Do subjective expectations explain asset pricing puzzles?

The structural uncertainty model with Bayesian learning, advanced by Weitzman (AER 2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums. This paper provides an operational version of this approach that incorporates realistic priors about consumption growth volatility, while guaranteeing finite asset pricing quantities. In contrast to the extant literature, the resulting asset pricing model with subjective expectations yields well-defined expected utility, finite moment generating function of the predictive distribution of consumption growth, and tractable expressions for equity premium and risk-free return. Our quantitative analysis reveals that explaining the historical equity premium and risk-free return, in the context of subjective expectations, requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs result in consumption disaster probabilities that virtually coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications.     

Bounds for Ratios of Posterior Expectations: Applications in the Collective Risk Model

This paper considers the collective risk model for the insurance claims process. We will adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question. The robust Bayesian approach uses a class of prior distributions which model uncertainty about the prior, instead of a single distribution. Relatively little research has dealt with robustness with respect to ratios of posterior expectations as occurs with the Esscher and Variance premium principles. Appropriate techniques are developed in this paper to solve this problem using the k -contamination class in the collective risk model.     

A Bayesian analysis of a variance decomposition for stock returns

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.     

WEIGHTED‐AVERAGE LEAST SQUARES (WALS): A SURVEY

Model averaging has become a popular method of estimation, following increasing evidence that model selection and estimation should be treated as one joint procedure. Weighted‐average least squares (WALS) is a recent model‐average approach, which takes an intermediate position between frequentist and Bayesian methods, allows a credible treatment of ignorance, and is extremely fast to compute. We review the theory of WALS and discuss extensions and applications.     

Additivity with multiple priors

The functional defined as the `min' of integrals with respect to probabilities in a given non-empty closed and convex class appears prominently in recent work on uncertainty in economics. In general, such a functional violates the additivity of the expectations operator. We characterize the types of functions over which additivity of this functional is preserved. This happens exactly when `integrating' functions which are positive affine transformations of each other (or when one is constant). We show that this result is quite general by restricting the types of classes of probabilities considered. Finally, we prove that with a very peculiar exception, all the results hold more generally for functionals which are linear combinations of the `min' and the `max' functional.