Frontier Estimation of a Cost Function System Model with Local Least Squares: An Application to Dutch Secondary Education

Abstract

In this paper, we propose a method for cost efficiency measurement that is based on local estimation in several stages. The method is based on weighted least squares where weights depend on the distance of an observation to all other observations and on the distance to the cost frontier. The new element in the method is that it also includes the information from the cost share equations and includes cost efficiency in the weighting matrix. The latter is derived from a first stage and implemented in a second stage analysis. An application to a data set of Dutch school boards in secondary education shows that it works well in practice. It produces a number of reliable estimates. It also shows a variation in outcomes that would be hard to cover with, for instance, traditional procedures such as SFA on a translog cost function.