The Role of Confounders and Linearity in Ecological Inference: A Reassessment
Shiro Kuriwaki, Cory McCartan
TL;DR
This paper reframes ecological inference (EI) as a specific instance of causal inference and linear regression, highlighting that confounding must be addressed for credible population-level conditional means to be identified from aggregated data. It formalizes identification conditions under coarsening at random (CAR) and shows that aggregation induces a partially linear conditional expectation in the predictor, enabling regression-based estimation with covariates. The authors compare King’s 2×2 model, count-based R×C models, and semiparametric EI, showing how each can be understood within a unified linear-regression framework, and they advocate flexible, covariate-rich approaches (e.g., double/debiased machine learning) to robustly control for confounders. Empirically, using political-science datasets with ground-truth proxies, they demonstrate persistent biases in EI—such as overestimating racial polarization and nationalization—though covariates can mitigate some errors, underscoring the importance of sensitivity analyses and flexible modeling. The work provides a principled framework for diagnosing and improving EI in applied settings, with practical implications for policy-relevant inferences from aggregate data.
Abstract
Estimating conditional means using only the marginal means available from aggregate data is commonly known as the ecological inference problem (EI). We provide a reassessment of EI, including a new formalization of identification conditions and a demonstration of how these conditions fail to hold in common cases. The identification conditions reveal that, similar to causal inference, credible ecological inference requires controlling for confounders. The aggregation process itself creates additional structure to assist in estimation by restricting the conditional expectation function to be linear in the predictor variable. A linear model perspective also clarifies the differences between the EI methods commonly used in the literature, and when they lead to ecological fallacies. We provide an overview of new methodology which builds on both the identification and linearity results to flexibly control for confounders and yield improved ecological inferences. Finally, using datasets for common EI problems in which the ground truth is fortuitously observed, we show that, while covariates can help, all methods are prone to overestimating both racial polarization and nationalized partisan voting.