(in Applications and Case Studies)
## On the Determination of General Scientific Models
with Application to Asset Pricing

A. Ronald Gallant, Robert E. McCulloch

*Journal of the American Statistical Association*,
104, 117--131.

### Abstract

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.
**Keywords: ** Scientific models, simulation, Bayes, MCMC, estimation,
inference, asset pricing.