Optimal Redistribution with a Shadow Economy

We extend the theory of the optimal redistributive taxation to economies with an informal labor market. The optimal tax formula contains two new terms capturing reported income responses of informal workers on an intensive and an extensive margin. Both terms decrease the optimal tax rates. We quantitatively show that this reduction can be substantial, exceeding 30 percentage points, and we document a large welfare gain of up to 6.4% of consumption from following our tax formula rather than the standard formula. We also provide a novel decomposition of the welfare impact of the shadow economy into labor efficiency and redistribution components. In the quantitative model estimated with Colombian data the shadow economy benefits efficiency at the expense of redistribution. As a result, conditional on the optimal tax policy, the presence of the informal sector does not substantially affect social welfare unless social preferences for redistribution are strong.