Robust Estimation and Inference in Panels with Interactive Fixed Effects

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.