JRC statistical audit of the 2020 gender equality index.
Date: 2020-10-27
Institutions: Joint Research Centre
Subjects: EU Member State, United Kingdom, audit, equal treatment, female work, gender equality, health policy, knowledge management, participation of women, performance measurement, research report, statistical method, work, work-life balance, working time

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JRC Statistical Audit of the 2020 
Gender Equality Index 

                               Papadimitriou, Eleni 

                                       Norlén, Hedvig  

                                    Del Sorbo, Maria 

2020 

EUR 30423 EN 

 
 
 
              
This  publication  is  a  Technical  report  by  the  Joint  Research  Centre  (JRC),  the  European 
Commission’s  science  and  knowledge  service.  It  aims  to  provide  evidence-based  scientific 
support to the European policymaking process. The scientific output expressed does not imply 
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authorities, or concerning the delimitation of its frontiers or boundaries. 

Contact information  
European Commission 
Joint Research Centre 

Directorate for Competences 
Monitoring, Indicators and Impact Evaluation Unit 
Competence Centre on Composite Indicators and Scoreboards 
E-mail: jrc-coin@ec.europa.eu 

Competence Centre on Composite Indicators and Scoreboards 
https://ec.europa.eu/knowledge4policy/composite-indicators 

EU Science Hub 
https://ec.europa.eu/jrc 

JRC122232 
EUR 30423 EN 

PDF 

ISBN 978-92-76-24507-0 

ISSN 1831-9424 

doi:10.2760/39645 

Luxembourg: Publications Office of the European Union, 2020 

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How to cite this report: Papadimitriou, E.; Norlén, H.; Del Sorbo, M. JRC Statistical Audit of the 
2020 Gender Equality Index, EUR 30423 EN, Publications Office of the European Union, 
Luxembourg, 2020, ISBN 978-92-76-24507-0, doi:10.2760/39645, JRC122232. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Contents 

Abstract ..................................................................................................................................................................................................................... 1 

1 

Introduction ...................................................................................................................................................................................................... 2 

2  Conceptual framework, data analysis and rationale for the choices supporting the Gender Equality Index 
construction............................................................................................................................................................................................................. 3 

3  Statistical coherence of the Gender Equality Index framework ............................................................................................ 8 

3.1  First statistical coherence test for the Gender Equality Index framework............................................................ 8 

3.1.1 

Principal component analysis .................................................................................................................................... 13 

3.2  Second statistical coherence test in the Gender Equality Index framework ..................................................... 14 

3.3  JRC recommendations based on the statistical coherence tests ........................................................................... 15 

4 

Impact of modelling assumptions on the Gender Equality Index results ...................................................................... 17 

5  Conclusions ................................................................................................................................................................................................... 24 

References ............................................................................................................................................................................................................ 25 

i 

 
 
 
 
 
 
 
 
 
 
 
 
 
Abstract 

The  2020  Gender  Equality  Index  ranks  the  27  EU  member  states  and  the  UK  on  31 
performance  indicators  measuring  gender  equalities  in  the  six  domains  of  work,  money, 
knowledge, time, power, health and additionaly the domain of violence, as well as intersecting 
inequalities. By providing relevant statistics, data and measures, all essential components for 
evidence-based  policymaking  and  successful  gender  mainstreaming,  it  supports  the 
assessment of policy outcomes on women and men. Since 2013 the Gender Equality Index 
is released biannually by the European Institute for Gender Equality (EIGE) while from 2019 
and on, the releases will be on annual basis. The European Commission’s Competence Centre 
on  Composite  Indicators  and  Scoreboards  (COIN)  at  the  Joint  Research  Centre  (JRC)  was 
invited by the European Institute for Gender Equality  to audit the 2020 edition of the index. 
The statistical audit presented herein aims to contribute to ensuring the transparency of the 
methodology and the reliability of the results. The report touches upon data quality issues, 
the  conceptual  and  statistical  coherence  of  the  framework  and  the  impact  of  modelling 
assumptions on the results. The analysis suggests that meaningful inferences can be drawn 
from the Gender Equality Index. It confirms that the 2020 Index meets the quality standards 
for statistical soundness and acknowledges it as a reliable composite indicator to measure 
gender equality in the European Union. 

1 

1 

Introduction 

Equality between women and men is and has always been at the core values of the European 
Union  (EU).  It  goes  back  to  the  beginning  of  European  Communities,  in  1957,  when  the 
principle of equal pay for equal work became part of the Treaty of Rome (Article 157) . Over 
the last 63 years, European legislation and changes to the Treaties have reinforced this core 
value and its implementation in the EU; “In all its activities, the Union shall aim to eliminate 
inequalities and to promote equality, between men and women” (Article 8).  

The Gender Equality Index, developed by the European Institute for Gender Equality (EIGE), 
assesses the levels of gender equality across the Member States of the EU based on the EU 
policy framework. It is the benchmark index of gender equality in the EU.  

The statistical assessment of the fifth edition of the index (version 2020) was performed by 
the European Commission’s Competence Centre on Composite Indicators and Scoreboards at 
the Joint Research Centre (JRC) and was conducted upon invitation of the index developers. 
The  first  version  of  the  index,  published  in  2013  (European  Institute  for  Gender  Equality, 
2013),    and  the  following  four  editions  were  published  biannually,  the  last  being  in  2019 
(European  Institute  for  Gender  Equality,  Gender  Equality  Index  2019  Work-life  balance, 
2019). From 2019, the index will be updated annually. The JRC pre-audited an earlier version 
of the index in 2017. The present statistical audit is assessing the last available data where 
most data points are deriving from 2018.  

The index is hierarchically structured and is composed of six core domains (d) (work, money, 
knowledge, time, power and health) and each core domain is sub-divided into two or three 
sub-domains (subd), in total there are 14 sub-domains. Further, each sub-domain is divided 
into one to three indicators. In total, there are 31 indicators across the sub-domains in the 
last  version  of  the  index.  There  are  also  two  satellite  domains,  violence  and  intersecting 
inequalities,  likewise  important  domains  of  gender  equality  but  due  to  data  unavailability, 
they are left apart from the index calculation. 

The Gender Equality Index provides a comprehensive framework of gender equality, in line 
with the EU’s framework on gender equality for both women and men.  No distinction is made 
as to the direction of the gender gap, meaning that the gender approach takes into account 
the situation of women and men in various domains of economic and social life, including 
those where men are in disadvantaged situations. The target is the equality point, and a given 
Member State is equally treated whether a gap is to the advantage of women, or men. The 
JRC  audit  of  the  Gender  Equality  Index  2020  focuses  on  two  main  issues:  the  statistical 
coherence  of  the  hierarchical  structure  of  indicators  and  the  impact  of  key  modelling 
assumptions  on  the  index  ranking.  The  JRC  analysis  complements  the  reported  country 
rankings for the index with confidence intervals in order to better appreciate the robustness 
of these ranks to the calculation methodology (in particular construction of the metric with 
or withought the correctin coeficient, weights and aggregation formula at the domain level). 

2 

2  Conceptual framework, data analysis and rationale for the choices supporting 

the Gender Equality Index construction  

The Gender Equality index is based on a hierarchical structure of six domains and 14 sub-
domains (Table 1). The six domains —work, money, knowledge, time, power and health — 
constitute the core index.   

The index is aggregated at sub-domain level with an arithmetic mean of the metrics of the 
indicators,  while  at  domain  level  a  simple  geometric  mean  is  used  and  at  index  level  a 
weighted  geometric  mean,  with  weights  derived  from  expert  opinions  (analytic  hierarchy 
process AHP). 

Table 1. Conceptual framework of the Gender Equality Index. 

Domain 

Sub-domain 

Indicator  

Full-time equivalent employment rate 

Participation 

Duration of working life  

Code 

Fte 

Dwl 

Work 

Employed people in Education, Human Health and Social 
Work activities 

Seg_W 

Segregation  and 
quality of work 

Ability to take an hour or two off during working hours 
to take care of personal or family matters 

Flexibility 

Money 

Financial 
resources 

Economic 
situation 

Career Prospects Index 

Mean monthly earnings  

Mean equivalised net income  

Prospects 

Earnings 

Income 

Not-at-risk-of-poverty, ≥60% of median income 

Poverty 

S20/S80 income quintile share  

Graduates of tertiary education 

S20/80 

Grad 

Attainment  and 
participation  

Knowledge 

People participating in formal or non-formal education 
and training 

Part 

Segregation 

Tertiary students in the fields of Education, Health and 
Welfare, Humanities and Art (tertiary students) 

Seg_E 

People  caring  for  and  educating  their  children  or 
grandchildren,  elderly  or  people with  disabilities,  every 
day  

Care 

Care activities 

Time 

People doing cooking and/or housework, every day  

Cooking 

Social activities 

Workers  doing  sporting,  cultural  or  leisure  activities 
outside of their home, at least daily or several times a 
week  

Leisure 

3 

 
Domain 

Sub-domain 

Indicator  

Code 

Workers involved in voluntary or charitable activities, at 
least once a month 

Voluntary 

Share of ministers 

Political 

Share of members of parliament  

Share of members of regional assemblies  

Min 

Parl 

Reg 

Economic 

Share  of  members  of  boards  in  largest  quoted 
companies, supervisory board or board of directors 

Boards 

Power 

Share of board members of central bank  

Banks 

Share  of  board  members  of 
organisations  

research  funding 

Res 

Social 

Share  of  board  members 
broadcasting organisations 

in  publically  owned 

Media 

Share of members of highest decision making body of 
the national Olympic sport organisations 

Sport 

Self-perceived health, good or very good 

Status 

Life expectancy in absolute value at birth  

Healthy life years in absolute value at birth  

People who don’t smoke and are not involved in harmful 
drinking 

Health 

Behaviour 

SelfPerc 

Life ex 

HLY 

Risk 

People doing physical activities and/or consuming fruits 
and vegetables  

Behav 

Access 

Population  without  unmet  needs 
examination 

for  medical 

Medical 

People without unmet needs for dental examination 

Dental 

The data sources of the index include several European institutions and agencies, such as the 
Eurostat, Eurofound, and the European Institute of Gender Equality (EIGE). The source of the 
data is a key element when building composite indicators; the quality and adequacy of the 
index lies not only on its development, but also on gathering reliable data.  

The  dataset  already  included  –very  few  –  imputations  for  missing  data  made  by  the 
developers; these concern the values of BE, NL and FR for two indicators only (People who 
don’t  smoke  and  are  not  involved  in  harmful  drinking  and  People  doing  physical  activities 
and/or  consuming  fruits  and  vegetables)  that  were  estimated  with  the  Expectation–

4 

 
maximization1 (EM) algorithm (European Institute of Gender Equality,  2017, p11). In other 
cases, when data were not available, the last available data were used from the available 
time series. Then, for some variables, the EU-28 average was not available. In those cases 
the un-weighted average of the 28 values was used instead. 

For this edition, the developers still consider UK in the analysis, and use EU+UK as aggregate 
for comparison, along with the EU2020 average. 

With regard to the direction, adjustments have been made, so that all variables move towards 
the same direction which means that they have a positive sign, i.e. higher value would indicate 
the ‘desirable situation’. For example, variables measuring ‘healthy life years’ have a positive 
direction,  as  it  is  desirable  to  live  a  long  healthy  life.  Quite  the  opposite,  the  variable 
measuring ‘being  at risk of poverty’ entails a negative sign or interpretation, which means 
that for the Index the indicator was changed to ‘not being at risk of poverty’.  

Each of the 31 indicators present in the framework is converted into a metric that combines 
the women and men figures in a single measure. The metric measures gender gaps by taking 
into  account  the  relative  position  of  women  and  men.  An  important  element  of  it,  is  the 
correcting  coefficient  that  makes  possible  to  take  into  account  the  country  context  by 
comparing  the  levels  achieved  in  all  Member  States  for  each  indicator.  In  this  way,  an 
indicator  with  a  good  score  is  the  reflection  of  both  low  gender  gaps  and  high  levels  of 
achievement.  The  purpose  of  the  correcting  coefficient  is  to  compare  the  performance  of 
each country with the best performer in the EU-28. This actually normalises the indicators 
allowing for comparability across them. 

The data analysis presented herein uses the ‘normalised’ by the metric dataset (1-100 scale) 
for the 27 European countries, and the UK, included in the Gender Equality Index. 

Table 2 shows summary statistics for the 31 indicators included in the Gender Equality Index 
using the ‘normalised’ indicator data (final metric) and highlights the cases in which specific 
issues were found, in terms of data coverage and presence of outliers.  

Table 2. Summary statistics of the metric scores included in the Gender Equality Index (2018 data) 

Code 

Countries 

% 
Missing 
data 

Mean 

Min. 
value 

Max. 
value 

Range 

Skewness 

Kurtosis 

Fte 

Dwl 

Seg_W 

30 

30 

30 

Flexibility 

30 

Prospects 

30 

0 

0 

0 

0 

0 

78.7 

62.1 

93.8 

31.8 

-0.4 

87.9 

75.1 

97.8 

22.7 

-0.2 

33.3 

20.8 

47.0 

26.1 

-0.1 

63.6 

42.6 

92.6 

50.0 

0.5 

92.5 

83.4 

98.3 

14.9 

-0.9 

0.4 

-0.7 

-1.3 

-0.5 

0.1 

1 The Expectation-Maximization (EM) algorithm (Little & Rubin, 2002)  is an iterative procedure that finds the maximum likelihood estimates 
of the parameter vector by repeating two steps. Step 1: The expectation E-step: Given a set of parameter estimates, such as a mean 
vector and covariance matrix for a multivariate normal distribution, the E-step calculates the conditional expectation of the complete-
data log likelihood given the observed data and the parameter estimates. Step 2: The maximization M-step: Given a complete-data 
log likelihood, the M-step finds the parameter estimates to maximize the complete-data log likelihood from the E-step. The two steps 
are iterated until the iterations converge. 

5 

 
                                         
Code 

Countries 

% 
Missing 
data 

Mean 

Min. 
value 

Max. 
value 

Range 

Skewness 

Kurtosis 

Earnings 

30 

Income 

Poverty 

S20/80 

Grad 

Part 

Seg_E 

Care 

30 

30 

30 

30 

30 

30 

30 

Cooking 

30 

Leisure 

30 

Voluntary 

30 

Min 

Parl 

Reg 

Boards 

Banks 

Res 

Media 

Sport 

30 

30 

30 

30 

30 

30 

30 

30 

SelfPerc 

30 

Life ex 

HLY 

Risk 

Behav 

Medical 

30 

30 

30 

30 

30 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

69.8 

47.4 

96.0 

48.7 

-0.1 

71.1 

46.5 

98.6 

52.1 

-0.1 

94.1 

87.0 

98.4 

11.4 

-0.8 

82.8 

65.3 

99.3 

34.0 

0.0 

77.7 

58.4 

95.0 

36.6 

-0.1 

62.7 

45.7 

80.9 

35.3 

53.9 

39.7 

69.0 

29.3 

81.6 

69.6 

97.6 

28.0 

0.3 

0.3 

0.3 

58.3 

31.0 

86.7 

55.7 

-0.1 

62.6 

31.6 

98.0 

66.4 

51.6 

25.5 

85.8 

60.3 

55.5 

9.7 

96.7 

87.0 

54.3 

21.2 

92.6 

71.4 

55.8 

22.6 

95.4 

72.8 

44.0 

14.7 

83.0 

68.3 

0.0 

0.3 

0.1 

0.2 

0.5 

0.1 

0.4 

39.0 

64.6 

67.1 

29.8 

1.0 

1.0 

1.0 

7.1 

89.8 

88.8 

96.5 

95.5 

-0.9 

96.5 

95.5 

-0.9 

90.1 

83.1 

1.4 

86.3 

66.9 

99.7 

32.8 

-1.0 

94.9 

89.2 

97.8 

8.6 

-0.8 

90.3 

82.2 

98.1 

16.0 

0.1 

77.1 

57.5 

89.6 

32.2 

-0.6 

70.7 

27.5 

93.4 

65.9 

-0.7 

97.5 

88.4 

99.9 

11.5 

-1.8 

6 

-1.0 

-0.9 

0.0 

-0.9 

-1.0 

-0.7 

-1.0 

-0.9 

-1.2 

-1.2 

-0.1 

-0.8 

-0.8 

-0.7 

-1.1 

-0.5 

0.2 

0.9 

2.5 

0.5 

-0.8 

-0.8 

-0.1 

0.5 

3.9 

Code 

Countries 

% 
Missing 
data 

Mean 

Min. 
value 

Max. 
value 

Range 

Skewness 

Kurtosis 

Dental 

30 

0 

97.6 

89.9 

100.0 

10.0 

-2.1 

4.6 

Notes: Data refer to year 2018, N=30 (27 EU countries, the UK, EU 2020 average, EU + UK average). Values in red colour indicate absolute 
skewness greater than 2.0 and kurtosis greater than 3.5.  
Source: European Commission, Joint Research Centre, 2020.    

Data coverage is excellent since the very few missing values were imputed beforehand, as 
already discussed.  

Potentially  problematic  indicators  that  could  bias  the  overall  index  results  are  usually 
identified  on  the  basis  of  two  measures  related  to  the  shape  of  the  distributions:  the 
skewness and kurtosis. A practical rule is that an indicator should be considered for treatment 
if it has an absolute skewness greater than 2.0 and kurtosis greater than 3.5 (Groeneveld & 
Meeden, 1984). 

Overall, indicator scores do not seem to have outliers or skewed distributions, except for the 
indicator ‘People without unmet needs for dental examination’ (Dental) which is at the limits 
of this threshold without that consisting a problem.  Our suggestion would be to monitor 
its distribution in the future editions and intervene in case the distribution becomes 
more skewed. 

The  developer’s  choices  on  the  framework,  the  use  of  the  specific  metric,  weights  and 
aggregation methods are very well justified. Nevertheless in the section 4 of this report we 
challenge  those  choices,  prerforming  a  robustness  analysis  to  show  how  stable  in  these 
choices the index is. 

7 

 
3  Statistical coherence of the Gender Equality Index framework 

The reliability of the Gender Equality Index depends - among other things – on the degree of 
coherence between the conceptual framework and the statistical structure of the data. The 
more the conceptual framework supports the statistical structure, the higher the reliability of 
the index will be. The coherence of the Gender Equality Index framework was assessed using 
two tests: (a) firstly, the analysis of the extent to which the indicators can explain a sufficient 
amount of variation in the aggregated scores (be those sub-domains, domains or the overall 
index). This first test entails correlation, cross-correlation and principal component analysis. 
Secondly,  (b)  the  analysis  of  the  impact  on  the  country  ranks  with  no  least  influential 
indicators (as identified in the first test) in the Gender Equality Index framework. The validity 
of the framework relies on the combination of both statistical and conceptual soundness. 

Given that the present statistical analysis of the Gender Equality Index is in part, though not 
exclusively,  based  on  correlations,  the  correspondence  of  the  index  to  a  real-world 
phenomenon  needs  to  be  critically  addressed  by  experts  in  the  field  because  ‘correlations 
need  not  necessarily  represent  the  real  influence  of  the  individual  indicators  on  the 
phenomenon being measured’. (OECD and JRC, 2008). In a nutshell, the argument is that the 
validity  of  the  framework  relies  on  the  combination  of  both  statistical  and  conceptual 
soundness. 

3.1  First statistical coherence test for the Gender Equality Index framework 

The  first  coherence  test  consists  of  correlation  and  cross-correlation  analyses,  which  was 
used to assess to what extent the data collected support the index’s conceptual framework.  
There is no redundancy of information in the Gender Equality Index framework given the lack 
of highly collinear (i.e. Pearson correlation coefficients greater than 0.92) pairs of indicators 
within the same sub-domain.  Indicators within most sub-domains exhibit modest to strong 
correlations between each other, see Table 3. 

8 

 
Table 3. Correlation matrix of the 31 indicators.  

Domain

Indicator

e
t
F

l

w
D

g
e
S

y
t
i
l
i

b
i
x
e
l
F

s
t
c
e
p
s
o
r
P

s
g
n

i

n
r
a
E

e
m
o
c
n

I

y
t
r
e
v
o
P

0
8
/
0
2
S

d
a
r
G

t
r
a
P

g
e
S

e
r
a
C

g
n

i
k
o
o
C

e
r
u
s
a
e
L

y
r
a
t
n
u

l

o
V

i

n
M

l
r
a
P

l
r
a
P
g
e
R

s
d
r
a
o
B

s
k
n
a
B

g
n

i

d
n
u
F

a

i

d
e
M

t
r
o
p
S

c
r
e
P
f
l
e
S

x
e
e
f
i
L

Y
L
H

k
s
i
R

v
a
h
e
B

l

a
c
i

d
e
M

l

a
t
n
e
D

k
r
o
W

y
e
n
o
M

l

e
g
d
e
w
o
n
K

e
m
T

i

r
e
w
o
P

h
t
l

a
e
H

Fte

Dwl

Seg

1.00

0.70

1.00

-0.15 0.15

1.00

Flexibility

-0.13 0.22

0.50

1.00

Prospects

0.39

0.35

0.25

0.19

1.00

Earnings

-0.16 0.07

0.85

0.48

0.28

1.00

Income

Poverty

S20/80

Grad

Part

Seg

Care

Cooking

Leasure

-0.01 0.26

0.81

0.48

0.32

0.91

1.00

-0.11 -0.09 0.35 -0.05 0.09

0.44

0.37

1.00

0.11

0.04

0.14

0.01

0.14

0.29

0.28

0.81

1.00

0.12

0.32

0.64

0.45

0.26

0.63

0.67

0.19

0.15

1.00

0.25

0.56

0.64

0.38

0.36

0.65

0.76

0.39

0.33

0.63

1.00

-0.20 -0.24 0.54

0.39

0.35

0.50

0.42

0.30

0.20

0.20

0.26

1.00

0.45

0.55

0.18

0.18

0.20

0.23

0.29 -0.20 -0.10 0.11

0.47 -0.05 1.00

0.37

0.59

0.36

0.47

0.54

0.38

0.46 -0.13 -0.04 0.47

0.60

0.19

0.47

1.00

0.08

0.43

0.60

0.60

0.42

0.69

0.73

0.24

0.29

0.60

0.81

0.42

0.46

0.66

1.00

Voluntary

0.16

0.43

0.46

0.43

0.33

0.56

0.55

0.37

0.51

0.33

0.65

0.22

0.41

0.50

0.74

1.00

Min

Parl

RegParl

Boards

Banks

Funding

Media

Sport

SelfPerc

Life ex

HLY

Risk

Behav

Medical

Dental

0.17

0.55

0.35

0.32

0.24

0.35

0.41

0.18

0.05

0.21

0.51

0.16

0.27

0.38

0.56

0.43

1.00

0.07

0.45

0.53

0.40

0.21

0.59

0.60

0.25

0.15

0.33

0.66

0.43

0.32

0.46

0.66

0.44

0.78

1.00

0.16

0.51

0.58

0.45

0.32

0.54

0.55

0.18

0.16

0.52

0.64

0.31

0.23

0.53

0.72

0.45

0.79

0.84

1.00

-0.04 0.30

0.42

0.27

0.18

0.52

0.50

0.38

0.29

0.18

0.45

0.37

0.22

0.33

0.55

0.55

0.68

0.74

0.69

1.00

0.14

0.25

0.31

0.22

0.04

0.24

0.25 -0.08 -0.31 0.22

0.28

0.20

0.39

0.33

0.37

0.07

0.60

0.49

0.57

0.42

1.00

0.15

0.18

0.38

0.45

0.32

0.52

0.48 -0.03 -0.10 0.31

0.28

0.32

0.14

0.42

0.44

0.20

0.57

0.54

0.57

0.40

0.52

1.00

0.33

0.45

0.17

0.39

0.37

0.20

0.21 -0.26 -0.17 0.24

0.28 -0.04 0.56

0.38

0.34

0.35

0.45

0.29

0.38

0.27

0.44

0.43

1.00

0.28

0.53

0.51

0.40

0.36

0.42

0.45

0.08 -0.06 0.47

0.61

0.34

0.38

0.58

0.58

0.52

0.68

0.66

0.70

0.62

0.62

0.45

0.49

1.00

-0.40 -0.29 0.58

0.36

0.05

0.66

0.55

0.50

0.33

0.51

0.27

0.51 -0.19 0.13

0.41

0.40

0.14

0.28

0.25

0.26

0.17

0.27

0.02

0.30

1.00

-0.29 -0.02 0.80

0.49 -0.06 0.84

0.79

0.52

0.38

0.54

0.57

0.49

0.09

0.18

0.58

0.53

0.32

0.53

0.44

0.41

0.24

0.35

0.04

0.34

0.77

1.00

-0.32 -0.43 0.50

0.20 -0.11 0.40

0.28

0.18

0.02

0.17

0.00

0.60 -0.19 -0.06 0.14

0.07

0.02

0.17

0.16

0.11

0.35

0.27 -0.17 0.25

0.65

0.55

1.00

-0.36 -0.23 0.33

0.25 -0.39 0.27

0.21

0.42

0.33

0.06

0.14

0.39 -0.06 -0.34 0.17

0.19

0.08

0.21

0.16

0.33

0.11 -0.17 -0.25 0.13

0.31

0.54

0.43

1.00

0.26

0.52

0.65

0.39

0.42

0.67

0.78

0.36

0.39

0.58

0.76

0.27

0.40

0.54

0.69

0.62

0.28

0.46

0.46

0.40

0.12

0.19

0.18

0.43

0.31

0.59

0.08

0.22

1.00

-0.18 -0.22 0.36

0.34 -0.06 0.42

0.41

0.38

0.23

0.16

0.09

0.33 -0.16 -0.25 0.10

0.06

0.18

0.17

0.12

0.24

0.07

0.43 -0.03 0.08

0.35

0.43

0.45

0.41

0.12

1.00

-0.18 -0.22 0.29

0.16

0.31

0.42

0.44

0.38

0.31

0.30

0.20

0.42 -0.23 -0.08 0.33

0.31

0.11

0.11

0.12

0.10 -0.10 0.10 -0.11 0.10

0.56

0.37

0.38

0.24

0.23

0.48

1.00

Notes: Numbers represent the Pearson correlations coefficients between the index indicators. Correlations that are not significant at the significance level of α = 0.10 are left light grey. Negative significant correlations 
are in red. Blue boxes show the conceptual grouping of the indicators into subdomains and black contour boxes the grouping of indicators into domains. Source: European Commission, Joint Research Centre, 2020. 

9 

 
 
 
Table 4 illustrates the index correlation structure within and across the 14 sub-domains and 
it confirms the expectation that most indicators, apart from two, are more associated with 
their own sub-domain than to any of the other sub-domains. The two conflicting indicators 
are  both  in  sub-domain  Quality  of  work  and  Segregation  (subd2):  indicator  Segregation  is 
more related to sub-domain Financial resources (subd3) and indicator Prospects is marginally 
higher correlated to sub-domain Care activities (subd7).  

At  the  next  level,  the  majority  of  the  indicators  are  more  associated  with  their  pertaining 
domain but seven indicators are in fact correlating better with other domains (in five cases 
only marginally). Indicator Segregation (Seg_W) is more related to the domains Money (d2), 
Knowledge  (d3)  and  Health  (d6),  than  to  its  pertaining  domain  Work  (d1).  Indicator 
Participation  (Part)  is  more  related  to  the  domains  Money  (d2)  and  Time  (d4)  than  to  its 
domain Knowledge (d3). Five out of the seven indicators in domain Health (d6) are marginally 
more related to either the Money (d2), or Knowledge (d3) domains and the related indicators 
are  Self-perceived  health  (SelfPerc),  Life  expectancy  (Life_ex),  Healthy  life  years  (HLY), 
Population  without  unmet  medical  examination  needs  (Medical)  and  Population  without 
unmet dental examination needs (Dental). For most indicators these results suggest that the 
allocation  of  the  indicators  to  the  specific  sub-domain,  and  allocation  of  sub-domains  to 
domains, is consistent both from conceptual and statistical perspectives.  

The majority of the indicators (24 out of 31) also are positively and significantly correlated 
with the overall index. However, seven indicators are found to be not sufficiently related to 
the  overall  index:  Full-time  equivalent  employment  (Fte)  in  the  Work  domain  (d1),  Not  at-
risk-of-poverty (Poverty) and Income distribution S20/S80 in the Money domain (d2), Healthy 
life years (HLY), Risk (Risk), Population without unmet medical examination needs (Medical) 
and Population without unmet dental examination needs (Dental) in the Health domain (d6). 
These  results  are  in  line  with  the  earlier  editions  of  the  index.  However,  given  that,  these 
seven indicators are influential at the first and second aggregation levels (sub-domains and 
domains),  their  inclusion  in  the  framework  is  partially  supported  by  the  analysis. 
Nevertheless, as mentioned above, it is noted that the three indicators of the Health domain 
(d6) were found to be correlating better with other domains. 

10 

 
Table 4. Correlations between indicators and other Gender Equality Index components. 

Domain

Subdomain

Indicator

subd1

subd2

subd3

subd4

subd5

subd6

subd7

subd8

subd9 subd10 subd11 subd12 subd13 subd14

d1

d2

d3

d4

d5

d6

Index

k
r
o
W

y
e
n
o
M

l

e
g
d
e
w
o
n
K

e
m
T

i

r
e
w
o
P

h
t
l

a
e
H

Participation          
(subd1)

Fte

Dwl

Quality of work 
& Segr. (subd2)

Financial 
resources 
(subd3)
Economic 
situation (subd4)

Seg

Flexibility

Prospects

Earnings

Income

Poverty

S20/80

Attainment & 
Partic. (subd5)
Segregation 
(subd6)
Care activities        
(subd7)

Grad

Part

Seg

Care

Cooking

Social activities      
(subd8)

Leasure

Voluntary

Min

Political                          
(subd9)

Parl

RegParl

Economic               
(subd10)

Boards

Banks

Funding

Social activities      
(subd11)

Media

Sport

SelfPerc

Status                      
(subd12)

Life ex

HLY

Risk
Behaviour                    
(subd13)

Behav

Access                      
(subd14)

Medical

Dental

0.94

0.91

-0.02

0.03

0.40

-0.06

0.12

-0.11

0.09

0.23

0.42

-0.23

0.54

0.51

0.26

0.31

0.37

0.26

0.35

0.12

0.20

0.18

0.41

0.43

-0.38

-0.19

-0.40

-0.33

0.41

-0.21

-0.06

-0.09

0.28

0.79

0.90

0.44

0.72

0.71

0.13

0.09

0.61

0.59

0.55

0.23

0.57

0.73

0.54

0.40

0.52

0.60

0.38

0.28

0.52

0.40

0.54

0.48

0.63

0.31

0.21

0.61

0.35

0.17

0.85

0.50

0.31

0.98

0.98

0.41

0.29

0.67

0.72

0.47

0.27

0.43

0.73

0.57

0.39

0.61

0.56

0.52

0.25

0.51

0.21

0.44

0.62

0.84

0.35

0.24

0.74

0.42

-0.22

0.28

0.44

0.06

0.01

0.19

0.00

0.13

0.33

0.31

0.89

0.99

0.17

0.35

0.23

-0.13

-0.06

0.29

0.49

0.08

0.18

0.17

0.32

-0.26

-0.08

-0.20

-0.03

0.38

0.43

0.06

0.36

0.40

0.27

0.34

0.20

0.48

0.71

0.47

0.34

0.71

0.79

0.31

0.26

0.91

0.89

0.25

0.31

0.58

0.77

0.53

0.38

0.54

0.64

0.34

0.27

0.33

0.29

0.59

0.44

0.61

0.10

0.11

0.73

0.14

0.28

-0.20

-0.24

0.54

0.39

0.35

0.50

0.42

0.30

0.20

0.20

0.26

1.00

-0.05

0.19

0.42

0.22

0.16

0.43

0.31

0.37

0.20

0.32

-0.04

0.34

0.51

0.49

0.60

0.39

0.27

0.33

0.42

0.45

0.66

0.34

0.43

0.49

0.38

0.46

-0.17

-0.07

0.40

0.63

0.13

0.73

0.94

0.68

0.54

0.39

0.47

0.49

0.33

0.40

0.38

0.50

0.59

0.03

0.17

-0.12

-0.28

0.56

-0.25

-0.15

0.12

0.46

0.58

0.57

0.41

0.68

0.70

0.31

0.41

0.52

0.79

0.36

0.47

0.64

0.95

0.91

0.54

0.61

0.65

0.59

0.27

0.36

0.37

0.59

0.43

0.60

0.12

0.19

0.71

0.09

0.35

0.15

0.54

0.51

0.42

0.28

0.52

0.55

0.21

0.12

0.37

0.64

0.31

0.29

0.48

0.69

0.47

0.93

0.93

0.94

0.75

0.60

0.60

0.41

0.73

0.23

0.45

0.12

0.15

0.42

0.17

0.12

0.07

0.32

0.43

0.28

0.12

0.43

0.42

0.14

-0.06

0.24

0.42

0.32

0.38

0.39

0.53

0.33

0.75

0.71

0.73

0.79

0.89

0.55

0.43

0.73

0.24

0.37

0.29

0.25

0.28

0.17

-0.02

0.31

0.47

0.43

0.52

0.44

0.48

0.47

-0.10

-0.14

0.41

0.47

0.25

0.44

0.57

0.56

0.43

0.70

0.61

0.68

0.52

0.65

0.81

0.81

0.77

0.24

0.30

0.14

-0.14

0.32

0.22

0.03

-0.40

-0.31

0.67

0.38

-0.02

0.69

0.58

0.46

0.28

0.47

0.28

0.59

-0.16

0.09

0.41

0.37

0.15

0.33

0.29

0.27

0.26

0.32

-0.03

0.33

0.96

0.84

0.81

0.43

0.33

0.44

0.53

0.08

0.35

0.67

0.42

0.21

0.67

0.74

0.46

0.46

0.51

0.69

0.38

0.32

0.32

0.65

0.59

0.26

0.47

0.45

0.46

0.14

0.10

0.06

0.41

0.38

0.71

0.23

0.56

0.93

0.26

0.29

-0.21

-0.25

0.38

0.29

0.13

0.48

0.49

0.44

0.31

0.26

0.16

0.43

-0.22

-0.20

0.24

0.21

0.17

0.17

0.14

0.21

-0.01

0.32

-0.08

0.11

0.52

0.47

0.49

0.39

0.20

0.88

0.84

0.46

0.72

0.61

0.72

0.57

0.54

0.63

0.04

0.12

0.61

0.69

0.30

0.48

0.73

0.71

0.59

0.53

0.56

0.67

0.38

0.34

0.51

0.55

0.67

0.17

0.40

0.02

-0.01

0.70

0.16

0.10

-0.06

-0.01

0.16

0.78

0.43

0.29

0.93

0.92

0.63

0.57

0.62

0.73

0.47

0.18

0.35

0.71

0.65

0.36

0.59

0.54

0.56

0.14

0.41

0.12

0.37

0.65

0.85

0.32

0.33

0.76

0.44

0.47

0.12

0.78

0.54

0.44

0.75

0.74

0.39

0.29

0.67

0.69

0.83

0.15

0.47

0.74

0.46

0.34

0.60

0.59

0.45

0.30

0.41

0.14

0.58

0.60

0.69

0.47

0.34

0.61

0.31

0.45

0.25

0.57

0.55

0.56

0.48

0.63

0.68

0.16

0.27

0.53

0.81

0.31

0.60

0.81

0.94

0.84

0.53

0.61

0.65

0.54

0.34

0.39

0.45

0.64

0.32

0.50

0.05

0.03

0.73

-0.03

0.20

0.18

0.48

0.51

0.43

0.28

0.52

0.52

0.11

-0.02

0.37

0.56

0.33

0.42

0.51

0.65

0.45

0.87

0.82

0.86

0.77

0.80

0.70

0.59

0.82

0.27

0.42

0.21

0.13

0.38

0.20

0.04

-0.07

0.16

0.75

0.46

0.15

0.77

0.80

0.54

0.49

0.56

0.64

0.49

0.19

0.24

0.65

0.58

0.25

0.47

0.44

0.46

0.17

0.18

0.01

0.40

0.60

0.84

0.45

0.62

0.85

0.42

0.46

0.17

0.49

0.72

0.61

0.44

0.77

0.78

0.26

0.20

0.60

0.78

0.50

0.45

0.66

0.87

0.67

0.74

0.83

0.85

0.73

0.59

0.65

0.50

0.79

0.45

0.65

0.26

0.19

0.67

0.25

0.24

Notes: Numbers represent Pearson correlations coefficients.. Correlations that are not significant at the significance level of α = 0.10 are left light grey. Negative significant correlations are in red. Blue boxes show 
the conceptual grouping of the indicators into subdomains and black contour boxes the grouping of indicators into domains. Source: European Commission, Joint Research Centre, 2020. 

11 

    
 
 
All sub-domains correlate moderately, or strongly with the respective domains (correlation 
coefficients from 0.51 to 0.96, Table 5). Nevertheless, sub-domain Access (subd14) is slightly 
more  associated  with  the  Money  domain  (d2)  than  to  its  Health  domain  (d6)  which  is  in 
alignment  with  previous  results  showing  that  these  indicators  were  higher  correlated  with 
the  Money  domain  (d2).  Further,  the  six  domains  strongly  correlate  and  in  a  relatively 
balanced way with the index (correlation coefficients ranging between 0.66 and 0.89, Table 
5). Further, it is noticed that the Power domain (d5) has the highest correlation with the index, 
and the Health domain (d6) has the lowest correlation and at the same time has the lowest 
experts’ weight. 

Table 5. Correlations between sub-domains, domains and index. 

GEI components

subd1 subd2 subd3 subd4 subd5 subd6 subd7 subd8 subd9 subd10 subd11 subd12 subd13 subd14 d1

d2

d3

d4

d5

d6 GEI

Participation

1.00

Quality of work & Segr. 0.10

1.00

Financial resources 

0.03

0.74

1.00

Economic situation 

0.04

0.11

0.33

1.00

Attainment & Partic.

0.35

0.67

0.77

0.28

1.00

0.63 0.04 0.05 0.43 0.34 0.04 0.34

0.84 0.66 0.76 0.69 0.55 0.64 0.79

0.60 0.95 0.76 0.67 0.54 0.80 0.79

0.10 0.61 0.32 0.25 0.02 0.52 0.22

0.72 0.74 0.75 0.73 0.50 0.67 0.76

Segregation

-0.23

0.55

0.47

0.23

0.25

1.00

0.30 0.47 0.83 0.31 0.33 0.49 0.50

Care activities 

0.59

0.52

0.43

-0.10

0.57

0.13

1.00

0.74 0.34 0.41 0.84 0.55 0.25 0.68

Social activities 

0.30

0.69

0.71

0.40

0.72

0.36

0.66

1.00

0.71 0.74 0.66 0.96 0.61 0.67 0.85

Political 

0.35

0.54

0.55

0.15

0.55

0.31

0.48

0.64

1.00

0.63 0.52 0.54 0.64 0.91 0.41 0.86

Economic 

0.20

0.38

0.44

-0.01

0.36

0.32

0.44

0.48

0.78

1.00

0.42 0.38 0.43 0.51 0.93 0.35 0.77

Social activities

0.41

0.61

0.49

-0.13

0.49

0.25

0.60

0.54

0.71

0.70

1.00

0.71 0.37 0.45 0.60 0.87 0.23 0.80

Status 

-0.39

0.52

0.65

0.34

0.42

0.59

0.01

0.42

0.27

0.31

0.25

1.00

0.19 0.66 0.65 0.31 0.31 0.67 0.48

Behaviour 

0.22

0.59

0.72

0.48

0.66

0.38

0.37

0.67

0.42

0.33

0.21

0.45

1.00

0.59 0.77 0.65 0.63 0.37 0.96 0.64

Access 

-0.25

0.37

0.50

0.35

0.24

0.43

-0.24

0.24

0.17

0.10

0.15

0.56

0.32

1.00

0.16 0.53 0.44 0.09 0.15 0.51 0.28

Notes: Numbers represent the Pearson correlations coefficients between the index components. Correlations that are not significant at the 
significance level of α = 0.10 are left light grey. Black contour boxes show the conceptual grouping of the indicators into sub-domains and 
domains.  Very  strong  correlations  (i.e.  Pearson  correlation  coefficients  greater  than  0,92)  are  marked  in  bold.  Negative  significant 
correlations are in red.            
Source: European Commission, Joint Research Centre, 2020. 

12 

 
 
 
Table 6. Correlations between domains and the index. 

Work

Money

Knowledge

Time

Power

Health

Work

Money

Knowledge

Time

Power

Health

1.00

0.55

0.63

0.78

0.63

0.52

1.00

0.75

0.66

0.47

0.85

1.00

0.64

0.52

0.72

1.00

0.64

0.58

1.00

0.38

1.00

GEI

0.81

0.75

0.78

0.86

0.89

0.66

Notes: Numbers represent the Pearson correlations coefficients.  
Source: European Commission, Joint Research Centre, 2020. 

3.1.1  Principal component analysis 

Next, the principal component analysis (PCA) was used to confirm whether there is a single 
statistical dimension in each index component, which would give the “statistical justification” 
for aggregating indicators into one number. Technically, the expectation here is that there is 
only  one  principal  component  with  eigenvalue  greater  than  1.0  (or  explained  variance  of 
around 70%).  

Indeed, PCA results confirm the presence of a single latent dimension within each of the 6 
domains that captures between 55% in the Work domain (d1) to 83% in the Time domain 
(d4)  of  the  total  variance  in  the  underlying  sub-domains.  The  results  of  the  six  PCAs 
performed in the sub-domains of the six domains are summarised in Table 7. 

Table 7. Results of the PCA (first PC) within each Gender Equality Index domain 

First principal 
component (PC1)

Eigenvalue

Percentage of 
variance

Work

Money

Knowledge

Time

Power

Health

1.1

1.33

1.25

1.66

2.47

1.89

0.55

0.66

0.63

0.83

0.82

0.63

Notes: Information is shown only for the first principal component (PC) of each of the analysis performed individually for each domain. The 
analysis was done at sub-domain level for each domain. 
Source: European Commission, Joint Research Centre, 2020. 

13 

 
 
 
 
 
Finally, as can be seen in Table 8, the six domains share a single statistical dimension that 
summarizes 69% of the total variance. This latter result supports the aggregation of the six 
domains into one number that would represent the common dimension that they share.  

Table 8. Results of the Principal component analysis at index level 

Eigenvalue

Percentage of 
variance

Cumulative percentage 
of variance

PC1

PC2

PC3

PC4

PC5

PC6

4.1

0.8

0.4

0.3

0.2

0.1

68.5

14.3

6.6

4.9

3.5

2.2

68.5

82.8

89.4

94.3

97.8

100

Notes: Information for all principal components (PC) of the analysis performed at domain level. 
Source: European Commission, Joint Research Centre, 2020. 

Concluding,  the  first  statistical  coherence  test  and  the  principal  component  analysis, 
corroborated  the  three-level  structure  of  the  Gender  Equality  Index  framework  and  the 
unidimensionality of all index components (sub-domains, domains and index). Furthermore, 
all 31 indicators were found to be influential at the first and second aggregation level (sub-
domains  and  domains).  However,  two  indicators  were  slightly  more  associated  with  other 
sub-domains with respect to their own sub-domains and seven indicators (in five cases only 
marginally) were more associated with other domains. At the last aggregation level, 24 out 
of  31  indicators  are  significantly  correlated  with  the  overall  index  while  seven  indicators 
explain  a  not  full  sufficient  amount  of  variation  in  the  index  scores.  Nevertheless,  the 
information  content  is  kept  at  all  levels  of  aggregation  in  the  index  framework  for  the 
majority of the underlying indicators.  

3.2  Second  statistical  coherence  test  in  the  Gender  Equality  Index 

framework 

A  second  coherence  test  aims  at  assessing  whether  the  seven  indicators  found  to  be  not 
significantly correlated with the overall index, are important in a different way in the overall 
index, for instance by influencing the overall index ranking.  

The  seven indicators that are found not to  be  sufficiently related to the  overall index are: 
Full-time equivalent employment (Fte), Not at-risk-of-poverty (Poverty), Income distribution 
S20/S80, Healthy life years (HLY), Risk (Risk), Population without unmet medical examination 
needs (Medical) and Population without unmet dental examination needs (Dental). However, 
given that these seven indicators are influential at the first and second aggregation levels 
(sub-domains  and  domains),  their  inclusion  in  the  Gender  Equality  Index  framework  is 

14 

 
 
 
 
supported  to  a  certain  extent  by  the  analysis.  The  test  consists  of  assessing  how  country 
ordering changes when these indicators are omitted one-at-a-time from the calculation.  

Table 9. Number of countries with a rank change when a selected indicator is omitted. 

Indicator

Ftc (ind1)

Poverty (ind8)

S20/80 (ind9)

HLY (ind27)

Risk (ind28)

Medical (ind30)

Dental (ind31)

Number of rank changes when omitted

4

8

4

0

8

0

0

Source: European Commission, Joint Research Centre, 2020. 

Two indicators are found to be somewhat more influential: Not at-risk-of-poverty (Poverty) 
and  Risk (Risk). When  omitting either of the indicators Not at-risk-of-poverty  or  Risk, eight 
Member  States  either  lose,  or  gain  one  position  in  ranking.  When  omitting  the  Full-time 
equivalent  employment  indicator  (Fte),  or  Income  distribution  S20/S80  indicator,  four 
Member  States  change  ranks  with  one  position.  Omitting  either  one  of  the  remaining 
indicators:  Healthy  life  years  (HLY),  Population  without  unmet  medical  examination  needs 
(Medical) and Population without unmet dental examination needs (Dental) has no impact on 
the index ranks, and as already discussed, these can explain only a small (negligible) amount 
of  variation  in  the  scores.  The  results  are  summarized  in  Table  9.  Although  these  three 
indicators are conceptually enriching the framework and their statistical impact contribute to 
the first and second aggregation levels, it is recommended to carefully monitor their 
performance in the coming releases of the index. 

3.3  JRC recommendations based on the statistical coherence tests 

Generally, the results of the two statistical coherence tests (correlation analysis and impact 
of excluding from the Gender Equality Index framework the least influential indicators one-
at-a time) suggest that the conceptual grouping of the indicators into 14 sub-domains and 
six domains is statistically confirmed, and that the index is in general influenced by most but 
not all of the underlying indicators.  

According  to  the  first  coherence  test,  24  out  of  the  31  indicators  are  positively  and 
significantly correlated with the overall index. The remaining seven indicators that are found 
to be the least influential at the index level are: Full-time equivalent employment (Fte), Not 
at-risk-of-poverty (Poverty), Income distribution S20/S80, Healthy life years (HLY), Risk (Risk), 
Population  without  unmet  medical  examination  needs    (Medical)  and  Population  without 
unmet  dental  examination  needs  (Dental).  However,  given  that  these  seven  indicators  are 
influential at the first two aggregation levels (sub-domains and domains), their inclusion in 
the  framework  is  to  a  certain  extent  corroborated  by  the  analyses.  Although  conceptually 
enriching  and  statistically informative  up to the  second  aggregation level, the information 
content  of  these  indicators  does  not  show  sufficiently  up  at  the  index  level.  The  second 

15 

 
 
coherence  test  offers  an  additional  perspective  on  the  impact  of  these  seven  indicators, 
showing that three of them have a low impact on the country ranks and can explain only a 
small (negligible) amount of variation in the scores. These three indicators follow Healthy life 
years (HLY), Population without unmet medical examination needs (Medical) and Population 
without  unmet  dental  examination  needs  (Dental).  Moreover,  these  three  indicators  were 
“puzzling” as they also  are more  associated with  other  domains  with  respect to their  own 
domains.  The  JRC  recommendation  to  the  Gender  Equality  Index  development  team  is  to 
monitor carefully  how these three indicators perform in the  coming releases  of the index, 
and eventually fine-tune the framework in this respect. 

16 

 
4 

Impact of modelling assumptions on the Gender Equality Index results 

A fundamental step of the statistical analysis of a composite indicator is to assess the effect 
of different modelling  assumptions among reasonable alternatives. The development  of  a 
composite  indicator,  like  any  model,  involves  assumptions  and  subjective  decisions.  The 
Gender Equality Index is the outcome of a number of choices concerning, among other things, 
the  theoretical  framework,  the  indicators  selected,  the  metric  construction,  the  weights 
assigned  and  the  aggregation  method.  Some  of  these  choices  may  be  based  on  expert 
opinion  or  other  considerations,  driven  by  statistical  analysis  or  by  the  need  for  ease  of 
communication or draw attention to specific issues. 

This section aims to test the impact of varying some of these assumptions within a range of 
plausible alternatives in an uncertainty analysis. The objective is therefore to try to quantify 
the uncertainty in the ranks of the Gender Equality Index, which can demonstrate the extent 
to which countries can be differentiated by their scores. 

As  suggested  in  the  relevant  literature  on  composite  indicators  (M  Saisana,  Tarantola,  & 
Saltelli,  2005;  Michaela  Saisana  &  Saltelli,  2011),  the  robustness  assessment  is  based  on 
Monte  Carlo  simulations  and  multi-modelling  approaches.  In  particular,  the  key  modelling 
issues  considered  in  the  assessment  of  the  Gender  Equality  Index  are  the  use  of  the 
correcting coefficient α, the aggregation formula and the weights at domain level, as outlined 
in Table 10. These were chosen as plausible alternative pathways in the construction of the 
index, which can be relatively easily investigated.  

Metric  construction.  The  metric  used  in  the  index  measures  gender  gaps  by  taking  into 
account the relative position of women and men. An important element of it, is the correcting 
coefficient that makes possible to take into account the country context by comparing the 
levels achieved in all Member States for each indicator. In this way, an indicator with a good 
score  is  the  reflection  of  both  low  gender  gaps  and  high  levels  of  achievement.  This 
construction  has  been  an  important  methodological  choice  of  the  developers  based  on 
evidence and experts’ opinion. It is important though to test its effect in the countries overall 
ranking and understand its contribution to a possible volatility of results. 

Aggregation  formula.  Regarding  the  aggregation  formula,  the  Gender  Equality  Index  team 
opted for the geometric average of the sub-domains into the domains and then again the 
geometric average of the six domains. This is a rather non-compensatory approach, since the 
geometric mean tends to penalize the existence of a low value, particularly when the other 
values are not so low. This choice is in line with relevant literature that challenges the use of 
simple arithmetic averages at higher aggregation levels because of their fully compensatory 
nature,  in  which  a  comparative  high  advantage  on  a  few  indicators  can  compensate  a 
comparative disadvantage on many indicators (Munda, 2008). To assess the impact of this 
choice,  a  comparison  with  the  arithmetic  mean  is  included  in  the  analysis.  The  arithmetic 
mean allows outstanding performance in some aspects to balance for weaknesses in others 
and  vice-versa.  The  comparison  of  the  two  aggregation  approaches  should  be  able  to 
highlight the individual countries with unbalanced profiles.  

Weights.  The  weighting  system  of  the  index  at  domain  level  is  based  on  experts’  opinion, 
using the analytic hierarchy process (AHP). The effect of randomly varying these weights by 
+/-25%  is  investigated:  Monte  Carlo  simulation  comprised  1,000  runs  of  different  sets  of 
weights for the six domains constituting the index. The weights are the result of a random 
extraction based on uniform continuous distributions centred in the reference value plus or 
minus 25% of this value. 

17 

Four models were tested comparing the different aggregation formulas and the presence or 
not of the correcting coefficient α in the metric, which resulted in a total of 4,000 runs of 
simulations, as can be seen in Table 10. 

Table 10. Sources of uncertainty examined in the robustness analysis. 

Assumption 

Reference 

Alternative 

I.  Uncertainty  in  the  use  of  the 
correcting coefficient 

Correcting coefficient  

II.  Uncertainty  in  the  aggregation 
method at domain and index level 

Geometric  mean  (at  both 
levels) 

III.  Uncertainty  intervals  for  the 
domain weights 

Work: 0.19 
Money: 0.15 
Knowledge: 0.22 
Time: 0.15 
Power: 0.19 
Health: 0.10 

Metric without the correcting 
coefficient α 

Arithmetic  mean  (at  both 
levels) 
U[0.14,0.24]2 
U[0.12,0.19] 
U[0.16,0.27] 
U[0.11,0.18] 
U[0.14,0.24] 
U[0.07,0.12] 

The main results obtained from the robustness analysis are shown in Figure 1, with median 
ranks and 90% intervals computed across the 4,000 Monte Carlo simulations. Countries are 
ordered  from  best  to  worst  according  to  their  original  index  rank  where  the  blue  dots 
represent the median rank among the iterations. For each country, the error bars represent 
the 90% interval across all simulations, that is, from the 5th to the 95th percentile. Countries 
for which the intervals have a range larger than 5 are highlighted with a red point.  

2 For the calculations, weights with 15 digits were used. In the table, they are rounded for simplification. 

18 

 
 
 
                                         
Figure 1.Robustness analysis on ranks (CRII rank vs median rank and 90% intervals) 

Source: European Commission, Joint Research Centre, 2020. 

Gender Equality Index ranks are shown to be representative of a plurality of scenarios and 
robust  to  changes  in  the  absence  or  presence  of  the  correcting  coefficient,  aggregation 
method and domain weights. If one considers the median rank across the simulated scenarios 
as being representative of these scenarios, then the fact that the index rank is very close to 
the  median  rank  (less  than  four  positions  away)  for  all  the  countries 3  included  in  the 
analysis,  suggests  that  the  Gender  Equality  Index  is  a  suitable  summary  measure. 
Furthermore, the reasonable narrow intervals for the majority of the countries’ ranks (less 
than 6 positions for 22 out of 30 countries3, including the EU averages) imply that the index 
ranks are also, for most countries, robust to the applied changes. However, it is also true that 
four country ranks, those of Bulgaria, Romania, Austria and Spain, vary significantly (seven 
and  more  positions)  with  the  changes  in  the  assumptions  and  four  other  (Cyprus,  Malta, 
Luxemburg and Czechia) have interval ranges of six positions.  

That could be due to the lack of balance among their values  on the six domains as in the 
case of Austria that shows a rather large range of different scores in the domains, varying 
from  44  in  the  Power  domain  to  92  in  the  Health  domain.  In  fact,  when  a  country  shows 
unbalanced values, it is particularly penalised by the geometric mean.  

The  reasons  of  the  presence  of  this  larger  volatility  in  the  four  countries  are  investigated 
further using sensitivity analysis. 

3  In  the  uncertainty  and  sensitivity  analysis  all  27  EU  MS,  the  UK  and  the  averages  EU2020  and  EU+UK  were 

used, giving in total 30 “countries”. 

19 

 
 
 
                                         
Overall, country ranks in the Gender Equality Index are fairly robust to changes in the domain 
weighs, the aggregation formula and the presence or not of the correcting coefficient in the 
metric  for  the  majority  of  the  countries  considered,  enough  to  allow  for  meaningful 
inferences to be drawn. For full transparency and information, Table 11 reports the original 
index country ranks together with the median rank and the simulated intervals (central 90 
percentiles observed among the 4,000 scenarios) in order to better appreciate the robustness 
of these ranks to the computation methodology, and to ease the analysis of the behaviour 
of specific countries respect to perturbations. 

20 

 
Table 11. Median rank of the countries and 90% confidence intervals. 

Country

Gender Equality 
Index rank

Median rank

90% Confidence Interval 
over the 4000 scenarios

SE

DK

FR

FI

NL

UK

IE

ES

BE

LU

EU+UK

SI

DE

EU_2020

AT

IT

MT

PT

LV

EE

BG

HR

CY

LT

CZ

PL

SK

RO

HU

EL

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

1

2.5

2.5

5

5

6

8.5

5

8

10

11

13

13

12

15

16

17

19

19

21

19

22

25

24

25

25

27

24.5

29

30

[1,1]

[2,4]

[2,5]

[3,8]

[4,7]

[5,7]

[6,10]

[3,10]

[7,10]

[8,14]

[10,14]

[11,15]

[10,15]

[11,15]

[11,19]

[15,17]

[16,22]

[17,20]

[18,21]

[18,23]

[13,23]

[21,25]

[21,27]

[24,25]

[22,28]

[25,27]

[26,30]

[20,29]

[28,30]

[29,30]

Notes: Confidence intervals with range larger than six positions are highlighted in red. 
Source: European Commission, Joint Research Centre, 2020. 

21 

 
 
The uncertainty analysis is complemented by a sensitivity analysis to identify which of the 
modeling assumptions presented in Table 10 have the highest impact on the countries with 
the most volatile Gender Equality Index ranks.  

In Figure 2, it is possible to compare the ranks derived from the Gender Equality Index with 
the  ranks  which  would  have  been  obtained  by  changing  the  metric  and  excluding  the 
correcting  coefficient  α  from  it.  The  use  of  the  correcting  coefficient  has  a  very  strong 
conceptual meaning and it can affect strongly the rank of some countries. The reason it was 
included in the JRC modelling assumptions to be tested, was to understand how drastically 
in can affect them and how much it contributes in the volatility of some of those ranks. From 
the figure though we see that although we do notice some rank changes, in most cases they 
are less than five positions. Only three countries stand out and these are Bulgaria, Romania 
and  Spain.  These  countries  have  a  better  ranking  by  eight,  seven  and  five  positions 
respectively, when the correcting coefficient is not in place. This would mean that in some 
specific indicators, the corr. coeff. α of these countries should be particularly low; and in this 
way it penalises them. 

Figure  2.  Comparison  of  ranks  according  to  the  use  of  a  metric  with  and  without  the  correcting 
coefficient α. 

Notes: Countries with rank changes more than four positions are highlighted in red. 
Source: European Commission, Joint Research Centre, 2020. 

22 

 
 
 
 
 
Next, we compare the original Gender Equality Index ranks (geometric aggregation) with the 
ranks  computed  using  arithmetic  aggregation  at  all  levels.  In  Figure  3  we  notice  that  the 
changes  are  even  more  subtle.  In  fact,  no  country  has  rank  changes  for  more  than  three 
positions, which lead us to the conclusion that although the  geometric mean do not really 
allows for compensations in the scores and it does affect the results; the aggregation method 
does not contribute significantly in the high volatility of the ranks of some countries. From 
the four countries identified at the uncertainty analysis, only Austria has a rank change of 3 
positions,  confirming  again  that  its  large  range  in  the  domain  scores  is  penalised  by  the 
geometric average. 

Figure 3. Comparison of ranks according to the use of geometric mean (default) and arithmetic mean 
at domain and index level. 

Source: European Commission, Joint Research Centre, 2020. 

Last,  we  looked  at  the  median  rank  produced  from  1,000  stimulations  where  the  domain 
weights  where  randomly  varying  ±25%  from  their  nominal  values,  keeping  unchanged  all 
other developers’ choices (metric, geometric aggregation at both top levels). The results show 
no actual changes in the ranking for any country.  

The overall implications of the uncertainty analysis are that the uncertainty in the rankings 
is  mostly  manageable;  only  the  ranks  of  three  countries  are  explicitly  affected  by  the 
assumption  made  on  the  metric  (RO,  BG,  ES).  Nevertheless,  the  index  allows  meaningful 
conclusions to be drawn from the index. 

23 

 
5  Conclusions 

The JRC statistical audit delves into the extensive work carried out by the developers of the 
Gender  Equality  Index  with  the  aim  of  suggesting  improvements  in  terms  of  data 
characteristics, structure and methods used. The analysis aims to ensure the transparency of 
the Gender Equality Index methodology and the reliability of the results.  

This report focused  on the assessment of the statistical coherence  of the Gender Equality 
index by carrying out a multilevel analysis of the correlations within and across the indicators, 
sub-  domains  and  domains  as  well  as  by  an  assessment  of  the  impact  of  key  modelling 
assumptions on the index ranking. 

The  analysis  suggests  that  the  Gender  Equality  Index  is  statistically  well  balanced  with 
respect to its structure. The results  of the two statistical coherence tests suggest that the 
conceptual grouping  of the indicators into 14 sub-domains and six domains is statistically 
confirmed, and that the index is in general influenced by most - though not all - underlying 
indicators. Seven indicators are found to be not so influential at the index level and for three 
of  those  -  Healthy  life  years,  Population  without  unmet  medical  examination  needs  and 
Population without unmet dental examination needs – it was shown that they also have a 
low impact on the index country ranks. Moreover, these three indicators are more associated 
with  other  domains  with  respect  to  their  own  domains.  Although  they  are  conceptually 
enriching, the JRC recommendation is to monitor carefully their performance in the future 
releases of the index, and eventually fine-tune the framework if needed. 

The results of the uncertainty analysis reveal that for most countries, the confidence intervals 
are narrow enough for meaningful inferences to be drawn from the index: there is a shift of 
fewer  than  six  positions  for  22  of  the  countries  included  in  the  Gender  Equality  Index. 
Nevertheless, there are four countries with 90% confidence interval widths of more than six 
positions, and thus their ranks vary significantly with changes in metric construction, weights 
and aggregation formula. The four countries are: Bulgaria, Romania, Austria and Spain. The 
sensitivity  analysis  that  followed  confirmed  that  Austria’s  volatility  is  due  to  the  uneven 
distribution of scores at domain level that is penalised with the use of geometric mean while 
the rest three countries have a significant rank change due to the use or not of the correcting 
coefficient in the metric. That volatility could be raising an issue in some cases, but given the 
fact  that  the  metric  with  the  addition  of  the  correcting  coefficient  is  based  in  a  strong 
conceptual choice, it is accepted. At the same time it should be aknowledged that a change 
in  the  construction  of  the  metric  could  result  in  significant  changes  in  the  ranking  of  the 
specific countries. 

In general, the present audit confirms that the 2020 Gender Equality Index meets the quality 
standards for statistical soundness and acknowledges it as a reliable composite indicator to 
measure gender equality in the EU context, tailored to fit the EU’s policy  goals. By looking 
beyond the overall index scores, the Gender Equality Index allows to provide insights on its 
underlying categories where the real essence of a composite indicator lies.  

24 

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Institute  for  Gender  Equality. 

(2013).  Gender  Equality 

Index  Report. 

https://doi.org/10.2839/9948 

European  Institute  for  Gender  Equality.  (2019).  Gender  Equality  Index  2019  Work  —  life 

balance European Institute for Gender Equality. https://doi.org/10.2839/44985 

European Institute of Gender Equality. (2017). Gender Equality Index 2017, Methodological 

report (Vol. 1). https://doi.org/10.2839/3514 

Groeneveld, R. A., & Meeden, G. (1984). Measuring Skewness and Kurtosis. The Statistician, 

33, 391–99. 

Little, R. J. A., & Rubin, D. B. (2002). Statistical Analysis with Missing Data Second Edition. 

Munda,  G. 

(2008).  Social  Multi-Criteria  Evaluation 

for  a  Sustainable  Economy. 

https://doi.org/10.1007/978-3-540-73703-2_2 

OECD and JRC. (2008). Handbook of Constructing Composite Indicators - Methodology and 

user guide. https://doi.org/10.1787/9789264043466-en 

Saisana, M, Tarantola, S., & Saltelli, A. (2005). Uncertainty and sensitivity techniques as tools 
for the analysis and validation of composite indicators. Journal of the Royal Statistical 
Society, 168(2), 307–323. 

Saisana,  Michaela,  &  Saltelli,  A.  (2011).  Rankings  and  ratings:  Instructions  for  use.  Hague 
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3(2), 

Law, 

on 

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of 
https://doi.org/10.1017/S1876404511200058 

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the 

25 

 
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