Political scientists often interpret coefficient shrinkage under fixed effects as evidence that pooled associations are confounded. This paper shows why that inference is unreliable for slow-moving, mismeasured regressors. Fixed effects can remove much of the signal and identify coefficients from within-unit variation that is disproportionately measurement error, attenuating estimates toward zero. A lone fixed effects coefficient may therefore be unable to distinguish confounding from measurement error. I show that the attenuation depends on a regressor's empirical intraclass correlation and measurement reliability. I then propose a default workflow for panel regression. Researchers estimate reliability when possible, report pooled and fixed effects estimates with corrected within reliability, use partial identification bounds when the estimates share a sign, and report fixed effects as a within-unit estimate when they do not. For variables with no reliability estimate, I introduce an autocorrelation frontier that bounds the attenuation factor directly. I conclude by applying this workflow to several published results to show that the data often cannot distinguish attenuation from confounding, and the workflow makes clear which case the researcher faces.
翻译:政治学家常将固定效应下的系数缩减解释为混合关联存在混杂。本文揭示了为何这一推断对于慢变且测量有误的解释变量不可靠:固定效应可能消除大部分真实信号,仅从单位内变异中识别系数,而这类变异主要由测量误差构成,从而将估计值向零衰减。单一的固定效应系数因此无法区分混杂与测量误差。研究表明衰减程度取决于解释变量的经验组内相关系数和测量信度。本文继而提出面板回归的默认工作流程:研究人员在可行时估计信度,报告经组内信度校正的混合效应与固定效应估计值;当两类估计符号一致时采用部分识别边界;符号不一致时以固定效应作为单位内估计。对于无法获得信度估计的变量,本文引入自相关边界以直接约束衰减因子。最后将该工作流程应用于若干已发表研究,结果表明现有数据往往无法区分衰减与混杂,而本文工作流程可明确研究者面临的具体情形。