Central Limit Theorems for Directional Distance Functions with and without Undesirable Outputs

Simar, LĂ©opold;Zelenyuk, Valentin;Zhao, Shirong
(2024) , 41 pages

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Abstract
We develop new central limit theorems (CLTs) for the aggregate directional distance functions (DDFs), which embed the CLTs for the aggregate efficiency and simple mean DDFs as special cases. Moreover, we develop new CLTs for the aggregate DDFs in the presence of the weak disposability of undesirable outputs. Our Monte-Carlo simulations confirm the good performance of statistical inference based on the new CLTs we have derived and illustrate how wrong the inference based on the standard CLTs can be. To our knowledge, this is the first study that provides both the asymptotic theory and the simulation evidence for the non-parametric frontier approaches when some outputs are undesirable. Finally, we provide an empirical illustration using a data set from large US banks as well as supply the computational code for alternative applications.
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Simar, L., Zelenyuk, V., & Zhao, S. (2024). Central Limit Theorems for Directional Distance Functions with and without Undesirable Outputs (LIDAM Discussion Paper ISBA 2024/10). https://hdl.handle.net/2078.5/30724