Treating non-discretionary variables one way or the other: implications for efficiency scores and their interpretation

Abstract

This paper explains the main DEA-techniques to model continuous and categorical non-discretionary variables as well as a related two-stage approach. The implications of using either alternative are demonstrated in practice using the pharmacy data from the original study by Banker and Morey (1986b) on categorical non-discretionary variables.

It is argued that the model appropriate for continuous non-discretionary variables rests on rather restrictive assumptions about the production technology. The model for categorical non-discretionary variables does not result in higher efficiency scores, i. e. a more robust assessment of the inefficiency of production units, as Banker and Morey claim. In addition, its efficiency scores can not be compared across observations with different values for the categorical variable as each category is evaluated by a differently sized data set. The bias resulting from this practice is discussed in Zhang and Bartels (1998).

The two-stage approach to modelling non-discretionary variables does not rest on more restrictive theoretical assumptions than the model for categorical non-discretionary variables. It does, however, use the full data set for the evaluation of each unit and is therefore recommended for the empirical analysis when non-discretionary variables are a relevant factor.