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A competing risks model with time‐varying heterogeneity and simultaneous failure

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  • Ruixuan Liu

Abstract

This paper proposes a new bivariate competing risks model in which both durations are the first passage times of dependent Lévy subordinators with exponential thresholds and multiplicative covariates effects. Our specification extends the mixed proportional hazards model, as it allows for the time‐varying heterogeneity represented by the unobservable Lévy processes and it generates the simultaneous termination of both durations with positive probability. We obtain nonparametric identification of all model primitives given competing risks data. A flexible semiparametric estimation procedure is provided and illustrated through the analysis of a real dataset.

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  • 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.
  • Handle: RePEc:wly:quante:v:11:y:2020:i:2:p:535-577
    DOI: 10.3982/QE1159
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    1. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    2. 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.
    3. Botosaru, Irene, 2011. "A Duration Model with Dynamic Unobserved Heterogeneity," TSE Working Papers 11-262, Toulouse School of Economics (TSE), revised Nov 2013.
    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. 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.
    6. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    7. Farzin, Y. H. & Huisman, K. J. M. & Kort, P. M., 1998. "Optimal timing of technology adoption," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 779-799, May.
    8. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    9. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    10. Geert Ridder, 1990. "The Non-Parametric Identification of Generalized Accelerated Failure-Time Models," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 167-181.
    11. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
    12. Reinganum, Jennifer F., 1981. "Dynamic games of innovation," Journal of Economic Theory, Elsevier, vol. 25(1), pages 21-41, August.
    13. Geert Ridder & Tiemen M. Woutersen, 2003. "The Singularity of the Information Matrix of the Mixed Proportional Hazard Model," Econometrica, Econometric Society, vol. 71(5), pages 1579-1589, September.
    14. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    15. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    16. Lundberg, Shelly & Pollak, Robert A, 1994. "Noncooperative Bargaining Models of Marriage," American Economic Review, American Economic Association, vol. 84(2), pages 132-137, May.
    17. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    18. Mark Y. An & Bent Jesper Christensen & Nabanita Datta Gupta, 2004. "Multivariate mixed proportional hazard modelling of the joint retirement of married couples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(6), pages 687-704.
    19. J. Heckman & B. Singer, 1984. "The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 51(2), pages 231-241.
    20. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    21. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
    22. Ryu, Keunkwan, 1993. "Structural duration analysis of management data," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 91-115.
    23. Reinganum, Jennifer F, 1982. "A Dynamic Game of R and D: Patent Protection and Competitive Behavior," Econometrica, Econometric Society, vol. 50(3), pages 671-688, May.
    24. 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.
    25. Basu, A. P. & Ghosh, J. K., 1978. "Identifiability of the multinormal and other distributions under competing risks model," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 413-429, September.
    26. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    27. Jensen, Richard, 1982. "Adoption and diffusion of an innovation of uncertain profitability," Journal of Economic Theory, Elsevier, vol. 27(1), pages 182-193, June.
    28. Fernando E. Alvarez & Katarína Borovičková & Robert Shimer, 2016. "Decomposing Duration Dependence in a Stopping Time Model," NBER Working Papers 22188, National Bureau of Economic Research, Inc.
    29. Ridder, Geert & Tunali, Insan, 1999. "Stratified partial likelihood estimation," Journal of Econometrics, Elsevier, vol. 92(2), pages 193-232, October.
    30. Torben Martinussen, 2002. "A flexible additive multiplicative hazard model," Biometrika, Biometrika Trust, vol. 89(2), pages 283-298, June.
    31. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
    32. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    33. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    34. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
    35. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    36. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    37. repec:dau:papers:123456789/6486 is not listed on IDEAS
    38. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
    39. 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.
    40. Courtney C. Coile, 2004. "Health Shocks and Couples' Labor Supply Decisions," NBER Working Papers 10810, National Bureau of Economic Research, Inc.
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