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Unformatted text preview: Inference on Randomly Censored Regression Models Using Conditional Moment Inequalities * Shakeeb Khan and Elie Tamer December 2006 ABSTRACT. Under a conditional quantile restriction, randomly censored regression models can be written in terms of conditional moment inequalities . We study the identified features of these moment inequalities with respect to the regression parameters. These inequalities restrict the parameters to a set. We then show regular point identification can be achieved under a set of inter- pretable sufficient conditions. Our results generalize existing work on randomly censored models in that we allow for covariate dependent censoring, endogenous censoring and endogenous regres- sors. We then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content. Our method obviates the need for nonparametric estimation, which would require the selection of smoothing parameters and trimming procedures. Maintaining the point identification conditions, we propose a quantile minimum distance estimator which converges at the parametric rate and has an asymptotically normal distribution. A small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance. Key Words: Conditional Moment Inequality models, quantile minimum distance, covariate dependent censoring, heteroskedasticity, endogeneity. * We thank K. Hirano, B. Honor e, J. Powell, and A. Rosen as well as seminar participants at Arizona, Cornell, Duke, OSU, NYU, Princeton, Syracuse, UIUC, University of Virginia and the 2005 World Congress meetings of the Econometric Society for many helpful comments. Both authors also gratefully acknowledge support from the National Science Foundation. Any errors are our own. Department of Economics, Duke University, 213 Social Sciences Building, Durham, NC 27708. Phone: (919) 660-1873. Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208. Phone: (847) 491-8218. 1 Introduction Much of the recent econometrics, statistics, and biostatistics literature has been concerned with distribution-free estimation of the parameter vector in the linear regression model y = x + (1.1) where the dependent variable y is subject to censoring that can potentially be random. For example, in the duration literature, this model is known as the accelerated failure time 1 (or AFT) model where y , typically the logarithm of survival time, is right censored at varying censoring points due usually either to data collection limitations or competing risks. The semiparametric literature which studies variations of this model is quite extensive and can be classified by the set of assumptions that a given paper imposes on the joint dis- tribution of ( x, ,c ) where c is the censoring variable. Under very weak assumptions on this joint distribution, one strand of the literature gives up on point (or unique) identification of...
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08