Optimal monetary policy under low trend inflation

In the monetary policy literature it is common to assume that trend inflation is zero, despite overwhelming evidence that zero inflation is neither empirically relevant nor a practical objective for central bank policy. We therefore extend the standard New Keynesian model to allow for positive trend inflation, showing that even low trend inflation has strong effects on optimal monetary policy and the dynamics of inflation, output and interest rates. Under discretion, the efficient policy deteriorates and there is no guarantee of determinacy. Even with commitment, targeting non-zero trend inflation leads to substantial welfare losses. Our results serve as a warning against indiscriminate use of models assuming zero trend inflation.