Estimating and testing a quantile regression model with interactive effects

This paper proposes a quantile regression estimator for a model with interactive effects potentially correlated with covariates. We provide conditions under which the estimator is asymptotically Gaussian and we investigate the finite sample performance of the method. An approach to testing the specification against a competing fixed effects specification is introduced. The paper presents an application to study the effect of class size and composition on educational attainment. The evidence suggests that while smaller classes are beneficial for low performers, larger classes are beneficial for high performers. The fixed effects specification is rejected in favor of the interactive effects specification.