Extremal Quantile Treatment Effects ∗ Job Market Paper

This paper establishes asymptotic theory and inference method for quantile treatment effect estimators when the quantile index is close or equal to zero. Such quantile treatment effects are of interest in many economic applications, such as the effect of maternal smoking on an infant’s adverse birth outcomes. When the quantile index is close to zero, the sparsity of data jeopardizes conventional asymptotic theory and bootstrap inference. When the quantile index is zero, there are no existing inference methods directly applicable in the treatment effect context. This paper establishes new estimation and inference theory for cases close or equal to zero. I illustrate the inference method with an application to estimate and test the effect of maternal smoking on the lower quantiles of infants’ birth weights.