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A Test for Endogeneity in Conditional Quantiles

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  • Tae-Hwan Kim

    ()
    (School of Economics, Yonsei University - Yonsei University)

  • Christophe Muller

    ()
    (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - École des Hautes Études en Sciences Sociales [EHESS] - Ecole Centrale Marseille (ECM))

Abstract

In this paper, we develop a test to detect the presence of endogeneity in conditional quantiles. Our test is a Hausman-type test based on the distance between two estimators, of which one is consistent only under no endogeneity while the other is consistent regardless of the presence of endogeneity in conditional quantile models. We derive the asymptotic distribution of the test statistic under the null hypothesis of no endogeneity. The finite sample properties of the test are investigated through Monte Carlo simulations, and it is found that the test shows good size and power properties in finite samples. As opposed to the test based on the IVQR estimator of Chernozhukov and Hansen (2006) in the case of more than a couple of variables, our approach does not imply an infeasible computation time. Finally, we apply our approach to test for endogeneity in conditional quantile models for estimating Engel curves using UK consumption and expenditure data. The pattern of endogeneity in the Engel curve is found to vary substantially across quantiles

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00854527.

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Date of creation: Aug 2013
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Handle: RePEc:hal:wpaper:halshs-00854527

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Related research

Keywords: regression quantile; endogeneity; two-stage estimation; Hausman test; Engel curve;

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  1. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 1131-1158, December.
  2. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, Econometric Society, vol. 71(3), pages 905-932, 05.
  3. Christophe Muller & Tae-Hwan Kim, 2004. "Two-Stage Quantile Regression When The First Stage Is Based On Quantile Regression," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2004-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Thanaset Chevapatrakul & Tae-Hwan Kim & Paul Mizen, 2009. "The Taylor Principle and Monetary Policy Approaching a Zero Bound on Nominal Rates: Quantile Regression Results for the United States and Japan," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 41(8), pages 1705-1723, December.
  5. Jaume Garcia & Pedro J. Hernández & Ángel López Nicolás, 1998. "How wide is the gap? An investigation of gender wage differences using quantile regression," Economics Working Papers 287, Department of Economics and Business, Universitat Pompeu Fabra.
  6. Omar Arias & Kevin F. Hallock & Walter Sosa Escudero, 1999. "Individual Heterogeneity in the Returns to Schooling: Instrumental Variables Quantile Regression using Twins Data," Department of Economics, Working Papers 016, Departamento de Economía, Facultad de Ciencias Económicas, Universidad Nacional de La Plata.
  7. Wolters, Maik Hendrik, 2010. "Estimating Monetary Policy Reaction Functions Using Quantile Regressions," MPRA Paper 23857, University Library of Munich, Germany.
  8. 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, Econometric Society, vol. 70(1), pages 91-117, January.
  9. Sakata, Shinichi, 2007. "Instrumental variable estimation based on conditional median restriction," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 350-382, December.
  10. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(3), pages 689-711, May.
  11. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, Econometric Society, vol. 75(4), pages 1191-1208, 07.
  12. Lee, Yoonseok & Okui, Ryo, 2012. "Hahn–Hausman test as a specification test," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 133-139.
  13. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 379-398, January.
  14. Tae-Hwan Kim & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," Working Papers halshs-00793372, HAL.
  15. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, Econometric Society, vol. 75(6), pages 1613-1669, November.
  16. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, Econometric Society, vol. 51(5), pages 1569-75, September.
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