آموزش و پرورش عمومی و نابرابری درآمد

This paper examines the evolution of inequality in an overlapping generations model where each individual's human capital investment depends on quality of schools. We consider an education regime where the quality of schools is a publicly provided input financed by an income tax. We show that the income gap between the rich and the poor may widen even when the quality of public education is the same across all individuals. Thus, in the short run, public education may not be the great equalizer as intended by its proponents, though it is in the long run. We also show that the effect of taxes on inequality is ambiguous.

In these days, it is doubtful that any child may reasonably be expected to succeed in life if he is denied the opportunity of an education. Such an opportunity where the state has undertaken to provide it, is a right which must be made available to all on equal terms. U.S. Supreme Court, Brown vs. Board of Education, 1954.1 In most industrialized countries, public education has been the dominant mode of providing educational services for the last century. In the U.S., for instance, over the last 100 years, the fraction of students at the elementary and secondary level who attend public schools has been around 90%. For OECD countries, public school enrollment typically exceeds 70%. As early as 1848, Horace Mann argued that public provision of education is “beyond all other devices of human origin, the great equalizer of the condition of men…” (Cremin, 1957, p. 87). Coons et al. (1970) argue that the purpose of public schools is to provide equality of opportunity and, therefore, unequal access to education ought to be eliminated. The essential idea behind their argument is that, under equal access to public education, some inputs to the learning technology are constant across all children, so the common input would make incomes converge.2 The main purpose of our paper is to study the evolution of income inequality in a model with public education and to evaluate whether equal access to public education yields income convergence. A secondary goal is to examine how such an economy behaves over time under different funding levels for public education. In Section 2, we construct an overlapping generations model with heterogeneous individuals. The basic framework is similar to that in Glomm and Ravikumar (1992). All individuals live for two periods. Their preferences over leisure in youth and consumption in old age are described by a CES utility function. Individuals within a generation are differentiated by the stock of human capital of their parents. This is the only source of heterogeneity in our model. Human capital of each individual depends on time allocated to learning, quality of schools and the stock of human capital of the individual's parents. Quality of schools is a publicly provided input financed by tax revenues from a uniform tax on income. The publicly provided input is common across all agents. Our model, by construction, has the forces suggested by proponents of public education. All agents have equal access to the public expenditures on education. All agents use the same learning technology. The quantity of the publicly provided input to the learning technology is the same for all agents. That is, we have eliminated, by assumption, the concern in Bowles (1978) or Wälde (2000). Thus, the common publicly provided input should potentially yield income convergence. Yet, we show for reasonable parameters that exactly the opposite occurs. Furthermore, we demonstrate the possibility of adverse distributional consequences without appealing to elitism. Our model is also different from Glomm and Ravikumar (1992), where we did not examine how an economy with public education behaves over time under different funding levels for public education. Rather, we compared public and private funding regimes, and endogenized public policy on education. Thus, there was exactly one resulting public policy. That model, therefore, cannot deliver comparative dynamic statements on how different public policies influence the evolution of income distribution. Since the model assumed Cobb–Douglas preferences and technology, time allocated to learning was constant over time and independent of parental human capital and the level of funding for public education. In this paper, time allocated to learning is a nontrivial function of parental human capital and public expenditures on education, and hence the implications for future income distributions are much more far reaching than in our 1992 paper. Moreover, the predictions concerning time allocations in the present paper are consistent with microevidence. In Section 3, we illustrate the possibility that, even under equal access to public education, the income gap between the rich and the poor may widen in the short run, even though public provision of education decreases inequality in the long run. (The short run in this framework may last for a few generations.) In our model, the evolution of inequality depends on the elasticity of substitution between consumption and leisure, and the elasticity of parental human capital in the learning technology. Under certain conditions on these two parameters, incomes below a critical level exhibit divergence, while those above the critical level exhibit convergence. The limiting distribution depends upon the evolution of critical income. In a growing economy, the critical income declines over time. Thus, income inequality increases for some periods, but eventually declines. The increase in income inequality occurs, although quality of public education is the same across all agents. We then numerically examine the effect of initial income distribution on the evolution of income inequality. We find that higher initial per capita income reduces future inequality and also reduces the number of periods over which the income gap widens. Moreover, higher initial income inequality increases future inequality and the income gap widens for more periods. The effect of taxes on the evolution of income inequality is ambiguous. For sufficiently small tax rates, an increase in the tax rate lowers the income inequality. This result is reversed for high tax rates. In our model, the tax rates affect the quality of public education directly. However, there is also an indirect effect because changes in tax rates affect the incentives to accumulate human capital. Section 4 contains concluding remarks.

We have used a simple overlapping generations model to show that, in the short run, public education may not be the “great equalizer” as intended by its proponents, even though in the long run it is equalizing. We showed that income inequality may increase for a few generations even when the quality of schools is the same across all individuals in an economy. Initial conditions as well as public policy affect the evolution of income inequality. Here, we have abstracted completely from self-selection by households into districts of differing public school quality. Such self-selection increases the tendency toward inequality, because the rich typically select better school districts. In our model, income inequality is transmitted from one generation to the next through human capital investment decisions of individuals. Individuals whose parents have low human capital allocate less time to learning than those whose parents have high human capital. One may conjecture that a policy of mandatory schooling would induce income convergence. See Eckstein and Zilcha (1994) for a model with compulsory schooling. It is true that many countries have mandatory schooling requirements. In European and North American countries, where mandatory schooling typically covers children from ages 6 to 15 or 16, enrollment ratios fall short of 100% (see Table 1). It seems that simply imposing mandatory schooling requirements does not in and of itself guarantee that the time input to learning is constant across individuals. We conclude from the data in Table 1 that divergence of income in a regime of equal public provision of educational expenditures is a possibility that should be taken seriously. The impact of public provision of education combined with imperfectly enforced mandatory schooling is an interesting extension of our paper.