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The Singularity of the Information Matrix of the Mixed Proportional Hazard Model

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Elbers and Ridder (1982) identify the Mixed Proportional Hazard model by assuming that the heterogeneity has finite mean. Under this assumption, the information matrix of the MPH model may be singular. Moreover, the finite mean assumption cannot be tested. This paper proposes a new identification condition that ensures non-singularity of the information bound. This implies that there can exist estimators that converge at rate root N. As an illustration, we apply our identifying assumption to the Transformation model of Horowitz (1996). In particular, we assume that the baseline hazard is constant near t=0 but make no no parametric assumptions are imposed for other values of t. We then derive an estimator for the scale normalization that converges at rate root N.

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  • Geert Ridder & Tiemen Woutersen, 2002. "The Singularity of the Information Matrix of the Mixed Proportional Hazard Model," University of Western Ontario, Departmental Research Report Series 20026, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20026
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    1. Burda, Martin & Harding, Matthew, 2014. "Environmental Justice: Evidence from Superfund cleanup durations," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PA), pages 380-401.
    2. Chen, Xiaohong & Liao, Zhipeng, 2014. "Sieve M inference on irregular parameters," Journal of Econometrics, Elsevier, vol. 182(1), pages 70-86.
    3. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.
    4. van den Berg, Gerard. J. & Janys, Lena & Mammen, Enno & Nielsen, Jens Perch, 2021. "A general semiparametric approach to inference with marker-dependent hazard rate models," Journal of Econometrics, Elsevier, vol. 221(1), pages 43-67.
    5. Chiappori, Pierre-Andre & Komunjer, Ivana, 2008. "Correct Specification and Identification of Nonparametric Transformation Models," University of California at San Diego, Economics Working Paper Series qt4v12m2rg, Department of Economics, UC San Diego.
    6. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
    7. James Wolter, 2015. "Kernel Estimation Of Hazard Functions When Observations Have Dependent and Common Covariates," Economics Series Working Papers 761, University of Oxford, Department of Economics.
    8. Bo E. Honoré & Aureo de Paula, 2009. ""Interdependent Durations" Third Version," PIER Working Paper Archive 09-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Feb 2008.
    9. Arkadiusz Szydłowski, 2019. "Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1086-1101, November.
    10. Arkadiusz Szydlowski, 2015. "Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance," Discussion Papers in Economics 15/06, Division of Economics, School of Business, University of Leicester.
    11. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    12. Bo E. Honore & Aureo de Paula, 2007. "Interdependent Durations, Second Version," PIER Working Paper Archive 08-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Nov 2008.
    13. Jaap H. Abbring, 2006. "The Event-History Approach to Program Evaluation," Tinbergen Institute Discussion Papers 06-057/3, Tinbergen Institute, revised 29 Oct 2007.
    14. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2017. "Modeling heaped duration data: An application to neonatal mortality," Journal of Econometrics, Elsevier, vol. 200(2), pages 363-377.
    15. Effraimidis, Georgios, 2016. "Nonparametric Identification of a Time-Varying Frailty Model," DaCHE discussion papers 2016:6, University of Southern Denmark, Dache - Danish Centre for Health Economics.
    16. 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.
    17. 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.
    18. Sasaki, Yuya, 2015. "Heterogeneity and selection in dynamic panel data," Journal of Econometrics, Elsevier, vol. 188(1), pages 236-249.
    19. Bo E. Honor & Áureo De Paula, 2010. "Interdependent Durations," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1138-1163.
    20. Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.

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