THIS PAPER REPORTS our initial efforts to use an explicitly Bayesian approach in estimating the asset demands of mutual savings banks and savings and loan associations. This is a part of a larger effort to construct and estimate a model of financial markets using flow of funds data. The general strategy followed in the construction of this model is somewhat different from that used in the design of most existing models. Each sector's allocation of its financial wealth among a variety of assets and liabilities is fully specified; the demand equations explicitly take into account the fact that a decision to hold funds in a particular form is simultaneously a decision to not hold these funds in an alternative form. Typically, the demand equations for a given sector include, as explanatory variables, rates of return on all assets held by the sector, and it is assumed that the assets are less than perfect substitutes. In contrast, most financial models focus attention on a subset of asset demands, the excluded assets being relegated to a residual category, and replace some of the markets by rate structure equations. Elsewhere, we have argued that specification of a complete set of sectoral demand and supply equations is a valuable safeguard against inadvertent use of inconsistent or nonsensical behavioral equations. Likewise, we have argued that for some of the policy questions being explored in large scale financial models, it is undesirable to assume the perfect substitution implied by rate structure equations. However, there is a major problem with the strategy we have advocated: it widens the already large gap between the number of parameters appearing in financial models and the number that can be reliably estimated from aggregate time series data. Indeed, it is undoubtedly the inadequacy of time series data which has led to the simplifications we find objectionable, and to the tireless search for the right combination of explanatory variables that will yield correctly signed and statistically significant coefficients. It has seemed to us that an attractive alternative to the simplification of structure and deletion of variables is the use of a priori information. In principle, this information could come from a variety of sources: theoretical calculation, crosssection studies, previous time series studies on different data, or even practical experience. The procedure we have followed in arriving at our priors is informal and subjective; we have tried to exploit ex ante the same information which gives rise to that almost inevitable disappointment one feels when confronted with a