Signing Distortions in Optimal Tax and other Adverse Selection Problems with Random Participation

We develop a methodology to sign output distortions in the random participation framework. We apply our method to monopoly nonlinear pricing problem, to the regulatory monopoly problem and mainly to the optimal income tax problem. In the latter framework, individuals are heterogeneous across two unobserved dimensions: their skill and their disutility of participation to the labor market. We derive a fairly mild condition for optimal marginal tax rates to be non negative everywhere, implying that in-work effort is distorted downwards. Numerical simulations for the U.S. confirm this property. Moreover, it is typically optimal to provide a distinct level of transfer to the non-employed and to workers with zero or negligible earnings.