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Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable


  • Tue Gorgens

    (Univ. of Iowa)

  • Joel L. Horowitz

    (Univ. of Iowa)


In this paper we develo psemiparametric estimators of L and y in the model L(Y) = min[b›X + U,C], where Y is a nonnegative dependent variable, X is a vector of explanatory variables, U is an unobserved random "error" term with unknown distribution function y, C is a random censoring variable, b is an unknown parameter vector, and L is an unknown strictly increasing function. This model includes as a special case the censored proportional hazards model with unobserved heterogeneity. Estimators of L and y already exist for the case where either L or y belongs to a known finite-dimensional parametric family, and methods for estimating b exist for the general case. In this paper we propose estimators of L and y which do not assume that L and y belong to known parametric families. We obtain their asymptotic distributions and investigate the small sample properties of the estimators by Monte Carlo simulation.

Suggested Citation

  • Tue Gorgens & Joel L. Horowitz, 1996. "Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable," Econometrics 9603001, EconWPA.
  • Handle: RePEc:wpa:wuwpem:9603001
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    References listed on IDEAS

    1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    2. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    3. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    4. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
    7. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    8. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    9. Kennan, John & Wilson, Robert, 1989. "Strategic Bargaining Models and Interpretation of Strike Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 87-130, Supplemen.
    10. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    11. J. L. HOROWITZ & Wolfgang HÄRDLE, 1994. "Direct Semiparametric Estimation of Single - Index Models with Discrete Covariates," SFB 373 Discussion Papers 1994,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    13. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs


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