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A Duration Model with Dynamic Unobserved Heterogeneity


  • Botosaru, Irene


The paper considers a new class of duration models in which unobserved heterogeneity changes with time. The class addresses two main questions: How does the exit probability from a state vary when unobserved heterogeneity evolves through time? And do changes in unobserved heterogeneity have a timing effect? We show the non- and semi-parametric identification of the new class by solving a nonlinear integral equation with unknown kernel. Both the function of observed covariates and the mean of the distribution of unobserved heterogeneity are nonparametrically identified. Identifying timing effects and the distribution of unobserved heterogeneity requires stronger assumptions on either one of the two. An extension to the case when unobserved heterogeneity is a function of observed covariates is also identified. We show that sieve maximum likelihood estimators are consistent and present Monte Carlo simulations for both correct specification and misspecification. The paper also presents an empirical model of unemployment duration in which individuals exit unemployment when total accumulated losses due to unemployment cross over a self-imposed spending limit.

Suggested Citation

  • Botosaru, Irene, 2011. "A Duration Model with Dynamic Unobserved Heterogeneity," TSE Working Papers 11-262, Toulouse School of Economics (TSE), revised Nov 2013.
  • Handle: RePEc:tse:wpaper:25316

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    References listed on IDEAS

    1. Bound, John & Stinebrickner, Todd & Waidmann, Timothy, 2010. "Health, economic resources and the work decisions of older men," Journal of Econometrics, Elsevier, vol. 156(1), pages 106-129, May.
    2. Ariga, Kenn & Ohkusa, Yasushi & Brunello, Giorgio, 1999. "Fast track: is it in the genes? The promotion policy of a large Japanese firm," Journal of Economic Behavior & Organization, Elsevier, vol. 38(4), pages 385-402, April.
    3. Aalen, Odd O. & Hjort, Nils Lid, 2002. "Frailty models that yield proportional hazards," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 335-342, July.
    4. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
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    Cited by:

    1. Ruixuan Liu, 2016. "A Single-index Cox Model Driven by Levy Subordinators," Emory Economics 1602, Department of Economics, Emory University (Atlanta).
    2. Ruixuan Liu, 2016. "A Competing Risks Model with Time-varying Heterogeneity and Simultaneous Failure," Emory Economics 1603, Department of Economics, Emory University (Atlanta).
    3. Effraimidis, Georgios, 2016. "Nonparametric Identification of a Time-Varying Frailty Model," COHERE Working Paper 2016:6, University of Southern Denmark, COHERE - Centre of Health Economics Research.

    More about this item


    duration analysis; Levy process; dynamic unobserved heterogeneity; identification; mixture;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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