On Vickrey’s Income Averaging
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.
We thank Hector Chade, Kjetil Storesletten, Georgii Riabov, Florian Scheuer, and Philipp Strack for useful discussions. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.