Identification and Inference for Algorithmic Frontiers with Selective Labels

This paper provides identification results to characterize a fairness-accuracy (FA) frontier, and statistical inference tools to test hypotheses and build a confidence set for the FA-frontier, when outcomes are observed only for selected individuals. When the selection process is unrestricted but loss is measured in specific ways, we provide a characterization of the sharp identification region of the FA-frontier. When the observed distribution rules out frontier membership for a binary status quo algorithm, we construct a single alternative algorithm that improves both groups' accuracy without worsening fairness, uniformly over all admissible distributions of missing labels. For any loss functions, under selection on observables and strict overlap assumptions, we obtain point identification and propose a debiased machine learning estimator, derive its asymptotic distribution, and show how this can be used to carry out inference for the FA-frontier.