Multicomponent production technologies with restricted allocations of shared inputs and outputs

We consider production technologies in which several parallel component processes are characterized by both component-specific and shared inputs and outputs. The recently developed multicomponent variable and constant returns-to-scale (MVRS and MCRS) models of such technologies are based on the assumption that we have no information about the actual allocation of the shared inputs and outputs to the component processes, which is a common scenario in many applications. The MVRS model treats each component process as a separate convex technology. The MCRS model additionally assumes that each process is a scalable technology. Both models account for the most conservative, or worst-case, allocation of the shared inputs and outputs to the individual processes, which does not require any knowledge of the actual allocation of such measures. In the current paper, we develop a new class of MVRS and MCRS models, by integrating a mechanism for the specification of lower and upper bounds on the proportions in which the shared inputs and outputs can be allocated to different component processes. We show that such bounds may be supported by data and generally lead to a larger model of technology and improved differentiation on efficiency. As an illustration, we discuss the application of the developed approach in the context of higher education.