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The Efficiency Bound of the Mixed Proportional Hazard Model

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  • Jinyong Hahn

Abstract

The semiparametric efficiency bound of the mixed proportional hazard model is derived. The density of the model factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation given the sufficient statistic. Applying this result to the single-spell Weibull mixed proportional hazard model, it is shown that its information matrix is singular and there cannot exist any ^/w-consistent estimator sequence. The information of the multi-spell Weibull mixed proportional hazard model is shown to be nonsingular in general.

Suggested Citation

  • Jinyong Hahn, 1994. "The Efficiency Bound of the Mixed Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 607-629.
  • Handle: RePEc:oup:restud:v:61:y:1994:i:4:p:607-629.
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    File URL: http://hdl.handle.net/10.2307/2297911
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    Cited by:

    1. Bo E. Honoré & Áureo de Paula, 2016. "A new model for interdependent durations with an application to joint retirement," CeMMAP working papers CWP07/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Bijwaard Govert E. & Ridder Geert & Woutersen Tiemen, 2013. "A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 1-23, July.
    3. Chen, Xiaohong & Liao, Zhipeng, 2014. "Sieve M inference on irregular parameters," Journal of Econometrics, Elsevier, vol. 182(1), pages 70-86.
    4. 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.
    5. 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.
    6. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    7. Hausman, Jerry A. & Woutersen, Tiemen, 2014. "Estimating a semi-parametric duration model without specifying heterogeneity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 114-131.
    8. Baker, Michael & Melino, Angelo, 2000. "Duration dependence and nonparametric heterogeneity: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 96(2), pages 357-393, June.
    9. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    10. Bo Honoré & Thomas Jørgensen & Áureo de Paula, 2020. "The informativeness of estimation moments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 797-813, November.
    11. Abbring, Jaap H. & Berg, Gerard J. van den, 2000. "The non-parametric identification of the mixed proportional hazards competing risks model," Serie Research Memoranda 0024, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    12. Jerry Hausman & Tiemen Woutersen, 2014. "Estimating the Derivative Function and Counterfactuals in Duration Models with Heterogeneity," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 472-496, August.
    13. 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.
    14. Sadat Reza & Paul Rilstone, 2016. "Semiparametric Efficiency Bounds and Efficient Estimation of Discrete Duration Models with Unspecified Hazard Rate," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 693-726, May.
    15. Bearse, Peter & Canals, Jose & Rilstone, Paul, 1998. "Consistent standard errors for semiparametric duration models with unobserved heterogeneity," Economics Letters, Elsevier, vol. 59(2), pages 153-156, May.

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