The Optimal Inflation Target and the Natural Rate of Interest

We study how changes in the steady-state real interest rate (henceforth r*) affect the optimal inflation target in a New Keynesian dynamic stochastic general equilibrium (DSGE) model with trend inflation and a lower bound on the nominal interest rate. In this setup, a lower r* increases the probability of hitting the lower bound. That effect can be counteracted by an increase in the inflation target, but the resulting higher steady-state inflation has a welfare cost in and of itself. We use an estimated DSGE model to quantify that trade-off and determine the implied optimal inflation target, conditional on the monetary policy rule in place before the financial crisis. The relation between r* and the optimal inflation target is downward sloping. While the increase in the optimal inflation rate is in general smaller than the decline in r*, 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 makeup strategies such as price level targeting, the optimal inflation target is significantly lower and less sensitive to r*.