Choosing among regularized estimators in empirical economics: The risk of machine learning

Many settings in empirical economics involve estimation of a large number of parameters. In such settings methods that combine regularized estimation and data-driven choices of regularization parameters are useful. We provide guidance to applied researchers on (i) the choice between regularized estimators and (ii) data-driven selection of regularization parameters. We characterize the risk and relative performance of regularized estimators as a function of the data generating process, and show that data-driven choices of regularization parameters yield estimators with risk uniformly close to the risk attained under the optimal (unfeasible) choice of regularization parameters. We illustrate using examples from empirical economics.