Variable selection in heterogeneous panel data models with cross-sectional dependence

This paper studies the Bridge estimator for a high-dimensional panel data model with heterogeneous varying coefficients, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We establish oracle efficiency and the asymptotic distribution of the Bridge estimator, when the number of covariates increases to infinity with the sample size in both dimensions. A BIC-type criterion is also provided for tuning parameter selection. We further generalise the marginal Bridge estimator for our model to asymptotically correctly identify the covariates with zero coefficients even when the number of covariates is greater than the sample size under a partial orthogonality condition. The finite sample performance of the proposed estimator is demonstrated by simulated data examples, and an empirical application with the US stock dataset is also provided.