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A Consistent Method for the Selection of Relevant Instruments

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Author Info
Alastair Hall (North Carolina State University)
Fernanda P. M. Peixe (Universidade de Evora)

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Abstract

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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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0790.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0790

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  1. James H. Stock & Jonathan Wright, 1996. "Asymptotics for GMM Estimators with Weak Instruments," NBER Technical Working Papers 0198, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July. [Downloadable!] (restricted)
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  5. Torben G. Andersen & Bent E. Sorensen, 1995. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Discussion Papers 95-19, University of Copenhagen. Department of Economics.
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  6. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
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  7. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
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  8. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September. [Downloadable!] (restricted)
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