Two-stage rank estimation of quantile index models

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This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246-269; Annals of Statistics 19 (1991b) 760-777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model. © 2001 Elsevier Science S.A. All rights reserved.






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Khan, S (2001). Two-stage rank estimation of quantile index models. Journal of Econometrics, 100(2). pp. 319–355. 10.1016/S0304-4076(00)00040-3 Retrieved from

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Shakeeb Khan

Professor of Economics

Professor Khan is on leave at Boston College for the 2016-17 academic year.

Professor Khan specializes in the fields of mathematical economics, statistics, and applied econometrics. His studies have explored a variety of subjects from covariate dependent censoring and non-stationary panel data, to causal effects of education on wage inequality and the variables affecting infant mortality rates in Brazil. He was awarded funding by National Science Foundation grants for his projects entitled, “Estimation of Binary Choice and Nonparametric Censored Regression Models” and “Estimation of Cross-Sectional and Panel Data Duration Models with General Forms of Censoring.” He has published numerous papers in leading academic journals, including such writings as, “Heteroskedastic Transformation Models with Covariate Dependent Censoring” with E. Tamer and Y. Shin; “The Identification Power of Equilibrium in Simple Games;” “Partial Rank Estimation of Duration Models with General Forms of Censoring” with E. Tamer; and more. He is currently collaborating with D. Nekipelov and J.L. Powell on the project, “Optimal Point and Set Inference in Competing Risk Models;” with A. Lewbel on, “Identification and Estimation of Stochastic Frontier Models;” and with E. Tamer on, “Conditional Moment Inequalities in Roy Models with Cross-Section and Panel Data.”

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