Multiplicity in New Keynesian Models

The common practice in monetary economics is to linearize a model around its deterministic equilibrium. In this paper, we show analytically that when central banks stabilize both output and inflation, a standard dynamic New Keynesian model has three deterministic equilibria under a realistic parameterization. One is associated with targeted inflation as is commonly found in the literature; the other two are associated with deflation and high inflation. Our findings suggest that empirical research should allow for multiple equilibria or regimes, including both the one with high inflation and the one with deflation, in modeling inflation dynamics.