Breakdown Reliability for Saturated Fixed-Effect Inference
饱和固定效应推断的崩溃可靠度AI 解读 ↓
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饱和固定效应推断的崩溃可靠度
- 研究问题
- 在大量固定效应与连续解释变量测量误差并存时，传统推断何时出现不可接受的尺寸失真，能否用已报告统计量进行诊断？
- 方法与思路
- 作者分析局部测量噪声下固定效应估计的非中心极限分布，反演尺寸失真得到可靠度门槛，并扩展至认证和聚类稳健推断。
- 材料陈述的贡献
- 摘要称提出仅由已报告 t 统计量计算的崩溃可靠度及认证版本，给出误认证概率界，并指出聚类修正可能改变诊断结论。
- 阅读关注点
- 应核对局部噪声设定、组内可靠度修正和容忍度定义，尤其检查聚类推广的投影兼容条件与应用所依赖的测量误差模型。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实。诊断针对连续解释变量的经典测量误差，不覆盖二元处理误分类；具体条件须查全文。
原文摘要
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.