Multiple Input-Output Frontier Analysis - From Generalized Deterministic to Stochastic Frontiers -
A. Dellnitz
A. Kleine
Data Envelopment Analysis
Computers & Industrial Engineering, Volume 135, September 2019, Pages 28-38

Stochastic Frontier Analysis (SFA) is a well-established parametric method designed to estimate (in)efficiency scores for the
activities of some economic entities. Here, most applications are based on explicit production functions taking into consideration multiple inputs and a single output - or vice versa. Although some authors have attempted to deal with multiple inputs and outputs, such models are actually reformulated in terms of explicit production functions to make it numerically tractable. In this contribution, we show that multiple inputs and outputs can be treated applying implicit
production relations. In particular, this can be construed as a generalization of the aforementioned attempts; we call this new approach Generalized Frontier Analysis - GFA for short. We prove that in some deterministic frontier cases the related maximum likelihood problems can be solved via goal programming. In the case of stochastic frontiers, we show that the estimation technique of Jondrow, J., Lovell, C.A.K., Materov, I.S. and Schmidt, P. [Journal of Econometrics 19, pp. 233-238, 1982] is reusable. Furthermore, we provide a link between the new framework and the non-parametric method called Data Envelopment Analysis (DEA). Finally, the gist of the novel approach will be exemplified, studying the data from 125 Adult Education Centers (AECs).

Franziska Fricke | 09.03.2021