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

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). We derive the limit distribution of the QTE estimator under MPDs, highlighting the difficulties that arise in analytical inference due to parameter tuning. We show that the naïve weighted bootstrap fails to approximate the limit distribution of the QTE estimator under MPDs because it ignores the dependence structure within the matched pairs.To address this difficulty we propose two bootstrap methods that can consistently approximate the limit 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 knowledge of the pair 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 coverage rates. We demonstrate their finite sample performance using simulations and provide an empirical application to a well-known dataset in microfinance.