A METHOD OF STRUCTURAL ESTIMATION UNDER LINEAR RESTRICTIONS
1973 年 23 巻 3 号 p. 72-78
詳細
1973 年 23 巻 3 号 p. 72-78
This paper treats the problem of the estimation of the 1-st structural equation y=Zα+u subject to linear inhomogeneous restrictions Φα=λ and shows its consistency and asymptotic normality. In the case of a simultaneous equation system the usual Lagrangean method cannot be easily applied to the derivation of the estimate, since the matrix of explanatory variables Z'X(X'X)-1X'Z cannot have its inverse. On the other hand, our estimate contains that of conditional regression y=Xβ+u subject to Φβ=λ by Lagrangean method ([8], [14]). It also contains 2SLSE when Φ is given as zero restrictions. Further our approach can be easily extended to the whole equation system, in which 3SLSE and Zellner-type estimate are contained ([15], [16]). It will enable us to get a test statistic for the identifiability under the linear restrictions.
