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Fixed-Effect Saturation Is Not Weak Identification: Certifying Inference under Measurement Error

Stanisław M. S. Halkiewicz

arXiv 6 Aug 2026 · Econometrics

arXiv:2608.06053 · PDF · Extracted main text

Abstract

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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37
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82
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37
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Griliches, Z., Hausman, J.A (1986) Errors in variables in panel data1.00074100%
2Bound, J., Krueger, A.B (1991) The extent of measurement error in longitudinal earnings data: Do two wrongs make a right?1.00064100%
3Bound, J., Brown, C., Duncan, G.J., Rodgers, W.L (1994) Evidence on the validity of cross-sectional and longitudinal labor market data1.00064100%
4Cattaneo, M.D., Jansson, M., Newey, W.K (2018) Inference in linear regression models with many covariates and heteroscedasticity0.92843100%
5Kline, P., Saggio, R., Slvsten, M (2020) Leave-out estimation of variance components0.8434475%
6Jochmans, K (2022) Heteroscedasticity-robust inference in linear regression models with many covariates0.84333100%
7Pemstein, D., Meserve, S.A., Melton, J (2010) Democratic compromise: A latent variable analysis of ten measures of regime type0.84333100%
8Staiger, D., Stock, J.H (1997) Instrumental variables regression with weak instruments0.73732100%
9Stock, J.H., Yogo, M (2005) Testing for weak instruments in linear IV regression0.73732100%
10Acemoglu, D., Naidu, S., Restrepo, P., Robinson, J.A (2019) Democracy does cause growth0.64441100%

Showing the top 10 of 37 scored citations.