Dynamic probabilities of restrictions in state space models: an application to the Phillips curve

G.M. Koop, Roberto Leon-Gonzalez, Rodney W. Strachan

Research output: Contribution to journalArticle

16 Citations (Scopus)
32 Downloads (Pure)

Abstract

Empirical macroeconomists are increasingly using models (e.g. regressions or Vector Autoregressions) where the parameters vary over time. State space methods are frequently used to specify the evolution of parameters in such models. In any application, there are typically restrictions on the parameters that a researcher might be interested in. This motivates the question of how to calculate the probability that a restriction holds at a point in time without assuming the restriction holds at all (or any other) points in time. This paper develops methods to answer this question. In particular, the principle of the Savage-Dickey density ratio is used to obtain the time-varying posterior probabilities of restrictions. We use our methods in a macroeconomic application involving the Phillips curve. Macroeconomists are interested in whether the long-run Phillips curve is vertical. This is a restriction for which we can calculate the posterior probability using our methods. Using U.S. data, the probability that this restriction holds tends to be fairly high, but decreases slightly over time (apart from a slight peak in the late 1970s). We also calculate the probability that another restriction, that the NAIRU is not identi…ed, holds. The probability that it holds fluctuates over time with most evidence in favor of the restriction occurring after 1990.
Original languageEnglish
Pages (from-to)370-379
Number of pages10
JournalJournal of Business and Economic Statistics
Volume28
Issue number3
DOIs
Publication statusPublished - 2010

Keywords

  • bayesian
  • state space model
  • Savage-Dickey density ratio
  • time varying parameter mode
  • economics

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