Prior Selection for Vector Autoregressions

TLDR

Vector autoregressions capture complex macroeconomic dynamics, but their dense parameterization causes unstable inference and inaccurate out‑of‑sample forecasts, especially in large‑variable models. The paper proposes using informative priors to shrink VARs toward a naive benchmark, thereby reducing estimation uncertainty, and investigates the optimal informativeness of these priors within a hierarchical framework. By treating the prior informativeness as additional parameters and applying hierarchical modeling, the authors derive a theoretically grounded, easily implemented shrinkage scheme. This method markedly reduces subjective choices, delivers strong out‑of‑sample forecasting performance—including for factor models—and yields accurate impulse‑response estimates.

Abstract

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-of-sample forecasts, particularly for models with many variables. A solution to this problem is to use informative priors in order to shrink the richly parameterized unrestricted model toward a parsimonious naıve benchmark, and thus reduce estimation uncertainty. This paper studies the optimal choice of the informativeness of these priors, which we treat as additional parameters, in the spirit of hierarchical modeling. This approach, theoretically grounded and easy to implement, greatly reduces the number and importance of subjective choices in the setting of the prior. Moreover, it performs very well in terms of both out-of-sample forecasting—as well as factor models—and accuracy in the estimation of impulse response functions.