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Bayesian Analysis of the Output Gap

Our objective is to build output gap estimates that benefit from information provided by Phillips curve theory and business cycle studies. For this, we develop a Bayesian analysis of the bivariate Phillips curve model proposed by Kuttner for estimating potential output. Given our priors, we obtain samples from parameters and state variables joint posterior distribution following a Gibbs sampling strategy. We sample the state variables given parameters using the Carter–Kohn procedure, and we exploit a likelihood factorization to draw parameters given the state. A Metropolis–Hastings step is used to remove the conditioning on starting values. To accommodate the variance moderation that has been observed on U.S. gross domestic product, Kuttner's model is extended for a change in variance parameters. We apply this methodology to the analysis of the output gap in the United States and in the European Monetary Union. Finally, some important extensions to the original Kuttner model are discussed.