Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations
Abstract
This paper analyzes a model in which an outcome equals a frontier function of inputs minus a nonnegative unobserved deviation. The inputs may be endogenous (statistically dependent on the deviation). If zero lies in the support of the deviation given the inputs -- an assumption we term assignment at the frontier -- then the frontier is identified by the supremum of the outcome given those inputs, obviating the need for instruments. We then consider estimation with random error that is mean-independent of the inputs. Motivated by the assignment at the frontier assumption, we regularize estimation by requiring the fitted distribution of the deviation to maintain a minimum probability mass in a neighborhood of zero. Finally, we derive a lower bound on mean deviation, using only variance and skewness, that is robust to scarcity of data near the frontier. We apply our methods to estimate a frontier production function and mean inefficiency.
Cite
@article{arxiv.2504.19832,
title = {Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations},
author = {Dan Ben-Moshe and David Genesove},
journal= {arXiv preprint arXiv:2504.19832},
year = {2026}
}