Sufficient Statistics for Nonlinear Tax Systems with Preference Heterogeneity

Abstract

This paper provides general and empirically implementable sufficient statistics formulas for optimal nonlinear tax systems in the presence of preference heterogeneity. We study unrestricted tax systems on income and savings (or other commodities) that implement the optimal direct-revelation mechanism, as well as simpler tax systems that impose common restrictions like separability between earnings and savings taxes. We characterize the optimum using familiar elasticity concepts and a sufficient statistic for across-income preference heterogeneity: the difference between the cross-sectional variation of savings with income, and the causal effect of income on savings. The Atkinson-Stiglitz Theorem is a knife-edge case corresponding to zero difference, and a number of other key results in optimal tax theory are subsumed as special cases. Our formulas also apply to other sources of across-income heterogeneity, including heterogeneity in rates of return on savings, inheritances, and the ability to shift income between tax bases. We provide tractable extensions of these results that include multidimensional heterogeneity, additional efficiency rationales for taxing heterogeneous returns, and corrective motives to encourage more saving. Applying these formulas in a calibrated model of the U.S. economy, we find that the optimal savings tax is positive and progressive.