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Consistent Estimation with a Large Number of Weak Instruments

  • John Chao

    ()

    (University of Maryland)

  • Norman Swanson

    ()

    (Rutgers University)

This paper analyzes the conditions under which consistent estimation can be achieved in instrumental Variables (IV) regression when the available instruments are weak, in the local-to-zero sense of Staiger and Stock (1997) and using the many-instrument framework of Morimune (1983) and Bekker (1994). Our analysis of an extended k-class of estimators that includes Jackknife IV (JIVE) establishes that consistent estimation depends importantly on the relative magnitudes of rn, the growth rate of the concentration parameter, and Kn, the number of instruments: In particular, LIML and JIVE are consistent when (Kn)^.5 /rn goes to zero, while two-stage least squares is consistent only if (Kn)^.5 /rn goes to zero, as n goes to infinity. We argue that the use of many instruments may be bene¯cial for estimation, as the resulting concentration parameter growth may allow consistent estimation, in certain cases.

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200421.

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Length: 20 pages
Date of creation: 16 Sep 2004
Date of revision:
Handle: RePEc:rut:rutres:200421
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  1. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  3. 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.
  4. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  5. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  6. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
  7. 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..
  8. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation for Research in Economics, Yale University.
  9. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
  10. 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.
  11. 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.
  12. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
  13. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
  14. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  15. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  16. 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.
  17. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  18. 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.
  19. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
  20. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  21. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  22. 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.
  23. 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.
  24. 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.
  25. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  26. Portnoy, Stephen, 1987. "A central limit theorem applicable to robust regression estimators," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 24-50, June.
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