Skip to main content Accessibility help
×
Home

NONPARAMETRIC IDENTIFICATION OF ACCELERATED FAILURE TIME COMPETING RISKS MODELS

  • Sokbae Lee (a1) and Arthur Lewbel (a2)

Abstract

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.

Copyright

Corresponding author

*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.

References

Hide All
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, 701710.
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.
Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 17951843.
Andrews, D.W.K. & Schafgans, M.M.A. (1998) Semiparametric estimation of the intercept of a sample selection model. Review of Economic Studies 65, 497517.
Athey, S. & Haile, P.A. (2002) Identification of standard auction models. Econometrica 70(6), 21072140.
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), 201215.
Berger, M.S. (1977) Nonlinearity and Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis. Academic Press.
Bond, S.J. & Shaw, J.E.H. (2006) Bounds on the covariate-time transformation for competing risks survival analysis. Lifetime Data Analysis 12, 285303.
Buera, F.J. (2006) Non-parametric Identification and Testable Implications of the Roy Model. Working paper, Northwestern University and UCLA.
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, 55495632.
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289314.
Chernozhukov, V., Imbens, G., & Newey, W. (2007) Instrumental variable identification and estimation of nonseparable models via quantile conditions. Journal of Econometrics 139, 414.
Clayton, D. & Cuzick, J. (1985) Multivariate generalization of the proportional hazard model. Journal of the Royal Statistical Society, Series A 148, 82117.
Cox, D.R. (1962) Renewal Theory. Methuen.
Elbers, C. & Ridder, G. (1982) True and spurious duration dependence: The identifiability of the proportional hazard model. Review of Economic Studies 49, 403409.
Femanian, J.-D. (2003) Nonparametric estimation of competing risks models with covariates. Journal of Multivariate Analysis 85, 156191.
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.
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, 537617.
Gallant, A.R. & Nychka, D. (1987) Semi-non-parametric maximum likelihood estimation. Econometrica 55, 363390.
Han, A. & Hausman, J.A. (1990) Flexible parametric estimation of duration and competing risks models. Journal of Applied Econometrics 5, 128.
Heckman, J.J. (1990) Varieties of selection bias. American Economic Review 80, 313318.
Heckman, J.J. & Honoré, B.E. (1989) The identifiability of the competing risks model. Biometrika 76, 325–30.
Heckman, J.J. & Honoré, B.E. (1990) The empirical content of the Roy model. Econometrica 58, 11211149.
Honoré, B.E. & Lleras-Muney, A. (2006) Bounds in competing risks models and the war on cancer. Econometrica 74, 16751698.
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. 349. Cambridge University Press.
Khan, S. & Tamer, E. (2009) Inference on endogenously censored regression models using conditional moment inequalities. Journal of Econometrics 152, 104119.
Khan, S. & Tamer, E. (2010) Irregular identification, support conditions, and inverse weight estimation. Econometrica 78, 20212042.
Komunjer, I. (2012) Global identification in nonlinear models with moment restrictions. Econometric Theory 28, 719729.
Lee, S. (2006) Identification of a competing risks model with unknown transformations of latent failure times. Biometrika 93, 9961002.
Matzkin, R.L. (2007) Nonparametric identification. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics, vol. 6, p. 2, chap. 73, pp. 53075368. Elsevier.
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71, 15651578.
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, 1113.
Shen, X. (1997) On methods of sieves and penalization. Annals of Statistics 25, 25552591.
Tsiatis, A.A. (1975) A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences 72, 2022.
Zheng, M. & Klein, J.P. (1995) Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika 82, 127138.
Zeidler, E. (1986) Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems. Springer Verlag.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed