Efficiency analysis with ratio measures

Abstract

In applications of data envelopment analysis (DEA) data about some inputs and outputs is often available only in the form of ratios such as averages and percentages. In this paper we provide a positive answer to the long-standing debate as to whether such data could be used in DEA. The problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions, e.g., that the technology is a convex set. Our approach is based on the formulation of new production assumptions that explicitly account for ratio measures. This leads to the estimation of production technologies under variable and constant returns-to-scale assumptions in which both volume and ratio measures are native types of data. The resulting DEA models allow the use of ratio measures "as is", without any transformation or use of the underlying volume measures. This provides theoretical foundations for the use of DEA in applications where important data is reported in the form of ratios.

A multilevel and multistage efficiency evaluation of innovation systems: A multiobjective DEA approach

“…It should be noted that certain values such as expenditures in R&D are usually used in a ratio (%) form (e.g., % of GDP). However, in these cases there is no special adaptation of the DEA model as required (see Olesen, Petersen, & Podinovski, 2015 ).…”

An illustration of multiple-stakeholder perspective using a survey across Australia, China and Japan

“…As in the case of this paper, ratio measures are direct measures of outputs, rather than complementing volume measures. Olesen et al (2015) point out that if ratio measures are used in conventional radial DEA, it could lead to the underlying technology being incorrectly modeled (this paper uses nonradial DEA). They then proceed to develop new ratio-based radial DEA models and leave the door open to further studies that can develop other DEA models capable of accepting ratio measures.…”

“…Olesen et al (2015) point out that DEA undertaken with ratio measures can introduce some potential limitations such as violation of the assumed convexity in production technology and an efficient frontier that could end up being arbitrary. As in the case of this paper, ratio measures are direct measures of outputs, rather than complementing volume measures.…”

“…Olesen et al (2015) acknowledge that performance analysis of the financial sector frequently uses ratio measures. Banking is a tightly regulated sector, and as such, it is often scrutinized and criticized by a range of stakeholders including customers and regulators.…”

Nonparametric Production Technologies with Multiple Component Processes

“…A principal problem with ratio measures is that they generally do not satisfy the standard convexity assumption and need to be modeled differently to the volume measures. A range of DEA models with a single proportional process and nonproportional ratio inputs and outputs is developed by Olesen et al (2015Olesen et al ( , 2017 who extend earlier ideas of Ruggiero (1996) and Podinovski (2005).…”