On the determination of general scientific models with application to asset pricing

We consider a consumption-based asset pricing model that uses habit persistence to overcome the known statistical inadequacies of the classical consumption-based asset pricing model. We find that the habit model fits reasonably well and agrees with results reported in the literature if conditional heteroskedasticity is suppressed but that it does not fit nor do results agree if conditional heteroskedasticity, well known to be present in financial market data, is allowed to manifest itself.We also find that it is the preference parameters of the model that are most affected by the presence or absence of conditional heteroskedasticity, especially the risk aversion parameter. The habit model exhibits four characteristics that are often present in models developed from scientific considerations: (1) a likelihood is not available; (2) prior information is available; (3) a portion of the prior information is expressed in terms of functionals of the model that cannot be converted into an analytic prior on model parameters; (4) the model can be simulated. The underpinning of our approach is that, in addition, (5) a parametric statistical model for the data, determined without reference to the scientific model, is known. In general one can expect to be able to determine a model that satisfies (5) because very richly parameterized statistical models are easily accommodated. We develop a computationally intensive, generally applicable, Bayesian strategy for estimation and inference for scientific models that meet this description together with methods for assessing model adequacy. An important adjunct to the method is that a map from the parameters of the scientific model to functionals of the scientific and statistical models becomes available. This map is a powerful tool for understanding the properties of the scientific model.