  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.
