On Vickrey's Income Averaging

25 Pages Posted: 20 Apr 2020 Last revised: 18 Nov 2021

See all articles by Stefan Steinerberger

Stefan Steinerberger

University of Washington

Aleh Tsyvinski

Yale University - Cowles Foundation; Yale University

Date Written: April 2020


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.

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Suggested Citation

Steinerberger, Stefan and Tsyvinski, Aleh and Tsyvinski, Aleh, On Vickrey's Income Averaging (April 2020). NBER Working Paper No. w27024, Available at SSRN: https://ssrn.com/abstract=3580582 or http://dx.doi.org/10.2139/ssrn.3580582

Stefan Steinerberger (Contact Author)

University of Washington ( email )

box 354350
Seattle, WA 98195-4350
United States

Aleh Tsyvinski

Yale University ( email )

493 College St
New Haven, CT CT 06520
United States

Yale University - Cowles Foundation ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-9163 (Phone)

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