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A test for endogeneity in conditional quantile models

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  • Tae-Hwan Kim

    (School of Economics, Yonsei University)

  • Christophe Muller

    (DEFI, University of Aix-Marseille)

Abstract

In this paper we develop a test to detect the presence of endogeneity in conditional quantile models. The proposed test is a Hausman-type test in that it is based on the distance between two estimators in which one is consistent only under no endogeneity while the other estimator 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 is investigated by Monte Carlo simulations and it is found that the test shows reasonably good size and power properties in finite samples. Finally, we apply our approach to test for endogeneity in a conditional quantile model for estimating Engel curves using the UK consumption and expenditure data. It is revealed that the pattern of endogeneity found in the Engel curve varies across different quantiles.

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Bibliographic Info

Paper provided by Yonsei University, Yonsei Economics Research Institute in its series Working papers with number 2012rwp-49.

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Length: 19 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:yon:wpaper:2012rwp-49

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

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  1. 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, vol. 26(1), pages 7-40.
  2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
  3. Lingjie Ma & Roger Koenker, 2004. "Quantile regression methods for recursive structural equation models," CeMMAP working papers CWP01/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, 05.
  5. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  6. 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.
  7. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
  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, vol. 70(1), pages 91-117, January.
  9. Christophe Muller & Tae-Hwan Kim, 2004. "Two-Stage Quantile Regression When The First Stage Is Based On Quantile Regression," Working Papers. Serie AD 2004-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  11. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
  12. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
  13. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
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