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REGULAR VARIATION AND THE IDENTIFICATION OF GENERALIZED ACCELERATED FAILURE-TIME MODELS

Published online by Cambridge University Press:  16 September 2014

Jaap H. Abbring  and
Geert Ridder
Jaap H. Abbring*
Affiliation:
Tilburg University
Geert Ridder*
Affiliation:
University of Southern California
*
*Address correspondence to Jaap Abbring, centER, Department of Econometrics & OR, Tilburg university, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e-mail: jaap@abbring.org or to Geert Ridder, Department of Economics, University of Southern California, Los Angeles, CA 90089, USA; e-mail: ridder@usc.edu.
*Address correspondence to Jaap Abbring, centER, Department of Econometrics & OR, Tilburg university, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e-mail: jaap@abbring.org or to Geert Ridder, Department of Economics, University of Southern California, Los Angeles, CA 90089, USA; e-mail: ridder@usc.edu.
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Abstract

Ridder (1990, Review of Economic Studies 57, 167–182) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder’s proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at 0 and ∞. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the nonparametric identification of the GAFT and MPH models.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1229 - 1248
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Abbring, J.H. (2012, March) Mixed hitting-time models. Econometrica 80(2), 783–819.Google Scholar
Abbring, J.H. & Van den Berg, G.J. (2003) The identifiability of the mixed proportional hazards competing risks model. Journal of the Royal Statistical Society, Series B 65, 701–710.Google Scholar
Brinch, C.N. (2011) Non-parametric identification of the mixed proportional hazards model with interval-censored durations. Econometrics Journal 14(2), 343–350.CrossRefGoogle Scholar
Chen, S. (2002) Rank estimation of transformation models. Econometrica 70(4), 1683–1697.Google Scholar
Chiappori, P.-A., Komunjer, I., & Kristensen, D. (2013, March) Nonparametric Specification and Identification of Transformation Models. Mimeo, Department of Economics, Columbia University, New York, NY.Google Scholar
Cox, D.R. (1972) Regression models and life-tables (with discussion). Journal of the Royal Statistical Society 34, 187–220.Google Scholar
De Haan, L. (1970) On Regular Variation and Its Application to the Weak Convergence of Sample Extremes. Mathematical Centre.Google Scholar
Ekeland, I., Heckman, J.J., & Nesheim, L. (2004) Identification and estimation of hedonic models. Journal of Political Economy 112(1), S60–S109.Google Scholar
Elbers, C. & Ridder, G. (1982) True and spurious duration dependence: The identifiability of the proportional hazards model. Review of Economic Studies 49, 403–409.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, vol. II, 2nd ed. Wiley.Google Scholar
Heckman, J.J. & Honoré, B.E. (1989) The identifiability of the competing risks model. Biometrika 76, 325–330.Google Scholar
Heckman, J.J. & Singer, B. (1984) The identifiability of the proportional hazard model. Review of Economic Studies 51, 231–241.Google Scholar
Honoré, B.E. & de Paula, A. (2010) Interdependent durations. Review of Economic Studies 77(3), 1138–1163.CrossRefGoogle Scholar
Horowitz, J. (1996) Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64, 103–137.CrossRefGoogle Scholar
Jacho-Chavez, D., Lewbel, A., & Linton, O. (2010) Identification and nonparametric estimation of a transformed additively separable model. Journal of Econometrics 156(2), 392–407.CrossRefGoogle Scholar
Kortram, R., Lenstra, A., Ridder, G., & van Rooij, A. (1995) Constructive identification of the mixed proportional hazard model. Statistica Neerlandica 49, 269–281.CrossRefGoogle Scholar
Krantz, S.G. & Parks, H.R. (2002) A Primer of Real Analytic Functions. Birkhäuser.CrossRefGoogle Scholar
Lancaster, T. (1979) Econometric methods for the duration of unemployment. Econometrica 47, 939–956.Google Scholar
Ridder, G. (1990) The non-parametric identification of generalized accelerated failure-time models. Review of Economic Studies 57, 167–182.CrossRefGoogle Scholar
Ridder, G. & Woutersen, T. (2003) The singularity of the information matrix of the mixed proportional hazard model. Econometrica 71, 1579–1589.Google Scholar
Ye, J. & Duan, N. (1997) Nonparametric n -1/2-consistent estimation for the general transformation models. Annals of Statistics 25(6), 2682–2717.CrossRefGoogle Scholar