Optimal Taxation with Heterogeneous Skills and Elasticities: Structural and Sufficient Statistics Approaches Previous versions of this paper has circulated under the titles “Optimal Nonlinear Income Taxation with Multidimensional Types: The Case with Heterogeneous Behavioral Responses” (2014) and “Optimal Income Taxation when Skills and Behavioral Elasticities are Heterogeneous” (2015)

The usual approach to calibrate optimal tax formulae consists in using the observed sufficient statistics, which is only correct as long as they correspond to the optimal sufficient statistics. In the very general case where agents are heterogeneous in many dimensions, we propose a new structural method (based on an allocation perturbation) from which we derive the optimal income tax formula and its optimal sufficient statistics computed from the observed ones. This allows us to quantify the error in the marginal tax rates entailed by using observed rather than optimal sufficient statistics. On US data, we show that this error can be considerable (up to 10 percentage points). We also call for a change of focus in the empirical analysis of top tax rates. Since individuals are heterogeneous along multiple dimensions, one needs to estimate the elasticity of those whose income density has the fatter tail.