Chasing the gap: speed limits and optimal monetary policy

Speed limit monetary policy rules incorporate a response to the change in the output gap. They have been widely used in the recent DSGE literature, for example in the influential model of Smets and Wouters. However, the optimality of these rules is unclear. Using a simple New-Keynesian DSGE model with habit persistence, we: (a) derive an optimal speed limit policy rule under discretion that has the same functional form as speed limit rules in the recent literature; and (b) show that the type of speed limit policy rule used in the recent literature are not optimal in our model, mainly because they assume a relatively low policy weight on inflation.