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Instrumental Variables Estimation and Weak-Identification-Robust Inference Based on a Conditional Quantile Restriction

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  • Marmer, Vadim
  • Sakata, Shinichi

Abstract

Extending the L1-IV approach proposed by Sakata (1997, 2007), we develop a new method, named the $rho_{tau}$-IV estimation, to estimate structural equations based on the conditional quantile restriction imposed on the error terms. We study the asymptotic behavior of the proposed estimator and show how to make statistical inferences on the regression parameters. Given practical importance of weak identification, a highlight of the paper is a proposal of a test robust to the weak identification. The statistics used in our method can be viewed as a natural counterpart of the Anderson and Rubin's (1949) statistic in the $rho_{tau}$-IV estimation.

Suggested Citation

  • Marmer, Vadim & Sakata, Shinichi, 2011. "Instrumental Variables Estimation and Weak-Identification-Robust Inference Based on a Conditional Quantile Restriction," Microeconomics.ca working papers vadim_marmer-2011-26, Vancouver School of Economics, revised 28 Sep 2011.
  • Handle: RePEc:ubc:pmicro:vadim_marmer-2011-26
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    File URL: http://microeconomics.ca/vadim_marmer/cqriv-20110817-2-ss.pdf
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
    2. Sakata, Shinichi, 2007. "Instrumental variable estimation based on conditional median restriction," Journal of Econometrics, Elsevier, vol. 141(2), pages 350-382, December.
    3. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    4. Sakata, S., 1998. "Instrumental Variable Estimation Based on Mean Absolute Deviation," Papers 98-08, Michigan - Center for Research on Economic & Social Theory.
    5. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
    6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    8. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    9. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-1194, September.
    10. 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.
    11. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
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    Cited by:

    1. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.

    More about this item

    Keywords

    quantile regression; instrumental variables; weak identification;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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