Cory McCartan, Shiro Kuriwaki
arXiv 24 Sep 2025 · Statistics — Methodology
arXiv:2509.20194 · PDF · Extracted main text
We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing methods for this problem, also known as ecological inference, implicitly make strong assumptions about the aggregation process. We first formalize weaker conditions for identification, which motivates estimators that can efficiently control for many covariates. We propose a debiased machine learning estimator that is based on nuisance functions restricted to a partially linear form. Our estimator also admits a semiparametric sensitivity analysis for violations of the key identifying assumption, as well as asymptotically valid confidence intervals for local, unit-level estimates under additional assumptions. Simulations and validation on real-world data where ground truth is available demonstrate the advantages of our approach over existing methods. Open-source software is available which implements the proposed methods.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | King, G (1997) A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data | 0.950 | 7 | 4 | 86% |
| 2 | Chernozhukov, V., Cinelli, C., Newey, W., Sharma, A., and Syrgkanis, V (2024) Long story short: Omitted variable bias in causal machine learning | 0.894 | 7 | 4 | 71% |
| 3 | Goodman, L. A (1953) Ecological regressions and behavior of individuals | 0.843 | 3 | 3 | 100% |
| 4 | Jbaily, A., Zhou, X., Liu, J., Lee, T.-H., Kamareddine, L., Verguet,… (2022) Air pollution exposure disparities across us population and income groups | 0.811 | 4 | 2 | 100% |
| 5 | Rosen, O., Jiang, W., King, G., and Tanner, M. A (2001) Bayesian and frequentist inference for ecological inference: The R$$C case | 0.811 | 4 | 2 | 100% |
| 6 | Chernozhukov, V., Newey, W. K., and Singh, R (2022) Debiased machine learning of global and local parameters using regularized riesz representers | 0.644 | 4 | 1 | 100% |
| 7 | Ansolabehere, S. and Rivers, D (1995) Bias in ecological regression | 0.644 | 2 | 2 | 100% |
| 8 | Duncan, O. D. and Davis, B (1953) An alternative to ecological correlation | 0.644 | 2 | 2 | 100% |
| 9 | Goodman, L. A (1959) Some alternatives to ecological correlation | 0.644 | 2 | 2 | 100% |
| 10 | Kuriwaki, S. and McCartan, C (2025) The role of confounders and linearity in ecological inference: A reassessment self | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 45 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model10pt | 0.405 | 1 | 1 |