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

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Abstract

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 “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 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 to build new social indicators of well-being and to interpret them considering the original time observations as a continuous function. 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 “subjective well-being” within the Italian “BES project” The final aim of this research is to provide scholars and policy-makers with additional tools for assessing the “Equitable and Sustainable Well-being” over time.

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Notes

  1. Focusing on the case of an Hilbert space with a metric \(d(\cdot ,\cdot )\) associated with a norm so that \(d(x_1(t), x_2 (t)) = \Vert x_1(t) - x_2(t)\Vert\), and where the norm \(\Vert \cdot \Vert\) is associated with an inner product \(\langle \cdot ,\cdot \rangle\) so that \(\Vert x(t)\Vert =\langle x(t),x(t) \rangle ^{1/2}\), we can obtain as specific case the space \(L_2[a,b]\) of real square-integrable functions defined on [a, b] by \(\langle x_1(t),x_2(t) \rangle =\int _{a}^{b} x_1(t)x_2(t)dt\).

  2. Some examples of classical statistical concepts adapted to the FDA framework are: the functional mean \(\overline{x}(t)=\frac{1}{N}\sum _{i=1}^N x_i(t)\), functional variance \(\sigma ^2_x(t)=\frac{1}{N}\sum _{i=1}^N\Bigl (\widehat{x}_i(t)-\overline{x}(t)\Bigr )^2\), functional covariance \(\sigma (s,t)=cov\Bigl (x(s),x(t)\Bigr )=\frac{1}{n}\sum _{i=1}^n \Bigl (x_i(s)-\overline{x}(s)\Bigr )\Bigl (x_i(t)-\overline{x}(t)\Bigr )\), and functional correlation \(\rho (s,t)=\frac{\sigma (s,t)}{\sqrt{\sigma (s,s)}\sqrt{(\sigma (t,t)}}\).

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Authors and Affiliations

  1. Biostatistics Unit, National University of Ireland Galway, Galway, Ireland

    Fabrizio Maturo

  2. University of Campania “Luigi Vanvitelli”, Caserta, Italy

    Antonio Balzanella

  3. “G. d’ Annunzio” University, DISFPEQ, Pescara, Italy

    Tonio Di Battista

Authors
  1. Fabrizio Maturo
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  2. Antonio Balzanella
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  3. Tonio Di Battista
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Correspondence to Fabrizio Maturo.

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Maturo, F., Balzanella, A. & Di Battista, T. Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework. Soc Indic Res 146, 449–471 (2019). https://doi.org/10.1007/s11205-019-02137-5

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  • DOI: https://doi.org/10.1007/s11205-019-02137-5

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