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Choosing instrumental variables in conditional moment restriction models

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  • Donald, Stephen G.
  • Imbens, Guido W.
  • Newey, Whitney K.

Abstract

Properties of GMM estimators are sensitive to the choice of instrument. Using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and/or variance in small samples. In this paper we develop and implement asymptotic mean square error (MSE) based criteria for instrument selection in estimation of conditional moment restriction models. The models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity. We develop moment selection criteria for the familiar two-step optimal GMM estimator (GMM), a bias corrected version, and generalized empirical likelihood estimators (GEL), that include the continuous updating estimator (CUE) as a special case. We also find that the CUE has lower higher-order variance than the bias-corrected GMM estimator, and that the higher-order efficiency of other GEL estimators depends on conditional kurtosis of the moments.

Suggested Citation

  • Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
  • Handle: RePEc:eee:econom:v:152:y:2009:i:1:p:28-36
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    References listed on IDEAS

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    Cited by:

    1. Stefan Boes, 2010. "Count Data Models with Correlated Unobserved Heterogeneity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 382-402, September.
    2. repec:eee:econom:v:200:y:2017:i:1:p:1-16 is not listed on IDEAS
    3. Canay, Ivan A., 2010. "Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel," Journal of Econometrics, Elsevier, vol. 156(2), pages 284-303, June.
    4. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    5. repec:bla:devpol:v:37:y:2019:i:2:p:225-244 is not listed on IDEAS
    6. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    7. Richard Ashley & Christopher Parmeter, 2015. "Sensitivity analysis for inference in 2SLS/GMM estimation with possibly flawed instruments," Empirical Economics, Springer, vol. 49(4), pages 1153-1171, December.
    8. Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
    9. Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
    10. Francis DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 15-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Aug 2015.
    11. repec:gam:jecomi:v:6:y:2018:i:4:p:55-:d:174430 is not listed on IDEAS
    12. Cho, Hyunkeun, 2016. "The analysis of multivariate longitudinal data using multivariate marginal models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 481-491.
    13. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    14. Mary, Sébastien, 2018. "Does Agricultural (Food) Trade Openness Reduce Child Stunting?," 2018 Annual Meeting, August 5-7, Washington, D.C. 274282, Agricultural and Applied Economics Association.
    15. Creel, Michael, 2017. "Neural nets for indirect inference," Econometrics and Statistics, Elsevier, vol. 2(C), pages 36-49.
    16. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    17. Kun Xu & Yanyuan Ma & Liqun Wang, 2015. "Instrument Assisted Regression for Errors in Variables Models with Binary Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 104-117, March.
    18. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.
    19. Michael Creel, 2016. "Neural Nets for Indirect Inference," UFAE and IAE Working Papers 960.16, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 18 Jul 2016.
    20. Varvara Isyuk, 2014. "Resuming bank lending in the aftermath of the Capital Purchase Program," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01093414, HAL.
    21. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    22. repec:bla:ecorec:v:91:y:2015:i:s1:p:1-24 is not listed on IDEAS
    23. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

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