Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations

Dan Ben-Moshe; David Genesove

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arXiv · 2504.19832

Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations

Dan Ben-Moshe·David Genesove

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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.

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Dan Ben-Moshe, David Genesove. 2026-04-26. Assignment at the Frontier: Identifying the Frontier Structural Function and Bounding Mean Deviations. https://arxiv.org/abs/2504.19832

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