🤖 AI Summary
Existing methods for panel data with interactive fixed effects (i.e., factor structures) suffer from severe estimation bias and distorted confidence intervals when factors are weak. This paper proposes a robust estimator with improved convergence rate and constructs a bias-aware confidence interval, achieving the first uniformly valid inference with respect to factor strength—thereby overcoming the theoretical breakdown of conventional approaches under weak factors. Our method operates within a minimax linear estimation framework and incorporates a nuclear-norm constraint to correct initial estimation errors in the interactive effects. Monte Carlo simulations demonstrate substantial gains in inferential accuracy under weak factors, near-lossless estimation efficiency under strong factors, and stable coverage rates at nominal levels across the full spectrum of factor strengths—delivering both robustness and efficiency.
📝 Abstract
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.
