Lasso under Multi-way Clustering: Estimation and Post-selection Inference

Abstract: This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method based on a post-double-selection procedure and show its asymptotic validity. Our procedure can be easily implemented with existing statistical packages. Simulation results demonstrate that the proposed procedure works well in finite sample. We illustrate the proposed method with a couple of empirical applications to development and growth economics.