Effective Federal Individual Income Tax Functions: an Exploratory Empirical Analysis

We define and statistically estimate a nonlinear relationship between individual effective income tax rates and economic income for United States tax return data for tax years 1979-89. The relationship, which we call the effective tax function, has three parameters and was theoretically derived from the theory of equal sacrifice by Young (1988, 1990) and more generally by Berliant and Gouveia (1993). Annual graphs of the statistically estimated effective tax functions are presented and used to characterize empirically the evolution of the United States federal tax system with respect to four characteristics of the tax system: average marginal tax rates, redistributional elasticities, revenue elasticities, and horizontal equity. For each characteristic, we present a preliminary assessment of the impact of the 1986 tax reform. The major empirical finding is that the effective income tax function exhibits a trend toward less progressivity for the years studied. This gen*Department of Economics, University of PennsylvanIa, 3718 Locust Walk, Philadelphia, PA 19104 **Department of Economics, University of Rochester, Rochester, NY 14627 and the Heinz School, Carnegie-Mellon University, Pittsburgh, PA 152 13 eral conclusion is also valid for indexes that measure the redistributive impact of the tax system (the elasticity of after-tax income with respect to before-tax income) and the revenue effects of the system (the elasticity of fiscal revenue with respect to before-tax income). I, . . a tax law is a mapping from a vector whose elements are the income characteristics of the individual (wage income, dividends, capital gains, and all the other items in the income tax form) to tax liabilities. It is supposed to be a well defined function; no economic analysis is needed. (. . .) In fact, to use this information one wants to know the distribution of the burden by some classification of lower dimensionality than that used in the tax law.” in Arrow (1980, p. 265).