend to acquire more skills, there will be a correlation between human capital level and earnings. In the standard signaling literature, it is commonly assumed that a higher ability person would get more benefit from acquiring skill. In addition, recently, DiNardo and Tobias (2001) and Tobias (2003) examined whether the returns from schooling are higher for high-ability individuals than for low-ability individuals by using a nonparametric method. They found that the returns are higher for high-ability individuals than for low-ability individuals. This suggests that assuming the presence of comparative advantage is not unrealistic as an approximation of the reality. At this point, one might wonder about the difference between Naito (1999) and the present paper. In the case of Naito (1999), each type of worker is attached to a different labor market. As a result, skilled workers can supply only skilled labor, and unskilled workers can supply only unskilled labor. However, in the present paper, both high-ability persons and low-ability persons have options to accumulate both types of human capital or either type of human capital. Thus, the reasoning that an increase of the return from unskilled human capital and a decrease of the return from skilled human capital always increases efficiency is not obvious. The organization of this paper is as follows. In Section 2, we present the model in a small open economy and analyze the production efficiency theorem by Diamond and Mirrlees (1971) when two factors are imperfect substitutes. In Section 3, we analyze the same issue when two factors are perfect substitutes. In Section 4, we shall give the implications, and, in Section 5, we will give a brief conclusion.

In this paper, we have examined whether indirect redistribution such as tariffs and production subsidies can complement income taxation in the long run where human capital accumulation is endogenous. For that purpose, I developed two models where individuals can choose the amount of both skilled and unskilled human capital based on their comparative advantage. In the first model, we assumed that skilled human capital and unskilled human capital are imperfect substitutes and that individuals accumulate both skilled and unskilled human capital. In the second model, we assumed that skilled human capital and unskilled human capital are perfect substitutes and that individuals accumulate only one type of human capital. Assuming that individuals with higher ability have comparative advantage in accumulating skilled human capital, we have shown that indirect redistribution such imposing a tariff on an unskilled human capital intensive good can increase the efficiency and complement an income tax system. This suggests that the validity of the production efficiency theorem depends on how the process of human capital accumulation is modelled. The result of this paper also suggests that empirical studies such as DiNardo and Tobias (2001) and Tobias (2003) that showed the returns from human capital were different among individuals with different abilities have important implications for public policy.