Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve

Using the Savage Dickey density ratio and an alternative approach that uses more relaxed assumptions, we develop methods to calculate the probability that a restriction holds at a point in time without assuming that the restriction holds at any other points in time. Both approaches use MCMC output only from the unrestricted model to compute the time-varying posterior probabilities for all models of interest. Using U.S. data, we find the probability that the long-run Phillips curve is vertical to be fairly high, but decreases over time. The probability that the NAIRU is not identified fluctuates over time, but increases after 1990.