固定效应饱和并非弱识别：测量误差下的推断验证

中文摘要 AI 辅助

仅固定效应饱和并非弱识别：在基准模型中，固定效应残差化OLS是无偏的，且对于每个残差处理方差τ²=nQ_K>0，传统推断是渐近精确的。处理中的经典测量误差会恢复弱识别，我们推导了τ²的Stock-Yogo型临界值。在局部漂移σ_ν²=c²/n下，衰减产生非中心极限，其非中心度η随τ²减小，且在处理平衡条件下，η仅通过整体√(1-ρ)缩放依赖于固定效应维度ρ，使组内可靠性与ρ无关。反转主导二次规模失真得到闭式阈值；失效可靠性仅在报告的t统计量中具有不动点形式。该诊断仅需可靠性的下界，而偏差校正需要点估计。我们将描述性“点通过”与“形式证书”区分，后者在上置信界处评估，且虚假认证概率最多为γ。聚类水平得分CLT和Arellano方差在可检验投影兼容性条件下的一致性得出η_CR=η/√ψ。模拟验证了该阈值；在饱和民主-增长面板中，总体V-Dem polyarchy在γ=0.05下获认证，而其司法约束子指数在独立同分布和聚类误差下被标记。该诊断涵盖连续回归元的经典误差，不涵盖二元处理误分类。

英文摘要

Fixed-effect saturation does not itself distort conventional inference, but classical measurement error does. Under a local noise drift $σ_ν^2=c^2/n$, the FE-OLS $t$-statistic converges to a non-central normal; saturation contributes a common $\sqrt{1-ρ}$ scaling rather than preferentially destroying signal or noise. Inverting the size distortion gives a Stock--Yogo-style critical value. Self-consistency of the within-reliability-corrected pilot yields a breakdown reliability $λ^{\dagger}=|t|/(|t|+η^{\dagger})$ --- the minimum within reliability at which conventional inference retains nominal size within the chosen tolerance --- computable from the reported $t$-statistic alone and algebraically $ρ$-free conditional on it; $η^{\dagger}\approx0.65$ at $5\%$ size and a 5-point tolerance. Replacing $|t|$ by $|t|+z_{1-γ_β}$ gives a certified breakdown reliability; with a lower-reliability bound whose coverage error is $γ_λ$, false certification is at most $γ_β+γ_λ$. Under a checkable projection-compatibility condition, a cluster-level score CLT and consistency of the Arellano variance estimator in the many-fixed-effect regime justify applying the same map to the reported cluster-robust $t$-statistic; clustering can reverse a verdict. In a saturated democracy--growth panel, aggregate V-Dem polyarchy is certified at $γ_β=0.05$, conditional on the supplied measurement model, while its judicial-constraints sub-index is flagged under i.i.d.\ and clustered standard errors. In a twin-pair wage design, the specification is flagged under both independent and correlated reporting-error models, although implied coverage of the nominal-$95\%$ interval ranges from $8\%$ to $68\%$. The diagnostic covers classical error in a continuous regressor, not binary-treatment misclassification.

发表机构

• Jagiellonian University（雅盖隆大学）

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