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

47 Pages Posted: 20 Dec 2021 Last revised: 30 Oct 2024

See all articles by Antoine Ferey

Antoine Ferey

Ludwig Maximilian University of Munich (LMU)

Benjamin B Lockwood

University of Pennsylvania - The Wharton School

Dmitry Taubinsky

University of California, Berkeley - Department of Economics

Date Written: December 2021

Abstract

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) 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 general across-income 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. 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.

Suggested Citation

Ferey, Antoine and Lockwood, Benjamin B and Taubinsky, Dmitry, Sufficient Statistics for Nonlinear Tax Systems with General Across-Income Heterogeneity (December 2021). NBER Working Paper No. w29582, Available at SSRN: https://ssrn.com/abstract=3989590

Antoine Ferey (Contact Author)

Ludwig Maximilian University of Munich (LMU) ( email )

Geschwister-Scholl-Platz 1
Munich, DE Bavaria 80539
Germany

Benjamin B Lockwood

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

Dmitry Taubinsky

University of California, Berkeley - Department of Economics ( email )

579 Evans Hall
Berkeley, CA 94709
United States

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