  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) 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 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 inflation measures vary nonlinearly with changes in the effect
modifiers.
