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Major central banks remunerate reserves at negative interest rates and it is increasingly likely that they will keep rates negative for many more years. To study the long run implications of negative rates, we construct a dynamic general equilibrium model with commercial banks funding investment projects and a central bank issuing reserves. Negative rates distort investment decisions resulting in lower output and welfare. These findings sharply contrast the short-run expansionary effects ascribed to negative rate policies by most of the existing literature. Negative rates also reduce commercial bank profitability. Exempting a fraction of reserves from negative rates can resolve profitability concerns without affecting the central bank's ability to control the money market rate. However, exemption thresholds do no mitigate the investment distortions created by negative rates.

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 United States. 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 rises during downturns, 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 racial unemployment gap and the magnitude of its response to shocks.

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