Instrumental variable quantile regression for clustered data

Abstract

The purpose is to enable inference in case of quantile regression with endogenous covariates and clustered data. It is proven that the instrumental variable quantile regression estimator is consistent where there is correlation of errors within clusters, and an asymptotic distribution for the estimator, which may be used for inference for a given quantile $\tau ,$ is derived. As regards inference based on the entire instrumental variable quantile regression process, it is proven that cluster-based resampling of a statistic of a certain class offers a computationally tractable approach for implementing asymptotic tests. The theoretical results concerning the asymptotic properties of the instrumental variable quantile regression estimator for clustered data are supported by simulation analysis. An empirical illustration shows the use of the proposed technique in order to estimate the earning equations of US men and women where female labor supply is endogenous and subject to the shock of World War II.