مقاله سال ۲۰۱۶

مجله امگا – Omega

Production processes that generate multiple outputs are typically characterized by jointly used inputs, i.e. inputs that simultaneously benefit different outputs. These joint inputs give rise to economies of scope, which actually form a prime economic motivation for Decision Making Units (DMUs) to produce more than one output. In the current paper, we establish a methodology for multi-output profit efficiency evaluation that explicitly accounts for jointly used inputs. In particular, our methodology distinguishes between joint inputs and inputs that are allocated to specific outputs.

DEA analysis of multi-output production: The method that we develop fits within the popular Data Envelopment Analysis (DEA, after [8]) approach to productive efficiency measurement. This DEA approach is intrinsically nonparametric, which means that it does not require a parametric/functional specification of the (typically unknown) production technology. It “lets the data speak for themselves” by solely using technological information that is directly revealed by the observed production units. It then reconstructs the production possibility sets by (only) assuming standard production axioms (such as monotonicity and convexity).1 A DMU’s efficiency is measured as the distance of the corresponding input-output combination to the efficient frontier of this empirical production set. Typically, a DMU’s efficiency can be computed by simple linear programming. Its nonparametric nature and its easy computation largely explain DEA’s widespread use as an analytical research instrument and decision-support tool.

ool. Recently, Cherchye et al. [10,9] introduced a novel DEA methodology to analyze cost efficiency in multi-output settings. The methodology assumes output-specific production technologies, accounts for joint inputs in the production process, and incorporates specific information on how inputs are allocated to individual outputs. As such they provide a formal modeling of the economies of scope that characterize the multi-output production process.2 These authors have also shown that their cost efficiency measure evaluated at shadow prices is dually equivalent to a specific multi-output version of the [21–۳۰] measure of (radial) input efficiency. This is an attractive feature, as DEA practitioners often use this Debreu–Farrell measure for evaluating the technical efficiency of a DMU’s input use (when assuming a fixed output).