Bayesian model selection for unit root testing with multiple structural breaks

A fully Bayesian approach to unit root testing with multiple structural breaks is presented. For this purpose the number of breaks, the corresponding break dates as well as the number of autoregressive lags are treated as model indicators, whose posterior distributions are explored using a hybrid Markov chain Monte Carlo sampling strategy. The performance of the sampling algorithm is demonstrated on the basis of several Monte Carlo experiments. In a next step the most likely model is used to test for a unit root with possible multiple breaks by computing the posterior probability of this point hypothesis under different prior distributions. The sensitivity of the test results with regard to the assumed prior distribution is analyzed and the Bayes test is compared with some classical unit root tests by means of power functions. Finally, in an empirical application the yearly unemployment rates of 17 OECD countries are analyzed to answer the question if there is persistence after a labor market shock.