A Causal Bootstrap

TL;DR

This paper introduces a bootstrap method tailored for causal estimands, addressing the unique uncertainty source from treatment variability rather than sampling, and compares it to the classical bootstrap.

Contribution

It develops a novel bootstrap procedure that accounts for treatment assignment randomness in causal inference, extending traditional bootstrap methods.

Findings

The causal bootstrap better captures treatment-related uncertainty.

It provides more accurate confidence intervals for causal estimands.

The method shows improved performance over classical bootstrap in causal settings.

Abstract

The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling uncertainty. We argue that for causal estimands the uncertainty arises entirely, or partially, from a different source, corresponding to the stochastic nature of the treatment received. We develop a bootstrap procedure that accounts for this uncertainty, and compare its properties to that of the classical bootstrap.