Who Gains from Growth: A Dynamic Model of Kuznets' Hypothesis*

This paper uses an overlapping generations model to analyze the relationship between economic development and income distribution and the effect of government taxation and transfers on the distribution of income. Individuals differ in their inherited stocks of human capital and therefore in their productivity and income, and their leisure and investment decisions. Individual productivity depends on inheritance, on investment in education and on society's average productivity. Consequently relative incomes and the distribution of income changes as the level of income changes. Government taxes and redistributes income intertemporally and intratemporally based on decisions made by majority voting. These decisions affect productivity but also produce a welfare class. In his presidential address to the American Economic Association and in subsequent writings, Simon Kuznets (1955, 1966, 1979) suggested that the relation of economic development to income inequality is an inverted U. In the early stages of economic development, inequality increases. As growth proceeds, the spread of the distribution slows, stops and, in the late stages of development, reverses. *We thank Torsten Persson and Matthew Canzoneri for helpful comments. tween groups are relatively large, the disincentive effects of taxes dominate the positive effects of growth on redistribution. Persson and Tabellini use an overlapping generations model to study the relation of income distribution to the growth rate of income, rather than the level as in Kuznets' hypothesis. Everyone saves at the same rate; individuals with more skill and income invest more per period. Individual investment in education does not directly change the distribution of income. Majority rule redistributes income and, therefore, lowers the growth rate. The authors' model implies, and their tests suggest, that inequality lowers the growth rate. We also use an overlapping generations model, but we study the effects of the level of income or productivity on the distribution of income as the level of income changes. Productivity (or human capital) is a continuous variable. As in Perotti (1990) there is an externality, but the externality arises here directly from the effects of education on average productivity; individual investment in education increases both individual and average productivity. Both the level and distribution of income change. Voters respond to these changes by setting tax rates to provide redistribution in the second period of life. These political decisions affect incentives thereby changing the level of income and the distribution of income before and after taxes. Since both generations pay taxes, voters' decisions cause both intragenerational and intergenerational redistribution. Section 1 presents the model of an economy with overlapping generations and investment in education. Section 2 considers the effect of government taxes and transfers. In Section 3, we extend the results in Meltzer and Richard (1981) to a growing economy. The median voter determines the tax rate and amount of redistribution that maximizes his utility and sustains the equilibrium. This section also presents some evidence on the relation of income to income distribution and the equilibrium tax rate. A conclusion summarizes our results. The Model and Its Implications The model we develop has two periods with equal numbers of people living in each period. Population is constant . Each period consists of a unit of time. In the first period, individuals allocate time between labor and investment in human capital. Investment increases second period productivity. In the second period, allocation of time is between labor and leisure. There are no bequests, debt or physical capital. Each person inherits an endowment of human capital from his family. Endowments differ across individuals, so productivity differs across individuals in each generation. A government collects taxes on the earnings of both generations to finance