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Constructive identification of the mixed proportional hazards model

Author

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  • R. A. Kortram
  • A. C. M. van Rooij
  • A. J. Lenstra
  • G. Ridder

Abstract

We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base‐line hazard, and distribution of the individual effect—from the observed cumulative distribution functions. We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist. Finally we show that the MPH model is even identifiable from two‐sided censored observations. This proof is constructive, too.

Suggested Citation

  • R. A. Kortram & A. C. M. van Rooij & A. J. Lenstra & G. Ridder, 1995. "Constructive identification of the mixed proportional hazards model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(3), pages 269-281, November.
    • Handle: RePEc:bla:stanee:v:49:y:1995:i:3:p:269-281
    DOI: 10.1111/j.1467-9574.1995.tb01469.x
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    Cited by:

    1. Bhattacharjee, Arnab, 2004. "A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models," MPRA Paper 3937, University Library of Munich, Germany.
    2. J. H. Abbring & P.-A. Chiappori & J. J. Heckman & J. Pinquet, 2002. "Testing for Moral Hazard on Dynamic Insurance Data," THEMA Working Papers 2002-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Florens, Jean-Pierre & Fougère, Denis & Mouchart, Michel, 2007. "Duration Models and Point Processes," IZA Discussion Papers 2971, Institute of Labor Economics (IZA).
    4. Christian N. Brinch, 2011. "Non‐parametric identification of the mixed proportional hazards model with interval‐censored durations," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 343-350, July.
    5. Abbring, Jaap H & van den Berg, Gerard J, 2005. "Social experiments and intrumental variables with duration outcomes," Working Paper Series 2005:11, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    6. Abbring, J.H., 2009. "Mixed Hitting-Time Models," Other publications TiSEM 6c745572-a041-4990-a767-6, Tilburg University, School of Economics and Management.
    7. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
    8. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    9. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    10. 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.
    11. Gerard J. van den Berg & Bettina Drepper, 2022. "A unique bond: Twin bereavement and lifespan associations of identical and fraternal twins," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 677-698, April.
    12. van den Berg, Gerard J. & Drepper, Bettina, 2018. "A Unique Bond: Twin Bereavement and Lifespan Associations of Identical and Fraternal Twins," IZA Discussion Papers 11448, Institute of Labor Economics (IZA).
    13. Abbring, Jaap H., 2002. "Stayers versus defecting movers: a note on the identification of defective duration models," Economics Letters, Elsevier, vol. 74(3), pages 327-331, February.
    14. Jaap H. Abbring, 2006. "The Event-History Approach to Program Evaluation," Tinbergen Institute Discussion Papers 06-057/3, Tinbergen Institute, revised 29 Oct 2007.

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