The statistical properties and empirical performance of double regression

Abstract

Voting rights litigation requires ecological inference to estimate the voting preferences of minority and nonminority groups within the electorate. Double regression has been the procedure most commonly employed for this purpose. This article presents the first formal examination of this procedure. The underlying structural model reveals that double regression estimators are neither unbiased nor consistent estimators of true within-group vote preferences or polarization. Simulations demonstrate that they can substantially exaggerate the differences between minority and nonminority vote choices when none are present, and dramatically understate them when differences exist. In sum, double regression cannot meet conventional statistical standards for reliability. Consequently, it should be abandoned. © Society for Political Methodology 2005; all rights reserved.