We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and size-distorted when some of the factors are weak. We propose estimators with improved rates of convergence and bias-aware CIs that remain valid uniformly, regardless of factor strength. Our approach applies the theory of minimax linear estimation to form a debiased estimate, using a nuclear norm bound on the error of an initial estimate of the interactive fixed effects. Our resulting bias-aware CIs take into account the remaining bias caused by weak factors. Monte Carlo experiments show substantial improvements over conventional methods when factors are weak, with minimal costs to estimation accuracy when factors are strong.

翻译：本文研究了具有交互固定效应（即因子结构）的面板数据中回归系数的估计与推断问题。我们证明，当部分因子为弱因子时，现有估计量与置信区间（CIs）可能存在严重偏差与尺度失真。我们提出了具有改进收敛速度的估计量，以及无论因子强度如何均能保持统一有效性的偏误感知置信区间。我们的方法应用极小极大线性估计理论，通过利用交互固定效应初始估计误差的核范数界，构建去偏估计量。所得偏误感知置信区间考虑了弱因子引起的剩余偏误。蒙特卡洛实验表明，在因子较弱时，本方法较传统方法有显著改进；而在因子较强时，其估计精度损失极小。