Bayesian VARs: Specification Choices and Forecast Accuracy

Abstract

Summary In this paper we discuss how the point and density forecasting performance of Bayesian vector autoregressions (BVARs) is affected by a number of specification choices. We adopt as a benchmark a common specification in the literature, a BVAR with variables entering in levels and a prior modeled along the lines of Sims and Zha (International Economic Review 1998; 39: 949–968). We then consider optimal choice of the tightness, of the lag length and of both; evaluate the relative merits of modeling in levels or growth rates; compare alternative approaches to h‐step‐ahead forecasting (direct, iterated and pseudo‐iterated); discuss the treatment of the error variance and of cross‐variable shrinkage; and assess rolling versus recursive estimation. Finally, we analyze the robustness of the results to the VAR size and composition (using also data for France, Canada and the UK, while the main analysis is for the USA). We obtain a large set of empirical results, but the overall message is that we find very small losses (and sometimes even gains) from the adoption of specification choices that make BVAR modeling quick and easy, in particular for point forecasting. This finding could therefore further enhance the diffusion of the BVAR as an econometric tool for a vast range of applications. Copyright © 2013 John Wiley & Sons, Ltd.

Hierarchical Shrinkage in Time‐Varying Parameter Models

“…Carriero et al. () is a recent paper which (among other things) compares direct and iterated forecasts in VARs using US macroeconomic data. For inflation, they find direct forecasts to be much better than iterated ones.…”

Empirical Bayesian Density Forecasting in Iowa and Shrinkage for the Monte Carlo Era

“…In our case, it has indeed turned out that the results are insensitive, not just to hyperparameters of a Minnesota prior as in Carriero et al , (), but even to direct manipulation of prior probabilities in an unabashed attempt to improve forecast performance.…”

“…Robust predictions provide a little more realism, but the effort to design a better‐performing prior by pursuing this goal directly did not improve out‐of‐sample forecasts appreciably. A more positive interpretation of the findings is similar to a main finding in Carriero et al , (), which demonstrated limitations to benefits of the Minnesota prior over the diffuse‐prior, noting: ‘We find that simple works …This finding that simple methods work well could therefore further enhance the diffusion of the BVAR as an econometric tool for a vast range of applications.’ Here we note that beyond more heuristic and hierarchical models such as the Minnesota prior, the fully Bayesian diffuse‐prior forecasts compare favorably (in out‐of‐sample performance) to even methodical, direct, nonparametric manipulation of the forecast distributions themselves.…”

Can a Data-Rich Environment Help Identify the Sources of Model Misspecification?

“…There are more ways to specify w Once we have selected the tightness of λ 1 and λ 2 , we can obtain the posterior distribution for M via Gibbs sampling and then verify for which coefficients in A 21 the 90% credible set does not include zero 7 . We can also measure how relevant the impact of the missing channels is in the dynamics of the model's driving processes, for example by analysing a forecast error variance decomposition (FEVD) and verifying how much weight is given to other variables.…”

“…We can also measure how relevant the impact of the missing channels is in the dynamics of the model's driving processes, for example by analysing a forecast error variance decomposition (FEVD) and verifying how much weight is given to other variables. 7 The 90% credible set is the narrowest interval around the mode of the posterior distribution such that the probability that a coefficient lies within that interval is 90%. We then assume that the econometrician estimates a prototypical new-Keynesian model, such as the one in An and Schorfheide (2007), which is characterized by the following log-linearized equations.…”