Practical Optimal Income Taxation

We review approaches to formulating and solving optimal tax problems in heterogeneous-agent economies. We first show that whether worker heterogeneity is represented through a small or a large number of different productivity types controls the tightness of incentive constraints facing the Mirrlessian planner and therefore has an important impact on policy prescriptions. A popular computational approach that iterates on the Diamond-Saez implicit optimal tax formula does not deliver the constrained efficient allocation when a coarse productivity grid is used. For the purpose of providing quantitative policy recommendations, one safe approach is to solve for the Mirrleesian optimum assuming a very fine grid of productivity types. Alternatively, one can formulate the problem assuming that the distribution of types is continuous, and search for a numerical solution to the system of ordinary differential equations that then define the optimal policy. If these options are infeasible, then optimizing within a flexible parametric class for taxes is preferable to a coarse grid Mirrleesian approach.