An Investigation into the Bias and Variance of Almost Matching Exactly Methods

The development of interpretable causal estimation methods is a fundamental problem for high-stakes decision settings in which results must be explainable. Matching methods are highly explainable, but often lack the accuracy of black-box nonparametric models for causal effects. In this work, we propose to investigate theoretically the statistical bias and variance of Almost Matching Exactly (AME) methods for causal effect estimation. These methods aim to overcome the inaccuracy of matching by learning on a separate training dataset an optimal metric to match units on. While these methods are both powerful and interpretable, we currently lack an understanding of their statistical properties. In this work we present a theoretical characterization of the finite-sample and asymptotic properties of AME. We show that AME with discrete data has bounded bias in finite samples, and is asymptotically normal and consistent at a root-n rate. Additionally, we show that AME methods for matching on networked data also have bounded bias and variance in finite-samples, and achieve asymptotic consistency in sparse enough graphs. Our results can be used to motivate the construction of approximate confidence intervals around AME causal estimates, providing a way to quantify their uncertainty.