Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework

In recent decades, the role of gross domestic product (GDP) as an indicator of well-being has been sharply questioned by both researchers and institutions. This theoretical discussion leads to the international debate ``emph{Beyond GDP}'', which aims to assess the progress of a country considering fundamental social and environmental dimensions of well-being, inequality, and sustainability. According to this perspective, well-being and quality of life, in general, deserve great attention at the institutional level; hence, this topic attracted also the consideration of methodological researchers, and thus many statistical indicators have been proposed. Recently, most insiders have dealt with the problem of the multidimensionality of well-being, and many research has also stressed the importance of assessing trends and changes over time rather than observing indices in single instants. For this reason, this research proposes the use of functional data analysis that is an exciting tool to build new social indicators of well-being and interpret them considering the original time observations as a continuous function to be treated as a whole. Indeed, repeated measures of social indicators of well-being can be considered as functions in the time domain. Moreover, this approach adds to the existing techniques interesting instruments of analysis, e.g. the derivatives and the functional principal components, and overcomes some strong assumptions of the time series analysis. To demonstrate the appropriateness of this approach, this study proposes an application to real data concerning ``emph{subjective well-being}'' within the Italian ``emph{BES project}'' The final aim of this research is to provide scholars and policy-makers with additional tools for assessing the ``emph{Equitable and Sustainable Well-being}'' over time.