Efficiency measurement in stochastic input-output systems†

Abstract

Measuring efficiency of systems with multiple inputs and multiple outputs is most difficult when market, prices for these inputs and outputs are unavailable as for example in most public sector decision-making units. Two types of measures related to Pareto-efficiency could still be defined in such a framework, one related to the productivity of a common set of inputs and the other to a ratio of weighted index of outputs and inputs. These measures however are ordinal and useful in ranking purposes only and may have stochastic variations when the multivariate input-output system contains random components. Some characterizations and theoretical results are derived here for some specific types of random variations. Potential applications are also briefly indicated.

Notes

†This is an enlarged and modified version of a paper : ‘ Problems in measuring frontier production functions : some theoretical results ’ originally presented at the Joint National Meeting of CORS-TIMS-ORSA held in Toronto, Canada. 3-6 May 1981.