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Measuring the State of the Future in the
European Union countries: comparing different
methods
Leonardo Salvatore Alaimo1[0000−0002−9785−0436], Yuri
Calleo2[0000−0002−0190−6061], and Simone di Zio3[0000−0002−9139−1451]
1Sapienza University of Rome, Rome, Italy,
2University College Dublin, Dublin, Ireland
3University ”G. d’Annunzio”, Chieti-Pescara, Chieti, Italy.
leonardo.alaimo@uniroma1.it
Abstract. This paper addresses the challenge of analyzing future tra-
jectories, crucial for goal attainment. While some models like the State
of the Future Index (SOFI) provide insights into potential trends, they
necessitate complementarity with qualitative methods for comprehensive
understanding. Despite its efficacy, SOFI’s condensation of diverse vari-
ables into a single index may obscure nuances and regional disparities,
potentially oversimplifying systemic dynamics. Critique has been leveled
against its construction, particularly regarding its weighting system. This
study aims to mitigate these concerns by comparing synthesis methods
and proposing a statistically rigorous framework for measuring SOFI at
the European Union level. By employing those techniques, this paper
endeavors to enhance the precision and reliability of SOFI as a tool for
identifying future dynamics and evaluating present policies.
Keywords: Futures Studies, SOFI, Aggregative-compensative approach.
1 Introduction
The analysis of future trajectories for understanding potential developments in
society is a challenging but crucial task for developing appropriate policies and
facilitating/counteracting designated objectives. In these terms, some quantita-
tive models assist in understanding the dynamics over time that some phenomena
may exhibit, proving extremely useful when combined with additional qualita-
tive methods (e.g., participation). Among the various methods used in Futures
Studies (FS), the State of the Future Index (SOFI), developed by [1], offers a
glimpse into projected trends over a medium-term horizon (i.e., a decade), draw-
ing from two decades of historical data on a selected set of variables indicative
of potential systemic changes. It is worth emphasizing that it combines individ-
ual key indicators suggesting the potential magnitude and direction of change;
therefore, they must be treated as indicators rather than projections because the
future is unpredictable [2]. The ultimate goal is to clarify systemic dynamics and
2 Leonardo Salvatore Alaimo et al.
the interaction among different variables, showing possible alterations in one or
more variables and how they influence the overall system. However, as emerged
from the study, condensing numerous (and diverse) variables into a single index
could lead to obscuring nuances, masking variations among sectors, regions, or
nations, simplifying what is a complex phenomenon. Despite such limitations,
SOFI is useful for evaluating policies and presenting potential trajectories as
preliminary results. Since 2000, the Millennium Project has managed the index
and its selection of variables with their respective weights within the system,
assessing the “best” and “worst” values predicted for future decades through
Real-Time Delphi studies [3], evaluating their consistency and robustness. In
particular, some criticism arises with regard to the way the index is constructed.
Specifically, SOFI is defined as the weighted sum of the normalised values of the
elementary indicators used; thereafter, the annual value is obtained as a fixed-
base index number based on a reference value. The higher the SOFI, the greater
the level of achievement of a better future state. Another point of criticism is
the weighting system adopted.
The aim of this paper is twofold. On the one hand, we want to compare differ-
ent synthesis methods, taking into consideration different levels of compensation
between the elementary indicators. On the other hand, it is intended to propose
a framework and a system of indicators valid for measuring SOFI at European
Union level. The paper is organised as follows. Section 2 presents the indicators
and the methods used. In Section 3 the application and the main findings are
shown. Conclusions in Section 4 summarise the obtained results.
2 Data description and methods
The starting point of this work was the definition of a system of indicators for
measuring SOFI for EU countries. Obviously, the selection of elementary in-
dicators was guided by two basic requirements: to maintain as much as pos-
sible the logic behind SOFI and to identify suitable measures at European
level. Moreover, this selection must meet the need to have data for all Euro-
pean nations and in annual historical series. Table 1 reports the 26 indicators
selected for this work, their description and polarity, i.e. the sign of the re-
lation between the basic indicator and the phenomenon we want to measure
by means of the synthetic indicator (for more information, please see: [4]).
Data are available from 2012 to 2022. Thus, we deal with a three-way time
data array Xof the type ”27 countries ×26 indicators ×10 years”, formally:
X≡ {xijt :i= 1,...,27; j= 1, . . . 26; t= 2012,...,2022}. We want to con-
struct a synthetic index adopting an aggregative-compensative approach [5] [6]
[4], a step by step process that consists of the mathematical combination of
the set of indicators, obtained by applying specific methodologies known as
composite indicators (CIs). Formally, given X≡ {xijt}, the objective is to
obtain a bi-dimensional data matrix of the type ”27 countries ×10 years”,
V≡ {vit :i= 1,...,27; t= 2012,...,2022}, where vit is the synthetic value of
the i-th country at the t-th year.
Measuring SOFI in the EU countries 3
From the operational point of view, after the definition of the phenomenon
and the framework, the first operational step in composites construction is the
normalisation of basic indicators, which makes the indicators comparable and
mathematically operational in aggregation [7] and allows all basic indicators have
positive polarity, i.e. an increase in the normalised indicators corresponds to an
increase in the composite index. The objective is to obtain an array R≡ {rijt},
in which the generic element rijt is the normalised value of the generic element
xijt of the array X. Dealing with a three-way time data array X≡ {xijt}, the
most commonly used normalisation method is the M in −Max or re-scaling [6]:
rijt =
(xijt −M inxij t
it
)
(Maxxijt
it
−Minxijt
it
)rijt =
(Maxxijt
it
−xijt )
(Maxxijt
it
−Minxijt
it
)(1)
where xijt is the value of the indicator j-th in the unit ith at the time t-th;
Minxijt
it
is the minimum value of the indicator j-th for all units iin all temporal
occasions t;M axxij t
it
is the maximum value of the indicator j-th for all units
iin all temporal occasions tand rij t is the normalised value of the indicator
j-th in the unit i-th at the time t-th. Obviously, this method presents pros
and cons. For instance, it is particularly sensitive to the outliers. At the same
time, reporting all indicators at the range [0,1], it facilitates the reading of the
phenomenon (for more information, please see: [4]). In this step, the weights of
the individual indicators must be defined. The choice of weighting has a large
impact on values and, consequently, on the meaning of the composites and, as
previously written, it is also an open question for SOFI. In this work, we decided
to use the most common weighting strategy, i.e. attributing equal weight to all
basic indicators, thus considering them equally important [8], leaving a more
in-depth reflection on this point to a future work. At this point, the next step is
the aggregation of the normalised indicators. We use three different aggregation
methods as they involve different levels of compensability or substitutability (for
more information, please see: [9]):
–the minimum (no compensatory): vit = min rijt
–the arithmetic mean (full compensatory): vit =PM
j=1 rijt
–the geometric mean (partially compensatory): vit = (QM
j=1 rijt )1/M
where Mis the number of basic indicators. To compare the results of the different
methods, we use the Kendall rank correlation, τ, given by the following:
τ=c−d
c+d=2S
n(n−1) (2)
where cis the number of concordant pairs; dis the number of discordant pairs
and S= (c−d) [10]. Kendall’s τmeasures the degree of a monotone relationship
between variables, and like Spearman’s ρ, it calculates the dependence between
ranked variables [11].
4 Leonardo Salvatore Alaimo et al.
Table 1. SOFI indicators for EU countries: code, variable name, description, polarity.
Code Variable name Description Polarity
X1 GNI per capita Gross national income divided by midyear popula-
tion. POS
X2 Income distribution
ratio of total income received by the 20% of the pop-
ulation with the highest income (the top quintile) to
that received by the 20% of the population with the
lowest income (the bottom quintile).
NEG
X3 At risk of poverty rate
Share of people with an equivalised disposable income
(after social transfer) below the 60% of the national
median equivalised disposable income.
NEG
X4 Foreign direct invest-
ment
Direct investment equity flows in the reporting econ-
omy. POS
X5 Long-term unemploy-
ment rate
Share of the economically active population aged 15
to 74 who has been unemployed for 12 months or
more.
NEG
X6 Employment rate Share of the population aged 20 to 64 which is em-
ployed. POS
X7 NEET Percentage of the population aged 15-29 not employed
and not involved in further education or training. NEG
X8 Employment rate of low
skilled people
Number of persons in employment with at most lower
secondary education (i.e. ISCED 0-2) and aged 20-
64 by the total population in the same age and skill
group.
POS
X9 Early school leavers
Share of the population aged 18-24 with at most lower
secondary education who were not involved in any
education or training during the four weeks preceding
the survey.
NEG
X10 Tertiary education rate Share of the population aged 25-34 who have success-
fully completed tertiary studies. POS
X11 Adult participation in
learning
Share of people aged 25-64 who stated that they re-
ceived formal or non-formal education and training in
the four weeks preceding the survey.
POS
X12 Healthy life expectancy Healthy life years in absolute value at birth. POS
X13 Infant mortality rate Number of infant deaths for every 1,000 live births. NEG
X14
Self reported unmet
meet for medical exams
and care
Share of the population aged 16 and over reporting
unmet needs for medical care. NEG
X15 Crude rate of net migra-
tion
Ratio of net migration (including statistical adjust-
ment) during the year to the average population in
that year
POS
X16 Population growth rate
Rate at which the number of individuals in a popula-
tion increases in a given time period, expressed as a
fraction of the initial population.
POS
X17 Total fertility rate
The mean number of children that would be born alive
to a woman during her lifetime if she were to survive
and pass through her childbearing years conforming
to the fertility rates by age of a given year.
POS
X18 Forest area Percentage of forest areas in the territory on total
land area POS
X19 Emissions of CO2 Air emissions of CO2, kilograms per capita NEG
X20 Years of life lost due to
PM2.5 exposure
Years of life lost due to exposure to particulate matter
(PM2.5). NEG
X21 Use of renewable for
electricity
Gross electricity production by means of renewable
sources. POS
X22 Energy efficiency Indicator measuring the energetic efficiency of a coun-
try. POS
X23 Energy productivity Amount of economic output that is produced per unit
of gross available energy. POS
X24 Corruption Perceptions
index
Composite index measuring how corrupt a country’s
public sector is perceived to be. POS
X25 People never use Inter-
net Percentage of individuals never use Internet. NEG
X26 Positions held by women
in management board
Share of female board members in the largest publicly
listed companies. POS
Measuring SOFI in the EU countries 5
3 Results
In Figure 1, we report the τKendall correlation coefficients among synthetic
measures obtained by using different aggregation methods. The correlation was
calculated by taking the average of the repeated measures data for each obser-
vation and perform a standard Kendall correlation on average data. In doing so,
we can evaluate if observations with high ranks in one measure also tend to have
high ranks in the others.
The quite low values of the coefficients indicate that the aggregation method
selected and, consequently, the level of compensability admitted, highly influence
the results, generating different rankings and different future scenarios.
Fig. 1. Corrplot of τKendall correlation coefficients of synthetic measures of SOFI with
different aggregations: minimum (MIN); arithmetic mean (ARIT); geometric mean
(GEOM).
To highlight this result, we show in Figure 2 the values achieved by 4 countries
over the time period considered using the three methods: Italy (ITA), Spain
(ESP), France (FRA) and Germany (DEU). The difference between the values
according to the selected method is evident (in particular, the minimum deviates
significantly from the other two).
4 Conclusions
The results of this preliminary study are the basis for future developments and
insights. In particular, the weighting of elementary indicators will be addressed;
we think that the better weighting method is the one based on the stakehold-
ers/experts’ opinion. Another in-depth aspect will be that of forecasts based
on SOFIs obtained with the different aggregation methods. In this case, meth-
ods suitable for forecasting short time series and taking into account the spatial
correlation between statistical units will be identified. Moreover, employing suit-
able AHP methodologies can enable the assignment and assessment of weights,
actually sourced directly from experts without a direct comparison.
6 Leonardo Salvatore Alaimo et al.
Fig. 2. SOFI values based on different aggregation methods for 4 countries: DEU, ESP,
FRA, ITA.
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