Inference in High-Dimensional Panel Data Models

Panel data sets with both individual and time effects are ubiquitous in applied economics. At the same time, modern data sources often provide many potential instruments or control variables, so that the number of regressors may be comparable to or larger than the sample size. In such high-dimensional environments classical instrumental variables (IV) procedures break down because ordinary least squares (OLS) is ill-defined and overfitting destroys the quality of first-stage predictions. Recent developments have introduced regularization methods to mitigate the overfitting problem in a high-dimensional feature space by exploiting the sparsity of important covariates, thereby substantially improving the performance of IV estimators. An active line of research in the econometrics literature has been concerned with the use of regularization and shrinkage methods for estimating optimal instruments in the context of estimating a low-dimensional parameterv