This paper considers models for unobservables in duration models. It demonstrates how cross-section and time-series variation in regressors facilitates identification of single-spell, competing risks and multiple spell duration models. We also demonstrate the limited value of traditional identification studies by considering a case in which a model is identified in the conventional sense but cannot be consistently estimated.
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References
1.
David HA, Moeschberger MLThe theory of competing risks. High Wycombe: Griffin, 1978.
2.
Kalbfleisch JD, Prentice RLThe statistical analysis of failure time data. New York : Wiley, 1980.
3.
Cox DR, Oakes D.Analysis of survival data. London: Chapman and Hall, 1984.
4.
Flinn CJ, Heckman JJAre unemployment and out of the labor force behaviorally distinct labor force states?Journal of Labor Economics1983; 1: 28-42.
5.
Cox DRRenewal theory. London: Methuen , 1962.
6.
Tsiatis A.A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences1975; 72: 20-2.
7.
Yashin AI, Manton KG, Stallard E.Dependent competing risks: a stochastic process model. Journal of MathematicalBiology1986; 24: 119-64.
8.
Flinn CJ, Heckman JJModels for the analysis of labor force dynamics. In Advances in econometrics, 1, Ed. Bassman R, Rhodes G, 35-95, Greenwich, CT: JAI Press, 1982.
9.
Basu AP, Ghosh JKIdentifiability of the multinormal and other distributions under competing risks model. Journal of MultivariateAnalysis1978; 8: 413-29.
10.
Arnold B., Brockett P.Identifiability for dependent multiple decrement/competing risk models. Scandinavian Actuarial Journal1983; 10: 117-27.
11.
Heckman JJ, Honoré B.The identifiability of the competing risks model. Biometrika1989; 76: 325-30.
12.
Cox DRRegression models and life-tables (with discussion). Journal of the Royal Statistical Society Series B 1972; 34: 187-202.
13.
Flinn CJ, Heckman JJThe likelihood function for the multistate-multiepisode model in 'Models for the analysis of labor force dynamics'. In Advances in econometrics , 3, Ed. Bassman R, Rhodes G. pp. 225-31, Greenwich, CT: JAI Press, 1983.
14.
Clayton D., Cuzick J.Multivariate generalizations of the proportional hazard model. Journal of the Royal Statistical Society Series A 1985; 148: 82-117.
15.
Manton KG, Stallard E., Woodbury M.Chronic disease evolution and human aging: a general model for assessing the impact of chronic disease in human populations. International Journal ofMathematical Modelling1986; 17: 406-52.
16.
Elbers C., Ridder G.True and spurious duration dependence: the identifiability of the proportional hazard model. Review of Economic Studies1982 ; 49: 403-10.
17.
Heckman JJ, Singer B.The identifiability of the proportional hazard model. Review of Economic Studies1984; 51(2): 231-43.
18.
Honoré B.Identification of duration models with unobserved heterogeneity. Unpublished manuscript, Northwestern University, 1990.
19.
Feller W.An introduction to probability theory and its applications. New York: Wiley, Vol. II, 1971.
20.
Heckman JJ, Singer B.Social science duration analysis. In Longitudinal analysis of labor market data. Ed. Heckman JJ, Singer B.New York: Cambridge University Press, 1985.
21.
Ridder G.The non-parametric identification of generalized hazard models. Review of Economic Studies1990; 57: 167-82.
22.
Heckman JJIdentifying the hand of past: distinguishing state dependence from heterogeneity. American Economic Review. Papers and Proceedings1991; 106(3): 75-79.
23.
Yashin AI, Arjas A.A note on random intensities and conditional survivor functions. Journal of Applied Probability1988; 25: 630-35.
24.
McCall B.Identifying state dependence in duration models with time-varying regressors, Industrial Relations Section. University of Minnesota, 1993.
25.
McCall B.The identifiability of the mixed proportional hazards model with time-coefficients, unpublished manuscript, Industrial Relations Section, University of Minnesota, 1993.
26.
Honoré B.Identification results for duration models with multiple spells. Review of Economic Studies1993; 60(1): 241-46.
27.
Heckman JJ, Hotz VJ, Walker JRNew evidence on the timing and spacing of births. American Economic Review1985; 72: 179-84.
28.
Heckman JJ, Borjas GJDoes unemployment cause future unemployment? Definitions, questions and answers for a continuous time model of heterogeneity and state dependence. Economica1980; 47: 247-83.
29.
Kiefer J., Wolfowitz J.Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics1956; 27: 363-66.
30.
Heckman JJ, Singer B.A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica1984 ; 52(2): 271-320.
31.
Meyer B.Semiparametric estimation of hazard models. Econometrica1992; 60(3): 64-67.
32.
Honoré 1993. Rates of convergence in Weibull mixture models , unpublished manuscript, Northwestern, 1993 .
33.
Ishwaran H.Rates of convergence in semiparametric mixture models, published Ph.D. Thesis , Yale University, Department of Statistics, 1993.
34.
Lindsey B.The geometry of mixture likelihoods, Part I. Annals of Statistics1983; 11: 86-94.
35.
Lindsey B.The geometery of mixture likelihoods, Part II. Annals of Statistics1983; 11(3): 783-92.
36.
Heckman JJ, Robb R., Walker J.Testing the mixture of exponentials hypothesis and estimating the mixing distribution by the method of moments. Journal of The American Statistical Association1990; 85: 410, 582-89.
37.
Honoré B.Simple estimation of a duration model with unobserved heterogeneity. Econometrica1990; 58: 453-74.
38.
Heckman JJ, Walker J.The relationship between wages and income and the timing and spacing of births: evidence from Swedish longitudinal data. Econometrica1990; 58(6): 1411-41.
39.
Steinberg D., Colla P. "CTM" A supplementary module for SYSTA T. Evanston, Illinois: SYSTAT, 1994.
40.
Heckman JJ, Taber C.Identification in binary choice models and their extensions, unpublished manuscript , University of Chicago, 1994.