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The Unobserved Heterogeneity Distribution in Duration Analysis

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  • Abbring, Jaap H
  • van den Berg, Gerard J

Abstract

In a large class of hazard models with proportional unobserved heterogeneity, the distribution of the heterogeneity among survivors converges to a gamma distribution. This convergence is often rapid. We derive this result as a general result for exponential mixtures and explore its implications for the specification and empirical analysis of univariate and multivariate duration models.

Suggested Citation

  • 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.
  • Handle: RePEc:cpr:ceprdp:6219
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    References listed on IDEAS

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    1. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    2. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
    3. Newman, John L & McCulloch, Charles E, 1984. "A Hazard Rate Approach to the Timing of Births," Econometrica, Econometric Society, vol. 52(4), pages 939-961, July.
    4. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    5. 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.
    6. 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.
    7. Nickell, Stephen J, 1979. "Estimating the Probability of Leaving Unemployment," Econometrica, Econometric Society, vol. 47(5), pages 1249-1266, September.
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    11. Lee Lillard & Constantijn Panis, 1996. "Marital status and mortality: The role of health," Demography, Springer;Population Association of America (PAA), vol. 33(3), pages 313-327, August.
    12. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    13. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
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    More about this item

    Keywords

    duration analysis; exponential mixture; gamma distribution; limit distribution; mixed proportional hazard;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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