THE OBSERVATION that large disparity in the variances of the disturbances from different structural equations in a simultaneous system can aid identification is as old as the discovery of the identification problem itself. Thus, in the classic example of E. J. Working [10], it is observed that whereas in the Marshallian cross neither the supply nor the demand curve is identified, this is not the case if one of the curves shifts about a great deal relative to the other. If such shifts do occur, then the relatively stable relationship is approximately traced out by the equilibrium points of intersection. This can, of course, be taken as an early statement of the fact that if one of the equations contains a shifting variable not in the other, the latter equation will be identified by the usual rank condition criterion;2 however, it is clear that even if there is no such explicit variable and all shifts come from the disturbance terms, something is still gained towards the identification of the relatively stable relationship. In other words, the example can be read as implying that information on the variances of the disturbance terms of a multiple equation system can be used for identification of the equation with the smallest disturbance variance.

The paper extends the results of the Solow-Samuelson article [12], reinterpreting their balanced growth model in terms of prices rather than output and weakening their monotonicity assumption to consider cases in which the production system is decomposable, completely decomposable, or approximates one of these. It is shown, among other things, that results similar to those obtained by Simon and Ando [11] and Ando and Fisher [1] for linear systems hold for the asymptotic behavior of this sort of nonlinear system of difference equations.

According to Wold, information on some of the variables at time t cannot be used for prediction of the values of the remaining variables at t, in a simultaneous equation system. This, however, is not the case with his causal model. This paper considers the stochastic processes underlying the two models, uses the theory of canonical correlation to discuss Wold's criticism, and suggests the type of additional information necessary to remove these objections. It further shows how both these models are complementary to each other. IN A SERIES of papers, Wold [9, 10, 11, 12] has recently proposed a new type of econometric model, which he calls the implicit causal chain model. The main incentive for this model was an attempt to combine the advantages of Tinbergen's causal model with those of the simultaneous equation systems initiated by Haavelmo [3, 4]. This latter model, which has been studied in detail by the Cowles Commission, is also known as the system. Wold has raised some objections, mainly from the point of view of prediction, against the simultaneous equation system; and in order to remedy these, he relaxed some of the restrictions on the correlational properties of the residuals in the simultaneous equation system. In this paper, these two models are discussed from an angle which offers a possibility for reconciling them. It is shown how the merits of both systems can be utilized by effecting some synthesis of them with the help of the stochastic process underlying both models. Furthermore, by using canonical analysis, it is shown how both these models are complementary. It must, of course, be added that the prediction problem has been considered purely on the basis of the stochastic model assumed, and the possible applicability of different representations of such models, for example, in economic contexts, under wider conditions is not discussed. Wold has objected to interdependent models on grounds other than prediction, especially from the point of view of the interpretation of structural parameters as elasticities, etc. The present paper, however, will not deal with this aspect of the problem. Instead, it deals primarily with the stochastic processes underlying economic models, and the demand and supply model, considered in the next section, is only for illustration.

This paper considers the problem of criteria for the identifiability of a structural equation which is one of a set of equations linear in the parameters but not in the variables. The criteria are developed in terms of parameter restrictions of the rank condition type. By expansion in Taylor's series and combination with the results of Fisher [2], these results can be easily extended to far more general nonlinear systems. THE USUAL treatment of identifiability criteria is one of linear structures and homogeneous linear restrictions on the coefficients of a single structural equation.2 Recently, I generalized this to the case where restrictions on such coefficients merely have continuous first derivatives; however, it was still the case that only linear structural equations were considered.3 While Anderson and Rubin showed how to obtain limited information, maximum likelihood estimates for the parameters of a linear equation which is part of a nonlinear system and have shown that such estimates have the usual consistency properties,4 they assumed that the equation in question was identifiable under coefficient restrictions of the usual type and did not consider the prior question of the application of the rank and order conditions for identifiability to nonlinear systems.5 This paper considers that question explicitly for a restricted (but highly important) class of nonlinear systems, namely, for systems linear in the unknown coefficients and in the residuals, but not necessarily linear in the variables. Extension to far more general nonlinear cases can be readily accomplished by expansion in Taylor series in the parameters and combina