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Inference in Censored Models with Endogenous Regressors

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Author Info
Han Hong ()
Elie Tamer

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Abstract

This paper analyzes the linear regression model y = x&bgr;+ε with a conditional median assumption med (ε| z) = 0, where z is a vector of exogenous instrument random variables. We study inference on the parameter &bgr; when y is censored and x is endogenous. We treat the censored model as a model with interval observation on an outcome, thus obtaining an incomplete model with inequality restrictions on conditional median regressions. We analyze the identified features of the model and provide sufficient conditions for point identification of the parameter &bgr;. We use a minimum distance estimator to consistently estimate the identified features of the model. We show that under point identification conditions and additional regularity conditions, the estimator based on inequality restrictions is normal and we derive its asymptotic variance. One can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring. A Monte Carlo analysis illustrates our estimator in the censored and the uncensored case. Copyright Econometric Society, 2002.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 3 (05)
Pages: 905-932
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:3:p:905-932

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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. Blundell, Richard W & Smith, Richard J, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," Review of Economic Studies, Blackwell Publishing, vol. 56(1), pages 37-57, January. [Downloadable!] (restricted)
  2. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  3. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November. [Downloadable!] (restricted)
  4. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March. [Downloadable!] (restricted)
  5. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July. [Downloadable!] (restricted)
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  6. Honore, Bo E, 1992. "Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects," Econometrica, Econometric Society, vol. 60(3), pages 533-65, May. [Downloadable!] (restricted)
  7. James Tobin, 1956. "Estimation of Relationships for Limited Dependent Variables," Cowles Foundation Discussion Papers 3R, Cowles Foundation, Yale University. [Downloadable!]
  8. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-63, July. [Downloadable!] (restricted)
  9. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July. [Downloadable!] (restricted)
  10. Vella, Francis & Verbeek, Marno, 1999. "Two-step estimation of panel data models with censored endogenous variables and selection bias," Journal of Econometrics, Elsevier, vol. 90(2), pages 239-263, June. [Downloadable!] (restricted)
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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. Mitali Das, 2002. "Estimators and inference in a censored regression model with endogenous covariates," Discussion Papers 0102-61, Columbia University, Department of Economics. [Downloadable!]
  2. Patrick Bajari & Han Hong & Ahmed Khwaja, 2006. "Moral Hazard, Adverse Selection and Health Expenditures: A Semiparametric Analysis," NBER Working Papers 12445, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. 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!]
    Other versions:
  4. Sokbae 'Simon' Lee, 2004. "Endogeneity in quantile regression models: a control function approach," CeMMAP working papers CWP08/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  5. 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:
  6. Andrew Chesher, 2005. "Identification with excess heterogeneity," CeMMAP working papers CWP19/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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