Overlap in Observational Studies with High-Dimensional Covariates

TL;DR

This paper investigates how the overlap assumption in high-dimensional observational studies limits covariate distribution differences, revealing that high dimensionality makes satisfying overlap more challenging and affects causal inference validity.

Contribution

It formalizes the impact of high dimensionality on overlap, deriving bounds on covariate imbalance using information theory, and discusses implications for causal inference methods.

Findings

Overlap constraints tighten as covariate dimension increases

Explicit bounds on covariate imbalance are derived

High-dimensional settings pose challenges for causal assumptions

Abstract

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming.