Endogenous dynamic inefficiency and optimal resource allocation: An application to the European Dietetic Food Industry

Abstract

The conventional dynamic cost inefficiency model relies on the directional distance function with an exogenous directional vector to measure technical and allocative inefficiency. However, this approach may lead to contradictory recommendations for firms to become technically and allocatively efficient. By definition, the conventional model forces firms to reduce their inputs and increase their investments in order to become technically efficient; for some firms this is followed by the reverse recommendation to become allocatively efficient. This paper proposes a model that endogenizes the directional vector to solve for the cost minimizing combination of inputs and investments. In contrast to the conventional model with an exogenous directional vector, our model provides managers with monotonic prescriptions. We illustrate the superiority of the endogenous directional vector model over its conventional counterpart using a dataset of EU firms in the dietetic food industry. The differences in the managerial prescriptions are striking, with the conventional model wrongly recommending reductions in inputs that are underused with respect to their optimal amounts minimizing cost.