Time consistent monetary policy with endogenous price rigidity

I characterize time consistent equilibrium in an economy with price rigidity and an optimizing monetary authority operating under discretion. Firms have the option to increase their frequency of price change, at a cost, in response to higher inflation. Previous studies, which assume a constant degree of price rigidity across inflation regimes, find two time consistent equilibria—one with low inflation, the other with high inflation. In contrast, when price rigidity is endogenous, the high inflation equilibrium ceases to exist. Hence, time consistent equilibrium is unique. This result depends on two features of the analysis: (1) a plausible quantitative specification of the fixed cost of price change, and (2) the presence of an arbitrarily small cost of inflation that is independent of price rigidity.