Using Ecological Inference Point Estimates as Dependent Variables in Second-Stage Linear Regressions

The practice of using point estimates produced by the King ecologicalinference technique as dependent variables in second-stage linearregressions leads to second-stage results that, in general,are inconsistent. This conclusion holds even when all assumptionsbehind King's ecological technique are satisfied. Second-stageinconsistency is a consequence of the fact that King-based pointestimates of disaggregated quantities contain errors correlatedwith the true quantities the estimates measure. Our findingson second-stage inconsistency, as well as a fix that we propose,follow from econometric theory in conjunction with an analysisof simulated and real ecological data sets.