سیاست مالی، ترکیب انتقال بین نسلها و توزیع درآمد

In this paper, we characterize the relationship between the initial distribution of human capital and physical inheritances among individuals and the long-run distribution of these two variables. In a model with indivisible investment in education, we analyze how the initial distribution of income determines the posterior intergenerational mobility in human capital and the evolution of intragenerational income inequality. This analysis enables us in turn to characterize the effects of fiscal policy on future income distribution and mobility when the composition of intergenerational transfers is endogenous. To this end, we consider the following government interventions: a pay-as-you-go social security system, a tax on inheritance, a tax on capital income, a tax on labor income, and a subsidy on education investment

1. Introduction The question of how inequality is generated and evolves over time is one of the major concerns in economic analysis. In the last decades a large number of studies have provided evidence supporting the presumption that intergenerational transfers are key to explain the empirical distribution of income and wealth.3 Moreover, as intergenerational transfers could take the form of either physical capital (through bequests) or human capital (through investment in education), there is also empirical evidence documenting that both types of transfers affect the distribution of relevant economic variables among individuals. For instance, the empirical analysis of d’Addio (2007) confirms both the importance of education on mobility and the intergenerational persistence of inequality. In this paper, we follow this line of research and show analytically how the joint initial distribution of bequest and human capital, as well as fiscal policy, determines the average level and the intragenerational distribution of income in the long run. Investment in education is a key factor of income inequality.4 As was pointed out by Galor and Zeira (1993), and many other papers, there are two main features that give rise to this relationship. On the one hand, the technology of human capital accumulation exhibits a non-convexity since the investment in education is indivisible. This technological feature implies that access to education by the poorest individuals depends on whether they can borrow or not. On the other hand, when there are capital market imperfections resulting in borrowing constraints, those individuals with an income below some threshold value cannot afford the cost of education.5 Therefore, the initial distribution of wealth determines the number of individuals who can acquire education and, thus, the aggregate stock of human capital and the rate of economic growth. This mechanism linking education with income distribution and growth was already widely analyzed in the literature by authors like Galor and Zeira, 1993, García-Peñalosa, 1995 and Galor and Tsiddon, 1997, and Owen and Weil (1998), among others. Intergenerational transfers from parents to children account for a part of the observed inequality since these transfers help to ameliorate the negative effects of borrowing constraints on the accumulation of human capital. In an environment with credit market imperfections, only those individuals who receive a sufficiently large inheritance can invest in human capital (see Becker and Tomes, 1976 and Eckstein and Zilcha, 1994; or Behrman et al., 1995). Regarding the dynamics of income distribution, Galor and Zeira (1993) show that, if one assumes credit market imperfections and a non-convex education technology, then the inherited distribution of wealth entirely determines the accumulation of human capital and the dynamics of the distribution of income. The literature that we have reviewed above has not considered simultaneously the two types of intergenerational transfers we have mentioned: (i) transfers of physical capital by means of bequests; and (ii) transfers of human capital by means of the parents’ investment in the education of their children. In this paper, we consider the interaction between the composition of intergenerational transfers and income distribution when education is financed by parents.6 To this end, our paper develops a model of a small open economy populated by overlapping generations of individuals who differ in the amount and composition of inherited transfers from parents. In this economy the disposable lifetime income of an individual is fully determined by the bequest and human capital inherited from his parent. In addition to the imperfection of the capital market and the non-convexity of the education technology, we introduce two crucial assumptions. One is that the intergenerational transfers arise because individuals care about the starting opportunities of their children and thus they take into account the disposable income of their offspring. More precisely, we assume that parents derive utility from their contribution to the future lifetime income of their children without discriminating between the two types of intergenerational transfers used for making such a contribution. The second important assumption is that there exists an asymmetry between the two types of intergenerational transfers as they take place at different moments of individual's lifetime and they exhibit different contributions to the offspring's lifetime income. Individuals can only attend to the school before going to the labor market and receiving a physical inheritance from their parents. Moreover, due to the borrowing constraints, individuals can only have access to education if their parents pay its cost. Finally, as it is standard in the literature, we assume the marginal return on human capital investment is larger than the marginal return on physical capital investment. Given our motive for intergenerational transfers, parents obtain thus larger marginal gains from investing in their children's education than from leaving bequest. The income of parents then drives the total contribution to the future lifetime income of their children. The composition of this contribution between the two types of transfers is endogenous in our model and depends on the relative returns of these transfers. However, since we assume that the investment in education is indivisible and that parents cannot force their children to give them transfers, if the cost of education is sufficiently large, parents will not finance the cost of education and, thus, they will only leave bequest to their offspring. Obviously, this occurs to parents with an income level below some threshold. In this way, the initial distribution of income drives the evolution of the composition of intergenerational transfers and, thus, the size of the educated population along the equilibrium path. This simple mechanism explains how the initial distribution of income determines the posterior evolution of intragenerational income inequality and of intergenerational mobility in terms of human capital. This dynamics implies that, under reasonable parameter values, non-educated but sufficiently rich parents will educate their descendents and educated parents will always educate their descendents. Therefore, only upward mobility is possible in our simple model, which explains the increasing access to education in most countries during the second half of the last century. Our model also implies that social mobility ends when the economy reaches the steady state, which is characterized by a two-class society composed of rich educated individuals and poor non-educated individuals. Our mechanism behind the dynamics of income distribution delivers two important insights for human capital accumulation, inequality, and growth. First, since the income of parents depends on the composition of their initial inheritance, the dynamics of economic activity depends not only on the initial distribution of wealth, but also on the initial distribution of human capital. Our model then characterizes a new mechanism relating the distribution of human capital with growth and inequality. Second, and probably more important, the relative return of human capital accumulation determines the access to education of the middle class. This result is quite intuitive. Since there is a wedge between the returns from the two types of transfers, there exists a non degenerated interval of income levels for which all the parents with those levels of income optimally choose to pay the education costs and to leave no physical bequest. Outside this interval, those parents with a larger income level educate and leave bequest, whereas those parents with a smaller income level leave bequest and do not educate. Therefore, both the accumulation of human capital and the dynamics of income inequality crucially depend on the initial mass of individuals with a level of income inside the aforementioned interval. Furthermore, the length of this interval is fully determined by the wedge between the contributions of each transfer to the lifetime income of children. Thus, for a given distribution of income, any shock altering the relative marginal return of education will change the fraction of individuals who will have access to education and, therefore, it will affect inequality, mobility, and growth. This is a feature that distinguishes our contribution from the one of Galor and Zeira (1993) since in their model the access to education only depends on the fixed cost of education, whereas in our model investment in education also depends on preference and fiscal policy parameters.7 Therefore, in our paper, fiscal policy will affect the education decision in a non-trivial way, which makes our framework particularly suitable to conduct the analysis of the effects of fiscal policy. Our model is closely related to those in Galor and Moav, 2004 and Galor and Moav, 2006, who also consider the two types of intergenerational transfers. However, they assume a joy of giving motive for intergenerational transfers, where parents’ marginal utility from physical bequest and from human capital transfers are identical. Therefore, in those papers the composition of intergenerational transfers relies on an ad-hoc assumption, so that it does not depend on the relative return of investing in education. Moreover, these papers assume a convex technology of education, which implies that the composition of intergenerational transfers does not affect the mobility in earnings. In contrast, we provide a framework where fiscal policy affects mobility through the induced change in the composition of intergenerational transfers of the middle class. In our setup all individuals are assumed to have the same learning ability so that the only difference among individuals arises from the predetermined initial income and education level of their parents. This assumption allows us to focus on the role of the composition of intergenerational transfers for the distribution of income in the long run. Allowing for random individually idiosyncratic abilities will deliver a stochastic version of the deterministic model considered in this paper. In this case the resulting dynamics and intergenerational mobility would be richer. However, we assume identical, non-stochastic abilities to make more transparent the mechanism driving the relation between the composition of intergenerational transfers and the subsequent dynamics of the economy. A natural question to ask in our model is how different fiscal policies affect the evolution of both income distribution and mobility, where the latter determines in turn aggregate income in the long run. In this paper we analyze the effects of the following government instruments: a pay-as-you-go social security system, a tax on inheritances, a tax on capital income, a tax on labor income, and a subsidy on education investment. Note that our analysis is purely positive as we focus exclusively on the effects on human capital accumulation, inequality, and mobility of traditional macroeconomic tax instruments. This analysis is performed in 5 and 6. In Section 5, we study the effects of modifying only one of the aforementioned government instruments and, among other results, we obtain that raising the tax rate on either inheritance or labor income results in a larger fraction of non-educated individuals in the total population, in a smaller individual amount of bequest, and in smaller inequality in initial wealth between educated and non-educated individuals. Therefore, these taxes have some equalizing effects but decrease the accumulation of human capital as individuals enjoy less disposable income to pay for the indivisible cost of education of their children. We characterize the effects of a pay-as-you-go social security system, which will depend on whether the economy is dynamically efficient or inefficient. When it is dynamically efficient, the introduction of a pension system implies a reduction in human capital accumulation and, hence, an income loss. We also analyze the quite neutral role on human capital accumulation played by the tax on capital income and the disequalizing effects triggered by education subsidies. These subsidies only benefit the educated families and hence they increase inequality. Finally, in Section 6 we study the effects of financing either government spending or education subsidies through labor income taxes instead of through inheritance taxes. We show that this substitution increases human capital and aggregate income, whereas the effect on income inequality between educated and non-educated individuals depends on the initial frequency distribution of these two types of individuals. The paper is organized as follows. Section 2 presents the model of overlapping generations with altruistic individuals. Section 3 solves the intertemporal choice problem faced by an individual. In Section 4 we describe the dynamics of the joint distribution of bequest and human capital following a given initial distribution. In 5 and 6 we analyze the effects of fiscal policy on the intergenerational mobility in human capital and on the stationary distribution of income. Section 7 concludes the paper.