Multiple Equilibria and the Phillips Curve: Do Agents Always Underreact?

We study a New Keynesian Phillips curve in which agents deviate from the rational expectation paradigm and forecast inflation using a simple, potentially misspecified autoregressive rule. Consistency criteria à la Hommes and Zhu (2014) between perceived and actual laws of motion of inflation might allow for multiple expectational equilibria. Unfortunately, multiple equilibria models pose challenges for empirical validation. This paper proposes a latent Markov chain process to dynamically separate such equilibria. Moreover, an original Bayesian inference approach based on hierarchical priors is introduced, which naturally offers the possibility of incorporating equilibrium-identifying constraints with various degrees of prior beliefs. Finally, an inference procedure is proposed to assess a posteriori the probability that the theoretical constraints are satisfied and to estimate the equilibrium changes over time. We show that common prior assumptions regarding structural parameters favor the separation of equilibria, thereby making the Bayesian inference a natural framework for Markov-switching Phillips curve models. Empirical evidence obtained from observed inflation, output gap, and the consensus expectations from the Survey of Professional Forecasters supports multiple equilibria, and we find evidence of temporal variation in over-and under-reaction patterns, which, to the best of our knowledge, have not been previously documented. Specifically, we observe that agents tend to underreact to shocks when inflation is high and persistent, whereas they behave substantially as fully informed forecasters when the inflation level is low and stable, i.e., after the mid-nineties. We also find that the model does not suffer from the missing disinflation puzzle during the Great Recession.