Optimal Monetary Policy Response to Distortionary Tax Changes

We analyze the trade-offs faced by a monetary policy authority when a value added tax rate is increased. In the short run, such an increase acts as a cost push shock from the perspective of a central bank that is concerned with stabilizing the welfare relevant output gap. We develop a New Keynesian monetary model with real wage rigidity and consider the effects that obtain under a simple interest rate rule, on the one hand, and those that obtain under an optimal monetary policy from a timeless perspective (in the terminology of Woodford, 2003). The implications for the dynamic response of the economy differ in the presence of real wage rigidity. While under a rule inflation is higher for about eight quarters, the optimal policy involves an adjustment that is about half as long, and is followed by a slight deflation. The reason is that this policy can be shown to include a commitment to target a certain price-level, which helps contain inflation expectations. We treat the tax shock as permanent, so that the central bank does not fully revert the price level to its orginal level.