arXiv 6 Aug 2026 · Econometrics
arXiv:2608.06053 · PDF · Extracted main text
Fixed-effect saturation alone is not weak identification: in the baseline model, fixed-effect--residualized OLS is unbiased and conventional inference is asymptotically exact for every residual treatment variance $τ^2=nQ_K>0$. Classical measurement error in the treatment restores it, and we derive Stock--Yogo-style critical values for $τ^2$. Under the local drift $σ_ν^2 = c^2/n$, attenuation produces a non-central limit whose non-centrality $η$ decreases in $τ^2$ and, under a treatment-balance condition, depends on the fixed-effect dimension $ρ$ only through an overall $\sqrt{1-ρ}$ scaling, leaving the within reliability $ρ$-free. Inverting the leading quadratic size distortion gives a closed-form threshold; the breakdown reliability has a fixed-point form in the reported $t$-statistic alone. The diagnostic needs only a lower bound on reliability, where bias correction needs a point estimate. We separate a descriptive point pass from a formal certificate, evaluated at an upper confidence bound and carrying false-certification probability at most $γ$. A cluster-level score CLT and Arellano-variance consistency under a checkable projection-compatibility condition yield $η_{CR}=η/\sqrtψ$. Simulations confirm the threshold; in a saturated democracy--growth panel, aggregate V-Dem polyarchy is certified at $γ=0.05$ while its judicial-constraints sub-index is flagged under i.i.d.\ and clustered errors. The diagnostic covers classical error in a continuous regressor, not binary-treatment misclassification.
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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 | Griliches, Z., Hausman, J.A (1986) Errors in variables in panel data | 1.000 | 7 | 4 | 100% |
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| 6 | Jochmans, K (2022) Heteroscedasticity-robust inference in linear regression models with many covariates | 0.843 | 3 | 3 | 100% |
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| 9 | Stock, J.H., Yogo, M (2005) Testing for weak instruments in linear IV regression | 0.737 | 3 | 2 | 100% |
| 10 | Acemoglu, D., Naidu, S., Restrepo, P., Robinson, J.A (2019) Democracy does cause growth | 0.644 | 4 | 1 | 100% |
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