Risk, uncertainty, and the dynamics of inequality

The dynamics of wealth inequality are studied in a continuous-time Blanchard/Yaari model. Investment returns are idiosyncratic and subject to Knightian uncertainty. In response, agents formulate robust portfolio policies. These policies are nonhomothetic; wealthy agents invest a higher fraction of their wealth in uncertain assets yielding higher mean returns. This produces a feedback mechanism that amplifies inequality. It also produces an accelerated rate of convergence, which helps resolve a puzzle recently identified by Gabaix et al. (2016). An empirically plausible increase in uncertainty can account for about half of the recent increase in top wealth shares.