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Quantile Regression With Censoring And Endogeneity

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Executive Summary

In this paper, the authors develop a new Censored Quantile Instrumental Variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) Censored Quantile Regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity.

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