Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-29T03:07:33.540Z Has data issue: false hasContentIssue false

ESTIMATING PANEL DATA DURATION MODELS WITH CENSORED DATA

Published online by Cambridge University Press:  11 June 2008

Sokbae Lee*
Affiliation:
Centre for Microdata Methods and Practice, Institute for Fiscal Studies, and University College London
*
Address correspondence to Sokbae Lee, Department of Economics, University College London, London, WC1E 6BT, United Kingdom; e-mail: l.simon@ucl.ac.uk

Abstract

This paper presents a method for estimating a class of panel data duration models, under which an unknown transformation of the duration variable is linearly related to the observed explanatory variables and the unobserved heterogeneity (or frailty) with completely known error distributions. This class of duration models includes a panel data proportional hazards model with fixed effects. The proposed estimator is shown to be n1/2-consistent and asymptotically normal with dependent right censoring. The paper provides some discussions on extending the estimator to the cases of longer panels and multiple states. Some Monte Carlo studies are carried out to illustrate the finite-sample performance of the new estimator.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abbring, J.H, Chiappori, P.A., & Pinquet, J. (2003) Moral hazard and dynamic insurance data. Journal of the European Economic Association 1, 767820.CrossRefGoogle Scholar
Billingsley, P. (1968) Weak convergence of probability measures. Wiley.Google Scholar
Chamberlain, G. (1985) Heterogeneity, omitted variable bias, and duration dependence. In Heckman, J.J. & Singer, B. (eds.), Longitudinal Analysis of Labor Market Data, pp. 338. Cambridge University Press.CrossRefGoogle Scholar
Cheng, S.C., Wei, L.J., & Ying, Z. (1995) Analysis of transformation models with censored data. Biometrika 82, 835845.CrossRefGoogle Scholar
Dabrowska, D. (1989) Uniform consistency of the kernel conditional Kaplan-Meier estimate. Annals of Statistics 17, 11571167.CrossRefGoogle Scholar
Fleming, T.R. & Harrington, D.P. (1991) Counting Processes and Survival Analysis. Wiley.Google Scholar
Gill, R. (1983) Large sample behaviour of the product-limit estimator on the whole line. Annals of Statistics 11, 4958.CrossRefGoogle Scholar
Heckman, J.J. & Borjas, G.J. (1980) Does unemployment cause future unemployment? Definitions, questions and answers for a continuous time model of heterogeneity and state dependence. Economica 47, 247283.CrossRefGoogle Scholar
Horowitz, J.L. (1996) Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64, 103137.CrossRefGoogle Scholar
Horowitz, J.L. (1998) Semiparametric Methods in Econometrics. Springer-Verlag.CrossRefGoogle Scholar
Horowitz, J.L. & Härdle, W. (1996) Direct semiparametric estimation of single-index models with discrete covariates. Journal of the American Statistical Association 91, 16321640.CrossRefGoogle Scholar
Horowitz, J.L. & Lee, S. (2004) Semiparametric estimation of a panel data proportional hazards model with fixed effects. Journal of Econometrics 119, 155198.CrossRefGoogle Scholar
Hristache, M., Juditski, A., & Spokoiny, V. (2001) Direct estimation of the index coeffcients in a single index model. Annals of Statistics 29, 595623.CrossRefGoogle Scholar
Ichimura, H. (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single index models. Journal of Econometrics 58, 71120.CrossRefGoogle Scholar
Jain, D. & Vilcassim, N.J. (1991) Investigating household purchase timing decisions: A conditional hazard function approach. Marketing Science 10, 123.CrossRefGoogle Scholar
Kalbfleisch, J.D. & Prentice, R.L. (1980) The Statistical Analysis of Failure Time Data. Wiley.Google Scholar
Khan, S. & Tamer, E. (2007) Partial rank estimation of duration models with general forms of censoring. Journal of Econometrics 136, 251280.CrossRefGoogle Scholar
Klein, R.W. & Spady, R.H. (1993) An efficient semiparametric estimation for binary response models. Econometrica 61, 387421.CrossRefGoogle Scholar
Koul, H., Susarla, V., & Van Ryzin, J. (1981) Regression analysis with randomly right-censored data. Annals of Statistics 9, 12761288.CrossRefGoogle Scholar
Lancaster, T. (2000) The incidental parameter problem since 1948. Journal of Econometrics 95, 391413.CrossRefGoogle Scholar
Lin, D.Y., Sun, W., & Ying, Z. (1999) Nonparametric estimation of the gap time distributions for serial events with censored data. Biometrika 86, 5970.CrossRefGoogle Scholar
Murphy, S.A. (1995) Asymptotic theory for the frailty model. Annals of Statistics 23, 182198.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D.L. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 21112245. North-Holland.Google Scholar
Newman, J.L. & McCullogh, C.E. (1984) A hazard rate approach to the timing of births. Econometrika 52, 939961.CrossRefGoogle Scholar
Powell, J.L. (1994) Estimation of semiparametric models. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 24432521. North-Holland.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrika 51, 14031430.CrossRefGoogle Scholar
Ridder, G. & Tunalı, .I. (1999) Stratified partial likelihood estimation. Journal of Econometrics 92, 193232.CrossRefGoogle ScholarPubMed
Srinivasan, C. & Zhou, M. (1994) Linear regression with censoring. Journal of Multivariate Analysis 49, 179201.CrossRefGoogle Scholar
Topel, R.H. & Ward, M.P. (1992) Job mobility and the careers of young men. Quarterly Journal of Economics 107, 439479.CrossRefGoogle Scholar
Van der Berg, G.J. (2001) Duration models: Specification, identification, and multiple durations. In Heckman, J.J. & Leamer, E. (eds.), Handbook of Econometrics, vol. V, pp. 33813460. North-Holland.Google Scholar
Visser, M. (1996) Nonparametric estimation of the bivariate survival function with application to vertically transmitted AIDS. Biometrika 83, 507518.CrossRefGoogle Scholar
Wang, W. & Wells, M.T. (1998) Nonparametric estimation of successive duration times under dependent censoring. Biometrika 85, 561572.CrossRefGoogle Scholar
Wei, L.J., Lin, D.Y., & Weissfeld, L. (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association 84, 10651073.CrossRefGoogle Scholar
Wooldridge, J.M. (2002) Inverse probability weighted M-estimators for sample selection, attrition, and stratification. Portuguese Economic Journal 1, 117139.CrossRefGoogle Scholar
Zhou, M. (1991) Some properties of the Kaplan-Meier estimator for independent non-identically distributed random variables. Annals of Statistics 19, 22662274.CrossRefGoogle Scholar