Timing Transitions Between Determinate and Indeterminate Equilibria in an Empirical DSGE Model: Benefits and Implications

Abstract

We extend Lubik and Schorfheide's (2004) likelihood-based estimation of dynamic stochastic general equilibrium (DSGE) models under indeterminacy to encompass a sample period including both determinacy and indeterminacy by implementing the change-point methodology (Chib, 1998). This feature is useful because DSGE models generally are estimated with data sets that include the Great Inflation of the 1970s and the surrounding low inflation periods. Timing the transitions between determinate and indeterminate equilibria is one of the key contributions of this paper. Moreover, by letting the data provide estimates of the state transition dates and allowing the estimated structural parameters to be the same across determinacy states, we obtain more precise estimates of the differences in characteristics, such as the impulse responses, across the states. In particular, we find that positive interest rate shocks were inflationary under indeterminacy. While the change-point treatment of indeterminacy is applicable to all estimated linear DSGE models, we demonstrate our methodology by estimating the canonical Woodford model with a time-varying inflation target. Implementation of the change-point methodology coupled with Tailored Metropolis-Hastings provides a highly efficient Bayesian MCMC algorithm. Our prior-posterior updates indicate substantially lower sensitivity to hyperparameters of the prior relative to other estimated DSGE models.