Bayesian Analysis of Business Cycle in Japan Using Markov Switching Model with Stochastic Volatility and Fat-tail Distribution

Abstract

This article analyzes the business cycle in Japan by applying Markov switching (MS) models to the monthly data on the coincident indicator of composite index (CI) during the period of 1985/01-2012/12 calculated by Economic and Social Research Institute (ESRI), Cabinet Office, the Government of Japan. It is shown that the impact of the financial crisis in 2008 and the Tohoku earthquake in 2011 on this index is so large that the simple MS model with normal error and constant volatility cannot detect the business cycle turning points properly. The MS model is extended by incorporating Student's t-error and stochastic volatility (SV), and a Bayesian method via Markov chain Monte Carlo is developed for the analysis of the extended models. It is also shown that the MS model provides the estimates of the business cycle turning points close to those published by ESRI once t-error or SV is introduced. Bayesian model comparison based on marginal likelihood provides evidence that the MS model with both t-error and SV fits the data best.