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A Bayesian analysis of a variance decomposition for stock returns

Hollifield, B. and Koop, G.M. and Li, K. (2003) A Bayesian analysis of a variance decomposition for stock returns. Journal of Empirical Finance, 10 (5). pp. 583-601. ISSN 0927-5398

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We apply Bayesian methods to study a common vector autoregression (VAR)-based approach for decomposing the variance of excess stock returns into components reflecting news about future excess stock returns, future real interest rates, and future dividends. We develop a new prior elicitation strategy, which involves expressing beliefs about the components of the variance decomposition. Previous Bayesian work elicited priors from the difficult-to-interpret parameters of the VAR. With a commonly used data set, we find that the posterior standard deviations for the variance decomposition based on these previously used priors, including ''non-informative'' limiting cases, are much larger than classical standard errors based on asymptotic approximations. Therefore, the non-informative researcher remains relatively uninformed about the variance decomposition after observing the data. We show the large posterior standard deviations arise because the ''non-informative'' prior is implicitly very informative in a highly undesirable way. However, reasonably informative priors using our elicitation method allow for much more precise inference about components of the variance decomposition.