Racial unemployment gaps and the disparate impact of the inflation tax

We study the nonlinearities present in a standard monetary labor search model modified to have two groups of workers facing exogenous differences in the job finding and separation rates. We use our setting to study the racial unemployment gap between Black and white workers in the US. A calibrated version of the model is able to replicate the difference between the two groups both in the level and volatility of unemployment. We show that the racial unemployment gap is counter-cyclical and that its reaction to shocks is state-dependent. In particular, following a negative productivity shock, when aggregate unemployment is above average the gap increases by 0.6pp more than when aggregate unemployment is below average. In terms of policy, we study the implications of different inflation regimes on the racial unemployment gap. Higher trend inflation increases both the level of the unemployment gap and the magnitude of its response to shocks.