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Business Cycle Filtering of Macroeconomic Data Via A Latent Business Cycle Index

We use Markov Chain Monte Carlo methods to augment, via a novel multi-move sampling scheme, a vector autoregressive 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.

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