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Random Effects Estimators with many Instrumental Variables

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  • Gary Chamberlain
  • Guido Imbens

Abstract

In this paper we propose a new estimator for a model with one endogenous regressor and many instrumental variables. Our motivation comes from the recent literature on the poor properties of standard instrumental variables estimators when the instrumental variables are weakly correlated with the endogenous regressor. Our proposed estimator puts a random coefficients structure on the relation between the endogenous regressor and the instruments. The variance of the random coefficients is modelled as an unknown parameter. In addition to proposing a new estimator, our analysis yields new insights into the properties of the standard two-stage least squares (TSLS) and limited-information maximum likelihood (LIML) estimators in the case with many weak instruments. We show that in some interesting cases, TSLS and LIML can be approximated by maximizing the random effects likelihood subject to particular constraints. We show that statistics based on comparisons of the unconstrained estimates of these parameters to the implicit TSLS and LIML restrictions can be used to identify settings when standard large sample approximations to the distributions of TSLS and LIML are likely to perform poorly. We also show that with many weak instruments, LIML confidence intervals are likely to have under-coverage, even though its finite sample distribution is approximately centered at the true value of the parameter. In an application with real data and simulations around this data set, the proposed estimator performs markedly better than TSLS and LIML, both in terms of coverage rate and in terms of risk. Copyright Econometric Society 2004.

Suggested Citation

  • Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, January.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:1:p:295-306
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00485.x
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    References listed on IDEAS

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    1. Phillips, P.C.B., 1984. "The exact distribution of the Stein-rule estimator," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 123-131.
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    Cited by:

    1. Anthony Strittmatter & Uwe Sunde, 2013. "Health and economic development—evidence from the introduction of public health care," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1549-1584, October.
    2. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics.
    3. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    4. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    5. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    6. Anirban Basu & James J. Heckman & Salvador Navarro-Lozano & Sergio Urzua, 2007. "Use of instrumental variables in the presence of heterogeneity and self-selection: An application in breast cancer patients," Health, Econometrics and Data Group (HEDG) Working Papers 07/07, HEDG, c/o Department of Economics, University of York.
    7. 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.
    8. Grant Hillier & Giovanni Forchini, 2004. "Ill-posed Problems and Instruments' Weakness," Econometric Society 2004 Australasian Meetings 357, Econometric Society.
    9. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    10. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 711-724, July.
    11. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    12. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," American Economic Review, American Economic Association, vol. 105(5), pages 486-490, May.
    13. Taylor, Eric, 2014. "Spending more of the school day in math class: Evidence from a regression discontinuity in middle school," Journal of Public Economics, Elsevier, vol. 117(C), pages 162-181.
    14. 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.
    15. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, 03.
    16. Susan Athey & Guido Imbens, 2016. "The State of Applied Econometrics - Causality and Policy Evaluation," Papers 1607.00699, arXiv.org.
    17. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    18. Rietveld, Cornelius A. & Webbink, Dinand, 2016. "On the genetic bias of the quarter of birth instrument," Economics & Human Biology, Elsevier, vol. 21(C), pages 137-146.

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