Beyond the Weights : A Multi-criteria Approach to Evaluate Inequality in Education

This paper proposes the use of a new technique, the Stochastic Multi-criteria Acceptability Analysis (SMAA), to evaluate education quality at school level out of the PISA multidimensional database. SMAA produces rankings with Monte Carlo Generation of weights to estimate the probability that each school is in a certain position of the aggregate ranking, thus avoiding any arbitrary intervention of researchers. We use the rankings in 4 waves of PISA assessment to compare SMAA outcomes with Benefit of Doubt (BoD), showing that differentiation of weights matters. Considering the whole set of feasible weights by means of SMAA, we then estimate multidimensional inequality in education, and we disentangle inequality into a ‘within' and a ‘between' country component, in addition to a component due to overlapping, using the multidimensional ANOGI. We find that, over time, inequality within countries has increased substantially. Overlapping among countries, particularly in the upper part of the distribution has also increased quite substantially suggesting excellence is spreading among countries