Trend-Cycle Decompositions of Real GDP Revisited : Classical and Bayesian Perspectives on an Unsolved Puzzle

While Perron and Wada's (2009) maximum likelihood estimation approach suggests that postwar U.S. real GDP follows a trend stationary process (TSP), our Bayesian approach based on the same model and the same sample suggests that it follows a difference stationary process (DSP). We first show that the results based on the maximum likelihood approach should be interpreted with caution, as they are relatively more subject to the ‘pile-up problem' than those based on the Bayesian approach.We then directly estimate and compare the two competing TSP and DSP models of real GDP within the Bayesian framework. We focus on out-of-sample prediction performance of the two competing models, and we employ the predictive likelihood as a criterion for model comparison. We also compare the out-of-sample predictive power of the cyclical components implied by the two models estimated. Our empirical results suggest that a DSP model is preferred to a TSP model. Furthermore, the cycle from the DSP model, unlike the cycle from the TSP model, has out-of sample predictive power for future output growth and has information beyond the historical mean for output growth