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Endogeneity in Quantile Regression Models: A Control Function Approach

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Sokbae Lee

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Abstract

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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Keywords: Endogeneity; partially linear regression; quantile regression; series estimation.;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09. [Downloadable!] (restricted)
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  3. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb.. [Downloadable!]
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  6. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  7. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September. [Downloadable!] (restricted)
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  10. 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. [Downloadable!]
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  11. 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. [Downloadable!] (restricted)
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  12. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July. [Downloadable!] (restricted)
  13. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, 05. [Downloadable!] (restricted)
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  14. David Card, 2000. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," NBER Working Papers 7769, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Whitney Newey & Guido Imbens, 2004. "Identification and Estimation of Triangular Simultaneous Equations Models without Additivity," Econometric Society 2004 North American Summer Meetings 594, Econometric Society. [Downloadable!]
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  16. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  17. 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. [Downloadable!]
  18. Graddy, K., 1993. "Testing for Imperfect Competition at the Fulton Fish Market," Papers 137, Princeton, Department of Economics - Financial Research Center.
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  19. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June. [Downloadable!] (restricted)
  20. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Joel Horowitz & Sokbae 'Simon' Lee, 2007. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," CeMMAP working papers CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Kathryn Graddy & Peter E. Kennedy, 2006. "When are Supply and Demand Determined Recursively Rather than Simultaneously? Another look at the Fulton Fish Market Data," Economics Series Working Papers 297, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  3. Vincenzo Atella & Noemi Pace & Daniela Vuri, 2008. "Are employers discriminating with respect to weight? European Evidence using Quantile Regression," CEIS Research Paper 123, Tor Vergata University, CEIS, revised 14 Jul 2008. [Downloadable!]
    Other versions:
  4. Kathryn Graddy & George Hall, 2009. "A Dynamic Model of Price Discrimination and Inventory Management at the Fulton Fish Market," NBER Working Papers 15019, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  5. Victor Chernozhukov & Roberto Rigobon & Thomas Stoker, 2009. "Set identification with Tobin regressors," CeMMAP working papers CWP12/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  6. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  7. Andrew Chesher, 2004. "Identification of sensitivity to variation in endogenous variables," CeMMAP working papers CWP10/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  8. Kathryn Graddy, 2006. "Markets : The Fulton Fish Market," Economics Series Working Papers 254, University of Oxford, Department of Economics. [Downloadable!]
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  9. Kamhon Kan & Chihwa Kao, 2005. "Simulation-Based Two-Step Estimation with Endogenous Regressors," Center for Policy Research Working Papers 76, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  10. Katleen Van den Broeck, 2007. "Child Height and Maternal Health Care Knowledge in Mozambique," Discussion Papers 07-30, University of Copenhagen. Department of Economics. [Downloadable!]
  11. Hunt, Priscillia, 2008. "Are immigrants so stuck to the floor that the ceiling is irrelevant?," The Warwick Economics Research Paper Series (TWERPS) 838, University of Warwick, Department of Economics. [Downloadable!]
  12. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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