Bayesian modeling of time-varying parameter vector autoregressions using regression trees

Abstract

In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper develops a semiparametric TVP vector autoregression (VAR) using Bayesian additive regression trees (BART) that models the TVPs as an unknown function of effect modifiers. The novelty of this model arises from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to U.S. macroeconomic data, we illustrate the use of our model in tracking the evolving nature of the Phillips curve trade-off between inflation and unemployment in response to business cycle shocks.