Estimating scale economies and the optimal size of school districts: A flexible form approach

This paper investigates estimation methods to model the relationship between school district size, costs per student and the organisation of school districts. We show that the assumptions on the functional form strongly affect the estimated scale economies and offer two possible solutions to allow for more flexibility in the estimation method. First, we introduce a model by adding higher-degree district size polynomials, allowing for multiple optima. Second, we develop a Fourier cost function, innovative in the literature on scale economies in education. We then compare both models to classical approaches in the literature. We illustrate how a minor change in the estimation method can alter policy conclusions significantly using Flemish school district data. In doing so, we find sizeable potential cost savings from the consolidation of school districts, especially at the lower tail of the district-size distribution. The organisational transition from small to large school districts is characterised by an interval between two optima. Beyond an apparent slowdown in cost savings in medium-sized school districts, cost savings from school district consolidation increase again, up to the optimal size of around 6,500 students. Beyond this optimum, school districts incur diseconomies of scale. The commonly used quadratic form (U'-shaped cost function) overestimates scale economies, and fails to identify the interval between both optima.