A Well-Being Indicator for the Italian Provinces

The acronym NUTS (from the French "Nomenclature des unités territoriales statistiques"—NUTS) stands for Nomenclature of Territorial Units for Statistics, that is the European Statistical System official classification for the territorial units. The NUTS is a partitioning of the EU territory for statistical purposes based on local administrative units. The NUTS codes for Italy have three hierarchical levels: NUTS-1 (Groups of regions); NUTS-2 (Regions); NUTS-3 (Provinces). The current NUTS 2013 classification is valid from 1 January 2015, and for Italy at the NUTS-3 level it includes 110 territorial units, which coincides with the 110 provinces that existing in Italy at the reference date.

“Sbilanciamoci!” involves associations, NGOs and networks active on social issues, solidarity, environment, civil rights promotion, education and health monitoring, consumer protection and alternative economic activities, from fair trade to ethical banking (Rondinella et al. 2014).

See Daniele and Malanima (2014), Felice (2011), and Pianta (2012), among others.

See Sen (1999), Alkire (2002), OECD (2014) and Nissi and Sarra (2016).

Ballas (2013) provides an extensive overview of well-being and quality of life in cities and regions.

In 2014 total spending by provinces and municipalities amounted at around 73 billion of Euro, that is about 4% of GDP [Ministry of Economy and Finance, Update Notre on the Economic and Financial Document (DEF) 2017].

The provincial BES is constructed trying to adapt the existing regional BES to large cities and provinces. Currently, only 29 Statistical Offices of Italian Provinces and Metropolitan areas, located in 14 different Italian regions, are contributing to the development of the prototype BES indicator at NUTS-3 level made for the province of Pesaro and Urbino. More details on the project can be found in Chelli and Gigliarano (2016), ISTAT (2015), Taralli (2015), and Taralli et al. (2015).

The standardization methodology transformed each indicator as follows: where x_ij is the value of indicator j for the region i:\( \mu_{i} \) is the average value of indicator j; \( \sigma_{{x_{j} }} \) is the standard deviation for the indicator j; and \( z_{i,j} \) is the standardized value of indicator j for the region i

The issue of equal weighting is discussed in Sect. 3.

During this process, we made the necessary directional adjustment, as some variables, such as newspaper diffusion, correspond to increases in overall well-being, whereas increases in other variables, such as unemployment, correspond to decreases in overall well-being. In other words, we change the sign of the normalized value by multiply it by − 1 if the variable is negatively correlated with the multidimensional phenomenon.

The QUARS indicator and its composition in the seven dimensions is reported in Table 5 in “Appendix”.

According to ISTAT classification Italy is divided into five macro regions or areas: the North-West (which comprises the regions of Piemonte, Valle d’Aosta, Lombardia and Liguria), the North-East (Trentino-Alto-Adige, Veneto, Friuli-Venezia Giulia and Emilia-Romagna), the Centre (Toscana, Umbria, Marche and Lazio), the South (Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria), and the Islands (Sicilia and Sardegna). For simplicity, in the rest of the paper the South area includes the Islands. Also, we use the term North for indicating the sum of the North-West and the North-East areas.

See for instance the seminal paper of Putnam (1993), and Brida et al. (2014) among others.

The values of the mean absolute differences of rank for the other dimensions are the following: for the “environment" 22, for the “economy and labour” 16, for the “health” 24, for the “education and culture” 19, for the “gender equity”, and for the “democratic participation” 12.

A similar geographical distribution of the well-being indicator emerges once we take into account the spatial autocorrelation of the data. Using a k-nearest neighbors weighting matrix, with 10 as the critical cut-off for each province, the Moran's I autocorrelation coefficient is equal to 0.649 and is strongly significant (Anselin 1995). The Moran scatter plot and the Moran scatter map are both available from the authors upon request.

Orr et al. (1991) suggests that data are more likely to be representative of the population as a whole if outliers are not removed.

With the minmax method the scaled values for each province is expressed in the following way: where \( x_{i, max} \) and \( x_{i, min} \) are the maximum and the minimum values observed for variable I, respectively.

Under the geometric average case, variables are normalized with the min–max transformation, noting that the standardization procedure produce same results. As required, variables are standardized under the PCA and the MPI cases (see Johnson and Wichern 2002; De Muro et al. 2010).

More details are available from the authors upon request. For a similar procedure see Ferrara and Nisticò (2014).

The scree plot is available from the authors upon request.

We also computed the accumulated proportion of variance of the first eigenvalue, which accounts for 48 percent of the original data variability. However, as noted by Rencher (2002, p. 398) and Jackson (1991, p. 44) the method of the accumulated proportion of variance is too arbitrary because the challenge lies in selecting an appropriate threshold percentage, so we do not rely on this method for selecting the correct number of components.

Under the null hypothesis, the dimensions are not correlated, i.e., the correlation matrix is the same as the identity matrix, and the observed dimensions cannot be really transformed by PCA into linear combinations in a lower-dimensional space (Johnson and Wichern 2002).

The box plots of the rank differences between the standardized QUARS computed in Sect. 2 with each one of the alternative four methods (minmax, minmaxg, PCA, and MPI) are shown in Fig. 4 in “Appendix”.

The distribution of the well-being indicator obtained with methods 1–4 are available from the authors upon request.

For a review, see Daniele and Malanima (2014), Felice (2011), and Pianta (2012), among others.

The anomaly of the Italian case is well documented by Iuzzolino et al. (2011), who analyzes the data of 147 regions in 14 countries between 1955 and 2005.

Well-being differences at sub-national level have also being documented. See, for instance, Casmiri et al. (2013), and Rizzi and Popara (2006).

See also Schyns (2002). Aslam and Corrado (2012) also present a regional study of subjective well-being in Europe and find a statistically significant relationship between subjective life satisfaction and regional characteristics.

The weighted average of provincial data does not differ from the official regional data. However, in some cases we were not able to aggregate the provincial data, nor to recover the information from the official sources, being the variables indexes. More specifically, for variable 3 (Environmental illegality) listed in Table 3 in “Appendix”, which is an index, we do not aggregate the provincial data but we use the regional ones from the official source Legambiente; variable 5 (Eco management) is also an index, so data are again obtained from Legambiente and are dated 2008; for variable 16 (School ecosystem), data are from Legambiente and are dated 2009. Finally, for variable 9 (Income inequality), data have been aggregated using a weighted average of provincial data, using the number of taxpayers as weights. The values of the obtained Gini index are very similar to those calculated by ISTAT.

The Spearman's rank correlation coefficient between our result and the QUARS indicator of Segre et al. (2011) is about 0.92.

Besides the number of variables used, differences between our regional QUARS^R and the QUARS in Segre et al. (2011) are also due to the year data are collected: in most cases, we use 2011 data while Segre et al. (2011) used data from 2003 to 2009. Also, because data at provincial level are in some cases not available, some of the differences with Segre et al. (2011) are due to differences in the variable used. More specifically: for variable 3 (Environmental illegality) listed in Table 3 in “Appendix” we do not take into account environmental crime as in Segre et al. (2011); for variable n.7 (Sustainable mobility) we do not take into account CO2 emissions from transport, and we replace the “use of rail, cars and bikes to go to work or school” with “public transport (number of passengers using public transport), and car ownership rate”; for variable n.12 (Migrant integration) we do not take into account the attractiveness of a province; for variable n.15 (Avoidable mortality) we replace the “average of per capita number of days of life lost due to causes that may be actively opposed by the public health system and that led to death at an age between 5 and 69 years” indicator with the “number of avoidable mortality for persons aged 0-74 years”; for variable n.18 (Higher education) we also take into account the number of under graduated students; for variable n.19 (Student migration) we consider the number of under graduated and graduated students instead of the number of undergraduates studying; finally, for variable n.21 (Theater and music) we use the number of tickets sold instead of “per capita expenditure for theatrical and musical performances”.

For the box plot as well as for the calculation of the Theil index we use data aggregated with the minmax method, since the Theil Index cannot be computed on negative or zero values, like in the standardize case, because of the logarithmic terms in their formulas. Data are reported in Table 2, column 6.

The Theil’s T statistic is given by: where n is the number of provinces in the population, \( wb_{p} \) is the well-being indicator of the province indexed by p, and \( \mu_{wb} \) is the population’s average well-being index. If every province has exactly the same well-being value, T will be zero; this represents perfect equality and is the minimum value of Theil’s T. If one province has all of the well-being, T will equal ln n; this represents utmost inequality and is the maximum value of Theil’s T statistic.

The decomposition of the Theil coefficient in well-being calculated with the minmax transformation method is shown in Table 6 in “Appendix”.

See Fig. 5 in “Appendix”.