Ridder and Woutersen (Ridder, G., and T. Woutersen. 2003. “The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model.” Econometrica 71: 1579–1589) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the linear rank estimator (LRE) of Tsiatis (Tsiatis, A. A. 1990. “Estimating Regression Parameters using Linear Rank Tests for Censored Data.” Annals of Statistics 18: 354–372) and Robins and Tsiatis (Robins, J. M., and A. A. Tsiatis. 1992. “Semiparametric Estimation of an Accelerated Failure Time Model with Time-Dependent Covariates.” Biometrika 79: 311–319) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.
Aalen, O. O., O. Borgan, and H. K. Gjessing. 2009. Survival and Event History Analysis. New York: Springer Verlag.
Amemiya, T. 1974. “The Nonlinear Two-Stage Least-Squares Estimator.” Journal of Econometrics 2: 105–110.
Amemiya, T. 1985. “Instrumental Variable Estimation for the Nonlinear Errors-in-Variables Model.” Journal of Econometrics 28: 273–289.
Andersen, P. K., O. Borgan, R. D. Gill, and N. Keiding. 1993. Statistical Models Based on Counting Processes. New York: Springer Verlag.
Baker, M., and A. Melino. 2000. “Duration Dependence and Nonparametric Heterogeneity: A Monte Carlo Study.” Journal of Econometrics 96: 357–393.
Bearse, P., J. Canals-Cerda, and P. Rilstone. 2007. “Efficient Semiparametric Estimation of Duration Models with Unobserved Heterogeneity.” Econometric Theory 23: 281–308.
Bijwaard, G. E. 2009. “Instrumental Variable Estimation for Duration Data.” In Causal Analysis in Population Studies: Concepts, Methods, Applications, edited by H. Engelhardt, H.-P. Kohler, and A. Fürnkranz-Prskawetz, 111–148. New York: Springer Verlag.
Bijwaard, G. E. 2010. “Immigrant Migration Dynamics Model for The Netherlands.” Journal of Population Economics 23: 1213–1247.
Bijwaard, G. E., and G. Ridder. 2005. “Correcting for Selective Compliance in a Re–employment Bonus Experiment.” Journal of Econometrics 125: 77–111.
Bijwaard, G. E., C. Schluter, and J. Wahba. 2013. “The Impact of Labour Market Dynamics on the Return–Migration of Immigrants.” Review of Economics & Statistics, forthcoming.
Chen, S. 2002. “Rank Estimation of Transformation Models.” Econometrica 70: 1683–1697.
Chiaporri, P. A., and B. Salanie. 2000. “Testing for Asymmetric Information in Insurance Markets.” Journal of Political Economy 108: 56–78.
Cox, D. R., and D. Oakes. 1984. Analysis of Survival Data. London: Chapman and Hall.
Elbers, C., and G. Ridder. 1982. “True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model.” Review of Economic Studies 49: 403–410.
Feller, W. 1971. An Introduction to Probability Theory and its Applications. 3rd ed. John Wiley and Sons.
Hahn, J. 1994. “The Efficiency Bound of the Mixed Proportional Hazard Model.” Review of Economic Studies 61: 607–629.
Han, A. K. 1987. “Non–parametric Analysis of a Generalized Regression Model: The Maximum Rank Correlation Estimator.” Journal of Econometrics 35: 303–316.
Hausman, J. A., and T. Woutersen. 2005. “Estimating a Semi–Parametric Duration Model without Specifying Heterogeneity.” CeMMAP, working paper, CWP11/05.
Heckman, J. J. 1991. “Identifying the Hand of the Past: Distinguishing State Dependence from Heterogeneity.” American Economic Review 81: 75–79.
Heckman, J. J., and B. Singer. 1984a. “Econometric Duration Analysis.” Journal of Econometrics 24: 63–132.
Heckman, J. J., and B. Singer. 1984b. “A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data.” Econometrica 52: 271–320.
Honoré, B. E. 1990. “Simple Estimation of a Duration Model with Unobserved Heterogeneity.” Econometrica 58: 453–473.
Horowitz, J. L. 1996. “Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable.” Econometrica 64: 103–137.
Horowitz, J. L. 1999. “Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity.” Econometrica 67: 1001–1018.
Horowitz, J. L. 2001. The Bootstrap in Handbook of Econometrics, Vol. 5, edited by J. J. Heckman and E. Leamer. North-Holland: Amsterdam.
Khan, S. 2001. “Two Stage Rank Estimation of Quantile Index Models.” Journal of Econometrics 100: 319–355.
Khan, S., and E. Tamer. 2007. “Partial Rank Estimation of Duration Models with General forms of Censoring.” Journal of Econometrics 136: 251–280.
Klein, J. P., and M. L. Moeschberger. 1997. Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer Verlag.
Lai, T. L., and Z. Ying. 1991. “Rank Regression Methods for Left–Truncated and Right-Censored Data.” Annals of Statistics 19: 531–556.
Lancaster, T. 1976. “Redundancy, Unemployment and Manpower Policy: A Comment.” Economic Journal 86: 335–338.
Lancaster, T. 1979. “Econometric Methods for the Duration of Unemployment.” Econometrica 47: 939–956.
Lin, D. Y., and Z. Ying. 1995. “Semiparametric Inference for the Accelerated Life Model with Time-Dependent Covariates.” Journao of Statistical Planning and Inference 44: 47–63.
Lindsay, B. G. 1983. “The Geometry of Mixture Likelihoods: A General Theory.” Annals of Statistics 11: 86–94.
Manton, K. G., E. Stallard, and J. W. Vaupel. 1981. “Methods for the Mortality Experience of Heterogeneous Populations.” Demography 18: 389–410.
Meyer, P. 1963. “Decomposition of Supermartingales: The Uniqueness Theorem.” Illinois Journal of Mathematics 7: 1–17.
Newey, W. K., and D. McFadden. 1994. “Large Sample Estimation and Hypothesis Testing.” In Handbook of Econometrics,Vol. 4, edited by R. F. Engle and D. MacFadden. North-Holland: Amsterdam.
Powell, M. J. D. 1964. “An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives.” The Computer Journal 7: 155–162.
Prentice, R. L. 1978. “Linear Rank Tests with Right Censored Data.” Biometrika 65: 167–179.
Press, W. H., B. P. Flannert, S. A. Teukolsky, and W. T. Vetterling. 1986. Numerical Recipes: The Art of Scientific Computing. Cambridge: Cambridge University Press.
Protter, P. 2005. Stochastic Integration and Differential Equations. New York: Springer Verlag, 107–113.
Ramlau-Hansen, H. 1983. “Smoothing Counting Process Intensities by Means of Kernel Functions.” Annals of Statistics 11: 453–466.
Ridder, G., and T. Woutersen. 2003. “The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model.” Econometrica 71: 1579–1589.
Robins, J. M., and A. A. Tsiatis. 1992. “Semiparametric Estimation of an Accelerated Failure Time Model with Time-Dependent Covariates.” Biometrika 79: 311–319.
Sherman, R. P. 1993. “The Limiting Distribution of the Maximum Rank Correlation Estimator.” Econometrica 61: 123–137.
Therneau, T., and P. Grambsch. 2000. Modeling Survival Data: Extending the Cox Model. New York: Springer Verlag.
Tsiatis, A. A. 1990. “Estimating Regression Parameters using Linear Rank Tests for Censored Data.” Annals of Statistics 18: 354–372.
van der Vaart, A. W. 1998. Asymptotic Statistics. Cambridge: Cambridge University Press.
Wooldridge, J. M. 2005. “Unobserved Heterogeneity and Estimation of Average Partial Effects.” In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, edited by D. W. K. Andrews and J. H. Stock, 27–55. Cambridge University Press.
Woutersen, T. 2000. Consistent Estimators for Panel Duration Data with Endogenous Censoring and Endogenous Regressors. Dissertation Brown University.
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