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Estimating the Derivative Function and Counterfactuals in Duration Models with Heterogeneity

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  • Jerry Hausman
  • Tiemen Woutersen

Abstract

This paper presents a new estimator for counterfactuals in duration models. The counterfactual in a duration model is the length of the spell in case the regressor would have been different. We introduce the structural duration function, which gives these counterfactuals. The advantage of focusing on counterfactuals is that one does not need to identify the mixed proportional hazard model. In particular, we present examples in which the mixed proportional hazard model is unidentified or has a singular information matrix but our estimator for counterfactuals still converges at rate N -super-1/2, where N is the number of observations. We apply the structural duration function to simulate important policy effects, including a change in welfare benefits.

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  • Jerry Hausman & Tiemen Woutersen, 2014. "Estimating the Derivative Function and Counterfactuals in Duration Models with Heterogeneity," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 472-496, August.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:5-6:p:472-496
    DOI: 10.1080/07474938.2013.825120
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    1. Geert Ridder, 1990. "The Non-Parametric Identification of Generalized Accelerated Failure-Time Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 167-181.
    2. J. Heckman & B. Singer, 1984. "The Identifiability of the Proportional Hazard Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 231-241.
    3. Meyer, Bruce D, 1996. "What Have We Learned from the Illinois Reemployment Bonus Experiment?," Journal of Labor Economics, University of Chicago Press, vol. 14(1), pages 26-51, January.
    4. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    5. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
    6. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    7. 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.
    8. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    9. Jinyong Hahn, 1994. "The Efficiency Bound of the Mixed Proportional Hazard Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 607-629.
    10. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
    11. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    12. Bo E. HonorÈ & Luojia Hu, 2010. "Estimation of a transformation model with truncation, interval observation and time-varying covariates," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 127-144, February.
    13. Han, Aaron & Hausman, Jerry A, 1990. "Flexible Parametric Estimation of Duration and Competing Risk Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(1), pages 1-28, January-M.
    14. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    15. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    16. Honore, Bo E, 1990. "Simple Estimation of a Duration Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 58(2), pages 453-473, March.
    17. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    18. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    19. 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. Lo Simon M.S. & Stephan Gesine & Wilke Ralf A., 2017. "Competing Risks Copula Models for Unemployment Duration: An Application to a German Hartz Reform," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-20, January.
    3. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.

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