Non-discretionary and discretionary factors and scale in data envelopment analysis

This paper discusses the interpretation of exogenously fixed, non-discretionary factors in data envelopment analysis (DEA) and suggests a generalised model for incorporating different types of input and outputs in DEA. The paper first compares two approaches to the inclusion of continuous non-discretionary factors in a one-stage model, one introduced by Banker and Morey and the other by Lovell and Ruggiero. The appoaches are compared theoretically, on the basis of axiomatic systems, and empirically, on the basis of examples and simulated data. The key difference is that some models require non-discretionary factors to be scale independent, i.e. indices, and some require them to be scale dependent, i.e. volume measures. Also, the returns to scale properties vary depending on the manner in which non-discretionary factors are treated. In practice, we may want to utilise the properties of the different models simultaneously. A generalised DEA model allowing for this possibility is presented.