Equilibrium determinacy and inflation measures for interest rate rules

Empirical evidence suggests that goods are highly heterogeneous with respect to the degree of price rigidity. We develop a two-sector dynamic general equilibrium model to study the equilibrium determinacy properties of interest rate rules that respond to inflation measures differing in their degree of price rigidity. We find that rules responding to a headline measure, which puts some weight on the inflation of the sector with low price stickiness, are more prone to generate endogenous aggregate instability—in the form of fluctuations driven by self-fulfilling expectations and equilibria where fluctuations are unbounded—than rules that respond exclusively to a core measure, which includes only the inflation of the sector with high price stickiness. We discuss how our results depend on the elasticity of substitution across goods, the timing of the policy rule, and reacting to aggregate activity.