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Estimation With Many Instrumental Variables

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  • Hansen, Christian
  • Hausman, Jerry
  • Newey, Whitney

Abstract

Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker to nonnormal disturbances, that adjust for many instruments. We find that this adjustment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors in t-ratios leads to an asymptotic approximation order that is the same when the number of instrumental variables grows as when the number of instruments is fixed. We also give a version of the Kleibergen weak instrument statistic that is robust to many instruments.

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File URL: http://pubs.amstat.org/doi/abs/10.1198/073500108000000024
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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 26 (2008)
Issue (Month): ()
Pages: 398-422

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Handle: RePEc:bes:jnlbes:v:26:y:2008:p:398-422

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  1. Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Departmental Working Papers 201111, Rutgers University, Department of Economics.
  2. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  4. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  5. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  6. John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics.
  7. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  8. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  9. 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.
  10. Norman R. Swanson & John C. Chao, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions with Many Weak Instruments," Econometric Society 2004 Far Eastern Meetings 668, Econometric Society.
  11. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
  12. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  13. John C. Chao & Norman R. Swanson, 2003. "Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments," Departmental Working Papers 200312, Rutgers University, Department of Economics.
  14. 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.
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