A Model of Public Education and Income Inequality with a Subsistence Constraint

1. Introduction "Deep in a citrus grove, law officers crept up on Dionatan Rocha and caught him redhanded. Dionatan, a 12-year-old wearing a baseball cap and T-shirt, was picking oranges, in plain violation of Brazil's child-labor code.... Says Mr. Grajew: `Brazil's chronically unequal wealth distribution has one root cause: Millions of children are working instead of studying.' (Moffett 1998). To reduce income inequality and spur economic development, many have advocated increased support for public education. However, public education may not be a silver bullet to eliminate poverty or lower income inequality. Fields (1980) reports that income inequality in several developing countries did not lessen even after an increased allocation of resources to public education. Sylwester (2002) considers how education expenditures are associated with subsequent changes in income inequality within a cross-section of countries. After dividing the sample into OECD and less-developed-country subsamples, he finds that education expenditures are more strongly associated with falling income inequality in the former group. One possible reason for these differing outcomes is that even when public education is freely provided, attendance is not guaranteed, especially in poorer nations. As in the above account, families may place their children in the labor force even if this is illegal, since the income that these children generate is nontrivial to the welfare of the family. Consequently, a subset of the population may exist that has little if any formal schooling, thereby limiting opportunities for these individuals later in life and possibly creating a permanent underclass. Poor children work rather than attend school and thus remain poor as adults. These adults then need their children to work to help support the family, and this poverty persists through another generation. Therefore, a better understanding of this cycle and of the policies that can break this cycle is needed to help alleviate poverty in these nations. This is not the first paper to examine how public education affects income inequality or poverty. Glomm and Ravikumar (1992) develop a model in which agents vote for a public or private education system and in which a public education system benefits low-income agents relative to high-income agents. Consequently, a public education system unambiguously decreases the level of income inequality. Saint-Paul and Verdier (1992) and Zhang (1996) also conclude that public education helps to lower income inequality over time. A critical assumption of these models is that attending public school is costless and so all agents attend. However, Jimenez (1986) finds that this assumption is questionable in many developing countries. Although public education is often provided freely, it is not necessarily costless. Those attending school forgo income that could have been used to help support a family, and in some cases this income is necessary for the family's survival. Jimenez (1986) also reports that taxation in many developing countries is regressive. Taken together, these assertions imply that in some countries poor families are hurt by the taxation used to support public education but do not receive many of the benefits. In fact, these public education systems might even be contributing to an increase in the level of income inequality. This paper creates a model that explores some of these issues. Like those of Perotti (1993) and Galor and Zeira (1993), this model does not assume that all agents partake in public education. Instead, agents face an opportunity cost associated with going to school and thus choose how much schooling to acquire. It is possible that the level of income inequality does not decline even in the presence of a public education system. Fernandez and Rogerson (1995) also capture some of these concerns in their model of public education with endogenous subsidies. In their model, only agents attending school receive education subsidies, and so highincome agents (who have the means to attend school) then have an incentive to vote for high subsidies. …