Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

This paper examines inference for quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). We derive the limiting distribution of the QTE estimator under MPDs and highlight the difficulty of analytical inference due to parameter tuning. We show that a naive weighted bootstrap fails to approximate the limiting distribution of the QTE estimator under MPDs because it ignores the dependence structure within the matched pairs. We then propose two bootstrap methods that can consistently approximate that limiting distribution: the gradient bootstrap and the weighted bootstrap of the inverse propensity score weighted (IPW) estimator. The gradient bootstrap is free of tuning parameters but requires the knowledge of pairs’ identities. The weighted bootstrap of the IPW estimator does not require such knowledge but involves one tuning parameter. Both methods are straightforward to implement and able to provide pointwise confidence intervals and uniform confidence bands that achieve exact limiting rejection probabilities under the null. We illustrate their finite sample performance using both simulations and a well-known dataset on microfinance.