The Role of Confounders and Linearity in Ecological Inference: A Reassessment
Estimating conditional means using only the marginal means available from aggregate data is known as the ecological inference problem. We reassess this literature, arguing that it has understudied two issues: how practitioners should control for confounding, and how methodologists can leverage the linearity inherent in the structure of the problem. On the former, we formalize ignorability conditions like those in causal inference and outline consistent plug-in estimators: These are credible when covariates make the ignorability condition plausible. On the latter, we show that aggregation restricts the target function to be partially linear. Such linearity clarifies the connections between King's (1997) methodology, its predecessors, and subsequent developments. That motivates a recent doubly-robust technique that enters covariates flexibly while leveraging linearity. Finally, we test these methods in datasets where the ground truth is fortuitously observed. In these common applications, all methods tested were prone to overestimating racial polarization and underestimating split-ticket voting.