Optimal income taxation with composition effects

Providing estimable sufficient statistics to give policy prescriptions has become a widespread approach over the recent years. A well-known limitation of this approach is the endogeneity of sufficient statistics to the policy. In this paper, using optimal tax policy as our field of application, we highlight a new source of endogeneity. It arises since, under multidimensional heterogeneity, optimal tax formulas are expressed as a function of weighted means of sufficient statistics computed at the individual level and the weights are endogenous to tax policy. We analytically show that ignoring these composition effects leads to underestimate the optimal linear tax and, under a restrictive set of assumptions, the optimal nonlinear tax as well. To relax these assumptions, we use an improved tax perturbation approach to study composition effects in the latter case. Our numerical simulations using U.S. data suggest the optimal tax rate may be underestimated by 6 percentage points for high incomes levels. As a secondary result, we show the equivalence between our improved tax perturbation method and the first order mechanism design method, two methods which have hitherto been used separately to derive optimal tax schedules.