Measuring efficiency in a general production possibility set allowing for negative data: An extension and a focus on returns to scale

Data envelopment analysis (DEA) is a technique used to measure the relative efficiency of a set of production units that applies multiple inputs to produce multiple outputs. In its original settings, the data is required to be nonnegative. To allow for negative data, several methods have been proposed. While these methods have merits, they also have weaknesses and limitations. This paper generalizes the construction of the production possibility set from production units with nonnegative observations to those with real values. Given the signs of the aggregate target and aggregate observed outputs of the production units to be evaluated, different models are developed to calculate the efficiencies under both variable and constant returns to scale technologies, and an additive model is used to identify the signs of the aggregate target and aggregate observed outputs. Since the efficiencies are calculated from the original observations without transformation or manipulation, the proposed method does not have the drawbacks of the existing methods. A case of the Detroit National Bank shows that the results obtained from the proposed method are more representative and reliable as compared to those obtained from a data transformation method.