Optimal Redistribution with a Shadow Economy

We extend the theory of optimal redistributive taxation to economies with an in- formal labor market. The optimal tax formula contains two novel terms capturing reported income responses of informal workers on an intensive and an extensive mar- gin. Both terms decrease the optimal tax rates. We estimate the model with Colombian data and show that the reduction of tax rates relative to the best-performing standard tax formula can be quantitatively large, reaching 25 pp and leading to a 1.9% welfare gain. We also provide a novel decomposition of the welfare impact of the shadow economy into an efficiency and a redistribution components. Conditional on the optimal tax policy, the Colombian shadow economy benefits efficiency at the expense of redistribution. Consequently, the presence of the informal sector reduces welfare only when preferences for redistribution are strong.