Note on Anderson's "Causal models in educational research: Nonrecursive models

Two comments are made concerning Anderson's article (1978) on the identification and estimation of nonrecursive models. First, Anderson's rule for identification is only a necessary but not sufficient condition. The necessary and sufficient conditions are presented using matrix notation and a modified version of Anderson's rule is offered. Second, contrary to Anderson's discussion, the choice of two-stage or ordinary least squares depends on the data results rather than the methodolog-ical properties of the estimators. A means for choosing between the estimates is provided. In discussing the identification and estimation of simultaneous equation models, Anderson (1978) presents a simple rule for determining whether or not an equation is identified: "In order for an equation to be identified, the number of predetermined variables excluded from the equation must be at least equal to the number of endogenous variables included on the right hand side of the equation " (p. 88). In fact, an equation can meet this requirement and still be unidentified. This is because the rule, often called the order condition, is only a necessary but not sufficient condition for identification. The necessary and sufficient conditions can be represented in matrix notation as follows. The relationship between the structural and reduced form coefficients (Anderson, p. 94) where n =-B-lT (1) n is the matrix of reduced form coefficients B is the matrix of endogenous coefficients T is the matrix of exogenous coefficient