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Consistent Estimation with a Large Number of Weak Instruments

  • John C. Chao
  • Norman R. Swanson

This paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables (IV) regression when the available instruments are weak and the number of instruments, K n, goes to infinity with the sample size. We show that consistent estimation depends importantly on the strength of the instruments as measured by r n, the rate of growth of the so-called concentration parameter, and also on K n. In particular, when K n→∞, the concentration parameter can grow, even if each individual instrument is only weakly correlated with the endogenous explanatory variables, and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature. Hence, the use of many weak instruments may actually improve the performance of certain point estimators. More specifically, we find that the limited information maximum likelihood (LIML) estimator and the bias-corrected two-stage least squares (B2SLS) estimator are consistent when $\sqrt{K_{n}}/r_{n}\rightarrow 0$ K n / r n → 0 , while the two-stage least squares (2SLS) estimator is consistent only if K n/r n→0 as n→∞. These consistency results suggest that LIML and B2SLS are more robust to instrument weakness than 2SLS. Copyright The Econometric Society 2005.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00632.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 5 (09)
Pages: 1673-1692

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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:5:p:1673-1692
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  1. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society.
  2. 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.
  3. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
  4. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  6. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  7. John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics.
  8. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
  9. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  10. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  11. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. 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.
  13. 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, vol. 13(2), pages 225-35, April.
  14. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March.
  15. In Choi & Peter C.B. Phillips, 1989. "Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations," Cowles Foundation Discussion Papers 929, Cowles Foundation for Research in Economics, Yale University.
  16. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-41, May.
  17. Peter C.B. Phillips, 1982. "Small Sample Distribution Theory in Econometric Models of Simultaneous Equations," Cowles Foundation Discussion Papers 617, Cowles Foundation for Research in Economics, Yale University.
  18. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
  19. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  20. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  21. 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..
  22. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  23. Portnoy, Stephen, 1987. "A central limit theorem applicable to robust regression estimators," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 24-50, June.
  24. Alastair Hall & Fernanda P. M. Peixe, 2000. "A Consistent Method for the Selection of Relevant Instruments," Econometric Society World Congress 2000 Contributed Papers 0790, Econometric Society.
  25. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 309-336.
  26. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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