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Instrumental variable estimation with heteroskedasticity and many instruments

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  • Jerry Hausman

    ()
    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Whitney Newey

    ()
    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Tiemen Woutersen

    (Institute for Fiscal Studies and John Hopkins University)

  • John Chao
  • Norman Swanson

Abstract

It is common practice in econometrics to correct for heteroskedasticity.This paper corrects instrumental variables estimators with many instruments for heteroskedasticity.We give heteroskedasticity robust versions of the limited information maximum likelihood (LIML) and Fuller (1977, FULL) estimators; as well as heteroskedasticity consistent standard errors thereof. The estimators are based on removing the own observation terms in the numerator of the LIML variance ratio. We derive asymptotic properties of the estimators under many and many weak instruments setups. Based on a series of Monte Carlo experiments, we find that the estimators perform as well as LIML or FULL under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered.

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File URL: http://cemmap.ifs.org.uk/wps/cwp2207.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP22/07.

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Date of creation: Sep 2007
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Handle: RePEc:ifs:cemmap:22/07

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  1. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-28, February.
  2. Daniel A. Ackerberg & Paul J. Devereux, 2008. "Improved Jive Estimators for Overidentified Linear Models with and without Heteroskedasticity," Working Papers 200817, School Of Economics, University College Dublin.
  3. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
  4. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  5. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
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Cited by:
  1. Crudu, Federico & Sándor, Zsolt, 2011. "On the finite-sample properties of conditional empirical likelihood estimators," MPRA Paper 34116, University Library of Munich, Germany.
  2. Bertille Antoine & Pascal Lavergne, 2011. "Conditional Moment Models under Semi-Strong Identification," Discussion Papers dp11-04, Department of Economics, Simon Fraser University, revised Dec 2012.
  3. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Centre de Recherche en Economie et Statistique.
  4. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
  5. Daniel A. Ackerberg & Paul J. Devereux, 2008. "Improved Jive Estimators for Overidentified Linear Models with and without Heteroskedasticity," Working Papers 200817, School Of Economics, University College Dublin.
  6. John Chao & Jerry Hausman & Whitney Newey & Norman Swanson & Tiemen Woutersen, 2013. "An Expository Note on the Existence of Moments of Fuller and HFUL Estimators," Departmental Working Papers 201311, Rutgers University, Department of Economics.
  7. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
  8. Eric French & Jae Song, 2012. "The effect of Disability Insurance receipt on labor supply: a dynamic analysis," Working Paper Series WP-2012-12, Federal Reserve Bank of Chicago.
  9. Abutaliev, Albert & Anatolyev, Stanislav, 2013. "Asymptotic variance under many instruments: Numerical computations," Economics Letters, Elsevier, vol. 118(2), pages 272-274.
  10. Naoto Kunitomo, 2012. "An optimal modification of the LIML estimation for many instruments and persistent heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(5), pages 881-910, October.
  11. Priebe, Jan, 2011. "Child Costs and the Causal Effect of Fertility on Female Labor Supply: An investigation for Indonesia 1993-2008," Proceedings of the German Development Economics Conference, Berlin 2011 67, Verein für Socialpolitik, Research Committee Development Economics.
  12. Hübler, Olaf, 2013. "Methods in empirical economics - a selective review with applications," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-513, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  13. Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
  14. Michal Kolesár & Raj Chetty & John N. Friedman & Edward L. Glaeser & Guido W. Imbens, 2011. "Identification and Inference with Many Invalid Instruments," NBER Working Papers 17519, National Bureau of Economic Research, Inc.
  15. 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.

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