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Two-Stage Huber Estimation

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Author Info

  • Christophe Muller

    ()
    (Universidad de Alicante)

  • Tae-Hwan Kim

    (Yonsei University)

Abstract

In this paper we study how the Huber estimator can be adapted to the presence of endogeneity in a two stage equations setting similar to that of 2SLS. We propose an estimation procedure that is at the same time relatively (i) simple, (ii) robust and (iii) efficient. Moreover, we deal with the case of random regressors and asymmetric errors, two extensions rarely present in this literature. The preliminary scale correction is implemented with median absolute deviation estimator, which is consistent with our above criteria and is a very robust estimator of scale. The resulting estimator is termed as the Two-Stage Huber (2SH) estimator. We explicitly establish the conditions for consistency and asymptotic normality of the 2SH estimator and we derive the formula of the asymptotic covariance matrix. We conduct Monte Carlo simulations whose results indicate that the 2SH estimator has smaller standard errors than the Two-Stage Least Squares (2SLS) estimator and than the Two-Stage Least Absolute Deviations (2SLAD) estimator in many situations. On the whole, the 2SH estimator appears to be a simple and useful alternative to 2SLS and 2SLAD in cases of two-stage estimation to deal with endogeneity when there are concerns for both robustness and efficiency.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2005-17.pdf
File Function: Fisrt version / Primera version, 2005
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2005-17.

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Length: 24 pages
Date of creation: Apr 2005
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2005-17

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Related research

Keywords: Two-stage estimation; Huber estimation; robustness; endogeneity;

This paper has been announced in the following NEP Reports:

References

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  1. 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, 06.
  2. 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.
  3. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  4. Krasker, William S, 1986. "Two-Stage Bounded-Influence Estimators for Simultaneous-Equations Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 437-44, October.
  5. Krasker, William S & Welsch, Roy E, 1985. "Resistant Estimation for Simultaneous-Equations Models Using Weighted Instrumental Variables," Econometrica, Econometric Society, vol. 53(6), pages 1475-88, November.
  6. repec:cup:etheor:v:12:y:1996:i:5:p:793-813 is not listed on IDEAS
  7. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  8. Duncan, Gregory M., 1987. "A simplified approach to M-estimation with application to two-stage estimators," Journal of Econometrics, Elsevier, vol. 34(3), pages 373-389, March.
  9. Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
  10. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July.
  11. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  12. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  13. Adrian Pagan, 1985. "Two Stage and Related Estimators and Their Applications," Cowles Foundation Discussion Papers 741, Cowles Foundation for Research in Economics, Yale University.
  14. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February.
  15. Marjorie Flavin, 1999. "Robust Estimation of the Joint Consumption / Asset Demand Decision," NBER Working Papers 7011, National Bureau of Economic Research, Inc.
  16. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
  17. 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.
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Citations

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Cited by:
  1. Pavel Cizek & Wolfgang Härdle, 2006. "Robust Econometrics," SFB 649 Discussion Papers SFB649DP2006-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.

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