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Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations

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  • Jinyong Hahn
  • Jerry Hausman
  • Guido Kuersteiner

Abstract

In this paper, we consider parameter estimation in a linear simultaneous equations model. It is well known that two-stage least squares (2SLS) estimators may perform poorly when the instruments are weak. In this case 2SLS tends to suffer from the substantial small sample biases. It is also known that LIML and Nagar-type estimators are less biased than 2SLS but suffer from large small sample variability. We construct a bias-corrected version of 2SLS based on the Jackknife principle. Using higher-order expansions we show that the MSE of our Jackknife 2SLS estimator is approximately the same as the MSE of the Nagar-type estimator. We also compare the Jackknife 2SLS with an estimator suggested by Fuller (Econometrica 45, 933--54) that significantly decreases the small sample variability of LIML. Monte Carlo simulations show that even in relatively large samples the MSE of LIML and Nagar can be substantially larger than for Jackknife 2SLS. The Jackknife 2SLS estimator and Fuller's estimator give the best overall performance. Based on our Monte Carlo experiments we conduct informal statistical tests of the accuracy of approximate bias and MSE formulas. We find that higher-order expansions traditionally used to rank LIML, 2SLS and other IV estimators are unreliable when identification of the model is weak. Overall, our results show that only estimators with well-defined finite sample moments should be used when identification of the model is weak. Copyright Royal Economic Socciety 2004

Suggested Citation

  • 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, June.
  • Handle: RePEc:ect:emjrnl:v:7:y:2004:i:1:p:272-306
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    2. José A. F. Machado & José Mata, 2001. "Earning functions in Portugal 1982-1994: Evidence from quantile regressions," Empirical Economics, Springer, pages 115-134.
    3. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    4. Cowell, Frank & Flachaire, Emmanuel, 2002. "Sensitivity of inequality measures to extreme values," LSE Research Online Documents on Economics 2213, London School of Economics and Political Science, LSE Library.
    5. Omar Arias & Walter Sosa-Escudero & Kevin F. Hallock, 2001. "Individual heterogeneity in the returns to schooling: instrumental variables quantile regression using twins data," Empirical Economics, Springer, pages 7-40.
    6. Tae-Hwan Kim & Christophe Muller, 2004. "Two-stage quantile regression when the first stage is based on quantile regression," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 218-231, June.
    7. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
    8. Buchinsky, Moshe, 1995. "Quantile regression, Box-Cox transformation model, and the U.S. wage structure, 1963-1987," Journal of Econometrics, Elsevier, vol. 65(1), pages 109-154, January.
    9. Angel López-Nicolás & Jaume García & Pedro J. Hernández, 2001. "How wide is the gap? An investigation of gender wage differences using quantile regression," Empirical Economics, Springer, vol. 26(1), pages 149-167.
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