Aggregation of Directional Distance Functions and Industrial Efficiency

Three main objectives are pursued in this paper. First, we intend to analyze the aggregation problem of directional distance functions from a constructive viewpoint. We provide necessary and sufficient conditions concerning the structural properties of the production technology and of the nature of groups of firms. Indeed, exact additive aggregation holds for a linear technology and for a direction solely defined in the output space. Second, since these conditions are somewhat restrictive, we are interested in providing a measure for the aggregation bias through the relationship between industrial and structural technical efficiency. Finally, we show that this aggregation bias is a lower bound for industrial allocative efficiency.