Overlap in observational studies with high-dimensional covariates

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