In the business cycle literature researchers often want to determine the extent to which models of the business cycle reproduce broad characteristics of the real world business cycle they purport to represent. Of considerable interest is whether a model’s implied cycle chronology is consistent with the actual business cycle chronology. In the US, a very widely accepted business cycle chronology is that compiled by the National Bureau of Economic research (NBER) and the vast majority of US business cycle scholars have, for many years, proceeded to test their models for their consistency with the NBER dates. In doing this, one of the most prevalent metrics in use since its introduction into the business cycle literature by Diebold and Rudebusch (1989) is the so-called quadratic probability score, or QPS. However, an important limitation to the use of the QPS statistic is that its sampling distribution is unknown so that rigorous statistical inference is not feasible. We suggest circumventing this by bootstrapping the distribution. This analysis yields some interesting insights into the relationship between statistical measures of goodness of fit of a model and the ability of the model to predict some underlying set of regimes of interest. Furthermore, in modeling the business cycle, a popular approach in recent years has been to use some variant of the so-called Markov regime switching (MRS) model first introduced by Hamilton (1989) and we therefore use MRS models as the framework for the paper. Of course, the approach could be applied to any US business cycle model.
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Diebold, Francis X & Rudebusch, Glenn D, 1989.
"Scoring the Leading Indicators,"
Journal of Business,
University of Chicago Press, vol. 62(3), pages 369-91, July.
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