The optimal inflation target and the natural rate of interest

We study how changes in the steady-state real interest rate affect the optimal inflation target in a New Keynesian DSGE model with trend inflation and a lower bound on the nominal interest rate. In this setup, a lower steady-state real interest rate increases the probability of hitting the lower bound. That effect can be counteracted by an increase in the inflation target, but the resulting higher steadystate inflation has a welfare cost in and of itself. We use an estimated DSGE model to quantify that tradeoff and determine the implied optimal inflation target, conditional on the monetary policy rule in place before the financial crisis. The relation between the steady-state real interest rate and the optimal inflation target is downward sloping. While the increase in the optimal inflation rate is in general smaller than the decline in the steady-state real interest rate, in the currently empirically relevant region the slope of the relation is found to be close to -1. That slope is robust to allowing for parameter uncertainty. Under "make-up" strategies such as price level targeting, the required increase in the optimal inflation target under a lower steady-state real interest rate is, however, much smaller.