Economic Cross-Efficiency

37 Pages Posted: 29 May 2019

See all articles by Juan Aparicio

Juan Aparicio

University Miguel Hernandez - Center of Operations Research

José L. Zofío

Universidad Autónoma de Madrid; Erasmus Research Institute of Management (ERIM)

Date Written: May 27, 2019


This paper is concerned with introducing a series of new concepts under the name of Economic Cross-Efficiency, which is rendered operational through Data Envelopment Analysis (DEA) techniques. To achieve this goal, from a theoretical perspective, we connect two key topics in the efficiency literature that have been unrelated until now: economic efficiency and cross-efficiency. In particular, it is shown that, under input (output) homotheticity, the traditional bilateral notion of input (output) cross-efficiency for unit l, when the weights of an alternative counterpart k are used in the evaluation, coincides with the well-known Farrell notion of cost (revenue) efficiency for evaluated unit l when the weights of k are used as market prices. This motivates the introduction of the concept of Farrell Cross-Efficiency (FCE) based upon Farrell’s notion of cost efficiency. One advantage of the FCE is that it is well defined under Variable Returns to Scale (VRS), yielding scores between zero and one in a natural way, and thereby improving upon its standard cross-efficiency counterpart. To complete the analysis we extend the FCE to the notion of Nerlovian cross-inefficiency (NCI), based on the dual relationship between profit inefficiency and the directional distance function. Finally, we illustrate the new models with a recently compiled dataset of European warehouses.

Keywords: Data Envelopment Analysis, Cross-efficiency, Farrell (Cost) Efficiency, Nerlove (Profit) Inefficiency, Warehousing

Suggested Citation

Aparicio, Juan and Zofío, Jose L., Economic Cross-Efficiency (May 27, 2019). ERIM Report Series Reference , Available at SSRN: or

Juan Aparicio (Contact Author)

University Miguel Hernandez - Center of Operations Research ( email )

Instituto CIO
Av. de la Universidad s/n.
Elche (Alicante), Alicante 03202

Jose L. Zofío

Universidad Autónoma de Madrid ( email )

Francisco Tomás y Valiente, 5
Madrid, Madrid 28049
914972406 (Phone)

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam

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