Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T04:07:43.713Z Has data issue: false hasContentIssue false

IDENTIFIABILITY OF THE SIGN OF COVARIATE EFFECTS IN THE COMPETING RISKS MODEL

Published online by Cambridge University Press:  03 October 2016

Simon M.S. Lo
Affiliation:
Lingnan University
Ralf A. Wilke*
Affiliation:
Copenhagen Business School
*
*Address correspondence to Ralf A. Wilke, Copenhagen Business School, Department of Economics, Porcelænshaven 16A, DK-2000, Frederiksberg; e-mail: [email protected].

Abstract

We present a new framework for the identification of competing risks models, which also include Roy models. We show that by establishing a Hicksian-type decomposition, the direction of covariate effects on the marginal distributions of the competing risks model can be identified under weak restrictions. Our approach leaves the marginal distributions and their joint distribution completely unspecified, except that the associated copula is invariant in the covariates. Results from simulations and two data examples suggest that our method often outperforms existing comparable approaches in terms of the range of durations for which the direction of the covariate effect is identified, particularly for long duration.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank the editor, a co-editor, two reviewers, Bernd Fitzenberger and Jaap Abbring for very useful comments and suggestions and Lutz Dümbgen for helpful discussions. Wilke is supported by the Economic and Social Research Council through the Bounds for Competing Risks Duration Models using Administrative Unemployment Duration Data (RES-061-25-0059) grant.

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, B 65, 701710.CrossRefGoogle Scholar
Alba-Ramirez, A., Arranz, J.M., & Munoz-Bullon, F. (2007) Exits from unemployment: Recall or new job. Labour Economics 14, 788810.CrossRefGoogle Scholar
Bond, S.J. & Shaw, J.E.H. (2006) Bounds on the covariate-time transformation for competing-risks survival analysis. Lifetime Data Analysis 12, 285303.CrossRefGoogle ScholarPubMed
Burda, M., Harding, M., & Hausman, J. (2015) A Bayesian semiparametric competing risk model with unobserved heterogeneity? Journal of Applied Econometrics 30, 353376.CrossRefGoogle Scholar
Butler, J.S., Anderson, K.H., & Burkhauser, R.V. (1989) Work and health after retirement: A competing risks model with semiparametric unobserved heterogeneity. The Review of Economics and Statistics 71, 4653.CrossRefGoogle Scholar
Cameron, A.C. & Trivedi, P.K. (2005) Microeconometrics. Cambridge University Press.CrossRefGoogle Scholar
Carling, K., Edin, P.A., Harkman, A., & Holmlund, B. (1996) Unemployment duration, unemployment benefits, and labor market programs in Sweden. Journal of Public Economics 59, 313334.CrossRefGoogle Scholar
Cox, D.R. (1962) Renewal Theory. Methuen and Co. Ltd.Google Scholar
D’Addio, A.C. & Rosholm, M. (2005) Exits from temporary jobs in Europe: A competing risks analysis. Labour Economics 12, 449468.CrossRefGoogle Scholar
Dabrowska, D.M. & Doksum, K.A. (1988) Estimation and testing in a two-sample generalized odds-rate model. Journal of the American Statistical Association 83, 744749.CrossRefGoogle Scholar
Dolton, P. & van der Klaauw, W. (1999) The turnover of teachers: A competing risks explanation. The Review of Economics and Statistics 81, 543552.CrossRefGoogle Scholar
Dorner, M., Heining, J., Jacobebbinghaus, P., & Seth, S. (2010) The sample of integrated labour market biographies. Schmollers Jahrbuch 130, 599608.CrossRefGoogle Scholar
Fermanian, J. (2003) Nonparametric estimation of competing risks models with covariates. Journal of Multivariate Anaysis 85, 156191.CrossRefGoogle Scholar
Heckman, J. & Honoré, B. (1989) The identifiability of the competing risks model. Biometrika 76, 325330.CrossRefGoogle Scholar
Heckman, J. & Honoré, B. (1990) The empirical content of the Roy model. Econometrica 58, 11211149.CrossRefGoogle Scholar
Heckman, J. & Singer, B. (1984) A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52, 271320.CrossRefGoogle Scholar
Henry, M. & Mourifie, I. (2014) Sharp Bounds in the Binary Roy Model. Working paper, Department of Economics, University of Toronto.Google Scholar
Honoré, B. & Lleras-Muney, A. (2006) Bounds in competing risks models and the war on cancer. Econometrica 74, 16751698.CrossRefGoogle Scholar
Kalbfleisch, J.D. & Prentice, R.L. (2002) The Statistical Analysis of Failure Time Data. Wiley.CrossRefGoogle Scholar
Lee, S. & Lewbel, A. (2013) Nonparametric identification of accelerated failure time competing risks models. Econometric Theory 29, 905919.CrossRefGoogle Scholar
Lo, S.M.S. & Wilke, R.A. (2010) A copula model for dependent competing risks. Journal of the Royal Statistical Society, C 59, 359376.CrossRefGoogle Scholar
Lo, S.M.S. & Wilke, R.A. (2011) Identifiability and Estimation of the Sign of a Covariate Effect in the Competing Risks Model. Discussion papers in Economics, No. 11/03, University of Nottingham, UK.CrossRefGoogle Scholar
McCall, B.P. (1996) Unemployment insurance rules, joblessness and part-time work. Econometrica 64, 647682.CrossRefGoogle Scholar
Mealli, F. & Pudney, S. (1996) Occupational pensions and job mobility in Britain: Estimation of a random-effects competing risks model. Journal of Applied Econometrics 11, 293320.Google Scholar
Meghir, C. & Whitehouse, E. (1997) Labour market transitions and retirement of men in the UK. Journal of Econometrics 79, 327354.CrossRefGoogle Scholar
Nelsen, R.B. (2006) An Introduction to Copulas, 2nd ed. Springer.Google Scholar
Park, B.G. (2015) Nonparametric Identification and Estimation of the Extended Roy Model. Working paper, Department of Economics, Suny Albany.Google 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 Science 73, 1113.CrossRefGoogle ScholarPubMed
Rivest, L. & Wells, M.T. (2001) A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. Journal of Multivariate Analysis 79, 138155.CrossRefGoogle Scholar
Roy, A.D. (1951) Some thoughts on the distribution of earnings. Oxford Economic Papers (New Series) 3, 135146.CrossRefGoogle Scholar
Schweizer, B. & Sklar, A. (1983) Probabilistic Metric Spaces. North-Holland.Google Scholar
Steiner, V. (2001) Unemployment persistence in the West German labor market: Negative duration dependence or sorting? Oxford Bulletin of Economics and Statistics 63, 91113.CrossRefGoogle Scholar
Tsiatis, A. (1975) A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences 72, 2022.CrossRefGoogle ScholarPubMed
Zheng, M. & Klein, J.P. (1995) Estimates of marginal survival for dependent competing risks based on assumed copula. Biometrika 82, 127138.CrossRefGoogle Scholar
Supplementary material: PDF

Lo and Wilke supplementary material

Lo and Wilke supplementary material

Download Lo and Wilke supplementary material(PDF)
PDF 86.3 KB