On the Estimation of Educational Technical Efficiency from Sample Designs: A New Methodology Using Robust Nonparametric Models

Average efficiency is popular in the empirical education literature for comparing the aggregate performance of regions or countries using the efficiency results of their disaggregated decision-making units (DMUs) microdata. The most common approach for calculating average efficiency is to use a set of inputs and outputs from a representative sample of DMUs, typically schools or high schools, in order to characterize the performance of the population in the analyzed education system. Regardless of the sampling method, the use of sample weights is standard in statistics and econometrics for approximating population parameters. However, weight information has been disregarded in the literature on production frontier estimation using nonparametric methodologies in education. The aim of this chapter is to propose a preliminary methodological strategy to incorporate sample weight information into the estimation of production frontiers using robust nonparametric models. Our Monte Carlo results suggest that current sample designs are not intended for estimating either population production frontiers or average technical efficiency. Consequently, the use of sample weights does not significantly improve the efficiency estimation of a population with respect to an unweighted sample. In order to enhance future efficiency and productivity estimations of a population using samples, we should define an independent sampling design procedure for the set of DMUs based on the population’s production frontier.