Prediction from Simultaneous Equation Systems and Wold's Implicit Causal Chain Model
联立方程系统与沃尔德隐式因果链模型的预测AI 解读 ↓
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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.