The hypothesis considered is that the utility function can be written as U U[VA (qai , * **, qX**, VM(q?1 , , q.,)], where the V's are utility functions depending on quantities of different commodities assigned to different branches (e.g., food, clothing). This hypothesis implies certain empirically meaningful and interesting conditions on the price coefficients of the demand functions. These conditions are, however, not subjected here to statistical test. A price index formula is next developed for measuring branch prices (e.g., the price of food, the price of clothing) and with the use of these indices a rationale is found for the individual doing his budgeting by first deciding how to allocate expenditure among the several branches and then making independent decisions as to how best to spend each branch allocation on the commodities within the branch. That this budgeting practice is both familiar and consistent with the proposed hypothesis is taken as evidence in support of the hypothesis and, therefore, of the implications for the price coefficients in demand functions.

PpT HIS note, pertinent to some recent literature on public goods,' presents two propositions which place the question of the optimal expenditure levels for public goods in a somewhat different perspective. By (pure) public goods or, synonymously, (pure) collective consumption goods, we mean those consumer goods having the property that, once produced, their enjoyment by each and every individual does not reduce their availability for the enjoyment of others. Public defense and public health measures may suggest cases in point.

In an earlier paper on "Interdependence as a Specification Error," Strotz has considered a recursive model with endogenous variables lagged by θ; letting θ go to 0, he argued that the likelihood function of the limit form of the model differed from the limit form of the likelihood function of the model. We show here that the two limits are obtained under different underlying assumptions; these alternative assumptions are brought out explicitly; under fixed assumptions, the two methods are shown to yield identical results.

This paper, which in part serves as a common introduction to the two papers following in this issue, attempts to define the meaning of the interpretability of a parameter in a system of simultaneous linear relationships. It attempts, moreover, to expound a basis for interpreting the parameters of a nonrecursive or interdependent system causally. This is done in terms of an underlying causal chain system to which the interdependent system is either an approximation or a description of the equilibrium state. OVER THE PAST fifteen years there has been an extended discussion of the meaning and applicability of nonrecursive as distinct from recursive systems in econometrics, and throughout this discussion there has been a marked divergence of views as to the merits of the two types of models. It is not the purpose of this note to extend that controversy further, but rather to attempt a constructive statement of the relationship betweenthe two approaches and the circumstances under which each is applicable. We assume that the reader is generally familiar with the past discussion' and that it will suffice here simply to recall that a recursive, or causalchain, system has the formal property that the coefficient matrix of the non-lagged endogenous variables is triangular (upon suitable ordering of rows and columns) whereas a nonrecursive, or interdependent, system is one for which this is not the case. While the triangularity of the coefficient matrix is a formal property of recursive models, the essential property is that each relation is provided a causal interpretation in the sense of a stimulus-response relationship. The question of whether and in what sense nonrecursive systems allow a causal interpretation is the main theme of this paper.