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Consistent Moment Selection Procedures for Generalized Method of Moments Estimation

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Abstract

This paper considers a generalized method of moments (GMM) estimation problem in which one has a vector of moment conditions, some of which are correct and some incorrect. The paper introduces several procedures for consistently selecting the correct moment conditions. The procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest. The paper specifies moment selection criteria that are GMM analogues of the widely used BIC and AIC model selection criteria. (The latter is not consistent.) The paper also considers downward and upward testing procedures. All of the moment selection procedures discussed in the paper are based on the minimized values of the GMM criterion function for different vectors of moment conditions. The procedures are applicable in time series and cross-sectional contexts. Application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables.

Suggested Citation

  • Donald W.K. Andrews, 1997. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Cowles Foundation Discussion Papers 1146R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1146r
    Note: CFP 979.
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    References listed on IDEAS

    as
    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. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    3. White, Halbert, 1982. "Instrumental Variables Regression with Independent Observations," Econometrica, Econometric Society, vol. 50(2), pages 483-499, March.
    4. 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.
    5. Kohn, Robert, 1983. "Consistent Estimation of Minimal Subset Dimension," Econometrica, Econometric Society, vol. 51(2), pages 367-376, March.
    6. Nishii, R., 1988. "Maximum likelihood principle and model selection when the true model is unspecified," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 392-403, November.
    7. Smith, Richard J, 1992. "Non-nested.Tests for Competing Models Estimated by Generalized Method of Moments," Econometrica, Econometric Society, vol. 60(4), pages 973-980, July.
    8. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
    9. Pesaran, M Hashem & Smith, Richard J, 1994. "A Generalized R[superscript]2 Criterion for Regression Models Estimated by the Instrumental Variables Method," Econometrica, Econometric Society, vol. 62(3), pages 705-710, May.
    10. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    12. Pesaran, M.H., 1992. "A Generalised R2 Criterion for Regression Models Estimated by the Instrumental Variable Method," Cambridge Working Papers in Economics 9220, Faculty of Economics, University of Cambridge.
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    More about this item

    Keywords

    Akaike information criterion; Bayesian information criterion; consistent selectionprocedure; downward testing procedure; generalized method of moments estimator; instrumental variables estimator; model selection; moment selection; test of over-identifyingrestrictions; upward testing procedure;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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