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Is the Flat Tax Optimal under Income Risk?

Author

Listed:
  • Dominique Henriet

    (École Centrale Marseille (Aix-Marseille School of Economics), CNRS & EHES)

  • Patrick Pintus

    (Aix-Marseille Université (Aix-Marseille School of Economics), CNRS & EHESS)

  • Alain Trannoy

    (Aix-Marseille Universite (Aix-Marseille School of Economics) CNRS EHESS)

Abstract

We derive testable conditions ensuring that the income tax is optimal when agents are ex-ante identical but face idiosyncratic income risk. The optimal tax depends positively on both absolute risk aversion and risk variance and negatively on labor supply elasticity and absolute prudence. The comparison with the formula of the optimal non-linear income tax provides the restrictions on both the preferences and the income distribution conditional on effort ensuring that the optimal tax is indeed linear. In general it requires that the ratio of absolute prudence to absolute risk aversion be no less than two; if the income density has a linear likelihood ratio, it requires a (generalized) logarithmic consumption utility. Under HARA utility and linear or logarithmic likelihood ratios, explicit solutions for the optimal non-linear income tax are derived.

Suggested Citation

  • Dominique Henriet & Patrick Pintus & Alain Trannoy, 2014. "Is the Flat Tax Optimal under Income Risk?," AMSE Working Papers 1420, Aix-Marseille School of Economics, France, revised 30 May 2014.
    • Handle: RePEc:aim:wpaimx:1420
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    References listed on IDEAS

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    1. Varian, Hal R., 1980. "Redistributive taxation as social insurance," Journal of Public Economics, Elsevier, vol. 14(1), pages 49-68, August.
    2. Monica Paiella & Luigi Guiso, 2004. "The Role of Risk Aversion in Predicting Individual Behaviour," Econometric Society 2004 Latin American Meetings 222, Econometric Society.
    3. Low, Hamish & Maldoom, Daniel, 2004. "Optimal taxation, prudence and risk-sharing," Journal of Public Economics, Elsevier, vol. 88(3-4), pages 443-464, March.
    4. Luigi Ventura & Joseph Eisenhauer, 2006. "Prudence and precautionary saving," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 30(2), pages 155-168, June.
    5. Merrigan, Philip & Normandin, Michel, 1996. "Precautionary Saving Motives: An Assessment from UK Time Series of Cross-Sections," Economic Journal, Royal Economic Society, vol. 106(438), pages 1193-1208, September.
    6. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    7. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    8. Dardanoni, Valentino, 1988. "Optimal Choices under Uncertainty: The Case of Two-Argument Utility Functions," Economic Journal, Royal Economic Society, vol. 98(391), pages 429-450, June.
    9. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
    10. John R. Conlon, 2009. "Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems," Econometrica, Econometric Society, vol. 77(1), pages 249-278, January.
    11. Eskander Alvi, 1997. "First-Order Approach to Principal-Agent Problems: A Generalization," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 22(1), pages 59-65, June.
    12. Diamond, Peter A, 1998. "Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates," American Economic Review, American Economic Association, vol. 88(1), pages 83-95, March.
    13. Jonathan Eaton & Harvey S. Rosen, 1980. "Optimal Redistributive Taxation and Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(2), pages 357-364.
    14. Mirrlees, J A, 1990. "Taxing Uncertain Incomes," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 34-45, January.
    15. Helmuth Cremer & Firouz Gahvari, 1999. "Uncertainty, Commitment, and Optimal Taxation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 51-70, January.
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    Cited by:

    1. Robin Boadway & Motohiro Sato, 2015. "Optimal Income Taxation with Risky Earnings: A Synthesis," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(6), pages 773-801, December.

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    More about this item

    Keywords

    Optimal Income Taxation; Income Risk; Linear and Nonlinear Income Tax.;
    All these keywords.

    JEL classification:

    • 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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