On Vickrey’s Income Averaging / Stefan Steinerberger, Aleh Tsyvinski.

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Steinerberger, Stefan

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Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w27024.Publication details: Cambridge, Mass. National Bureau of Economic Research 2020.Description: 1 online resource: illustrations (black and white)Subject(s):

H20 - General

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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.

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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.