Taxation, Sorting and Redistribution: Theory and Evidence

We develop a framework for optimal taxation when assignment of workers to firms is endogenous. In our model, workers are heterogeneous with respect to their productivity as well as their firm-specific cost of working. Firms have heterogeneous productivities and production exhibits complementarities between firm and worker productivity. Different workers assign to different firms and this assignment depends on the the distribution of workers characteristics. We show that the nature of the multi-dimensional heterogeneity of the workers implies that income taxes affect the way workers sort into jobs. As a result, taxes affect the allocation of workers among firms and thus aggregate productivity even when traditional notions of labor supply are fully inelastic. Our model allows us to define a notion of sorting elasticity with respect to taxes and technological changes. Furthermore, we can analyze optimal linear and non-linear taxes and provide formulas that relate optimal taxes to the sorting elasticity. Contrary to some results in the literature, technological change that changes firms' distribution of productivity does have an effect on marginal taxes through this sorting elasticity. Finally, we provide evidence on the magnitude of the sorting elasticity and its implications on optimal income taxes using employer-employee data.