Quantile regression with a one-sided misclassified binary regressor

Addressing misreporting of participation in social programs, which is common and has increased in all major surveys, is important to study intergenerational effects of policies. In this paper we propose a practical estimator for a quantile regression model with endogenous one-sided misreporting. The identification of the model uses a parametric first stage and information related to participation and misreporting. We show that the estimator is consistent and asymptotically normal. We also establish that a bootstrap procedure is asymptotically valid for approximating the distribution of the estimator. Simulation studies show the small sample behavior of the estimator in comparison with other methods. Finally, we illustrate the approach using U.S. survey data to estimate the intergenerational effect of a mother’s participation on welfare on her daughter’s adult income.