Local average causal effects and superefficiency

TL;DR

This paper demonstrates that adapting the inferential target based on data can lead to significant gains in precision when estimating local average causal effects, especially in the presence of heterogeneity.

Contribution

It shows that data-adaptive targeting of causal effects can achieve superefficiency, enhancing statistical certainty in causal inference.

Findings

Data-adaptive local effects can be estimated with superefficiency.

Asymptotically normal estimators are superefficient for local effects.

Fundamental gains in certainty arise from flexibility in the inferential target.

Abstract

Recent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root-$n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect. Our result illustrates the fundamental gain in statistical certainty afforded by indifference about the inferential target.