Beyond the weights: a multicriteria approach to evaluate inequality in education
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Beyond the weights: a multicriteria approach to evaluate inequality in education Giuseppe Coco1 · Raffaele Lagravinese2,3 · Giuliano Resce4 Received: 6 October 2019 / Accepted: 28 May 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper proposes the use of a new technique, the Stochastic Multicriteria 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. Keywords Education inequality · PISA · SMAA · ANOGI · Anywhere and somewhere
The authors wish to thank Paolo Liberati and the participants of the Workshop “Equity in Education” held at Faculty of Economics & Business, Katholieke Universiteit Leuven, Belgium. 30 November-1 December 2017 and the partecipants of the Italian Economic Society held in Palermo 24-26 October 2019. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10888-020-09449-4) contains supplementary material, which is available to authorized users. Raffaele Lagravinese
[email protected] 1
Dipartimento di Scienze per l’Economia e l’Impresa, Universit`a di Firenze, Florence, Italy
2
Dipartimento di Economia e Finanza, Universit`a di Bari, Bari, Italy
3
University of Bari “Aldo Moro” Largo Abbazia Santa Scolastica, 70124 - Bari, Italy
4
Italian Ministry of Economy and Finance, Italian National Research Council (CNR), Rome, Italy
G. Coco et al.
1 Introduction In the last decade, there has been an increase of detailed international surveys on cognitive achievement tests. Among them, the Programme for International Student Assessment (PISA) is one of the most influential and used to measure student performances in different subjects (mathematics, science and reading). The performances in different dimensions are usually averaged in order to obtain a composite indicator to be used for ranking and comparisons among schools and states (e.g., (Bloom et al. 2015)) However, the average score can hide different attitudes and specialisations. Thus, a crucial issue is how to define a proper set of weights to aggregate different subjects. (Decancq and
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