🤖 AI Summary
This paper addresses the robustness challenge of average treatment effect on the treated (ATT) estimation under the no-unconfoundedness assumption when high-dimensional covariates or poor overlap undermine conventional methods. We propose a finite-information aggregation estimation framework situated between Manski’s bounds and inverse probability weighting (IPW). Our approach integrates a constrained dependence function design with a variant of IPW to jointly achieve robustness against model misspecification and efficiency in information utilization. We establish asymptotically valid interval estimation theory for the resulting estimator. Simulation studies and empirical applications demonstrate that the proposed method substantially tightens the identification bounds, exhibits superior robustness to increasing covariate dimensionality and overlap deficiency, and consistently outperforms both classical Manski bounds and standard IPW estimators in finite-sample performance.
📝 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 an empirical application that our bounds are indeed robust and informative in practice.