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On the Cost of Approximate Specification in Simultaneous Equation Estimation

Franklin M. Fisher

Abstract

This paper considers the question of whether simultaneous equation estimation is possible in view of the fact that specification errors are always made in the construction of models which are supposed only to hold approximately. It is shown that, so far as consistency is concerned, good approximations give good results, but that different estimators have different sensitivities to specification errors of the types considered. It follows that the choice of an estimator may depend crucially on its properties in such situations. The problem leads naturally to a consideration of the positions of T. C. Liu and H. Wold on the prevalence of underidentification and recursiveness, respectively. The concept of recursiveness is generalized as is the Proximity Theorem, and it is shown that a position intermediate between the two just mentioned is highly tenable, such a position permitting the use of simultaneous equation estimators. The whole problem turns out to be related to the question of almost unilateral coupling of dynamic systems and some conjectures are presented on the possibility of generalizing the recent aggregation and partition theorem of H. Simon and A. Ando.