The measurement of profit, profitability, cost and revenue efficiency through data envelopment analysis: A comparison of models using BenchmarkingEconomicEfficiency.jl

Abstract

We undertake a systematic comparison of existing models measuring and decomposing the economic efficiency of organizations. For this purpose we introduce the package BenchmarkingEconomicEfficiency.jl for the open-source Julia language including a set of functions to be used by scholars and professionals working in the fields of economics, management science, engineering, and operations research. Using mathematical programming methods known as Data Envelopment Analysis, the software develops code to decompose economic efficiency considering alternative definitions: profit, profitability, cost and revenue. Economic efficiency can be decomposed, multiplicative or additively, into a technical (productive) efficiency term and a residual term representing allocative (or price) efficiency. We include traditional decompositions like the radial efficiency measures associated with the input (cost) and output (revenue) approaches, as well as new ones corresponding to the Russell measures, the directional distance function, DDF (including novel extensions like the reverse DDF, modified DDF, or generalizations based on Hölder norms), the generalized distance function, and additive measures like the slack based measure, their weighted variants, etc. Moreover, regardless the underlying economic efficiency model, many of these technical inefficiency measures are available for calculation in a computer software for the first time. This article details the theoretical methods and the empirical implementation of the functions, comparing the obtained results using a common dataset on Taiwanese Banks.