DEA with non-monotonic variables. Application to EU governments’ macroeconomic efficiency

Conventional Data Envelopment Analysis (DEA) considers monotonic variables, ie the lower the inputs and the larger the outputs, the better. There are, however, occasions when the monotonicity of a variable with respect to efficiency depends on the value of the variable, that is in a certain range of values an increase in the variable is desirable, while in another range it is a decrease of the variable that is desirable. In this paper, a DEA model that solves problems considering non‐monotonic variables is proposed. An application to assess the macroeconomic efficiency of European Union Member States, as regards taxation, gross debt, GDP growth and employment is presented.