Ecological Regression with Partial Identification

Citation:

Wenxin Jiang, Gary King, Allen Schmaltz, and Martin A. Tanner. 2019. “Ecological Regression with Partial Identification.” Political Analysis, Pp. 1--22. Copy at http://j.mp/2vh3O93
Ecological Regression with Partial Identification

Abstract:

Ecological inference (EI) is the process of learning about individual behavior from aggregate data. We relax assumptions by allowing for ``linear contextual effects,'' which previous works have regarded as plausible but avoided due to non-identification, a problem we sidestep by deriving bounds instead of point estimates. In this way, we offer a conceptual framework to improve on the Duncan-Davis bound, derived more than sixty-five years ago. To study the effectiveness of our approach, we collect and analyze 8,430  2x2 EI datasets with known ground truth from several sources --- thus bringing considerably more data to bear on the problem than the existing dozen or so datasets available in the literature for evaluating EI estimators. For the 88% of real data sets in our collection that fit a proposed rule, our approach reduces the width of the Duncan-Davis bound, on average, by about 44%, while still capturing the true district level parameter about 99% of the time. The remaining 12% revert to the Duncan-Davis bound. 

Easy-to-use software is available that implements all the methods described in the paper. 

DOI: 10.1017/pan.2019.19
Last updated on 12/04/2019