Linear production functions and the data envelopment analysis

Abstract

This paper shows that the Data Envelopment Analysis (or Farrell) method is not nonparametric in the sense that the method implicitly employs linear production functions (frontiers) to measure efficiency. Deriving positive-multiplier linear production frontiers and grouping the DMUs by their corresponding frontiers can simplify the estimation procedures when there are new DMUs included, and can easily determine how many inputs should be reduced or/and how many outputs should be increased to make an inefficient DMU efficiently. This procedure can also circumvent the problems of the non-Archimedean infinitesmal in the CCR literature. It is also shown that, because of the linear production functions, both Banker's and the Banker-Charnes-Cooper methods fail in testing for returns-to-scale.