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Nonparametric analysis of a duration model with stochastic unobserved heterogeneity

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  • Botosaru, Irene

Abstract

This paper develops nonparametric identification and estimation results for a single-spell hazard model, where the unobserved heterogeneity is specified as a Lévy subordinator. The identification approach solves a nonlinear Volterra integral equation of the first kind with an unknown kernel function. Both the kernel of the integral operator, which models the distribution of the unobserved heterogeneity, and the functions that enter it are identified given regularity conditions and minimal variation in the observed covariates. The paper proposes a shape-constrained nonparametric two-step sieve minimum distance estimator. Rates of convergence are derived and Monte Carlo experiments show the finite sample performance of the estimator.

Suggested Citation

  • Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    • Handle: RePEc:eee:econom:v:217:y:2020:i:1:p:112-139
    DOI: 10.1016/j.jeconom.2019.06.006
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    1. Wang, J. & Ghosh, S.K., 2012. "Shape restricted nonparametric regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2729-2741.
    2. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    3. 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.
    4. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    5. Singpurwalla, Nozer D., 2006. "The Hazard Potential: Introduction and Overview," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1705-1717, December.
    6. Lisa B. Kahn & Fabian Lange, 2014. "Employer Learning, Productivity, and the Earnings Distribution: Evidence from Performance Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1575-1613.
    7. Le‐Yu Chen & Sokbae Lee & Myung Jae Sung, 2014. "Maximum score estimation with nonparametrically generated regressors," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 271-300, October.
    8. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    9. 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.
    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. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    12. Hu, Yingyao & Schennach, Susanne M. & Shiu, Ji-Liang, 2017. "Injectivity of a class of integral operators with compactly supported kernels," Journal of Econometrics, Elsevier, vol. 200(1), pages 48-58.
    13. Aalen, Odd O. & Hjort, Nils Lid, 2002. "Frailty models that yield proportional hazards," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 335-342, July.
    14. Qingning Zhou & Tao Hu & Jianguo Sun, 2017. "A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 664-672, April.
    15. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    16. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    17. Hugo A. Hopenhayn & Francesco Squintani, 2011. "Preemption Games with Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 667-692.
    18. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    19. Y. Kebir, 1991. "On hazard rate processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(6), pages 865-876, December.
    20. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    21. Gwo Dong Lin, 2017. "Recent developments on the moment problem," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    22. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    23. Eduardo A. Haddad & Jaime Bonet & Geoffrey J. D. Hewings, 2023. "Introduction and Overview," Advances in Spatial Science, in: Eduardo A. Haddad & Jaime Bonet & Geoffrey J. D. Hewings (ed.), The Colombian Economy and Its Regional Structural Challenges, chapter 0, pages 1-16, Springer.
    24. Hahn, Jinyong & Liao, Zhipeng & Ridder, Geert, 2018. "Nonparametric Two-Step Sieve M Estimation And Inference," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1281-1324, December.
    25. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    26. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 403-409.
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    Cited by:

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    2. Nathalie Gimenes & Emmanuel Guerre, 2019. "Nonparametric identification of an interdependent value model with buyer covariates from first-price auction bids," Papers 1910.10646, arXiv.org.

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    More about this item

    Keywords

    Duration model; Lévy process; Nonlinear Volterra integral equation of the first kind; Shape restricted estimation;
    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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