Working Paper: CEPR ID: DP8894
Authors: Andrea Carriero; Todd Clark; Massimiliano Marcellino
Abstract: The estimation of large Vector Autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor. This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients, and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the resulting BVAR with common stochastic volatility (BVAR-CSV). Under the chosen prior the conditional posterior of the VAR coefficients features a Kroneker structure that allows for fast estimation, even in a large system. Using US and UK data, we show that, compared to a model with constant volatilities, our proposed common volatility model significantly improves model fit and forecast accuracy. The gains are comparable to or as great as the gains achieved with a conventional stochastic volatility specification that allows independent volatility processes for each variable. But our common volatility specification greatly speeds computations.
Keywords: Bayesian VARs; Forecasting; Prior Specification; Stochastic Volatility
JEL Codes: C11; C13; C33; C53
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| common volatility model (C58) | model fit (C52) |
| common volatility model (C58) | forecast accuracy (C53) |
| BVARCSV model (C29) | model fit (C52) |
| BVARCSV model (C29) | forecast accuracy (C53) |
| BVARCSV model (C29) | computational efficiency (C63) |