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

Abstract

While Perron and Wada (2009) show that postwar U.S. real GDP follows a trend stationary process (TSP) based on the maximum likelihood approach, our analysis based on the Bayesian approach shows that it is a difference stationary process (DSP) with the stochastic trend component explaining most of the variations in real GDP. One goal of this paper is to provide a comprehensive analysis on the sources of such different results and to suggest that more credibility should be conferred to the Bayesian inference. Another goal naturally is to re-investigate the trend-cycle decompositions within the Bayesian framework. This is done by employing a model that incorporates time variation in both the mean and variance. The Bayesian approach to model selection prefers a DSP model to a TSP model, even though the evidence is less than decisive. Empirical results also show that there exists convincing evidence that the cycle from the DSP model, which is small in magnitude and noisy, has out-of-sample predictive power for future output growth at short horizons. The highly persistent TSP cycle without any predictive power may be related to spurious periodicity discussed in Nelson and Kang (1981).