انتخاب آموزشی، نابرابری درون زا و توسعه اقتصادی

This paper investigates the mechanics through which wealth may, in the long run, trickle down from the rich to the poor. In the presence of indivisibilities in investment of human capital and impossibility of borrowing money, investment in education is financed through an intergenerational transfer. In an OLG model where aggregate production requires capital and both skilled and unskilled labor, it is shown that the long run equilibrium outcome depends on the values of few key parameters. A complete characterization of the steady state is provided. Under some configurations of the parameter values a unique invariant equilibrium exists where inequality vanishes asymptotically. Under others, multiple equilibria exist and the equilibrium outcome crucially depends on the initial conditions of the system. These equilibria are characterized by a negative relationship between inequality and economic development.

In the presence of imperfect credit markets, intergenerational transfers within the family are particularly important for economic development and income inequality. Investment in education has to be financed out of the savings of parents and consequently the income distribution crucially matters both at the individual and at the aggregate level. At the individual level, an unskilled dynasty may be unable to escape its inferior state leading to persistent inequality. At the aggregate level, underinvestment in education may result in underdevelopment and poor economic performance. This is all the more relevant today as technological capability depends on the availability of skilled workers.

In this paper, we investigated the mechanics through which wealth may, in the long run, trickle down from the rich to the poor. For sufficiently large values of the relative cost of education the model predicts endogenous and permanent separation of the population between the rich (skilled) and the poor (unskilled). For lower values of this cost, wealth eventually trickles down from the rich to the poor. In particular, we found that the larger is the size of the intergenerational transfer or the lower is the relative importance of the skilled labor in the production function, the larger is the set of initial conditions such that a trickle-down eventually occurs. Furthermore, the model predicts that if factors are gross-substitutes, then there exists always values for the relative cost of education allowing trickle-down irrespectively of initial conditions. Thus, for sufficiently low values of the relative educational cost, a unique, invariant equilibrium exists where inequality vanishes asymptotically. For larger values, besides the trickle-down equilibrium, a continuum of equilibria appears, where inequality persists forever. On the other hand, if factors are gross-complements, then the model predicts that for each level of the relative cost of education, the trickle-down equilibrium always coexists with a continuum of equilibria characterized by persistent inequality. In other words, the equilibrium outcome crucially depends on the initial conditions of the system.