Optimal resource allocation: Convex quantile regression approach

Optimal allocation of resources across sub-units in the context of centralized decision-making systems such as bank branches or supermarket chains is a classical application of operations research and management science. In this paper, we develop quantile allocation models to examine how much the output and productivity could potentially increase if the resources were efficiently allocated between units. We increase robustness to random noise and heteroscedasticity by utilizing the local estimation of multiple production functions using convex quantile regression. The quantile allocation models then rely on the estimated shadow prices instead of detailed data of units and allow the entry and exit of units. Our empirical results on Finland’s business sector show that the marginal products of labor and capital largely depart from their respective marginal costs and also reveal that the current allocation of resources is far from optimal. A large potential for productivity gains could be achieved through better allocation, especially for the reallocation of capital, keeping the current technology and resources fixed.