Sufficient Statistics for Nonlinear Tax Systems with General Across-Income Heterogeneity

This paper provides general and empirically implementable sufficient statistics formulas for optimal nonlinear tax systems in the presence of across-income heterogeneity in preferences, inheritances, income-shifting capabilities, and other sources. We study unrestricted tax systems on income and savings (or other commodities), 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 general across-income heterogeneity: the difference between the cross-sectional variation of savings with income, and the causal effect of income on savings. 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. Drawing on recent empirical work, we apply our formulas to savings and wealth taxation in the U.S., and find that the optimal savings tax is positive and progressive.