A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input–output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or ‘static’ DEA which assumes input–output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input–output dependence by using input–output ‘paths’ mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. It is suggested that a dynamic model captures the efficiency better than a static model.