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

Abstract

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.

Keywords: Pile-Up Problem, Profile Likelihood, Integrated Likelihood, Trend Stationary Process, Difference Stationary Process, Out-Of-Sample Prediction, Spurious Periodicity