This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section and panel data. The authors' analysis proves nonparametric identifiability for the closely related competing risks model.