The use of the scaling property in a frontier analysis of a system of equations

Abstract

This article presents a one-stage efficiency frontier analysis based on the scaling property. This type of analysis is a not very often applied in empirical work in spite of its nice features. Due to the scaling property the influence of exogenous (managerial) variables on efficiency can be modelled and estimated in one stage. It also opens the possibility of estimating a system of equations, consisting of a cost function and the corresponding cost share equations. The model is applied to a unique data set of Dutch secondary education school boards in the period 2007–10, not only consisting of regular data on cost, inputs and outputs, but also of specific data on operational management. The model provides reliable and plausible estimates for the cost efficiency, scale elasticity, and technical change. Average cost efficiency is about 96%. Economies of scale prevail for school boards with size less than 0.8 times average size, whereas annual productivity growth is 2.2% on average.