A Comparison of Approaches to Select the Informativeness of Priors in BVARs

Vector autoregressions (VARs) are richly parameterized time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, in small samples the rich parametrization of VAR models may come at the cost of overfitting the data, possibly leading to imprecise inference for key quantities of interest such as impulse response functions (IRFs). Bayesian VARs (BVARs) can use prior information to shrink the model parameters, potentially avoiding such overfitting. We provide a simulation study to compare, in terms of the frequentist properties of the estimates of the IRFs, useful strategies to select the informativeness of the prior. The study reveals that prior information may help to obtain more precise estimates of impulse response functions than classical OLS-estimated VARs and more accurate coverage rates of error bands in small samples. Strategies based on selecting the prior hyperparameters of the BVAR building on empirical or hierarchical modeling perform particularly well.