Linear expenditure systems are widely used to describe consumption and portfolio decisions. However, the complexity of these models makes estimation a formidable task. In earlier work, an exchangeability assumption was used to incorporate subjective a priori information into the estimation of asset demand equations. Here, an alternative hierarchical approach is described and illustrated. This procedure provides a framework in which the identification of a limited number of distinct reasons for prior uncertainty can be converted into a full prior covariance matrix. Such a matrix can then be combined with prior means and the sample data to yield Bayesian parameter estimates.

Douglas Purvis' discussion of an integrated approach to consumption and portfolio decisions is an attractive extension of the framework advocated by William Brainard and James Tobin. The pitfalls is concerned with the portfolio allocation of a level of wealth which is predetermined by beginning of period asset holdings and current period saving and capital gains. One of the innovative features of this is the inclusion of all asset yields and lagged asset holdings as explanatory variables in the asset demand equations. Purvis supplements the BrainardTobin asset demands with a consumptionsaving relationship that includes a similar list of explanatory variables and reinterprets this system as a of integrated rather than sequential decision making. Despite his observation that, when combined with a consumption-savings relationship such as (2), the Brainard-Tobin will in principle give rise to exactly the same shortand long-run behavior as the integrated model (p. 407), most of Purvis' discussion is concerned with alleged dissimilarities between the two approaches. This is apparently due to his implicit coupling of a simple consumption function and sequential decision making. In particular most of his comments on the BrainardTobin approach are actually concerned with whether or not lagged asset holdings should be included in a consumption function. This is rather unfair to Brainard and Tobin since there is no consumption function in the pitfalls model, and the two issues are really conceptually distinct. An integrated approach does not preclude, and a sequential approach does not require, a simple consumption function. The spirit of Brainard and Tobin's work is in fact that the inherited composition of wealth is very important to consumption, but consumption decisions precede asset demand decisions. The substance of their sequential approach is not that the composition of wealth is unimportant to consumption but rather that there are some variables which influence consumption and yet do not separately affect asset demands; only the net amount of saving motivated by these influences is important. In this paper I have consequently tried to separate these two issues: the use of an integrated or sequential framework and the imposition of parametric assumptions. One of the reasons for the merging of these two issues in Purvis' discussion is that he uses a deterministic scenario which makes the distinction between integrated and sequential decisions unimportant. In Purvis' integrated model, consumption and asset demands are constrained by lagged asset holdings plus income. In the relevant sequential interpretation of this model, consumption is first determined, setting the amount of saving and the level of end of period wealth. Asset demands are then decided upon, subject to the budget constraint that they sum to the predetermined end of period wealth. Thus the integrated asset demands include income as an explanatory variable while the sequential asset demands instead include end of period wealth. In a deterministic world there are no substantive differences between these approaches as long as income and wealth are related through a consumption-saving equation. This equivalence breaks down if the marginal propensity to save out of income is zero (since wealth is then no longer related to income) or if there is an unobserved disturbance term in the consumption *Yale University. Note that equations numbered (1) through (11) are in Purvis' paper. My equations are numbered in the same sequence.

In their well-known paper, William Brainard and James Tobin advocated 'general disequilibrium' framework for the dynamics of adjustment to a 'general equilibrium' system. The Pitfalls framework has subsequently been widely used in the construction of flow of funds models of financial markets. The Brainard-Tobin paper has also elicited notes from Mark Ladenson and Kevin Clinton in this Review which attempt to interpret and elaborate upon the Pitfalls model. However, these authors seriously misinterpret the model and seemingly obscure rather than extend the Pitfalls framework in a maze of unnecessary mathenatical techniques and notation. Ladenson and Clinton both attempt to work with linearly dependent explanatory variables whose coefficients are not identified and cannot be meaningfully interpreted. Clinton uses this indeterminacy to provide a superficial counterexample to a BrainardTobin argument. Ladenson, on the other hand, discusses two (of many possible) sets of expedient parameter restrictions which will allow him to assign values to all of the coefficients of the linearly dependent variables. He believes that estimation of the model necessitates substantive behavioral assumptions, whereas in fact the elimination of a redundant explanatory variable alters only the appearance of the model and the interpretation of individual coefficients. In addition to discussing the errors of Clinton and Ladenson, this paper will demonstrate the simplicity with which adding up constraints can be derived, the relationship between the form of a model and the interpretation of its coefficients, and how the parameters might be estimated subject to adding up constraints. In Section I the Pitfalls model is compared with the ClintonLadenson formulation; Sections II and III concern the respective details of the Clinton and Ladenson articles; and estimation procedures are discussed in Section IV.

ABSTRACT This paper discusses the consistent specification and estimation of asset demand equations in a disequilibrium model of financial markets. We estimate the effective asset demands of savings and loan associations, allowing for rationing in the mortgage market. These disequilibrium estimates are not very different from the estimates of notional demands with no rationing assumed. Savings and loans seem to be least affected by excess demand situations in that they are apparently not reluctant to raise mortgage rates and/or to ration borrowers.