A comparison of data envelopment analysis and stochastic frontiers as methods for assessing the efficiencies of organisational units

This thesis gives an overall view of the two most commonly used approaches for measuring the relative efficiencies of organisational units. The two approaches, data envelopment analysis (DEA) and stochastic frontiers (SF), are supposedly estimating the same underlying efficiency values but the natures of the two methods are very different. This can lead to different estimates for some, or all, of the units in an analysis. By identifying the nature of these differences this work shows that it is possible to gain some insight into the nature of the underlying data and to say more confidently which of the two estimates is closer to the true efficiency for individual units. In order to investigate the differences between the methods across different facets of the technology two important dimensions are chosen. Firstly differences across scale size are investigated. It is shown how it is possible to define a measure of scale size in both the single output and multiple input and output cases. This measure of scale size can then be used to split the technology into regions of differing scale size enabling, for example, tests for the true nature of returns to scale in DEA. The measure of scale size developed in multiple dimensions necessitates a method for estimating an homothetic, constant returns to scale function. Differences between the approaches across input mix are also investigated. These differences may highlight the abilities of the methods to correctly identify the elasticity of substitution between the inputs. The results of the comparisons between the methods are summarised. This summary gives possible reasons for differences which may be found between the results of the two approaches, and an indication of what the nature of the estimates may be to the true efficiency values. An algorithm is then developed for using a comparison of the results from the two methods to help to identify the better estimates