Inference on Quantile Treatment Effects with Small Treatment Groups
arXiv:2105.10965
Abstract
We develop inference for conditional quantile treatment effects that allows treatment groups to remain small as the overall sample grows. Such groups arise naturally in multivalued treatment models. Our procedure combines estimation of a conditional quantile function from a large reference group with an exact conditional Bernoulli representation of quantile indicators. We establish asymptotic size control and derive a power bound allowing treatment-group sizes to remain bounded. The framework accommodates nonseparable outcome functions, heteroskedasticity, and flexible error distributions across treatment profiles. We illustrate its scope through dynamic treatment models, nonseparable quantile models, and difference-in-differences designs with staggered adoption. Monte Carlo experiments assess finite-sample performance, and an application to temperature shocks and GDP growth illustrates inference on effects associated with distinct treatment histories.