Logical Inconsistency in EI‐Based Second‐Stage Regressions

Abstract

The statistical procedure EI–R, in which point estimates produced by the King (1997) ecological inference technique are used as dependent variables in a linear regression, can be logically inconsistent insofar as the assumptions necessary to support EI–R's first stage (ecological inference via King's technique) can be incompatible with the assumptions supporting its second stage (linear regression). In light of this problem, we develop a specification test for logical consistency of EI–R and describe options available to a researcher who confronts test rejection. We then apply our test to the implementation of EI–R in Burden and Kimball's (1998) study of ticket splitting and find that this implementation is logically inconsistent. In correcting for this problem we show that Burden and Kimball's substantive results are artifacts of a self‐contradictory statistical technique.