Optimal Monetary Policy in Response to Shifts in the Beveridge Curve

I build 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 results cover several cases depending on the reason for the shift. If the shift is due to a fall in the efficiency of matching, then the optimal response of the central bank is to stabilize inflation. On the other hand, if the shift arises from an increase in the elasticity of employment matches with respect to vacancies, then the policy maker faces a trade off between stabilizing inflation and unemployment. The optimal policy response to the efficient labor market shock changes when real wages are sticky but remains unchanged when home and market goods are imperfect substitutes, compared to the case when they are not. When contrasted to a Taylor rule that targets inflation and output growth, the optimal monetary policy is more aggressive in pursuit of its objectives