Inference in High-Dimensional Panel Models: Two-Way Dependence and Unobserved Heterogeneity

Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data further complicates high-dimensional estimation and inference. This paper proposes a toolkit for high-dimensional panel models with large cross-sectional and time sample sizes. To reduce the dimensionality, I propose a weighted LASSO using two-way cluster-robust penalty weights. Although consistent, the convergence rate of LASSO is slow due to the cluster dependence, rendering inference challenging in general. Nevertheless, asymptotic normality can be established in a semiparametric moment-restriction model by leveraging a clustered-panel cross-fitting approach and, as a special case, in a partial linear model using the full sample. In a panel estimation of the government spending multiplier, I demonstrate how high dimensionality could be hidden and how the proposed toolkit enables flexible modeling and robust inference.