Optimal long-run inflation and the New Keynesian model

Central banks typically have a long-run inflation target that is modestly positive. However, the standard New Keynesian framework prescribes that zero inflation is the optimal long-run target. In this paper, we show that when the baseline New Keynesian model is extended to allow for rule-of-thumb behavior by price setters, the optimality of zero long-run inflation ceases, and the monetary authority commits to a positive inflation target. The optimality of positive long-run inflation turns on the fact that the aggregate-supply relation does not imply an equivalence, up to first-order and regardless of policy, between the welfare-relevant measure of inflation and the discounted sequence of future output gaps.