Instrumental Variable Quantile Regression For Clustered Data

The purpose of the paper is to enable inference in case of quantile regression with endogenous covariates and clustered data. We prove that the instrumental variable quantile regression estimator is consistent where there is correlation of errors within clusters. We derive an asymptotic distribution for the estimator, which may be used for inference for a given tau. As regards inference based on the entire instrumental variable quantile regression process, we prove that cluster-based bootstrapping of a statistic of a certain class offers a computationally tractable approach for implementing asymptotic tests. Our theoretical results concerning the asymptotic properties of the instrumental variable quantile regression estimator for clustered data are supported by simulation analysis. The empirical part of the paper applies the technique to estimation of the earning equations of US men and women where female labor supply is endogenous and subject to the shock of World War II