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Weak identification robust tests in an instrumental quantile model

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  • Jun, Sung Jae

Abstract

We develop a testing procedure that is robust to identification quality in an instrumental quantile model. In order to reduce the computational burden, a multi-step approach is taken, and a two-step Anderson-Rubin (AR) statistic is considered. We then propose an orthogonal decomposition of the AR statistic, where the null distribution of each component does not depend on the assumption of a full rank of the Jacobian. Power experiments are conducted, and inferences on returns to schooling using the Angrist and Krueger data are considered as an empirical example.

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  • Jun, Sung Jae, 2008. "Weak identification robust tests in an instrumental quantile model," Journal of Econometrics, Elsevier, vol. 144(1), pages 118-138, May.
    • Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:118-138
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    Cited by:

    1. Galvao, Antonio F. & Montes-Rojas, Gabriel, 2015. "On the equivalence of instrumental variables estimators for linear models," Economics Letters, Elsevier, vol. 134(C), pages 13-15.
    2. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    3. Javier Alejo & Antonio F Galvao & Gabriel Montes-Rojas, 2023. "A first-stage representation for instrumental variables quantile regression," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 350-377.
    4. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    5. Muller, Christophe, 2018. "Heterogeneity and nonconstant effect in two-stage quantile regression," Econometrics and Statistics, Elsevier, vol. 8(C), pages 3-12.
    6. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    7. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP46/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    9. Philip Kostov & Julie Le Gallo, 2018. "What role for human capital in the growth process: new evidence from endogenous latent factor panel quantile regressions," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(5), pages 501-527, November.
    10. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    11. 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.
    12. Tae-Hwan Kim & Christophe Muller, 2013. "A Test for Endogeneity in Conditional Quantiles," Working Papers halshs-00854527, HAL.
    13. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    14. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers 46/17, Institute for Fiscal Studies.
    15. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    16. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.
    17. Jun, Sung Jae, 2009. "Local structural quantile effects in a model with a nonseparable control variable," Journal of Econometrics, Elsevier, vol. 151(1), pages 82-97, July.
    18. Joel L. Horowitz, 2018. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP52/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Tae-Hwan Kim & Christophe Muller, 2015. "A Particular Form of Non-Constant Effect in Two-Stage Quantile Regression," Working papers 2015rwp-82, Yonsei University, Yonsei Economics Research Institute.
    20. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84(4), pages 1571-1612, July.
    21. Diebolt, Claude & Mishra, Tapas & Perrin, Faustine, 2021. "Gender empowerment as an enforcer of individuals’ choice between education and fertility: Evidence from 19th century France," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 408-438.
    22. Javier Alejo & Antonio F. Galvao & Gabriel Montes-Rojas, 2020. "A first-stage test for instrumental variables quantile regression," Asociación Argentina de Economía Política: Working Papers 4304, Asociación Argentina de Economía Política.

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