Bounding Treatment Effects by Pooling Limited Information across Observations

TL;DR

This paper introduces robust bounds on average treatment effects that balance limited and extensive information pooling across observations, applicable even under challenging conditions like large covariate spaces or overlap violations.

Contribution

It proposes a novel method for constructing treatment effect bounds using limited pooling of information, bridging Manski bounds and inverse propensity score weighting.

Findings

Bounds are robust in scenarios with many covariates or overlap issues.

Monte Carlo experiments demonstrate the bounds' practical robustness and informativeness.

Empirical applications show the bounds' usefulness in real-world data analysis.

Abstract

We provide novel bounds on average treatment effects (on the treated) that are valid under an unconfoundedness assumption. Our bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on a large number of different values in the observed sample, or when the overlap condition is violated. This robustness is achieved by only using limited "pooling" of information across observations. Namely, the bounds are constructed as sample averages over functions of the observed outcomes such that the contribution of each outcome only depends on the treatment status of a limited number of observations. No information pooling across observations leads to so-called "Manski bounds", while unlimited information pooling leads to standard inverse propensity score weighting. We explore the intermediate range between these two extremes and provide corresponding inference methods. We show in Monte Carlo experiments and through two empirical application that our bounds are indeed robust and informative in practice.