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.
We develop multivariate time series models using Bayesian additive regression trees that posit nonlinearities among macroeconomic variables, their lags, and possibly their lagged errors. The error variances can be stable, feature stochastic volatility, or follow a nonparametric specification. We evaluate density and tail forecast performance for a set of US macroeconomic and financial indicators. Our results suggest that the proposed models improve forecast accuracy both overall and in the tails. Another finding is that when allowing for nonlinearities in the conditional mean, heteroskedasticity becomes less important. A scenario analysis reveals nonlinear relations between predictive distributions and financial conditions.
Recent decades have seen advances in using econometric methods to produce more timely and higher-frequency estimates of economic activity at the national level, enabling better tracking of the economy in real time. These advances have not generally been replicated at the sub–national level, likely because of the empirical challenges that nowcasting at a regional level presents, notably, the short time series of available data, changes in data frequency over time, and the hierarchical structure of the data. This paper develops a mixed– frequency Bayesian VAR model to address common features of the regional nowcasting context, using an application to regional productivity in the UK. We evaluate the contribution that different features of our model provide to the accuracy of point and density nowcasts, in particular the role of hierarchical aggregation constraints. We show that these aggregation constraints, imposed in stochastic form, play a key role in delivering improved regional nowcasts; they prove to be more important than adding region-specific predictors when the equivalent national data are known, but not when this aggregate is unknown.
The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial benefits, both overall and in the left tail, with nonparametric modeling of the conditional mean being of particular importance.
In the US, income and expenditure-side estimates of GDP (GDPI and GDPE) measure "true" GDP with error and are available at a quarterly frequency. Methods exist for using these proxies to produce reconciled quarterly estimates of true GDP. In this paper, we extend these methods to provide reconciled historical true GDP estimates at a monthly frequency. We do this using a Bayesian mixed frequency vector autoregression (MF-VAR) involving GDPE, GDPI, unobserved true GDP, and monthly indicators of short-term economic activity. Our MF-VAR imposes restrictions that reflect a measurement-error perspective (that is, the two GDP proxies are assumed to equal true GDP plus measurement error). Without further restrictions, our model is unidentified. We consider a range of restrictions that allow for point and set identification of true GDP and show that they lead to informative monthly GDP estimates. We illustrate how these new monthly data contribute to our historical understanding of business cycles and we provide a real-time application nowcasting monthly GDP over the pandemic recession.
We develop novel multivariate time series models using Bayesian additive regression trees that posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel nonparametric specification. Estimation is carried out using scalable Markov chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our results suggest that using nonparametric models generally leads to improved forecast accuracy. In particular, when interest centers on the tails of the posterior predictive, flexible models improve upon standard VAR models with SV. Another key finding is that if we allow for nonlinearities in the conditional mean, allowing for heteroskedasticity becomes less important. A scenario analysis reveals highly nonlinear relations between the predictive distribution and financial conditions.