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On Vickrey's Income Averaging

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  • Stefan Steinerberger
  • Aleh Tsyvinski

Abstract

We consider a small set of axioms for income averaging -- recursivity, continuity, and the boundary condition for the present. These properties yield a unique averaging function that is the density of the reflected Brownian motion with a drift started at the current income and moving over the past incomes. When averaging is done over the short past, the weighting function is asymptotically converging to a Gaussian. When averaging is done over the long horizon, the weighing function converges to the exponential distribution. For all intermediate averaging scales, we derive an explicit solution that interpolates between the two.

Suggested Citation

  • Stefan Steinerberger & Aleh Tsyvinski, 2020. "On Vickrey's Income Averaging," Papers 2004.06289, arXiv.org.
    • Handle: RePEc:arx:papers:2004.06289
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    References listed on IDEAS

    as
    1. Mark Huggett & Juan Carlos Parra, 2010. "How Well Does the U.S. Social Insurance System Provide Social Insurance?," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 76-112, February.
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    7. Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
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    JEL classification:

    • H20 - Public Economics - - Taxation, Subsidies, and Revenue - - - General

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