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. It is shown that both the naive multiplier bootstrap and the naive multiplier bootstrap of the pairs fail to approximate the limit distribution of the QTE estimator under MPDs because they do not preserve 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 multiplier 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 multiplier 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 macroinsurance .
This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities .
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We derive the limit distribution of the QTE estimator under MPDs, highlighting the difficulties that arise in analytical inference due to parameter tuning. It is shown that both the naive multiplier bootstrap and the naive multiplier bootstrap of the pairs fail to approximate the limit distribution of the QTE estimator under MPDs because they do not preserve the dependence structure within the matched pairs. To address this difficulty we propose
Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes
R
: the gradient bootstrap and
of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially,
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multiplier bootstrap of the
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(IPW) estimator. The gradient bootstrap is free of tuning parameters but requires knowledge of the pair identities. The multiplier 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 macroinsurance
multiplier bootstrap can be implemented without knowledge of pair identities