Duration Dependence in US Business Cycles: An Analysis Using the Modulated Power Law Process
Zhou, Haigang, Rigdon, Steven E., Journal of Economics and Finance
The modulated power law process is used to analyze the duration dependence in US business cycles. The model makes less restricting assumptions than traditional models do and measures both the local and global performance of business cycles. The results indicate evidence of positive duration dependence in the U.S. business cycles. Structural change after WWII in both expansion and contraction phases of business cycles is also documented. Hypothesis tests confirm that the model fits US business cycles.
Keywords Weibull process * Renewal process * Maximum likelihood estimation * Modulated power law process
JEL Classifications E3-C1
Previous studies have applied nonparametric and parametric methods to analyze the duration dependence in business cycles. Examples of early works that applied nonparametric χ^sup 2^-type goodness-of-fit tests include McCulloch (1975), Savin (1977), So (1994), Leeuw (1987), and Diebold and Rudebusch (1987).
Later parametric studies mainly used the Weibull distribution because of its parametric nature and of its flexibility in modeling different types of duration dependence. Using the National Bureau of Economic Research (NBER) monthly reference cycle chronology from 1854 to 1990, Sichel (1991) applied the Weibull hazard function to examine the duration dependence of business cycles and found positive duration dependence in prewar expansions and postwar contractions. Cochran and Defina (1995) also used the Weibull hazard function to investigate duration dependence in US stock market cycles over the January 1885 to July 1992 period. They found evidence of duration dependence in prewar expansions and in postwar contractions but did not find evidence of duration dependence in prewar contractions and postwar expansions. Using a generalized Weibull model to analyze the NBER monthly reference cycles chronology from December 1854 to March 2001, Zuehlke (2003) documented evidence of duration dependence for all samples in the study. Harman and Zuehlke (in press) applied the generalized Weibull model to analyze the US stock market data and document positive duration dependence for both prewar and postwar samples of stock market expansions and contractions.
One potential drawback of using a renewal process is that it assumes the sample observations are from an independent and identically distributed (i.i.d.) stochastic process, i.e., the durations between consecutive events are positive, independent, and identically distributed. This assumption is sound if a physical renewal process involves successive replacements of failed mechanical components. However, with business cycles of the past 150 years, it may not be reasonable to assume the interarrival times between economic troughs, or peaks, follow the same distribution. For example, Basu and Taylor (1999) have observed a significant decline in the volatility of measured US output.
Instead, this study uses a generalized model, the modulated power law process (MPLP), which is a compromise between a renewal process and a non-homogeneous Poisson process, to study the duration dependence in the US business cycles. Using the modulated power law process, the results indicate the presence of positive duration dependence in our samples of US business cycles. The results are robust to different sampling processes. Hypothesis tests of the parameters confirm that the MPLP model is appropriate in modeling US business cycles.
This study contributes to the literature in that it introduces a new statistical model to analyze the duration dependence of business cycles. The model relies on less restrictive assumptions about the underlying process of business cycles, but offers a more complete description of the statistical process. While traditional models measure only the local performance, the MPLP model measures both the global and local performance of the underlying statistical process. …