Binary Choice with Asymmetric Loss in a Data-Rich Environment: Theory and an Application to Racial Justice

We study the binary choice problem in a data-rich environment with asymmetric loss functions. In contrast to asymmetric regression problems, the binary choice with general loss functions and high-dimensional datasets is challenging and not well understood. Econometricians have studied nonparametric binary choice problems for a long time, but the literature does not offer computationally attractive solutions in data-rich environments. In contrast, the machine learning literature has many algorithms that form the basis for much of the automated procedures that are implemented in practice, but is focused mostly on loss functions that are independent of individual characteristics. We show that the theoretically valid predictions of binary outcomes with a generic loss function can be achieved via a very simple reweighting of the logistic regression or state-of-the-art machine learning techniques, such as LASSO, boosting, or deep learning. We apply our analysis to racial justice in pretrial detention.