Sensitivity Analysis for the Average Treatment Effect under Discrete Unobserved Confounders

2026-06-20

AI Summary

This study addresses the identification and sensitivity analysis of the average treatment effect (ATE) under discrete unobserved confounding by proposing a method grounded in the assumption of a finite number of latent types. By modeling the outcome distributions in both treatment and control groups as finite mixtures, the authors construct sharp bounds for the ATE and demonstrate that these bounds strictly improve upon the classical Manski bounds beyond a specific threshold, which grows only linearly with the number of mixture components. Integrating nonparametric identification theory with asymptotic inference, the paper develops an estimation and inference procedure with formal statistical guarantees. Empirical application to the LaLonde dataset yields substantially narrower ATE identification intervals, thereby enhancing the precision of causal inference.

Abstract

We model unobserved confounding through an unknown finite number of latent types. This assumption induces finite-mixture representations of the treated and control outcome distributions. Using the identified mixture components, we characterize the sharp identified set for the number of latent types and derive the sharp identified set for the average treatment effect (ATE) corresponding to each admissible value, thereby providing a natural framework for sensitivity analysis. We further obtain a cutoff beyond which the identified set for the ATE coincides with a version of the Manski bounds, whereas below the cutoff it is strictly smaller. This cutoff grows only linearly with the numbers of mixture components in the treated and control groups, although the maximum admissible number of latent types grows quadratically. We also provide estimation and inference procedures with asymptotic guarantees and illustrate our methodology using LaLonde's data.

Problem

• sensitivity analysis
• average treatment effect
• unobserved confounders
• latent types
• finite mixture

Innovation

• latent types
• finite mixture models
• sharp identified set
• sensitivity analysis
• average treatment effect