Preference Externality Estimators: A Comparison of Border Approaches and IVs

This paper compares two estimators-the Border Approach and an Instrumental Variable (IV) estimator-using a unified framework where identifying variation arises from "preference externalities," following the intuition in Waldfogel (2003). We highlight two dimensions in favor of the IV approach. First, an econometric model of the data-generating process reveals that the border approach requires a set of identification assumptions that are not easily satisfied in practice: the ignorance of some payoff-relevant information and conflicting spatial correlation assumptions. The IV approach, in contrast, exhibits greater internal validity because it is derived from the model that generates the data. Second, the border approach suffers from representative issues when the true effect sizes are different between border and off-border regions. We use a common political advertising example to evaluate these estimators and suggest ways to evaluate or limit the above concerns, such as excluding localities that are a large share of the policy making region and evaluating spatial correlations of observables. We find the border approach's representative issue to be substantial when the ignorance assumption is most plausible and observe that spatial correlations do not reflect those needed in the unobservables for consistency of the estimator. The IV, in contrast, does not exhibit concerns related to local average treatment effects. We also derive the specific conditions when the border approach can reduce bias relative to OLS.