Translational invariance in DEA DDF models: an application in eco-efficiency

In the presence of negative variables in DEA models, it is possible to translate axes so that all variables become positive. This is only possible under certain conditions of returns to scale and model orientation. The procedure is analogous in cases where the directional distance function (DDF) is the strategy for reaching the efficiency frontier. In this paper we propose a DEA DFF eco-efficiency score under variable returns to scale and translation to measure the performance of agricultural production systems in the presence of variables that can take on negative values. In addition to calculating the eco-efficiency measures, it is our interest to identify the determinants or causal factors of efficiency, which we did by fitting a fractional regression. We compared the results to a previous study, in which we modeled all DEA variables as ranks to avoid the presence of negative values.