Bayesian Modeling of Time-Varying Parameters Using Regression Trees
47 Pages Posted: 13 Jan 2023 Last revised: 19 Sep 2023
Date Written: January 11, 2023
Abstract
In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART). The novelty of this model stems 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. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty.
Keywords: Bayesian Vector Autoregression, Time-varying Parameters, Nonparametric Modeling, Machine Learning, Regression Trees, Phillips Curve, Business Cycle Shocks
JEL Classification: C11, C32, C51, E32
Suggested Citation: Suggested Citation