The ‘Pile-up Problem’ in Trend-Cycle Decomposition of Real GDP: Classical and Bayesian Perspectives

Prof. Chang-Jin Kim
Wednesday, November 27, 2013 - 2:00pm
Spandauer Strasse 1, Room 21b

Based on maximum likelihood estimation of an ARMA model of real GDP growth with a structural break in mean, Perron and Wada (2009) show that real GDP may be a trend stationary process. Based on Bayesian estimation of the same model, on the contrary, we show that most of the variations in real GDP can be explained by the stochastic trend component, as suggested by Nelson and Plosser (1982) and Morley et al. (2003). Our analysis indicates that Perron and Wada’s (2009) results may be due to the classical pile-up problem, while we can give more credibility to the results based on the Bayesian approach. If we take the posterior modes of the parameters as true values, the probability of the pile-up problem for the maximum likelihood method is calculated to be as high as 42.7%. We conclude that, even after taking a break in the mean growth rate of real GDP in the mid 1970s, the implications of Nelson and Plosser (1982) and Morley et al. (2003) on trend-cycle decomposition continue to hold within the Bayesian framework, which is relatively free from the pile-up problem in repeated sampling context. This conclusion is further strengthened if we incorporate the Great Moderation, i.e., a structural break in the conditional variance of real GDP in the mid-1980s, and uncertainty in the break dates.