A Bayesian analysis of a variance decomposition for stock returns |
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Authors: | Burton Hollifield Gary Koop Kai Li |
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Institution: | a Graduate School of Industrial Administration, Carnegie Mellon University, USA;b Department of Economics, University of Glasgow, Scotland, UK;c Faculty of Commerce, University of British Columbia, Canada |
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Abstract: | 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. |
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Keywords: | Vector autoregression Priors Initial conditions Nonlinear functions |
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