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Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments

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Author Info

  • Norman R. Swanson

    ()
    (Rutgers University)

  • John C. Chao

    ()
    (University of Maryland)

  • Jerry A. Hausman

    ()
    (MIT)

  • Whitney K. Newey

    ()
    (MIT)

  • Tiemen Woutersen

    ()
    (Johns Hopkins University)

Abstract

This paper derives the limiting distributions of alternative jackknife IV (JIV ) estimators and gives formulae for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005). We show that J IV estimators are asymptotically normal; and that standard errors are consistent provided that √Kn/rn → 0, as n → ∞, where Kn and rn denote, respectively, the number of instruments and the rate of growth of the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIML, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless Kn/rn → 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201110.

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Length: 20 pages
Date of creation: 15 May 2011
Date of revision:
Handle: RePEc:rut:rutres:201110

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Keywords: heteroskedasticity ; instrumental variables; jackknife estimation; many instruments; weak instruments;

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References

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  1. Chao, John Chao & Norman R. Swanson, 2003. "Consistent Estimation with a Large Number of Weak Instruments," Cowles Foundation Discussion Papers 1417, Cowles Foundation for Research in Economics, Yale University.
  2. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
  3. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Kajal Lahiri & Chuanming Gao, 2001. "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Discussion Papers 01-15, University at Albany, SUNY, Department of Economics.
  5. Daniel A. Ackerberg & Paul J. Devereux, 2008. "Improved Jive Estimators for Overidentified Linear Models with and without Heteroskedasticity," Working Papers, School Of Economics, University College Dublin 200817, School Of Economics, University College Dublin.
  6. 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., John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  7. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
  8. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, Econometric Society, vol. 70(5), pages 1781-1803, September.
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  10. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, Econometric Society, vol. 74(1), pages 147-192, 01.
  11. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, Econometric Society, vol. 72(1), pages 219-255, 01.
  12. Paul A. Bekker & Jan Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267.
  13. Christian Hansen & Jerry Hausman & Whitney Newey, 2006. "Estimation with many instrumental variables," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP19/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  14. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  15. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
  16. Russell Davidson & James G. MacKinnon, 2004. "The Case Against JIVE," Working Papers 1031, Queen's University, Department of Economics.
  17. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, Econometric Society, vol. 62(3), pages 657-81, May.
  18. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(2), pages 225-35, April.
  19. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 107(441), pages 503-19, March.
  20. 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.
  21. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  22. James G. MacKinnon & Russell Davidson, 2006. "Reply to Ackerberg and Devereux and Blomquist and Dahlberg on 'The case against JIVE'," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(6), pages 843-844.
  23. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(01), pages 140-168, February.
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Cited by:
  1. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
  2. Brian P. Poi, 2006. "Jackknife instrumental variables estimation in Stata," Stata Journal, StataCorp LP, StataCorp LP, vol. 6(3), pages 364-376, September.
  3. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2012. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," CREATES Research Papers 2012-02, School of Economics and Management, University of Aarhus.
  4. 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.
  5. John Chao & Jerry Hausman & Whitney Newey & Norman Swanson & Tiemen Woutersen, 2013. "Combining Two Consistent Estimators," Departmental Working Papers, Rutgers University, Department of Economics 201310, Rutgers University, Department of Economics.

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