Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity

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Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity

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Joel L. Horowitz

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Joel L. Horowitz

Abstract

The proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity. This paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically. The baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known, finite-dimensional, parametric families. Existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family. Thus, the estimators presented in this paper are more general than existing ones.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 67 (1999)
Issue (Month): 5 (September)
Pages: 1001-1028
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Handle: RePEc:ecm:emetrp:v:67:y:1999:i:5:p:1001-1028

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Jaap H. Abbring & Gerard J. van den Berg, 2006. "The Unobserved Heterogeneity Distribution in Duration Analysis," Tinbergen Institute Discussion Papers 06-059/3, Tinbergen Institute. [Downloadable!]
Other versions:
- Abbring, Jaap H & van den Berg, Gerard J, 2007. "The Unobserved Heterogeneity Distribution in Duration Analysis," CEPR Discussion Papers 6219, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
- Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Oxford University Press for Biometrika Trust, vol. 94(1), pages 87-99. [Downloadable!] (restricted)
Arnab Bhattacharjee, 2007. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," Discussion Paper Series, Department of Economics 0708, Department of Economics, University of St. Andrews. [Downloadable!]
Other versions:
- Bhattacharjee, Arnab, 2004. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," MPRA Paper 3937, University Library of Munich, Germany. [Downloadable!]
Carine Milcent, 2005. "Hospital ownership, reimbursement systems and mortality rates," Health Economics, John Wiley & Sons, Ltd., vol. 14(11), pages 1151-1168. [Downloadable!]
Bhattacharjee, A., 2004. "A Simple Test for the Absence of Covariate Dependence in Duration Models," Cambridge Working Papers in Economics 0401, Faculty of Economics, University of Cambridge. [Downloadable!]
Sokbae 'Simon' Lee, 2005. "Identification of a competing risks model with unknown transformations of latent failure times," CeMMAP working papers CWP17/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Other versions:
- Sokbae Lee, 2006. "Identification of a competing risks model with unknown transformations of latent failure times," Biometrika, Oxford University Press for Biometrika Trust, vol. 93(4), pages 996-1002, December. [Downloadable!] (restricted)
B. Dormont & D. Fougère & A. Prieto, 2001. "L'effet de l'allocation unique dégressive sur la reprise d'emploi," THEMA Working Papers 2001-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
Tue Gørgens, 1999. "Semiparametric Estimation of Single-Index Transition Intensities," Discussion Papers 99-25, University of Copenhagen. Department of Economics. [Downloadable!]
Other versions:
- Tue Gorgens, 2000. "Semiparametric Estimation of Single-Index Transition Intensities," Econometric Society World Congress 2000 Contributed Papers 0596, Econometric Society. [Downloadable!]
- Gorgens, T., 1999. "Semiparametric Estimation of Single-Index Transition Intensities," Papers 99-25, Carleton - School of Public Administration.
Joel L. Horowitz & Sokbae Lee, 2002. "Semiparametric Estimation of a Panel Data Proportional Hazards Model with Fixed Effects," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 A5-3, International Conferences on Panel Data. [Downloadable!]
Other versions:
- Joel Horowitz & Sokbae 'Simon' Lee, 2002. "Semiparametric estimation of a panel data proportional hazards model with fixed effects," CeMMAP working papers CWP21/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
- Horowitz, Joel L. & Lee, Sokbae, 2004. "Semiparametric estimation of a panel data proportional hazards model with fixed effects," Journal of Econometrics, Elsevier, vol. 119(1), pages 155-198, March. [Downloadable!] (restricted)
James E. Prieger, . "Conditional Moment Tests for Parametric Duration Models," Department of Economics 00-10, California Davis - Department of Economics. [Downloadable!]
Other versions:
- Prieger, James, 2000. "Conditional Moment Tests for Parametric Duration Models," Working Papers 00-10, University of California at Davis, Department of Economics. [Downloadable!]
Bhattacharjee, A. & Samarjit Das, 2002. "Testing Proportionality in Duration Models with Respect to Continuous Covariates," Cambridge Working Papers in Economics 0220, Faculty of Economics, University of Cambridge. [Downloadable!]
Van den Berg, Gerard J., 2000. "Duration Models: Specification, Identification, and Multiple Durations," MPRA Paper 9446, University Library of Munich, Germany. [Downloadable!]
Other versions:
- Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460 Elsevier. [Downloadable!] (restricted)
Zhang, Tao, 2003. "A Monte Carlo study on non-parametric estimation of duration models with unobserved heterogeneity," Memorandum 25/2003, Oslo University, Department of Economics. [Downloadable!]
Arnab Bhattacharjee, 2009. "Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity," Discussion Paper Series, Department of Economics 0904, Department of Economics, University of St. Andrews. [Downloadable!]
Jerry Hausman & Tiemen M. Woutersen, 2005. "Estimating a semi-parametric duration model without specifying heterogeneity," CeMMAP working papers CWP11/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Other versions:
- Tiemen Woutersen & Jerry Hausman, 2005. "Estimating a Semi-Parametric Duration Model without Specifying Heterogeneity," Economics Working Paper Archive 525, The Johns Hopkins University,Department of Economics. [Downloadable!]

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