A Consistent Method for the Selection of Relevant Instruments
Generalized Method of Moments (GMM) is widely applied in econometrics. In most cases, there is a vast array of population moments upon which to base estimation and so the researcher must decide which moments to use. Andrews (1999, Econometrica, 543-564) proposes a method for moment selection paper based on minimizing an information criterion which is the sum of the overidentifying restrictions test and a bonus term reflecting the number of overidentifying restrictions. In this paper, we consider the problem of moment selection in the case where generalized instrumental variables (GIV) estimation is used. In the literature on GIV, it is known that it is desirable to choose instruments on the basis of three attributes: orthogonality, relevance and uniqueness. It is shown that Andrews' method chooses instruments on the basis of the orthogonality property alone, and so leads to the inclusion of instruments which are irrelevant in the sense their inclusion has no impact on the asymptotic variance of the estimator. While this weakness is inconsequential asymptotically, it has an adverse effect on the finite sample properties. In this paper we propose a new method for selecting instruments on the basis of their relevance. This method is based on a canonical correlations information criterion which we believe to be new to the literature. It is shown that the method is consistent in the sense that it selects all relevant instruments from a candidate set of instruments which are orthogonal. It is also shown that the combination of Andrews' method and our own yields a consistent method for the selection of relevant, orthogonal instruments from a candidate set. Simulation evidence suggests the method works well.
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