Inflation persistence and optimal positive long-run inflation

Within New Keynesian economics, the optimality of a monetary policy that aims at zero inflation is surprisingly robust. Optimal monetary policy has this character despite the inefficiency of the nonstochastic steady state and despite the existence of a positively sloped long-run Phillips-curve trade-off. Full price stability remains optimal even under inflation persistence due to backward-looking price indexation by price setters. We show how extending a basic New Keynesian model to the case of inflation persistence due to backward-looking rule-of-thumb behaviour by price setters breaks the surprising robustness of zero long-run inflation target, namely backward-looking rule-of-thumb behaviour by price setters results in optimal positive long-run inflation. Comparing different theoretical explanations for structural inflation persistence suggests that the features that seem capable of delivering an endogenously optimal inflation target are costly disinflation, long-run Phillips-curve trade-off, and steady-state distortions.