Inference in high-dimensional two-way fixed effects panel data models

This paper studies a triangular simultaneous panel-data model with individual and time fixed effects and a high-dimensional set of instruments in the first stage. The endogenous regressor is driven by an unknown function of observable instruments and two sets of fixed effects, while the structural equation contains the same two-way fixed effects. We propose a two-step procedure: first, we remove both individual and time effects by a double-demeaning transformation; second, we estimate an optimal instrument for the endogenous regressor using Lasso or Cluster-Lasso and then apply two-stage least squares (2SLS). Under approximate sparsity and high-level regularity conditions, we show that the resulting 2SLS estimator is N T -consistent and asymptotically normal. The proofs adapt the panel Cluster-Lasso results of Belloni et al. (2016) to the two-way fixed effects transformation. • Two-way fixed effects panel model with high-dimensional instruments estimated via Lasso. • Double-demeaning removes individual and time effects before Lasso instrument selection. • Cluster-Lasso first stage yields a root-NT consistent and asymptotically normal estimator. • Time fixed effects add no asymptotic cost over the one-way fixed effects case. • Cross-validated penalty outperforms fixed tuning in finite-sample simulations.