Ramsey Optimal Monetary Policy in Response to Shifts in the Beveridge Curve

I use a dynamic stochastic general equilibrium model with search and matching frictions in the labor market and analyze the optimal monetary policy response to an outward shift in the Beveridge curve. The shift results from an exogenous deline in the efficiency of matching unemployed workers to vacant jobs. The results cover several cases depending on type of the shift, temporary versus permanent, and efficient versus inefficient. Whether the shock is temporary and persistent versus permanent affects the length of the adjustment, with the adjustment after a persistent temporary shift taking twice as long the adjustment after a permanent one. Whether the shock is efficient or not affects the goals of optimal monetary policy. In response to an efficient shock, it is optimal to maintain price stability while in response to an inefficient shock it is optimal to both stabilize prices and inefficient fluctuations in unemployment. The goals of monetary policy are critical for the way the shock affects inflation and, more importantly, for the way it affects fluctuations in unemployment and vacancies.