On the Measurement of Subset Input Overuse Using Data Envelopment Analysis

The input-based radial measure of technical inefficiency can be interpreted as the extent of input overuse by a firm. In recent years, researchers in applied economics have been particularly interested in overuse estimates for the subset of inputs (e.g. polluting agrochemical use in agriculture), and have used the radial measure constructed using Data Envelopment Analysis for such estimation. The problem of 'slacks' can, however, be severe in Data Envelopment Analysis. One of the solutions available is the 'Russell' nonradial measure that provides 'slack-free' technical efficiency estimates. Some authors researching subset input overuse have therefore used the Russell instead. We argue here that the Russell is not a suitable tool when the objective is to highlight the extent of overuse in a subset of inputs (e.g., polluting chemicals in agricultural production). We present three arguments in this demonstration, and use numerical examples and an empirical application based on UK cereal production to illustrate.