Extracting a Robust U.S. Business Cycle Using a Time-Varying Multivariate Model-Based Bandpass Filter

In this paper we investigate whether the dynamic properties of the U.S. business cycle have changed in the last fifty years. For this purpose we develop a flexible business cycle indicator that is constructed from a moderate set of macroeconomic time series. The coincident economic indicator is based on a multivariate trend-cycle decomposition model that accounts for time variation in macroeconomic volatility, known as the great moderation. In particular, we consider an unobserved components time series model with a common cycle that is shared across different time series but adjusted for phase shift and amplitude. The extracted cycle can be interpreted as the result of a model-based bandpass filter and is designed to emphasize the business cycle frequencies that are of interest to applied researchers and policymakers. Stochastic volatility processes and mixture distributions for the irregular components and the common cycle disturbances enable us to account for all the heteroskedasticity present in the data. The empirical results are based on a Bayesian analysis and show that time-varying volatility is only present in the a selection of idiosyncratic components while the coefficients driving the dynamic properties of the business cycle indicator have been stable over time in the last fifty years.