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

Author

Listed:
  • Antoine Ferey

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Benjamin Lockwood

    (The Wharton School - University of Pennsylvania [Philadelphia], NBER - The National Bureau of Economic Research)

  • Dmitry Taubinsky

    (UC Berkeley - University of California [Berkeley] - UC - University of California, NBER - The National Bureau of Economic Research)

Abstract

This paper provides 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 characterize optimal smooth tax systems on income and savings (or other commodities), as well as simpler tax systems. We use familiar elasticity concepts and a novel sufficient statistic for heterogeneity correlated with earnings ability: the difference between across-income variation in savings and the causal effect of income on savings. We apply these formulas to the United States and find that the optimal savings tax is mostly positive and progressive.

Suggested Citation

  • Antoine Ferey & Benjamin Lockwood & Dmitry Taubinsky, 2024. "Sufficient Statistics for Nonlinear Tax Systems with General Across-Income Heterogeneity," Sciences Po Economics Publications (main) hal-05020383, HAL.
    • Handle: RePEc:hal:spmain:hal-05020383
    DOI: 10.1257/aer.20221053
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    Cited by:

    1. is not listed on IDEAS
    2. Jacquet, Laurence & Lehmann, Etienne, 2021. "How to Tax Different Incomes?," IZA Discussion Papers 14739, Institute of Labor Economics (IZA).
    3. Hellwig, Christian & Werquin, Nicolas, 2022. "A Fair Day's Pay for a Fair Day's Work: Optimal Tax Design as Redistributional Arbitrage," CEPR Discussion Papers 16863, C.E.P.R. Discussion Papers.
    4. Ferey, Antoine, 2022. "Redistribution and Unemployment Insurance," Rationality and Competition Discussion Paper Series 345, CRC TRR 190 Rationality and Competition.
    5. Kevin Spiritus, 2025. "Optimal commodity taxation when households earn multiple incomes," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 32(1), pages 98-119, February.
    6. Hellwig, Christian & Werquin, Nicolas, 2022. "Using Consumption Data to Derive Optimal Income and Capital Tax Rates," TSE Working Papers 22-1284, Toulouse School of Economics (TSE), revised Jan 2026.
    7. Paweł Doligalski & Piotr Dworczak & Mohammad Akbarpour & Scott Duke Kominers*, 2025. "Optimal Redistribution via Income Taxation and Market Design," Bristol Economics Discussion Papers 25/787, School of Economics, University of Bristol, UK.
    8. Mallesh Pai & Philipp Strack, 2022. "Taxing Externalities Without Hurting the Poor," Cowles Foundation Discussion Papers 2377, Cowles Foundation for Research in Economics, Yale University.
    9. Matteo Dalle Luche & Demetrio Guzzardi & Elisa Palagi & Andrea Roventini & Alessandro Santoro, 2024. "Tackling the regressivity of the Italian tax system: An optimal taxation framework with heterogeneous returns to capital," World Inequality Lab Working Papers halshs-04753529, HAL.
    10. Ashley C. Craig & Thomas Lloyd & Dylan Moore & Ashley Craig, 2025. "Do Distributional Concerns Justify Lower Environmental Taxes?," CESifo Working Paper Series 12317, CESifo.

    More about this item

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies

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