Cost Efficiency, Urban Patterns and Population Density When Providing Public Infrastructure: A Stochastic Frontier Approach

Relying on stochastic frontier analysis we propose a methodology to study the technological characteristics and cost efficiency levels related to the provision of public infrastructure for basic utilities. The methodology assumes a cost minimizing behaviour on the part of public officials when planning the construction of local infrastructure, which is represented by way of a flexible translog cost function. Introducing relevant definitions of scale economies, associated with larger numbers of inhabitants and dwellings, as well as economies of density, brought about by reductions in urban dispersion, we analytically determine the optimal population densities for which average cost is minimized. We illustrate our model with the water cycle sector, including water distribution, sewage collection and cleansing of wastewater, and considering data at the municipality level for the Spanish region of Castilla y León. The obtained results indicate potential cost savings in the form of decreasing average costs, as relevant scale and density economies are present, along with large inefficiency levels. Relevant policy guidelines favouring larger and denser urban sizes are drawn, as the observed cost excess is the result of a general suboptimal urban size in terms of population density, and the negative effects of dispersed settlement patterns.