Modeling Inequality and Mobility with Stochastic Processes

This paper presents tractable two parameter stochastic processes of the drift-diffusion class in order to model economic processes with a focus on income. Starting from the resulting closed-form, cross-sectional distributions, easy-to-interpret expressions for mobility and inequality (including the popular Gini-coefficient) are derived. The general processes are applied to discuss income mobility and inequality and fitted to US evidence. Heteroscedasticity is crucial to explaining skewed distributions of log-income, while multiplicative risk is necessary for generating Pareto tails. Furthermore, introducing Poisson death jumps also generates Pareto tails in the low end of the distribution and therefore fits the evidence best. Finally, we develop a micro-founded model for income inequality that fits the current US evidence and permits discussing the welfare effects of tax reforms given that individuals also adjust their labor supply and human capital accumulation. According to the model current US taxation is close to its welfare optimum.