Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T23:26:58.581Z Has data issue: false hasContentIssue false
  • English
  • Français

NONPARAMETRIC IDENTIFICATION OF ACCELERATED FAILURE TIME COMPETING RISKS MODELS

Published online by Cambridge University Press:  21 February 2013

Sokbae Lee  and
Arthur Lewbel
Sokbae Lee*
Affiliation:
Seoul National University
Arthur Lewbel
Affiliation:
Boston College
*
*Address correspondence to Sokbae Lee, Department of Economics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-742, Republic of Korea; e-mail: sokbae@snu.ac.kr.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We provide new conditions for identification of accelerated failure time competing risks models. These include Roy models and some auction models. In our setup, unknown regression functions and the joint survivor function of latent disturbance terms are all nonparametric. We show that this model is identified given covariates that are independent of latent errors, provided that a certain rank condition is satisfied. We present a simple example in which our rank condition for identification is verified. Our identification strategy does not depend on identification at infinity or near zero, and it does not require exclusion assumptions. Given our identification, we show estimation can be accomplished using sieves.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 5 , October 2013 , pp. 905 - 919
Copyright
Copyright © Cambridge University Press 2013 

Footnotes

We would like to thank Xiaohong Chen for very helpful discussions at the early stage of this project. We also would like to thank Hidehiko Ichimura, Ivana Komunjer, Rosa Matzkin, Whitney Newey, Jean-Marc Robin, Elie Tamer, and two anonymous referees for helpful comments. This work was supported by the Economic and Social Research Council for the ESRC Centre for Microdata Methods and Practice (RES-589-28-0001) and a small research grant (RES-000-22-2761), by a European Research Council grant (ERC-2009-StG-240910-ROMETA), and by the National Research Foundation of Korea grant funded by the Korean Government (NRF-2011-327-B00073).

References

REFERENCES

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.CrossRefGoogle Scholar
Abbring, J.H. & Van den Berg, G.J. (2005) Social Experiments and Instrumental Variables with Duration Outcomes. Tinbergen Institute discussion paper TI 2005-047/3.Google Scholar
Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795–1843.CrossRefGoogle Scholar
Andrews, D.W.K. & Schafgans, M.M.A. (1998) Semiparametric estimation of the intercept of a sample selection model. Review of Economic Studies 65, 497–517.CrossRefGoogle Scholar
Athey, S. & Haile, P.A. (2002) Identification of standard auction models. Econometrica 70(6), 2107–2140.CrossRefGoogle Scholar
Bayer, P.J., Khan, S., & Timmins, C. (2011) Nonparametric identification and estimation in a Roy model with common nonpecuniary returns. Journal of Business and Economic Statistics 29(2), 201–215.CrossRefGoogle Scholar
Berger, M.S. (1977) Nonlinearity and Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis. Academic Press.Google Scholar
Bond, S.J. & Shaw, J.E.H. (2006) Bounds on the covariate-time transformation for competing risks survival analysis. Lifetime Data Analysis 12, 285–303.Google ScholarPubMed
Buera, F.J. (2006) Non-parametric Identification and Testable Implications of the Roy Model. Working paper, Northwestern University and UCLA.Google Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. In J.J. Heckman & E.E. Leamer (eds.), Handbook of Econometrics, vol. 6B, chap. 76, 5549–5632.CrossRefGoogle Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289–314.CrossRefGoogle Scholar
Chernozhukov, V., Imbens, G., & Newey, W. (2007) Instrumental variable identification and estimation of nonseparable models via quantile conditions. Journal of Econometrics 139, 4–14.CrossRefGoogle Scholar
Clayton, D. & Cuzick, J. (1985) Multivariate generalization of the proportional hazard model. Journal of the Royal Statistical Society, Series A 148, 82–117.CrossRefGoogle Scholar
Cox, D.R. (1962) Renewal Theory. Methuen.Google Scholar
Elbers, C. & Ridder, G. (1982) True and spurious duration dependence: The identifiability of the proportional hazard model. Review of Economic Studies 49, 403–409.CrossRefGoogle Scholar
Femanian, J.-D. (2003) Nonparametric estimation of competing risks models with covariates. Journal of Multivariate Analysis 85, 156–191.CrossRefGoogle Scholar
Fox, J. T. & Gandhi, A. (2009) Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures. Working paper, University of Chicago and University of Wisconsin.CrossRefGoogle Scholar
French, E. & Taber, C. (2011) Identification of models of the labor market. In Ashenfelter, O. & Card, D. (eds.), Handbook of Labor Economics, vol. 4A, chap. 6, 537–617.Google Scholar
Gallant, A.R. & Nychka, D. (1987) Semi-non-parametric maximum likelihood estimation. Econometrica 55, 363–390.Google Scholar
Han, A. & Hausman, J.A. (1990) Flexible parametric estimation of duration and competing risks models. Journal of Applied Econometrics 5, 1–28.CrossRefGoogle Scholar
Heckman, J.J. (1990) Varieties of selection bias. American Economic Review 80, 313–318.Google Scholar
Heckman, J.J. & Honoré, B.E. (1989) The identifiability of the competing risks model. Biometrika 76, 325–30.CrossRefGoogle Scholar
Heckman, J.J. & Honoré, B.E. (1990) The empirical content of the Roy model. Econometrica 58, 1121–1149.CrossRefGoogle Scholar
Honoré, B.E. & Lleras-Muney, A. (2006) Bounds in competing risks models and the war on cancer. Econometrica 74, 1675–1698.CrossRefGoogle Scholar
Ichimura, H. & Lee, L.-F. (1991) Semiparametric least squares estimation of multiple index models: single equation estimation. In Barnett, W.A., Powell, J., & Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 3–49. Cambridge University Press.Google Scholar
Khan, S. & Tamer, E. (2009) Inference on endogenously censored regression models using conditional moment inequalities. Journal of Econometrics 152, 104–119.Google Scholar
Khan, S. & Tamer, E. (2010) Irregular identification, support conditions, and inverse weight estimation. Econometrica 78, 2021–2042.Google Scholar
Komunjer, I. (2012) Global identification in nonlinear models with moment restrictions. Econometric Theory 28, 719–729.CrossRefGoogle Scholar
Lee, S. (2006) Identification of a competing risks model with unknown transformations of latent failure times. Biometrika 93, 996–1002.CrossRefGoogle Scholar
Matzkin, R.L. (2007) Nonparametric identification. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics, vol. 6, p. 2, chap. 73, pp. 5307–5368. Elsevier.CrossRefGoogle Scholar
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Peterson, A.V. (1976) Bounds for a joint distribution with fixed sub-distribution functions: Application to competing risks. Proceedings of the National Academy of Sciences 73, 11–13.CrossRefGoogle ScholarPubMed
Shen, X. (1997) On methods of sieves and penalization. Annals of Statistics 25, 2555–2591.Google Scholar
Tsiatis, A.A. (1975) A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences 72, 20–22.Google ScholarPubMed
Zheng, M. & Klein, J.P. (1995) Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika 82, 127–138.CrossRefGoogle Scholar
Zeidler, E. (1986) Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems. Springer Verlag.CrossRefGoogle Scholar