EFFECTIVE FEDERAL INDIVIDUAL INCOME TAX FUNCTIONS: AN EXPLORATORY EMPIRICAL ANALYSIS

TLDR

The effective tax function, a three‑parameter model derived from Young’s equal‑sacrifice theory and extended by Berliant and Gouveia, describes how individual effective income tax rates relate to economic income. The study defines and estimates this nonlinear function and preliminarily evaluates the impact of the 1986 tax reform on its characteristics. Using 1979‑89 U.S. tax return data, the authors estimate the function and present annual graphs to empirically chart changes in average marginal rates, redistributional and revenue elasticities, and horizontal equity.

Abstract

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 general 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).