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A Consistent Method for the Selection of Relevant Instruments

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  • Alastair R. Hall
  • Fernanda P. M. Peixe

Abstract

In many applications, a researcher must select an instrument vector from a candidate set of instruments. If the ultimate objective is to perform inference about the unknown parameters using conventional asymptotic theory, then we argue that it is desirable for the chosen instrument vector to satisfy four conditions which we refer to as orthogonality, identification, efficiency, and non-redundancy. It is impossible to verify a priori which elements of the candidate set satisfy these conditions; this can only be done using the data. However, once the data are used in this fashion it is important that the selection process does not contaminate the limiting distribution of the parameter estimator. We refer to this requirement as the inference condition. In a recent paper, Andrews [[Andrews, D. W. K. (1999)]. Consistent moment selection procedures for generalized method of moments estimation. Econometrica 67:543-564] has proposed a method of moment selection based on an information criterion involving the overidentifying restrictions test. This method can be shown to select an instrument vector which satisfies the orthogonality condition with probability one in the limit. In this paper, we consider the problem of instrument selection based on a combination of the efficiency and non-redundancy conditions which we refer to as the relevance condition. It is shown that, within a particular class of models, certain canonical correlations form the natural metric for relevancy, and this leads us to propose a canonical correlations information criterion (CCIC) for instrument selection. We establish conditions under which our method satisfies the inference condition. We also consider the properties of an instrument selection method based on the sequential application of [Andrews, D. W. K. (1999)]. Consistent moment selection procedures for generalized method of moments estimation. Econometrica 67:543-564 method and CCIC.

Suggested Citation

  • Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
  • Handle: RePEc:taf:emetrv:v:22:y:2003:i:3:p:269-287
    DOI: 10.1081/ETC-120024752
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    3. 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 283-298, May.
    4. James H. Stock & Jonathan Wright, 1996. "Asymptotics for GMM Estimators with Weak Instruments," NBER Technical Working Papers 0198, National Bureau of Economic Research, Inc.
    5. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    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.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    9. Fernanda Peixe & Alastair Hall & Kostas Kyriakoulis, 2006. "The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 117-138.
    10. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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