Robust Inference for High Dimensional Panel Data Models

In this paper, we propose a robust estimation and inferential method for high dimensional panel data models. Specifically, (1) we investigate the case where the number of regressors can grow faster than the sample size, (2) we pay particular attention to non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, and (3) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator. Methodologically and technically, we develop two Nagaev-types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we also derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator. Our study thus provides the relevant literature with a complete toolkit for conducting inference about the parameters of interest involved in a high-dimensional panel data framework. We also demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive fixed effects. Moreover, we conduct extensive numerical studies using simulated and real data examples.