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

Dan Ben-Moshe and David Genesove

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Abstract: This paper analyzes a model in which an outcome equals a frontier function of observed variables minus a nonnegative unobserved deviation. The observables may be endogenous (statistically dependent on the deviation). If zero lies in the support of the deviation given the observables -- an assumption we term assignment at the frontier -- then the frontier is identified by the supremum of the outcome given those variables, obviating the need for instruments. We then consider estimation with random error that is mean-independent of the observables. 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.

Date: 2025-04, Revised 2026-03
New Economics Papers: this item is included in nep-ecm and nep-eff
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