Business-Cycle Filtering Of Macroeconomic Data Via A Latent Business-Cycle Index

We use Markov chain Monte Carlo methods to augment, via a novel multimove sampling scheme, a vector autoregressive (VAR) system with a latent business-cycle index that is negative during recessions and positive during expansions. We then sample counterfactual values of the macroeconomic variables in the case where the latent business-cycle index is held constant. These counterfactual values represent posterior beliefs about how the economy would have evolved absent business-cycle fluctuations. One advantage is that a VAR framework provides model-consistent counterfactual values in the same way that VARs provide model-consistent forecasts, so data series are not filtered in isolation from each other. We apply these methods to estimate the business-cycle components of industrial production, consumer price inflation, the federal funds rate, and the spread between long-term and short-term interest rates. These decompositions provide an explicitly counterfactual approach to isolating the effects of the business cycle and to deriving empirical business-cycle facts.