Incorporating intermediate outputs into SFA using an equation system approach with application to transport

Conventional Stochastic Frontier Analysis conceptualizes a firm’s production process as a single stage of transforming inputs to final outputs. In practice many firms have a multi-stage production process and conceptualizing this as a single stage only assesses overall efficiency and does not provide insight into where inefficiency resides which is of greater interest to decision making units and policy makers. The paper addresses this issue by developing a Network Stochastic Frontier model into which intermediate output is incorporated. We propose a Network Stochastic Frontier model in which multiple stages of a production process are modelled as a system of equations. However, departing from Huang et al. (2017, 2018), our model focuses on how stage efficiency can be aggregated to measure overall efficiency and how the model exploits different data aggregations to yield more information about the performance of firms. Besides the model development, we make a contribution to the estimation method by introducing a simplified multi-step estimation procedure with an authors’ written package in Stata, “networkSFA”. The applicability of the model and the validity of the estimation method are demonstrated by an empirical example of English road maintenance.