Optimal Taxation with Private Insurance

We derive a fully nonlinear optimal income tax schedule in the presence of a private insurance market. The optimal tax formula is expressed in terms of sufficient statistics?such as the Frisch elasticity of labor supply, social preferences, and hazard rates of the income distributions?as in the standard Mirrleesian taxation without private insurance (e.g., Saez (2001)). However, in the presence of a private market, the standard sufficient statistics are no longer sufficient. The optimal tax rate also depends on how private savings interact with public insurance? through substitution and crowding in/out. Based on our formula, we compute the optimal tax schedule using a quantitative general equilibrium model calibrated to reproduce the U.S. income distribution.