Ecological Regression with Partial Identification

Wenxin Jiang, Gary King, Allen Schmaltz, Martin A. Tanner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 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.

Original languageEnglish (US)
Pages (from-to)65-86
Number of pages22
JournalPolitical Analysis
Issue number1
StatePublished - Jan 1 2020
Externally publishedYes


  • asymptotics
  • bounds
  • confidence intervals
  • contextual models
  • ecological inference
  • linear regression
  • partial identification

ASJC Scopus subject areas

  • Sociology and Political Science
  • Political Science and International Relations


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