The Weighting Role of Normalisation in a Multidimensional Analysis of Social Inclusion

Abstract

In the context of the multidimensional measurement of complex phenomena, the major focus of the recent literature has been on the choice of the dimensions’ weights and the shape of the aggregation function, while few studies have concentrated on how normalisation influences the results. With the aim of building a measure of Social Inclusion for European regions between 2004 and 2012, we adopt a CES aggregation framework and compare two alternative normalisation strategies: a data-driven min-max function, where the parameters depends solely on the available data, and an expert-based function where parameters are elicited through a survey at the University of Venice Ca’ Foscari. Regardless of the adopted strategy, we show that normalisation plays a crucial part in defining variables’ weighting and trade-offs. The data-driven strategy produces trade-offs that are hard to interpret in economic terms and debatable from a social desirability perspective, thus generating an aggregate measure with a “positive” interpretation. Moreover, it softens the aftermaths of the recent economic crisis on Social Inclusion, by putting a consistent weight on the longevity variable. Conversely, the expert-based normalisation has strikingly different parameters and allows for a normative interpretation of the resulting index. Furthermore, it emphasizes the worsening trends in long- term unemployment and the relevance of early school leaving in the Social Inclusion measure. As a result, numerous rank-reversals occur between regions when switching the normalisation methods.