Quantile Regression with Clustered Data

We study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.