Bayesian analysis of the consumption CAPM

In this paper we take up Bayesian inference for the consumption capital asset pricing model. The model has several econometric complications. First, it implies exact relationships between asset returns and the endowment growth rate that will be rejected by all possible realizations. Second, it was thought before that it is not possible to express asset returns in closed form. We show that Labadie's (1989) solution procedure can be applied to obtain asset returns in closed form and, therefore, it is possible to give an econometric interpretation in terms of traditional measurement error models. We apply the Bayesian inference procedures to the Mehra and Prescott (1985) dataset, we provide posterior distributions of structural parameters and posterior predictive asset return distributions, and we use these distributions to assess the existence of asset returns puzzles. The approach developed here, can be used in sampling theory and Bayesian frameworks alike. In fact, in a sampling-theory context, maximum likelihood can be used in a straightforward manner.