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The likelihood of mixed hitting times

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  • Abbring, Jaap H.
  • Salimans, Tim

Abstract

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of Lévy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan’s (1985) strike data.

Suggested Citation

  • Abbring, Jaap H. & Salimans, Tim, 2021. "The likelihood of mixed hitting times," Journal of Econometrics, Elsevier, vol. 223(2), pages 361-375.
    • Handle: RePEc:eee:econom:v:223:y:2021:i:2:p:361-375
    DOI: 10.1016/j.jeconom.2019.08.017
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    References listed on IDEAS

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    1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    2. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    3. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    4. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    5. Jaap H. Abbring & Tim Salimans, 2019. "The Likelihood of Mixed Hitting Times," Papers 1905.03463, arXiv.org, revised Apr 2021.
    6. Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    More about this item

    Keywords

    Duration analysis; First passage time; Identification; Laplace transform; Lévy process; Maximum likelihood; Mellin’s inverse formula; Mixture; Optimal stopping; Strike duration;
    All these keywords.

    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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