AI 中文总结
该研究针对饱和固定效应回归，通过构造干扰项消灭对比项解决精确推断问题，利用循环填充优化设计，在匹配雇主-雇员等数据上验证了方法的有效性。
AI 中文摘要
在饱和固定效应回归中，高斯推断不依赖于总识别变异，而依赖于其集中程度，该程度由去势处理的自归一化杠杆λₙ衡量。当有限个得分权重保持持续性时，t统计量收敛于原始误差与高斯分量的卷积。在完全集中的情况下，其零分布随具有相等方差的对称误差律变化，因此不存在统一有效的固定临界值。我们转而仅从设计中构造干扰项消灭对比项，这些对比项恒等消除固定效应，在对称、任意异方差误差下产生有限样本精确符号翻转推断，无需同质性假设或对固定效应维度的限制。在双向设计中，可容许对比项构成观测多重图的循环空间，其效率由可观测捕获率κ总结，κ等于皮特曼效率。由此产生的设计问题涉及捕获-粒度权衡：粗支撑集最大化捕获，但减少随机化符号的数量；循环填充提供足够粒度的支撑集。在匹配的雇主-雇员数据上，利用结构的算法实现κ≈0.51，而 naive 填充的κ为0.26。在Grunfeld投资回归中，实现的得分浓度为0.739，对应Nₑff^score=1.80，同时32个有效支撑集达到κ=0.627，所得精确95%置信区间为[0.150,0.450]。一项工人-企业应用证明了其对大型网络的可扩展性。
英文摘要
In fixed-effect regressions with many groups, fixed effects can absorb most identifying variation, leaving a handful of observations to carry what remains. When variation is this concentrated, conventional $t$-tests can reject a true null more than half the time, and any fixed critical value is either invalid or so conservative it has essentially no power. This paper builds an exact test from the design alone. A \textit{nuisance-annihilating contrast} is a linear combination of the treatment and fixed-effect dummies that eliminates the fixed effects without touching the outcome; sign-flipping these contrasts is then an exact symmetry of the null distribution at every sample size, under arbitrary heteroskedasticity. In two-way designs --- worker-firm, firm-time --- these contrasts are exactly the cycles of the bipartite mobility graph, so the movement that identifies the treatment effect is what makes exact inference possible. Exactness costs power: relative to an oracle test, a chosen set of cycles has an observable \textit{capture ratio} $\kap\in[0,1]$ and standard-error premium $\kap^{-1/2}$, and a packing algorithm resolves the capture-granularity trade-off. In the Grunfeld investment regression (single-observation score concentration $73.9\%$), 32 cycle contrasts capture $\kap=0.627$ of the identifying variation, giving an exact $95\%$ confidence interval of $[0.150,\,0.450]$.
