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Endogeneity in Quantile Regression Models: A Control Function Approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature and on possible extensions and limitations of the estimation approach. Finally, the numerical performance and usefulness of the estimator are illustrated by the results of Monte Carlo experiments and two empirical examples, demand for fish and returns to schooling

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 521.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:521
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  1. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, 09.
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  3. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Richard Blundell & James Powell, 2001. "Endogeneity in semiparametric binary response models," CeMMAP working papers CWP05/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Honore, Bo E & Hu, Luojia, 2004. "On the Performance of Some Robust Instrumental Variables Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 30-39, January.
  6. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  8. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  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. Alberto Abadie & Joshua Angrist & Guido Imbens, 1999. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Working papers 99-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  12. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
  13. Elie Tamer, 2000. "Inference in Censored Models with Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1815, Econometric Society.
  14. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(01), pages 1-31, February.
  15. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  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. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, 09.
  18. Kathryn Graddy, 1995. "Testing for Imperfect Competition at the Fulton Fish Market," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 75-92, Spring.
  19. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  20. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
  21. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  22. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
  23. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  24. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
  25. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
  26. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  27. 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.
  28. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  29. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  30. Moshe Buchinsky, 1998. "The dynamics of changes in the female wage distribution in the USA: a quantile regression approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 1-30.
  31. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 499-527.
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