Shaping inequality: Progressive taxation under human capital accumulation

In order to design optimal policy instruments that shape the distribution of income we require realistic income models. A comparison between popular stochastic processes for income shows that most of them fail to match inequality in the US, especially at the top. The Geometric Brownian Motion with reset, however, produces realistic outcomes at both ends of the distribution, while still permitting clear analytic results. Building on this observation, we develop a micro-founded model for endogenous income inequality that fits the current US evidence. It also permits discussing the welfare effects and trade-offs of tax reforms as individuals adjust their labor supply and human capital accumulation. We extend it in an incomplete market setup solved numerically, in which individuals can both form precautionary savings and adjust their labor supply. A calibrated version suggests that the progressivity of US income taxes is below its welfare optimum by around six percentage points.