Optimal Income Taxation with Composition Effects

Providing estimable sufficient statistics to give policy prescriptions has become a widespread approach, a well-known limitation of which is the endogeneity of sufficient statistics to the policy. Using optimal tax policy as our field of application, we highlight a new source of endogeneity. It arises under multidimensional heterogeneity, because optimal tax formulas are then expressed as functions of weighted means of sufficient statistics computed at the individual level and the weights are endogenous to the 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. In the latter case, we use an improved tax perturbation approach to study composition effects without these assumptions. Numerical simulations on U.S. data suggest the optimal tax rate may be underestimated by 6 p.p. for high incomes levels. We also relate our tax perturbation method to the first order mechanism design method, both methods having hitherto been used separately to derive optimal tax schedules.