Exact equivalence of instrumental variable estimators in an error component structural system

The paper establishes an equivalence result in the context of anm-equation error component structural system, whose disturbances have the usual three-component structure, and whose equations feature explanatory variables of the formz _i, z_t andz _it; the latter vary (respectively) only over individuals, only over time, and over both. Under the stochastic specification assumed, it is shown that the alternative instrumental variables (IV) estimators commonly used in the special cases of this system are all equivalent (numerically identical); the result is a generalization of the equivalences established previously for the special cases. In the single equation (m=1) context, the equivalence requires that the IV set contain variables of the formz _i and/orz _t, and further, in numbers determined by the ranks of (respectively) the individuals-mean and time-mean matrices of the instruments. If such an IV set is common to all equations, the equivalence also holds for the system under joint estimation. The result is used to recommend a couple of estimators for use in panel data, on grounds of computational simplicity.This is a revision of the December 1990 draft with the same title, and is a substantial revision of the April 1990 version entitled: Analysis of an error component structural system. This revision has benefited from comments received from a referee and a editor of this journal. I came to know from an anonymous reader that the equivalence criterion developed in my 1990 a article, used here and the two earlier versions, was infact obtained previously in an unpublished paper by Balestra (1988). Balestra's paper, which was made available to me by Badi Baltagi at the time of this revision, and subsequently by Balestra, considers the equivalence of ^b, ^c and one other estimator which differs from our ^a. Errors, if any, are my responsibility.