Using ecological inference point estimates as dependent variables in second-stage linear regressions

The practice of using point estimates produced by the King ecological inference technique as dependent variables in second-stage linear regressions leads to second-stage results that, in general, are inconsistent. This conclusion holds even when all assumptions behind King's ecological technique are satisfied. Second-stage inconsistency is a consequence of the fact that King-based point estimates of disaggregated quantities contain errors correlated with the true quantities the estimates measure. Our findings on second-stage inconsistency, as well as a fix that we propose, follow from econometric theory in conjunction with an analysis of simulated and real ecological data sets.