The parting of the ways between causal chain (recursive) and interdependent (nonrecursive) systems is reviewed from the point of view of explanatory relations specified in terms of conditional expectations. On the customary assumptions, a causal chain system is designed so that its relations both in the original form and in the reduced form can be specified in terms of conditional expectations, whereas the relations of interdependent systems allow such specification only in the reduced form. A third type of model is discussed, called conditional causal chains, which formally is similar to interdependent systems, with the important difference that the behavioural relations of the original system are specified in terms of conditional expectations.

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.

H. O. A. Wold, Harold Hotelling, Tjalling C. Koopmans, Rene Roy, De la theorie des choix aux budgets de familles: Discussion, Econometrica, Vol. 17, Supplement: Report of the Washington Meeting (Jul., 1949), pp. 187-191