Robust Estimation and Inference in Panels with Interactive Fixed Effects

We consider estimation and inference for a regression coefficient in a panel setting with time and individual specific effects which follow a factor structure. Previous approaches to this model require a "strong factor" assumption, which allows the factors to be consistently estimated, thereby removing omitted variable bias due to the unobserved factors. We propose confidence intervals (CIs) that are robust to failure of this assumption, along with estimators that achieve better rates of convergence than previous methods when factors may be weak. 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 individual effects. 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.