A Nonparametric Approach to Augmenting a Bayesian VAR with Nonlinear Factors

TL;DR

This paper introduces a Bayesian VAR model augmented with nonlinear factors modeled nonparametrically via regression trees, improving flexibility, parsimoniousness, and computational efficiency for economic forecasting and analysis.

Contribution

It presents a novel nonparametric Bayesian VAR with nonlinear factors using regression trees, enabling flexible modeling of nonlinearities with efficient computation.

Findings

Effective in modeling nonlinearities in macroeconomic data

Improves forecasting accuracy over linear models

Facilitates structural shock identification in nonlinear settings

Abstract

This paper proposes a Vector Autoregression augmented with nonlinear factors that are modeled nonparametrically using regression trees. There are four main advantages of our model. First, modeling potential nonlinearities nonparametrically lessens the risk of mis-specification. Second, the use of factor methods ensures that departures from linearity are modeled parsimoniously. In particular, they exhibit functional pooling where a small number of nonlinear factors are used to model common nonlinearities across variables. Third, Bayesian computation using MCMC is straightforward even in very high dimensional models, allowing for efficient, equation by equation estimation, thus avoiding computational bottlenecks that arise in popular alternatives such as the time varying parameter VAR. Fourth, existing methods for identifying structural economic shocks in linear factor models can be adapted for the nonlinear case in a straightforward fashion using our model. Exercises involving artificial and macroeconomic data illustrate the properties of our model and its usefulness for forecasting and structural economic analysis.