Carriero-Clark-Marcellino (2015) Bayesian VARs: Specification Choices and Forecast Accuracy

Summary

Carriero, Clark, and Marcellino examine how the forecasting performance of Bayesian VARs depends on a large set of specification choices. Their baseline uses a conjugate Normal–Inverted-Wishart (Minnesota-style) prior which, combined with a (pseudo-)iterated approach, makes analytical multi-step forecasts feasible and simple — especially with standard, fixed values for the prior tightness and the lag length. They then assess the value of optimizing the tightness, the lag length, or both; compare direct, iterated, and pseudo-iterated multi-step forecasting; discuss the treatment of the error variance and cross-variable shrinkage; and address the VAR size, modeling in levels versus growth rates, and the forecast bias induced by shrinkage. Across a large body of empirical results, the headline is that the quick-and-easy default choices lose very little accuracy — and sometimes gain — relative to elaborate, optimized alternatives, which should further encourage routine use of BVARs. (FRB Cleveland Working Paper 11-12, 2011; published in the Journal of Applied Econometrics 30(1): 46–73.)

Key Claims

• Conjugate NIW baseline is convenient and competitive. A Normal–Inverted-Wishart prior on the VAR coefficients and error covariance yields a closed-form posterior and, with the pseudo-iterated scheme, analytical multi-step forecasts — no simulation needed.
• Fixing the tightness costs little. Using a standard, fixed overall shrinkage (tightness) $\lambda$ forecasts about as well as data-based optimization of $\lambda$; the same holds for using a fixed, standard lag length. Optimizing both jointly rarely helps much.
• Multi-step forecasting: iterated ≈ pseudo-iterated ≥ direct. The (pseudo-)iterated approach is generally at least as accurate as direct multi-step regressions and is analytically cheaper under the conjugate prior.
• Cross-variable shrinkage and the error variance. Relaxing the Minnesota assumption of harsher shrinkage on other variables' lags (i.e., allowing cross-variable shrinkage) and the treatment of the residual variance matter only modestly for forecasts.
• Size, levels vs. growth rates, and bias. Larger VARs help up to a point; modeling in levels vs. growth rates and the (shrinkage-induced) forecast bias have second-order effects relative to the convenience gains of the simple setup.

Concepts Introduced or Extended

• Bayesian VAR
• Minnesota Prior
• Forecasting

Entities Mentioned

• Andrea Carriero
• Todd E. Clark
• Massimiliano Marcellino

Quotes

"We find very small losses (and sometimes even gains) from the adoption of specification choices that make BVAR modeling quick and easy."

My Take

This is the paper you cite to justify not agonizing over BVAR hyperparameters. Its value is negative-result reassurance backed by a big horse race: the conjugate Normal–Inverted-Wishart prior with a standard fixed tightness and lag length, forecast with the analytically convenient pseudo-iterated scheme, is hard to beat — so the elaborate machinery (optimizing $\lambda$, cross-variable shrinkage, direct multi-step regressions) mostly buys convenience costs without forecast gains. That conclusion is what made the conjugate-Minnesota setup the default for applied and central-bank BVAR forecasting, and it sets the practical baseline the large-BVAR literature (Bańbura–Giannone–Reichlin; Koop; Chan) builds on. The one caveat it flags for later work is that the fully conjugate structure ties cross-equation shrinkage together, which the asymmetric-conjugate and stochastic-volatility extensions later relax.