arXiv 12 Jun 2026 · Statistics — Methodology
arXiv:2606.14009 · PDF · DOI · OpenAlex · Extracted main text
Political scientists often interpret coefficient shrinkage under fixed effects as evidence that pooled associations are confounded. This paper shows why that inference is unreliable for slow-moving, mismeasured regressors. Fixed effects can remove much of the signal and identify coefficients from within-unit variation that is disproportionately measurement error, attenuating estimates toward zero. A lone fixed effects coefficient may therefore be unable to distinguish confounding from measurement error. I show that the attenuation depends on a regressor's empirical intraclass correlation and measurement reliability. I then propose a default workflow for panel regression. Researchers estimate reliability when possible, report pooled and fixed effects estimates with corrected within reliability, use partial identification bounds when the estimates share a sign, and report fixed effects as a within-unit estimate when they do not. For variables with no reliability estimate, I introduce an autocorrelation frontier that bounds the attenuation factor directly. I conclude by applying this workflow to several published results to show that the data often cannot distinguish attenuation from confounding, and the workflow makes clear which case the researcher faces.
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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 | Cornell, Agnes and Knutsen, Carl Henrik and Teorell, Jan (2020) Bureaucracy and Growth | 0.941 | 6 | 4 | 83% |
| 2 | Treier, Shawn and Jackman, Simon (2008) Democracy as a Latent Variable | 0.737 | 3 | 3 | 67% |
| 3 | Blundell, Richard and Bond, Stephen (1998) Initial Conditions and Moment Restrictions in Dynamic Panel Data Models | 0.644 | 2 | 2 | 100% |
| 4 | Callaway, Brantly and Sant'Anna, Pedro H. C (2021) Difference-in-Differences with Multiple Time Periods | 0.644 | 2 | 2 | 100% |
| 5 | Rosenberg, Andrew S (2026) ferobust: Measurement-Error Diagnostics for Fixed-Effects Regression self | 0.644 | 2 | 2 | 100% |
| 6 | Goodman-Bacon, Andrew (2021) Difference-in-Differences with Variation in Treatment Timing | 0.644 | 2 | 2 | 100% |
| 7 | Griliches, Zvi and Hausman, Jerry A (1986) Errors in Variables in Panel Data | 0.644 | 2 | 2 | 100% |
| 8 | Sun, Liyang and Abraham, Sarah (2021) Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects | 0.644 | 2 | 2 | 100% |
| 9 | Pemstein, Daniel and Marquardt, Kyle L. and Tzelgov, Eitan and Wang,… (2018) The V-Dem Measurement Model: Latent Variable Analysis for Cross-National and Cross-Temporal Expert-Coded Data | 0.567 | 11 | 3 | 18% |
| 10 | de Chaisemartin, Clément and D'Haultfœuille, Xavier (2020) Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 34 scored citations.