A New Approach to Dating the Reference Cycle

Abstract

Abstract–This article proposes a new approach to the analysis of the reference cycle turning points, defined on the basis of the specific turning points of a broad set of coincident economic indicators. Each individual pair of specific peaks and troughs from these indicators is viewed as a realization of a mixture of an unspecified number of separate bivariate Gaussian distributions whose different means are the reference turning points. These dates break the sample into separate reference cycle phases, whose shifts are modeled by a hidden Markov chain. The transition probability matrix is constrained so that the specification is equivalent to a multiple change-point model. Bayesian estimation of finite Markov mixture modeling techniques is suggested to estimate the model. Several Monte Carlo experiments are used to show the accuracy of the model to date reference cycles that suffer from short phases, uncertain turning points, small samples, and asymmetric cycles. In the empirical section, we show the high performance of our approach to identifying the US reference cycle, with little difference from the timing of the turning point dates established by the NBER. In a pseudo real-time analysis, we also show the good performance of this methodology in terms of accuracy and speed of detection of turning point dates.

Keywords:

• Business cycles
• Finite mixture models
• Turning points

Acknowledgments

We thank the editor and two referees for helpful comments and suggestions. We thank Gary Koop for sharing his GAUSS code to determine the number of breaks. All remaining errors are our responsibility. Data and codes that replicate our results are available from the authors’ websites. The views in this article are those of the authors and do not represent the views of the Bank of Spain or the Eurosystem.

Funding

M. Camacho and M. D. Gadea are grateful for the support of grants PID2019-107192GB-I00 (AEI/10.13039/501100011033) and 19884/GERM/15, and ECO2017-83255-C3-1-P and ECO2017-83255-C3-3-P (MICINU, AEI/ERDF, EU), respectively.