Bayesian Modeling of Time-varying Parameters Using Regression Trees

Florian Huber is a Professor of Economics at the University of Salzburg, focusing on Bayesian time series econometrics and its applications in macroeconomics and finance. He is also deputy head of the Department of Economics, a scientific consultant to the Austrian Central Bank and the European Commission, Associate Editor of Empirical Economics and Senior Scientist at the International Institute for Applied Systems Analysis (IIASA). His research has been published in international top journals such as the Journal of Business & Economic Statistics, the Journal of Econometrics, the International Economic Review, the Journal of Applied Econometrics, and the European Economic Review, among others.

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 arises from the law of motion driving the parameters being 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.