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In this paper, we examine two issues concerning business cycle research. First, a number of studies have demonstrated that more complicated non-linear models do not replicate business cycle features better than simpler linear models. In Harding and Pagan (2002), they showed that a random walk with drift model of real GDP for the U.S., U.K., and Australia can capture the main business cycle features of the respective countries quite well. Adding non-linear structure, such as Hamilton’s (1989) Markov-switching model produced cycles that are too extreme, especially with respect to the cumulative movements of the cycles, where cumulative movements are a measure of cumulated output losses from peak to trough of a business cycle. Furthermore, Harding and Pagan (2003a) argued that based on criteria, such as simplicity, transparency, robustness, and replicability, the non-parametric Bry and Boschan algorithm (1971) is in fact superior to the Markov-switching model in determining turning points in business cycles. Similarly, Hess and Iwata (1997) showed that a non-linear models such as the Markov-switching models are no better than a simple ARIMA(1,1,0) model in replicating business cycle features. We start by comparing how well the Hamilton’s Markov-switching model and the Bry and Boschan algorithm can replicate the U.S. business cycle features. One interesting finding that has not been shown before is that we are unable to replicate Hamilton’s original result for the same sample period using real GDP rather than real GNP as Hamilton did. Furthermore, we also found that Hamilton’s Markov-switching model is not robust with respect to different sample periods. The Bry and Boschan algorithm, on the other hand, replicated business cycle features consistently. Second, Burns and Mitchell (1946) and NBER’s Business Cycle Dating Committee suggested that a variety of time series representing economic activities should be used for the purpose of dating business cycle. Nevertheless, real GDP is by far the most popular and frequently used single series to represent aggregate economic activities in business cycle research. We compared the ability of the U.S. real GDP and a coincident index published by the Federal Reserve Bank of Philadelphia in replicating features of the U.S. business cycle. We found that a constructed quarterly version of the coincident index is slightly preferred over the real GDP, suggesting that the coincident index may be a better indicator than the commonly used real GDP as an overall indicator of U.S. economic activities.

Measuring U.S. business cycles: A comparison of two methods and two indicators of economic activities