  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
reveal a large potential for productivity gains through better allocation,
keeping the current technology and resources fixed.
