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Mixed Hitting‐Time Models

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  • Jaap H. Abbring

Abstract

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Levy process - a continuous-time process with stationary and independent increments - crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from optimal-stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards (MPH) structure. We show how strategies for analyzing the MPH model's identifiability can be adapted to prove identifiability of an MHT model with observed regressors and unobserved heterogeneity. We discuss inference from censored data and extensions to time-varying covariates and latent processes with more general time and dependency structures. We conclude by discussing the relative merits of the MHT and MPH models as complementary frameworks for econometric duration analysis.
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  • Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:2:p:783-819
    DOI: ECTA7312
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    Cited by:

    1. Jaap H. Abbring & Tim Salimans, 2019. "The Likelihood of Mixed Hitting Times," Papers 1905.03463, arXiv.org, revised Apr 2021.
    2. Yogo Purwono & Irwan Adi Ekaputra & Zaäfri Ananto Husodo, 2018. "Estimation of Dynamic Mixed Hitting Time Model Using Characteristic Function Based Moments," Computational Economics, Springer;Society for Computational Economics, vol. 51(2), pages 295-321, February.
    3. Jaap Abbring & James Heckman, 2008. "Dynamic policy analysis," CeMMAP working papers CWP05/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Marinescu, Ioana, 2016. "Divorce: What does learning have to do with it?," Labour Economics, Elsevier, vol. 38(C), pages 90-105.
    5. 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.
    6. Sebastian Galiani & Juan Pantano, 2021. "Structural Models: Inception and Frontier," NBER Working Papers 28698, National Bureau of Economic Research, Inc.
    7. Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.
    8. Abbring, Jaap H. & Salimans, Tim, 2021. "The likelihood of mixed hitting times," Journal of Econometrics, Elsevier, vol. 223(2), pages 361-375.
    9. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
    10. Jaap H. Abbring, 2006. "The Event-History Approach to Program Evaluation," Tinbergen Institute Discussion Papers 06-057/3, Tinbergen Institute, revised 29 Oct 2007.
    11. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    12. Renault, Eric & van der Heijden, Thijs & Werker, Bas J.M., 2014. "The dynamic mixed hitting-time model for multiple transaction prices and times," Journal of Econometrics, Elsevier, vol. 180(2), pages 233-250.
    13. Sasaki, Yuya, 2015. "Heterogeneity and selection in dynamic panel data," Journal of Econometrics, Elsevier, vol. 188(1), pages 236-249.
    14. Div Bhagia, 2023. "Duration Dependence and Heterogeneity: Learning from Early Notice of Layoff," Papers 2305.17344, arXiv.org, revised Jul 2024.

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    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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