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 the choice between regularized estimators and 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.

Policymakers are often interested in estimating how policy interventions affect the outcomes of those most in need of help. This concern has motivated the practice of disaggregating experimental results by groups constructed on the basis of an index of baseline characteristics that predicts the values of individual outcomes without the treatment. This paper shows that substantial biases may arise in practice if the index is estimated by regressing the outcome variable on baseline characteristics for the full sample of experimental controls. We propose alternative methods that correct this bias and show that they behave well in realistic scenarios.