“Ecological Inference : Minimum distance to first moment constraints approach"

Abstract

This paper presents a new approach to the ecological inference problem, particularly to estimating voter transition matrices between two elections. Our estimators choose the points that most closely conform to constraints derived from several first moment conditions arising from mild and natural assumptions. We show that under these assumptions our estimators are consistent, that our estimation procedure has properties that simplify their computation significantly, and derive estimators for the standard deviations of the true voter transitions. We also show that our estimators perform well in small samples through a simulation study and illustrate our approach with three applications. The first application is the well-known problem in the ecological inference literature of estimating the fraction of voter registrations among different demographic groups in the US. The second application uses data on the 2013 Chilean presidential election to analyze voter turnout between the first round and the runoff. We use this application to show that, unlike more computationally intensive approaches, our model can use large datasets without issue. We also show that our approach may be extended in a straightforward manner to the case of multiple clusters in the true values for the voter transitions across units. Both of the previous applications have known true voter transition matrices, and we find that our model performs similarly to more established approaches and provides superior estimates in some circumstances. Our final application estimates voter transitions between the 2021 Chilean presidential election runoff and the 2022 Constitutional Plebiscite, where voters decided whether to approve or reject the proposed draft for a new constitution. Our results for this application suggest that the compulsory voting policy put in place for the 2022 plebiscite significantly impacted its outcome. We find that close to 90% of voters who did not vote in the 2021 runoff but did vote in the 2022 plebiscite voted to reject the constitutional draft. Under the assumption that the bulk of these voters would not have voted had there not been a compulsory voting policy in place, in its absence the result would likely have been the approval of the draft rather than its rejection. Overall, our approach is a viable alternative to other ecological inference methods. It has good theoretical properties and a good performance in small samples, and it is simpler and less computationally intensive than prevailing simulation-based strategies.