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

Leopold Simar, Valentin Zelenyuk and Shirong Zhao

No 2024010, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Inference; Data Envelopment Analysis; Non-parametric Efficiency Estimators; Undesirable Outputs; Weak Disposability (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 (search for similar items in EconPapers)
Pages: 41
Date: 2024-03-04
New Economics Papers: this item is included in nep-ecm and nep-eff
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