Bayesian Analysis of Business Cycles in Japan by Extending the Markov Switching Model

This paper analyzes business cycles in Japan by applying Markov switching (MS) models to monthly data on the coincident indicator of composite index (CI) during the period of 1985/01-2025/05 calculated by Economic and Social Research Institute (ESRI), Cabinet Office, the Government of Japan. During the latter half of the sample period, the Japanese economy experienced major shocks such as the global financial crisis in 2008, the Great East Japan Earthquake in 2011 and the COVID-19 pandemic in 2020. CI fell sharply during these periods, which make it difficult to estimate business cycle turning points using the simple MS model. In this paper, the MS model is extended by incorporating Student's t-error and stochastic volatility (SV). Since it is difficult to evaluate the likelihood once SV is introduced, a Bayesian method via Markov chain Monte Carlo (MCMC) is employed. The MS model with t-error or SV is shown to provide the estimates of the business cycle turning points close to those published by ESRI. A new method for evaluating marginal likelihood is evaluated. Bayesian model comparison based on marginal likelihood provides evidence that t-error is not needed once SV is introduced. Using the MS model with normal error and SV, structural changes in CI's mean growth rates during booms and recessions are also analyezed and two break points are found in the both mean growth rates. One is 2008/10 and the other is 2010/02, during which the mean growth rate during recession falls and that during boom rises due to the global financial crisis.