Pro-cyclical emissions, real externalities, and optimal monetary policy

We study optimal monetary policy in an analytically tractable New Key-nesian DSGE-model with an emission externality. Empirically, emissions are strongly pro-cyclical and output in the flexible price equilibrium overreacts to productivity shocks, relative to the efficient allocation. At the same time, output under-reacts relative to the flexible price allocation due to sticky prices. Therefore, it is not optimal to simultaneously stabilize inflation and to close the natural output gap, even though this would be feasible. Real externalities affect the LQ-approximation to optimal monetary policy and we extend the analysis of Benigno and Woodford (2005) to inefficient flexible price equilibria. For central banks with a dual mandate, optimal monetary policy places a larger weight on output stabilization and targets a non-zero natural output gap, implying a higher optimal inflation volatility.