标题：Ecological Regression with Partial Identification
作者：Jiang, Wenxin; King, Gary; Schmaltz, Allen; Tanner, Martin A.
作者机构：[Jiang, Wenxin] Shandong Univ, Inst Finance Adjunct, Jinan, Shandong, Peoples R China.; [Jiang, Wenxin; Tanner, Martin A.] Northwestern Univ, Dept S 更多
通讯作者地址：[Schmaltz, A]Harvard Univ, Inst Quantitat Social Sci, Cambridge, MA 02138 USA.
关键词：asymptotics; bounds; confidence intervals; contextual models; ecological; inference; linear regression; partial identification
摘要：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 nonidentification, 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 65 years ago. To study the effectiveness of our approach, we collect and analyze 8,430 2\times 2 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.