Quantile regression with aggregated data

Administrative data can contain a wealth of information for empirical research. Just to cite two examples, administrative data on schools can be used to study pupils’ educational attainments while hospital data can be useful for health research. However, access to administrative information is often restricted to aggregated data and this can lead to biased results. The estimation bias caused by using aggregated rather than individual data is known
as the ecological bias. In this paper we consider for the first time this issue in the context of quantile regressions. We show how data can be aggregated to obtain unbiased estimation of quantile regressions with categorical covariates and how the bias can be reduced when researchers are interested to estimate quantile regression where some of the covariates are continuous.