Bayesian Modeling of Time-Varying Parameters Using Regression Trees

47 Pages Posted: 13 Jan 2023 Last revised: 19 Sep 2023

See all articles by Niko Hauzenberger

Niko Hauzenberger

University of Salzburg

Florian Huber

University of Salzburg

Gary Koop

University of Strathclyde, Glasgow - Strathclyde Business School - Department of Economics

James Mitchell

Federal Reserve Bank of Cleveland

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

Hauzenberger, Niko and Huber, Florian and Koop, Gary and Mitchell, James, Bayesian Modeling of Time-Varying Parameters Using Regression Trees (January 11, 2023). FRB of Cleveland Working Paper No. 23-05, https://doi.org/10.26509/frbc-wp-202305, Available at SSRN: https://ssrn.com/abstract=4322548 or http://dx.doi.org/10.2139/ssrn.4322548

Niko Hauzenberger

University of Salzburg ( email )

Akademiestraße 26
Salzburg, Salzburg 5020
Austria

Florian Huber

University of Salzburg ( email )

Akademiestraße 26
Salzburg, Salzburg 5020
Austria

Gary Koop

University of Strathclyde, Glasgow - Strathclyde Business School - Department of Economics ( email )

100 Cathedral Street
Glasgow G4 0LN
United Kingdom

James Mitchell (Contact Author)

Federal Reserve Bank of Cleveland ( email )

East 6th & Superior
Cleveland, OH 44101-1387
United States

HOME PAGE: http://https://www.clevelandfed.org/en/our-research/economists/james-mitchell.aspx

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