9.3.6 Empirical Performance of Bayesian VARs

9.3.6 Empirical Performance of Bayesian VARs

Ni and Sun (2005) provide a broad comparison of frequentist risks for Bayesian VAR estimates of regression coefficients and the variance–covariance matrix for VARs. In a Monte Carlo study they consider different priors, loss functions, and data distributions. Their results suggest that the choice of priors affects the Bayesian estimates more strongly than the choice of loss function. Interestingly, however, they find that the estimator of the slope coefficients based on an asymmetric Linex loss function performs better than the estimator based on quadratic loss.

Estimation error can make a very large difference in empirical studies. In the context of Federal funds rate forecasts, Rudebusch (1998) and others have found that structural VARs produce much greater forecast errors than the errors associated with forecasts based on prices in the Federal funds futures markets. Robertson and Tallman (2001) examine whether this finding could be due to parameter estimation error. They study the forecasting performance of flat prior VARs, i.e., the usual OLS estimates, and Bayesian methods based on more informative priors. Their model includes many highly persistent variables in levels and requires many lags and thus the estimation of a large number of coefficients. Empirically, they find that VAR models based on OLS estimates generate one-month-ahead MSE values nearly three times greater than the Federal funds futures benchmark. Shrinkage VAR models perform much better than VARs using OLS estimates, although they produce MSE values that are still between $\frac{1}{3}$ and 60% higher than their benchmark. Interestingly, a simple first-order autoregressive model for the change in the Federal funds rate produces forecasts comparable to the best forecasts from the multivariate models in levels.

In regional forecasting, VAR models have also been used to generate growth forecasts. Kinal and Ratner (1986) generate forecasts for New York state employment, output, retail sales, and consumer prices using both state-specific and national variables. They find relatively poor forecasting performance for the VARs which they attribute to overparameterization. Consistent with this, Bayesian VARs perform better.