How should monetary policy respond to changes in the relative price of oil? considering supply and demand shocks

This paper examines optimal monetary policy in a New Keynesian model, where the relative price of oil is affected by exogenous supply shocks and a productivity-driven demand shock. When wages are flexible, stabilizing core inflation is optimal and the nominal rate rises (falls) in response to a demand (supply) shock. When both prices and wages are sticky, core inflation falls (rises) in response to the demand (supply) shock. Stabilizing CPI inflation generates small welfare losses only if the demand shock is the main driver of oil prices. Based on a VAR estimated using post-1986 data for the U.S., both shocks have had minimal impacts on core inflation. The federal funds rate rises in response to the demand shock but falls in response to the supply shock, consistent with the predictions of the theoretical model for a policy that stabilizes core inflation.