Optimal Redistribution with a Shadow Economy

We examine the constrained efficient allocations in the Mirrlees (1971) model with an informal sector. There are two labor markets: formal and informal. The planner observes only income from the formal market. We show that the shadow economy can be welfare improving through two channels. It can be used as a shelter against tax distortions, raising the efficiency of labor supply, and as a screening device, benefiting redistribution. We calibrate the model to Colombia, where 58% of workers are employed informally. The optimal share of shadow workers is close to 22% for the Rawlsian planner and less than 1% for the Utilitarian planner. The optimal tax schedule is very different then the one implied by the Mirrlees (1971) model without the informal sector.