We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We show that previously developed estimators and confidence intervals (CIs) might 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 are uniformly valid regardless of whether the factors are strong or not. 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. We use the obtained estimate to construct a bias-aware CI taking into account the remaining bias due to weak factors. In Monte Carlo experiments, we find a substantial improvement over conventional approaches when factors are weak, with little cost to estimation error when factors are strong.

翻译：我们考虑具有交互固定效应（即因子结构）的面板数据中回归系数的估计与推断问题。研究表明，当部分因子较弱时，先前开发的估计量和置信区间可能存在严重偏差和尺寸扭曲。我们提出了具有改进收敛速度的估计量和偏差感知置信区间，无论因子强弱均能保持一致性。该方法应用极小化极大线性估计理论，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。基于此估计量，我们构建了考虑弱因子剩余偏差的偏差感知置信区间。蒙特卡洛实验表明，在弱因子情形下，该方法相比传统方法有显著改进，且在强因子情形下估计误差代价极小。