Critical Article Analysis
Journal of European Social Policy 2015, Vol. 25(4) 414 –430 © The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0958928715594545 esp.sagepub.com
Jo u r n a l O f E u ro p e a n
S o c i a l P o l i cy
Introduction
On 13 June 2013, the European Institute for Gender Equality (EIGE) launched the brand new ‘Gender Equality Index’ (GEI). The index was built with the purpose of assessing the levels of gender equality across the 27 member states of the European Union (EU-27 or EU for short) in a wide range of dimensions that are essential for human well-being. Among many other things, the new GEI is to be welcomed for bring- ing to the fore essential gender inequality information
that is comparable across all member states – an extremely difficult task that has quite successfully been achieved by the EIGE team. The index attempts
Why call it ‘equality’ when it should be ‘achievement’? A proposal to un-correct the ‘corrected gender gaps’ in the EU Gender Equality Index
Iñaki Permanyer Centre d’Estudis Demogràfics – Universitat Autònoma de Barcelona (UAB), Spain
Abstract This study critically reviews the new Gender Equality Index (GEI) proposed by the European Institute for Gender Equality (EIGE) in 2013, arguing that the way in which it has been defined can be misleading for its potential users. The GEI is defined to ensure that good scores in the index are reflective of both low gender gaps and high levels of overall achievement. The study finds that the GEI values are largely driven by differences in overall achievement levels between countries rather than by gender differences within them, a disturbing issue that unduly penalizes low-income countries for factors that are not related to gender norms or discriminatory practices and which might lead to the elaboration of ill-targeted policies. In order to overcome this problem, we introduce a new version of the GEI that gets rid of its achievement component and which is much simpler to interpret.
Keywords EIGE, Europe, gender equality, Gender Equality Index, measurement
Corresponding author: Iñaki Permanyer, Centre d’Estudis Demogràfics – Universitat Autònoma de Barcelona (UAB), Campus de la UAB, Edifici E-2, Cerdanyola del Valles, 08193 Barcelona, Spain. Email: inaki.permanyer@uab.es
594545ESP0010.1177/0958928715594545ArticleJournal of European Social PolicyPermanyer research-article2015
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to uncover existing gender inequalities across six core domains (‘work’, ‘money’, ‘knowledge’, ‘time’, ‘power’ and ‘health’) and in two satellite domains (‘intersecting inequalities’ and ‘violence’). These domains – the choice of which has been guided by dif- ferent theoretical frameworks like the ‘equality of con- dition’ perspective suggested by Baker et al. (2004) or Amartya Sen’s Capability Approach (see, for instance, Robeyns, 2003 or Nussbaum, 2003) – have been care- fully selected after an exhaustive literature review and an open dialogue with gender experts all over Europe. The accomplishment of gender equality in these areas is crucial to face current social challenges, secure social justice and reach the objectives set by the EU in the Europe 2020 growth strategy. To the extent that the new measure is taken up by policy-makers as an indi- cator of progress in the different EU member states, it could help to focus and inform policy debates on gen- der inequality, its causes and consequences. To this end, however, it is important that the new index is criti- cally scrutinized by different actors (including, but not limited to, policy-makers, Statistical Offices, non-gov- ernmental organizations (NGOs) and academics) so that its eventual limitations can be overcome in the near future. In this context, this article aims to criti- cally analyse the way in which the GEI and its main predecessors have been defined and indicate the impli- cations that the choice of one methodology or another entails for the interpretation of their values and the pro- posal of gender-related policies.
In the last few years, the growing interest in gen- der-related issues and the increasing availability of internationally comparable datasets have stimulated international institutions and individual researchers alike to propose different measures of gender (in) equality.1 Since these quite numerous measures have been designed with different purposes, it is impor- tant to analyse what aspects of the new GEI are shared with the currently existing measures and what other aspects stand out, making of it a truly differen- tiated entity. For that purpose, we will take an over- view of the literature on gender indices and briefly review the main conceptual issues that are involved in their creation (see sections ‘Literature overview’ and ‘Conceptual issues in the measurement of gen- der equality’). In the section entitled ‘Methodological issues in the measurement of gender inequality’, we
continue the discussion focusing on several meth- odological aspects that must be addressed when con- structing indices of gender equality.
Of particular interest for the purposes of this article is the study of the basic underlying metric that is used to measure the gender gaps in a given variable – an apparently minor technical point that has passed through seemingly unnoticed but which does have enormous implications both from a conceptual-theo- retical point of view and from a practical-empirical perspective (see the section on ‘Methodological issues in the measurement of gender inequality’). When defining this basic gender gap metric, the GEI design- ers have succinctly introduced the so-called correction coefficient to ensure that good scores in the index are reflective of both low gender gaps and high levels of overall achievement. At first sight, the term ‘correction coefficient’ might be suggestive of some small adjust- ments that have been introduced to control for some undesirable properties or irregularities of the raw dis- tribution but which, overall, are likely to have minor consequences on the main message conveyed by the index. Yet, this important point is not clarified any- where in the report. In this context, it seems natural to ask, ‘what is the extent of this correction?’ Are the original (i.e. un-corrected) gender gaps very different from the corrected ones? How much does the correc- tion factor contribute to the reported value of the index? Since the basic ingredients of the index are composed of equality and achievement components, it is fundamental to unravel which of them is more important in shaping the final values of the index (see section called ‘Disentangling the contribution of the ‘equality’ and ‘achievement’ components’). This arti- cle aims to address these different issues and frame the GEI methodology within currently existing approaches in the measurement of gender equality.
As will be argued in detail below, the way in which the new GEI has been defined can be mislead- ing for its potential users and might lead to inoppor- tune misinterpretations. In order to address such eventual confusions, in this article, we suggest rede- fining the GEI by un-correcting the ‘corrected gen- der gaps’ (i.e. getting rid of the overall achievement component) so that the new version of the index becomes a measure of gender inequality per se, which is more transparent and much easier to
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interpret. As is to be expected, the values of this new version of the GEI index do differ with respect to the current version. We will investigate the extent to which the two versions of the index diverge – both within and between countries – and whether or not they offer a coherent picture of the prevailing levels of gender inequality in the EU-27 (see the section entitled ‘Un-correcting the corrected gender gaps’). In this respect, we will also investigate the relation- ship between the economic performance of the dif- ferent member states and their gender equality levels according to the two versions of the GEI (the official one and the one proposed in this article). We con- clude the article in the last section ‘Discussion and concluding remarks’ with some final comments and remarks on the implications of our findings.
Literature overview
The United Nations Development Programme (UNDP) pioneered the construction of global-scope gender-related indices taking into account disparities between women and men in a large number of coun- tries. In 1995, the UNDP published the Gender- related Development Index (GDI), an indicator that measures development in the same dimensions as the well-known Human Development Index (HDI), discounting them for gender inequality. These dimensions are ‘longevity’ (measured by life expec- tancy at birth), ‘educational attainment’ (measured by adult literacy rate and school enrolment ratios) and ‘standard of living’ (measured by the gross domestic product (GDP) per capita). In that year, the UNDP also published the Gender Empowerment Measure (GEM). While the GDI takes into account the gender gaps in human development, the GEM focuses more specifically on women’s opportunities by taking into account the dimensions of ‘political participation and decision-making power’ (meas- ured by women’s and men’s percentage shares of parliamentary seats), ‘economic participation and decision-making power’ (measured by women’s and men’s percentage shares of positions as legislators, senior officials and managers and the percentage shares of professional and technical positions) and ‘power over economic resources’ (measured by women’s and men’s estimated earned income). The
impact of these two measures has been enormous in both academic and nonacademic circles, and their values have been widely used all over the world (Schüler, 2006). Among other things, these indices were particularly useful to raise awareness of gen- der-related issues in the context of human develop- ment. The launch of the GDI and GEM in 1995 set the stage for the proliferation of gender inequality indices among policy-makers and academia. Different authors have already made exhaustive reviews of these indices (e.g. Bericat, 2011; Dijkstra, 2002; Hawken and Munck, 2013; Mills, 2010; Permanyer, 2010), so here we will only summarize the ones which, for conceptual or technical reasons, are related to the GEI.
Despite their relevance, both the GDI and GEM have been criticized for not measuring gender ine- quality in itself, but rather a combination of gender equality and levels of overall achievement (Dijkstra, 2002; Dijkstra and Hanmer, 2000; Klasen, 2006). Such criticism motivated the proposal of new indices of gender equality both from individual researchers and international institutions. Among the scholarly contributions, Dijkstra and Hanmer (2000) proposed the Relative Status of Women (RSW) index, an inno- vative measure that uses the same components of the GDI but does not include a relation with absolute levels of achievement, that is, it simply averages the gender gaps. Two years later, Dijkstra (2002) pro- posed the Standardized Index of Gender Equality (SIGE), a new version of her own index aiming to control for the fact that those variables with higher variance had the strongest implicit weight in the overall index. Later on, Benería and Permanyer (2010) and Klasen and Schüler (2011) proposed improved versions of the RSW that coherently aggregated the gender gap ratios across alternative dimensions. In the last few years, different authors have proposed gender indices restricted to the European context only: Plantenga et al. (2009), who introduced the European Union Gender Equality Index (EUGEI), and Bericat (2011), who introduced the European Gender Equality Index (EGEI).
During the same period of time, different interna- tional institutions have also proposed their own indi- ces of gender inequality. One of them is the African Gender Status Index (AGSI), which was created in
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2004 by the United Nations Economic Commission for Africa but which has not yet seen the light of day. One year later, the World Economic Forum pub- lished the Global Gender Gap Index (GGGI), which is being updated on a yearly basis. Commemorating the twentieth anniversary of the Human Development Reports, the UNDP presented the new Gender Inequality Index (GII) in 2010, which has been criti- cally analysed by Permanyer (2013). Finally, in 2013, the EIGE launched the GEI that is being ana- lysed in this article.
Conceptual issues in the measurement of gender equality
As illustrated by the plethora of indices proposed in the last few years, the concept of ‘gender inequality’ is somewhat vague and means very different things to different people. Since the construction of com- posite indices of gender inequality is a complex pro- cess that involves many difficult and somehow arbitrary decisions, it is important for its designers to clarify and be explicit about the overarching concept they seek to measure. In what follows, we delineate some of the basic conceptual issues that must be addressed when constructing a coherent measure of gender equality.
Achievement versus gender equality
On many occasions, scholars have attempted to cre- ate gender-specific achievement indices to measure in absolute terms the level of status attained by women or men separately. For instance, if one wants to compare the achievements of women between countries, it is customary to create a composite index with women-specific indicators. Alternatively, when one is interested in assessing the relative position of women vis-à-vis men (or vice versa), it makes more sense to create a measure of gender equality compar- ing the achievements of both groups. For the sake of coherence and conceptual clarity, researchers agree that it is preferable to keep both approaches separate and use one or the other depending on the goal of the study (Benería and Permanyer, 2010; Bericat, 2011; Dijkstra, 2002; Dijkstra and Hanmer, 2000; Klasen, 2006; Klasen and Schüler, 2011; Permanyer, 2011,
2013; Schüler, 2006). Indeed, the individual research- ers’ proposals reviewed in the ‘Literature overview’ have only used the ‘gender equality approach’. In sharp contrast, the majority of indices proposed by international institutions (e.g. the GDI, GEM, GII and, as will be analysed below, the GEI itself) con- flate into a single measure an absolute achievement and a relative gender equality component, therefore muddying the waters and creating confusion on the meaning of the published results (Permanyer, 2013; Schüler, 2006).
Outcomes versus opportunities
The circumstances in which women and men are raised and educated are quite different from one another. Even if several efforts have been made to level the playing field in many regions of the world, women still face more difficulties than men in secur- ing a profitable job or in pulling the levers of power. For this reason, it has been argued that one should focus the attention on the distribution of opportuni- ties rather than on the distribution of outcomes. According to this perspective, what matters is not whether women and men get the same jobs or sala- ries but whether they regard the outcomes as fair because they have the same opportunities or face the same constraints when they have to make a relevant choice. Important as it is, one could argue that the equality of opportunities approach would be more suitable to construct a measure of gender equity rather than gender equality.2 So far, all existing indi- ces – including the GEI – have focused on the distri- bution of outcomes.
Agency versus well-being
Another debate that has permeated the construction of gender equality indices is whether they should focus on the factors that contribute to enhance human agency (i.e. an individual’s ability to act on behalf of goals that matter to them) (see Sen, 1999) or on human well-being. While some of the indices pro- posed so far have tended to favour the well-being approach (this is the case of the GDI, RSW, AGSI or GGGI) and others have given more emphasis to indi- viduals’ agency (for instance, the GEM, EUGEI and
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EGEI), one might argue that all indices partially sup- port both approaches at the same time because these are not mutually exclusive (for instance, education can empower individuals while simultaneously being a dimension of well-being). As shown in the section called ‘How is gender equality measured in the GEI?’ the GEI has many indicators that support both the agency and well-being approaches, without clearly favouring any of the two.
Geographical scope
The pioneering UNDP indices were very useful to make a broad brush assessment of global gender- related disparities. However, the use of the same set of indicators across the world does inevitably ques- tion their meaning and validity: are those indicators equally relevant and meaningful in all world regions and countries? As shown in Permanyer (2011), the GDI variables might be appropriate to capture gen- der inequalities for low-and middle-income coun- tries, but they are nowadays not very useful for most European countries where most gender gaps have either vanished or are measured on shaky grounds. This suggests that, for certain purposes, it might be more meaningful to define region-specific measures at the European level only, an issue that has already been attempted in other recent articles (e.g. Bericat, 2011; Plantenga et al., 2009). In this respect, the GEI is an index that has been specifically crafted to suit the context of the EU, so it is better equipped to cap- ture gender disparities in Europe than other global- scale indices like the GDI, GEM, GII or GGGI.
Methodological issues in the measurement of gender inequality
After clarifying the overarching concept one wants to measure, there are still a number of methodologi- cal decisions that must be taken for the construction of a composite index of gender equality. In particu- lar, one has to decide how to measure gender gaps in each indicator before aggregating across dimen- sions, a crucial decision that will determine not only the overall levels of gender equality but also their substantive meaning. The choice of the specific
measure has to be guided by the way in which the notion of ‘gender in/equality’ has been conceptual- ized (see the section entitled ‘Conceptual issues in the measurement of gender equality’). We will briefly discuss some of the issues involved in the construction of this kind of basic metric.3
Direction of inequality
When measuring gender disparities for a given indi- cator, one might be interested in capturing the extent to which the achievements of women and men are different irrespective of whether these differences favour one sex or the other: this is the so-called non- directional approach. In this approach, what matters is the extent of dissimilarity between both outcomes, but not their relative position (i.e. whether gender gaps go in one direction or another is not meaning- ful). Alternatively, in the ‘directional approach’, one wants to know not only whether disparities exist between women and men but also whether such dis- parities benefit the former or the latter. If we denote by x and y the average achievement levels of women and men, simple examples of directional gender gaps could be x − y or x/y (i.e. differences or ratios). The non-directional counterparts of those gaps would be |x − y| and min{x,y}/max{x,y}, respec- tively. One inconvenience of non-directional gender gaps is that it is not possibly to identify whether one sex is systematically discriminated against (i.e. if all inequalities go in the same direction). Alternatively, the problem with the directional approach is that gender gaps running in opposite directions might eventually cancel out each other giving a false impression of gender equality (see Klasen, 2006 and Permanyer, 2010, for extensive discussions on this problem). While there does not seem to be a consen- sus on whether one approach is indisputably better than the other, the directional approach has been adopted more often than the non-directional one (the former has been used in AGSI, GGGI, EGEI, RSW and its improved versions suggested by Benería and Permanyer, 2010 and Klasen and Schüler, 2011, while the latter has been used in Plantenga et al.’s (2009) EUGEI). Before being ‘corrected’, the gen- der gaps used in the GEI are non-directional (see equation (5) in Appendix 1). As a consequence, the
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values of GEI are not informative on the relative position of women vis-à-vis men. Interestingly, the directional/non-directional dichotomy is not exhaus- tive: as shown below, some well-known gender- related indices have followed a completely different approach.
Inequality-sensitive welfare indices
The GDI is not defined as a measure of gender ine- quality per se, but rather as a measure of overall well-being that penalizes the existence of disparities between the achievements of women and men (Dijkstra and Hanmer, 2000). In this respect, the GDI does not measure gender gaps for each indica- tor explicitly, but uses an overall achievement func- tion that is corrected downwards when the achievements between women and men differ (in technical terms, such a function is also known as an ‘inequality-sensitive welfare index’; see equation (9) in Appendix 1). As documented by Schüler (2006), this has generated widespread confusion because many users wrongly identify the GDI with a measure of gender inequality that simply averages gender gaps across dimensions. Despite the widely docu- mented criticism against the use of inequality-sensi- tive welfare indices as gender inequality measures, the UNDP successor of the GDI – the new GII – goes in the same direction. On this occasion, the values of the GII are conceptualized as the welfare loss that can be attributed to the different achievement levels of women and men, but the gender gaps are not being measured explicitly. For this reason, and since its methodology is particularly (and unnecessarily) complicated (Permanyer, 2013), the GII risks being misinterpreted as its predecessor. One of the adverse consequences of using inequality-sensitive welfare indices rather than simple gender gaps is that both the GDI and GII are very highly correlated with macro-economic performance indicators like the GDP per capita (Dijkstra and Hanmer, 2000; Permanyer, 2013).
Interestingly, the EIGE team has made an effort to start from scratch, and it has proposed a related – yet apparently different – approach to measure gen- der equality. As shown in the next subsection, rather than correcting overall achievement (i.e. welfare) by
existing disparities between women and men (as the GDI does), the GEI goes the other way around cor- recting the gender gaps depending on the corre- sponding overall achievement levels.
How is gender equality measured in the GEI?
The GEI is a hierarchically structured index composed of six core domains, each further sub-divided into two sub-domains (giving a total of 12 sub-domains). The domains (and corresponding sub-domains between parentheses) are ‘Work’ (‘Participation’, ‘Segregation and Quality of Work’), ‘Money’ (‘Financial Resources’, ‘Economic Situation’), ‘Knowledge’ (‘Educational Attainment and Segregation’, ‘Lifelong Learning’), ‘Time’ (‘Care Activities’, ‘Social Activities’), ‘Power’ (‘Political’, ‘Economic’) and ‘Health’ (‘Status’, ‘Access’). In addition, each sub-domain consists of several individual indicators that are disaggregated by sex. Overall, there are 27 individual indicators across all sub-domains (all details of the architecture of the index can be found in EIGE’s webpage: http://eige. europa.eu/). For each individual indicator, the GEI con- structs the so-called ‘gender gaps corrected by levels of achievement’ (from now onwards referred to as ‘cor- rected gender gaps’). Now, what is the nature of this correction? And more importantly, what are its implica- tions? According to the GEI technical report (see EIGE, 2013), for each individual indicator the corrected gen- der gaps are defined as
Γ = + −1 99 1[ ( )]α g (1)
where α is the so-called correcting coefficient and g is the gender gap between women and men in the corresponding indicator. The values of the gender gap g are bounded between 0 and 1. In a case of per- fect gender equality (i.e. when women and men per- form equally), g takes a value of 0, and in a case of extreme inequality (i.e. when the achievements of women and men are at opposite extremes of the dis- tribution), g takes a value of 1. The correcting coef- ficient is a normalized average of the achievements of women and men in that specific indicator. It takes values between 0 and 1 and penalizes those countries
420 Journal of European Social Policy 25(4)
with low overall achievement in the corresponding indicator – technical details are given in Appendix 1. Smaller values of α are conducive to higher penali- zations and vice versa (whenever α equals 1, there is no penalization whatsoever). By construction, the values of Γ are bounded between 1 and 100, and the latter can only be attained when women and men perform equally well at the top of the corresponding distribution. Essentially, the GEI is an average of the different corrected gender gaps that are defined for each of the 27 individual indicators composing the index.
An analytical result
As shown in Appendix 1, it is straightforward to prove that the corrected gender gaps presented in equation (1) can be exactly rewritten as
Γ x y c x y, { , }( ) = + ×1 min (2)
where x and y are the female and male achievement levels in the corresponding indicator, min {x, y} is the minimum between x and y and c is a normalization constant that bounds the values of Γ between 1 and 100. According to the welfare economics literature, equation (2) is an example of an inequality-sensitive welfare index known as the ‘Rawlsian social welfare function’ (see, for instance, Sen and Foster, 1997). This function ranks social states on the basis of the achievement of the least well-off member in a given society (where women and men are treated as a uni- form group). As is known, social welfare analysis takes into consideration the total amount of a certain good (i.e. the achievement part) as well as its degree of inequality. Therefore, the ranking of alternative dis- tributions on social welfare grounds is completely dif- ferent to ranking alternative distributions on inequality grounds. To clarify, consider a hypothetical case in which the achievement of women and men in a given indicator (bounded between 0 and 100) is equal to 40 (i.e. (x1, y1) = (40, 40), a case of perfect gender equal- ity). Imagine now that after a certain period of time, the achievement of men increases dramatically while the achievement of women remains constant, so that (x2, y2) = (40, 100). Interestingly, Γ(40, 40) = Γ(40,
100), that is, the corrected gender gap Γ is completely insensitive to the dramatic enlargement of the gender gap because such deterioration in equality is compen- sated by increases in overall achievement (40 = (40 + 40)/2 vs 70 = (40 + 100)/2).
Ironically, equations (1) and (2) show that cor- recting gender gaps by overall achievement as done by the GEI or correcting overall achievement by the gender gaps as done by the GDI end up being the same in analytical terms: in both cases, an inequal- ity-sensitive welfare index is used as a measuring rod to capture gender disparities. Yet, it is not entirely clear whether the potential users of the GEI who want to have an idea of the gender inequality levels prevailing in the EU would agree with this way of measuring gender disparities.
Results
Disentangling the contribution of the ‘equality’ and ‘achievement’ components
As can be seen in equation (1), the corrected gender gaps have two separate ingredients: gender inequality (as measured by g) and overall achievement of women and men (as measured by α). We are now going to pre- sent a very simple procedure to estimate the contribu- tion of these two components to the values of the corrected gender gaps Γ. Since g is a measure of gen- der inequality bounded between 0 and 1, 1 − g is a measure of gender equality. Defining e = 1 − g, the cor- rected gender gaps shown in equation (1) can be rewritten as Γ = 1 + 99α·e, which, in turn, can be rea- sonably rescaled and approximated as Γ/100≈α·e. In this form, it is clear that the corrected gender gaps used in the construction of the GEI are composed of an equality component (measured with the equality index ‘e’) and an achievement one (captured with the correc- tion function α). Taking natural logs in the previous expression, one obtains the additive decomposition: ln(Γ/100)≈ln(α) + ln(e). Therefore, the percent contri- bution of the correction coefficient to the corrected gender gap can be approximated as Cα = 100·ln(α)/ ln(Γ/100). Analogously, the contribution of the equal- ity component is approximated as Ce = 100·ln(e)/ ln(Γ/100). By construction, both contributions add up to 100 percent. The contribution of the achievement
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and gender equality components to the corrected gen- der gaps are therefore given by (Cα, Ce).
In Table 1, we show the contribution of the gen- der equality component to the corrected gender gaps (Ce) for all indicators and countries included in the GEI.4 As is clear, there is a big heterogeneity across indicators and countries. At one extreme, the gender equality component contributes as much as 80 per- cent (on average across countries) to the corrected gender gap associated with the ‘Domestic Activities’ indicator (labelled as I15 in Table 1). At the other extreme, that contribution barely reaches 7 percent (on average across countries) for the ‘Mean equival- ized net income’ indicator (labelled as I8 in Table 1). Despite such heterogeneity, it is remarkable that in most country-indicator cases shown in Table 1 (in 72.2% of the cells to be precise), the percent contri- bution of the gender equality component (e) to the corresponding corrected gender gaps (Γ) is below the threshold of 50 percent. Roughly speaking, this means that when constructing the GEI’s corrected gender gaps, in three out of four cases, the contribu- tion of the correction component is larger than the contribution of the gender equality one. Indeed, if one averages the values of Ce across all indicators and countries included in the dataset,5 one obtains a surprisingly low value of 31.6 percent. These quite remarkable results prove that the GEI’s correction coefficients α are not minor adjustments introduced to eventually correct small inadequacies or irregu- larities of the raw data, but a major and crucial factor that largely contributes to shape the final values reported in the GEI and which will eventually guide gender-related policies and analysis.
Un-correcting the corrected gender gaps
If we are interested in capturing gender equality per se, it is necessary to introduce another gender gap that is not contaminated by the achievement component – as is the case with Γ. A simple way of creating such a gender equality measure (while keeping all else equal) consists in un-correcting the corrected gender gaps. For this purpose, one can simply get rid of the correc- tion coefficient of Γ and define Γ* = 1 + 99e, which is an index that takes the maximal value of 100 whenever women and men attain the same level irrespective of
what this level is. An immediate consequence of sup- pressing the correction coefficient is that for many indicators, the distribution of the Γ* across countries is much less dispersed and more concentrated on the top of the distribution. Figure 1 clearly illustrates this point for the indicator ‘mean monthly earnings’: while the corrected gender gaps range between 20 and 100, the un-corrected ones just range between 80 and 100 (analogous figures arise when considering many other indicators included in the construction of the GEI). This noticeable loss of variability (which is reminis- cent of the problem identified in Permanyer (2011) regarding the lack of variability of the indicators included in UNDP’s GDI for Europe) might be one of the reasons that has motivated the introduction of a correction factor in the definition of the GEI.
Taking the un-corrected gender gaps (Γ*) rather than the corrected ones as the basic building blocks, one can use exactly the same averaging methodology across indicators, sub-domains and domains to con- struct a new version of the GEI, which will be denoted as GEI* to distinguish it from the official GEI. Unlike GEI, GEI* takes the normatively desirable value of 100 whenever there are no gaps between women and men across the different indicators. While the values of GEI are an average of 27 corrected gender gaps (which are a mixture between overall achievement and gender equality), the values of GEI* are simply an average of 27 gender gaps. The values of GEI and GEI* differ considerably across countries (see Table 2). As expected, the values of GEI* are substan- tially larger than those of GEI: the EU-27 average for the values of GEI equals 54, while for GEI* that aver- age equals 75.3. Since the potential maximum of those indices equals 100, EIGE (2013) concluded that the EU-27 was ‘halfway towards gender equal- ity’ according to the values of the GEI in 2010. Using the new GEI*, the message is clearly more optimistic: according to its values, the EU-27 would have already covered three quarters of its way towards complete gender equality.
The association between GEI and GEI* is moder- ately strong: the rank correlation coefficient equals 0.74 and Kendall’s tau coefficient of association equals 0.55.6 Overall, this means that although their absolute levels are quite different, both indices tend to rank countries in a relatively consistent way, although
422 Journal of European Social Policy 25(4)
T a b
le 1
. Pe
rc en
t co
nt ri
bu ti o n
o f th
e eq
ua lit
y co
m po
ne nt
t o t
he c
o rr
ec te
d ge
nd er
g ap
s as
m ea
su re
d by
C e.
C o un
tr y
I1 I2
I3 I4
I5 I6
I7 I8
I9 I1
0 I1
1 I1
2 I1
3 I1
4 I1
5 I1
6 I1
7 I2
3 I2
4 I2
5 I2
6 I2
7
B E
52 .9
27 .9
83 .5
14 .3
17 .9
32 .5
29 .6
5. 0
10 .9
0. 0
46 .4
88 .6
1. 7
71 .7
78 .8
22 .4
3. 8
20 .0
57 .0
8. 5
14 .3
6. 9
B G
36 .2
17 .4
54 .9
15 .7
7. 4
38 .3
5. 0
1. 1
15 .2
4. 2
30 .6
28 .9
0. 4
42 .3
75 .0
13 .6
1. 9
27 .4
31 .0
25 .6
1. 9
0. 0
C Z
83 .9
38 .8
61 .2
20 .9
4. 0
59 .8
12 .7
2. 7
10 0
47 .4
4. 8
57 .4
1. 7
50 .7
69 .3
22 .4
3. 4
12 .3
41 .7
13 .3
5. 9
14 .2
D K
72 .0
70 .2
10 0
26 .4
3. 6
10 0
10 0
3. 3
1. 8
15 .5
33 .8
10 0
10 0
60 .1
84 .5
12 .1
7. 9
13 .8
41 .2
4. 8
0. 0
29 .7
D E
61 .0
46 .2
66 .2
18 .1
14 .1
50 .3
48 .4
6. 5
13 .3
7. 5
34 .5
81 .0
1. 4
22 .9
79 .7
1. 2
3. 8
6. 6
57 .5
3. 3
4. 1
1. 8
EE 37
.3 7.
9 65
.5 20
.7 31
.2 22
.6 16
.5 2.
5 6.
5 11
.1 79
.5 58
.9 9.
9 83
.7 89
.9 24
.0 9.
1 9.
4 45
.1 13
.4 5.
3 4.
6 IE
50 .6
44 .0
78 .1
32 .3
19 .8
80 .2
97 .7
5. 1
5. 8
5. 6
10 0
72 .9
2. 4
45 .7
81 .7
17 .2
12 .1
10 0
61 .4
10 .4
17 .2
11 .6
EL 54
.8 42
.2 50
.0 19
.0 3.
0 32
.9 21
.3 2.
7 6.
1 0.
0 2.
1 46
.6 0.
0 57
.3 80
.6 4.
3 6.
4 24
.2 55
.6 14
.2 15
.0 4.
9 ES
47 .7
39 .5
53 .5
10 .0
18 .5
31 .3
20 .8
1. 6
4. 8
2. 9
16 .1
60 .7
5. 8
66 .7
92 .5
15 .2
4. 0
26 .4
94 .1
3. 5
13 .0
8. 0
FR 44
.2 26
.1 70
.0 22
.1 8.
7 33
.3 23
.8 5.
4 17
.9 0.
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.9 54
.4 2.
4 51
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.8 84
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4 0.
7 IT
53 .7
39 .2
60 .0
30 .3
7. 5
74 .6
18 .4
5. 3
15 .3
0. 0
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72 .5
76 .5
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7. 1
C Y
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56 .6
43 .1
15 .4
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27 .3
6. 3
22 .5
12 .5
63 .3
52 .9
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76 .4
81 .3
24 .5
8. 1
23 .5
73 .8
6. 6
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8. 3
LV 30
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21 .2
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6. 5
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48 .5
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82 .6
19 .4
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LU 69
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.9 4.
0 23
.2 14
.9 35
.5 8.
5 5.
2 12
.2 M
T 69
.3 53
.6 67
.6 9.
5 13
.3 54
.2 15
.7 2.
2 13
.0 0.
0 4.
3 66
.4 1.
1 52
.2 67
.3 32
.4 9.
2 13
.4 69
.2 58
.5 8.
8 10
.9 N
L 65
.6 72
.8 85
.5 18
.9 26
.4 93
.6 41
.6 5.
2 37
.5 16
.9 31
.6 76
.0 3.
5 10
0 78
.8 1.
5 10
0 31
.7 59
.1 5.
3 0.
0 17
.5 A
T 73
.5 42
.9 59
.9 15
.6 4.
8 50
.4 32
.1 6.
1 31
.9 11
.7 17
.4 57
.8 6.
5 46
.8 76
.4 4.
4 42
.3 16
.6 62
.9 5.
5 8.
6 1.
2 PL
57 .0
26 .0
61 .7
16 .4
4. 3
44 .7
9. 7
0. 9
3. 0
5. 0
24 .3
49 .4
3. 8
44 .4
74 .5
16 .0
0. 0
14 .2
43 .4
16 .0
5. 5
5. 7
PT 74
.4 36
.5 63
.5 13
.4 19
.7 30
.2 10
.8 1.
4 11
.8 1.
7 19
.3 56
.7 1.
4 74
.1 88
.1 12
.7 7.
8 18
.1 54
.4 10
.1 16
.6 9.
5 R
O 59
.2 27
.3 47
.5 6.
5 0.
3 4.
3 3.
7 0.
4 2.
8 0.
0 0.
0 23
.6 0.
0 63
.7 75
.8 17
.4 8.
0 31
.2 32
.2 0.
0 15
.1 9.
1 SI
70 .4
23 .8
60 .5
14 .9
12 .9
17 .1
4. 2
2. 1
29 .9
47 .4
26 .8
43 .6
12 .0
69 .1
82 .8
9. 0
37 .5
15 .3
56 .8
3. 8
10 0
10 0
SK 61
.1 30
.0 66
.2 16
.6 4.
2 46
.0 10
.9 2.
1 8.
3 23
.9 9.
8 66
.0 2.
8 58
.5 71
.0 1.
9 19
.7 21
.9 37
.1 0.
9 2.
9 4.
8 FI
53 .5
17 .4
83 .5
10 0
10 0
6. 8
37 .2
4. 5
11 .1
33 .6
89 .8
72 .5
31 .0
12 .0
73 .8
10 0
0. 0
9. 7
60 .8
1. 3
22 .4
5. 0
SE 76
.2 10
0 95
.6 27
.4 5.
9 18
.3 19
.4 5.
4 27
.1 0.
0 57
.7 90
.0 45
.9 13
.1 83
.7 13
.2 33
.8 42
.5 71
.8 10
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7 U
K 62
.1 58
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.5 65
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4 11
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6 65
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58 .4
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67 .3
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97 15
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93 56
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Permanyer 423
there are quite a lot of exceptions. In Table 2, we can see not only the rankings of the EU-27 member states according to the values of those indices but also the changes in ranking positions that take place when we move from the values of GEI to those of GEI*. As can be seen, some countries lose more than five ranking positions: Ireland (−6), Cyprus (−8), Austria (−8) and, most notably, Luxembourg (−14). On the opposite side, other countries advance more than five posi- tions: Portugal (+6), Slovakia (+6), Latvia (+7), Lithuania (+7) and, most notably, Bulgaria (+13). Given the fact that there are only 27 units of analysis, the changes experienced by those countries are quite substantial. In between, countries like Sweden, Finland, Denmark and the Netherlands do not suffer much alteration and consistently remain in the top four positions according to the values of both the GEI and GEI*. The good performance of these countries in both measures is explained by the fact that the corre- sponding achievements of women and men are not only very similar but also very near the top of the dif- ferent indicators’ distributions.
The fact that the relative position of countries like Luxembourg or Austria deteriorates when shifting from GEI to GEI* while countries like Bulgaria, Latvia and Lithuania greatly improve their positions does suggest that countries’ performance on those indicators might be linked to their economic wealth. In order to investigate this issue in more detail, Figure 2 plots the levels of countries’ GDP per capita (in Purchasing Power Standard – PPS) jointly with the corresponding shift in ranking positions when moving from GEI to GEI*. A clear negative relation- ship is observed (the correlation coefficient equals −0.73 and is statistically significant), therefore indi- cating that wealthy countries tend to occupy lower (i.e. better) positions with GEI and lower income countries tend to occupy better positions with GEI*. This stylized result does not change when Luxembourg (a strong outlier that because of its atyp- ical characteristics might bias the results) is elimi- nated from the sample. Given the strong influence that the correction coefficient α (a measure of aggre- gate achievement that is expected to be positively
Figure 1. Scatterplot of the corrected gender gap on earnings (horizontal axis) and the un-corrected gender gap on earnings (vertical axis) for the 27 EU member states. Source: Author’s calculations using EIGE (2013) data. Country labels follow the ISO3166 codes.
424 Journal of European Social Policy 25(4)
correlated with the GDP) has in shaping the values of the GEI, these results are not very surprising. Again, they confirm the previous findings that lower income countries are penalized by the GEI for their poor per- formance in aggregate achievement – a factor that, a priori, is not related to gender-related norms or dis- criminatory practices.
In this context, it is also interesting to comple- ment the previous analysis exploring the relationship between gender inequality measures and a relevant macro-economic variable like the GDP per capita. This way, one is able to ascertain the extent to which
economic performance is associated with higher gender equality levels – a matter of great concern among social scientists interested in development, economic growth and well-being (see, for instance, Berik et al., 2009). As shown in Figure 3 (right panel), the relationship between the values of GDP per capita (in PPS) and the official GEI is moder- ately strong: richer member states tend to have higher levels of gender equality as measured by that index. The correlation coefficient between them equals 0.48, and it increases to 0.75 if Luxembourg (the big outlier in the distribution) is dropped from
Table 2. Values of GEI, GEI*, GDP per capita and other related indicators for the 27 EU member states.
Country GEI GEI ranking
GEI* GEI* ranking
Δ Rank GDP per capita (PPS)
Kendall tau
BE 59.6 6 78.0 6 0 29,100 0.53 BG 37.0 26 70.3 13 13 10,700 0.35 CZ 44.4 14 68.9 19 −5 19,500 0.60 DK 73.6 2 82.9 3 −1 31,300 0.54 DE 51.6 11 70.0 14 −3 29,000 0.53 EE 50.0 16 69.9 17 −1 15,500 0.60 IE 55.2 9 70.0 15 −6 31,300 0.63 EL 40.0 25 65.5 23 2 21,200 0.46 ES 54.0 10 77.7 7 3 24,200 0.41 FR 57.1 7 79.1 5 2 26,500 0.58 IT 40.9 23 63.4 24 −1 24,700 0.63 CY 42.0 19 56.7 27 −8 23,600 0.62 LV 44.4 15 74.3 8 7 13,200 0.40 LT 43.6 18 71.7 11 7 15,000 0.49 LU 50.7 12 61.9 26 −14 64,200 0.64 HU 41.4 21 68.7 20 1 15,800 0.52 MT 41.6 20 63.3 25 −5 21,400 0.62 NL 69.7 4 80.6 4 0 32,000 0.58 AT 50.4 13 67.1 21 −8 31,100 0.61 PL 44.1 17 71.5 12 5 15,300 0.46 PT 41.3 22 69.9 16 6 19,700 0.49 RO 35.3 27 67.1 22 5 11,400 0.36 SI 56.0 8 72.6 10 −2 20,500 0.70 SK 40.9 24 69.7 18 6 17,900 0.50 FI 73.4 3 84.2 2 1 27,700 0.48 SE 74.3 1 85.6 1 0 30,200 0.56 UK 60.4 5 74.1 9 −4 27,500 0.67 EU-27 54.0 – 75.3 – – 24,500 0.56
GEI: Gender Equality Index; GDP: gross domestic product; PPS: purchasing power standard. Source: Author’s calculations from EIGE (2013) data. Country labels follow the ISO3166 codes.
Permanyer 425
the list of admissible observations. On the other hand, the association between GDP per capita and the new GEI* is not particularly strong (see left panel in Figure 3). The correlation coefficient equals 0.03 for the whole sample and increases up to 0.4 when Luxembourg is not taken into account. As expected, the wealth of a country is a worse predictor of the levels of gender equality if we shift from the official GEI to the GEI* proposed in this article. Therefore, the GEI* is more successful in capturing new infor- mation not encapsulated in the strictly economic dimension. These results are in line with the findings of Dijkstra and Hanmer (2000) and Permanyer (2013) showing analogous results for the cases of the GDI and GII, respectively.
So far, we have only explored changes between countries when shifting from GEI to GEI*. However, it is also illuminating to investigate the assessments of gender equality provided by those different indi- ces within each country. If the policy-makers of a given country guided the elaboration of gender- related policies on the basis of those indices, what
picture would emerge if we shifted from the values of GEI to those of GEI*? Stated in more precise terms, if the size of gender gaps were used to rank indicators within countries to decide what area of policy intervention should receive priority attention from the government, would the results provided by Γ and Γ* be consistent or not? To answer this ques- tion, Table 2 reports the values of Kendall’s tau coef- ficient of association between the corrected and un-corrected gender gaps for all indicators within each of the 27 EU member states.7 When that coef- ficient is close to its maximal value of 1, the two indicators’ rankings derived from the values of Γ and Γ* are highly consistent. When it approaches 0, there is no association and the two rankings look as if they were generated independently. As can be seen in Table 2, the values of Kendall’s tau range from a minimum of 0.35 observed in Bulgaria to a maxi- mum of 0.7 observed in Slovenia, with an EU-27 average of 0.56. Therefore, the country-level pic- tures that emerge when shifting from corrected to un-corrected gender gaps change to a sizeable extent,
Figure 2. Scatterplot of GDP per capita (PPS) versus the GEI rank minus GEI* rank across the 27 EU member states. Source: Author’s calculations using EIGE (2013) data. Country labels follow the ISO3166 codes.
426 Journal of European Social Policy 25(4)
so the policy interventions that would be derived from the values of those indices would not be par- ticularly consistent as they would prioritize alterna- tive areas of intervention.
Discussion and concluding remarks
On June 2013, the EIGE presented the new GEI to assess gender equality levels across the 27 member states of the EU. Being an index specifically crafted for the EU context, it is much better equipped to cap- ture gender disparities in Europe than other global- scale gender indices like the GDI, GEM, GII or GGGI. In order to make sure that the normatively desirable values of the index are only attainable when- ever women and men perform equally well on the top of the corresponding distribution, its designers have introduced the so-called correction coefficient: a com- ponent that penalizes those countries with low overall
(i.e. population level) achievement levels. Because of the way in which it has been designed, the GEI trades off gender equality by overall achievement, so it con- siders that a highly gender-unequal society where overall achievement is relatively high has the same level of gender inequality than another society where women and men perform equally but at a lower aggre- gate achievement level than in the former society. While perfectly defensible from a normative point of view in case one wanted to construct a gender ine- quality–sensitive overall welfare measure (something which has not been mentioned anywhere in the EIGE reports), we contend that this interpretation and opera- tionalization of gender inequality might create some misunderstandings among potential users of the index – in much the same way as it has already happened with UNDP’s GDI during the last 20 years (Schüler, 2006).
In this article, we have investigated in detail the ways in which the new GEI measures gender equality.
Figure 3. Scatterplot of GDP per capita (PPS) versus the GEI (left panel) and GEI* (right panel) across the 27 EU member states. Source: Author’s calculations using EIGE (2013) data. Country labels follow the ISO3166 codes.
Permanyer 427
In particular, we have quantified the contribution of the correction coefficient (i.e. the achievement com- ponent) to the values of the index. As demonstrated in our analysis, the values of the new GEIs are largely driven by the achievement component rather than the egalitarian one. Stated another way, the GEI values are basically determined by differences between countries in average achievement levels of women and men rather than by gender differences within them, a result that is somewhat disturbing for an index of gender equality. In light of these results – and mim- icking the name of UNDP’s GDI – it might be tempt- ing to rename EIGE’s measure as the ‘Gender-related Achievement Index’. We contend that the inclusion of an achievement component to an equality index does muddy the waters, creating confusion when interpret- ing the true meaning of its values. Among other things, the mixing of achievement and equality com- ponents in a single index makes comparisons over time particularly difficult. Whenever a corrected gen- der gap changes over time, one does not know whether such a change has been driven by improvements (or deteriorations) in the gap between women and men, by changes in overall achievement, or by changes in both of them.
When designing large-scale gender-related indices like the GEI, GDI, GEM or GII, international institu- tions like EIGE or UNDP seem reluctant to generate indices of gender inequality in itself: that is, indices that measure equality between women and men irre- spective of the level where such equality has been achieved. Arguably, this might be guided by political correctness and respond to the desire of preventing some countries where the status of women is very low to show up in a privileged position of the final rank- ing. However, in such countries, the status of men might be quite poor as well (i.e. the corresponding gender gaps might not be so large after all), so it is not entirely obvious that they should be expelled alto- gether from the better positions of a ranking that aims to order countries in terms of gender equality levels. As discussed elsewhere (e.g. Benería and Permanyer, 2010; Dijkstra and Hanmer, 2000), it is necessary to complement information on equality with other achievement and contextual indicators to clarify whether equality is achieved on the top or at the bot- tom of the distribution. In the context of economic
inequality measurement, income inequality indices are published for every country no matter if equality is achieved at any of the extremes of the distribution. If everyone takes the values of the Gini index (or any other inequality measure) at face value, why should one follow a different approach in the case of gender inequality measurement? In other words, why should countries be penalized for insufficient achievement, a factor that a priori is not related to gender-related norms or discriminatory practices? Echoing a recent reflection of William Easterly on the unfair treatment of Africa in the international assessments of welfare improvements (Easterly, 2009, 2010), one is left pon- dering whether the proposed ‘corrections’ to the gen- der gaps might be geared to provide a more ‘logical’ or ‘expected’ ordering of European countries that is in accordance with conventional wisdom. In this respect, the fact that none of the indices proposed by individ- ual researchers so far have attempted to ‘correct’ their assessments of gender equality by overall achieve- ments suggests that they might not be as constrained by political correctness as some international institu- tions might be.
In order to capture gender equality levels in Europe more accurately, we suggest un-correcting the corrected gender gaps and construct a new ver- sion of the GEI – denoted as GEI* – on the basis of that information alone (i.e. removing the achieve- ment component from the basic metric of the index). When comparing the values of the official GEI with the new GEI* proposed in this article, important dif- ferences arise. Since economic performance indica- tors like the GDP per capita naturally tend to be positively correlated with the achievement compo- nent of the GEI, it is not surprising to find that lower income countries tend to rank in better positions when shifting from the official index to the new one and vice versa. At the country level, it turns out that the corrected and un-corrected gender gaps are quite different across indicators. If the size of those gaps was used to rank indicators within countries to decide what area of policy intervention should receive priority attention from the government, the assessment provided by both indices would be quite inconsistent. In order to avoid mis-targeting the most urgent areas of policy intervention, it is essential to pursue the debate further, take a firmer stance and
428 Journal of European Social Policy 25(4)
decide consensually what is the most appropriate way of measuring gender equality.
As shown in this article, the values of GEI* are much larger than those of GEI (the EU-27 average for the former equals 75.3 and for the later 54). Essentially, this is caused by the surprisingly small size of the un-corrected gender gaps vis-à-vis their corrected counterparts – an issue that is reminiscent of the lack of variability of the indicators included in UNDP’s GDI for Europe identified in Permanyer (2011). Rather than being ‘halfway towards equality’ (as announced in the EIGE (2013) report), the values of GEI* suggest that the EU has already covered three quarters of its way towards complete gender equality – a much more optimistic message. While more optimistic messages are likely to be less telling and less efficient than the existing one in order to raise public awareness about gender differences – which is arguably one of the goals pursued with the construction of GEI – the values of the new GEI* have the advantage of being much more transparent and easy to understand, so they might be in a better position to guide and inform successful policies aim- ing at reducing real disparities between women and men in Europe.
Funding
This work was financially supported from the Spanish Ministry of Economy and Competitiveness ‘Ramón y Cajal’ Research Grant Program (RYC-2013-14196) and research projects ERC-2014-StG-637768, ERC-2009- StG-240978 and ECO2013-46516-C4-1-R.
Notes
1. Given their complementarity, the terms ‘gender equality index’ (GEI) and ‘gender inequality index’ will be used interchangeably in the text when no con- fusion arises.
2. According to McDonald (2013),
Gender equity is a more subtle and therefore more problematic concept because it allows for differ- ent outcomes for men and women, so long as men and women regard the outcomes as fair or at least not grossly unfair and so long as there is equality of opportunity rather than equality of outcome. Thus gender equity is about perceptions of fairness and opportunity rather than strict equality of outcome.
3. The technical discussion presented in this section is by no means exhaustive; it only deals with certain aspects that are pertinent for our analysis of the GEI. A more comprehensive analysis of the technical issues surrounding the construction of composite indices of gender inequality can be found in Permanyer (2010), Bericat (2011) and Hawken and Munck (2013).
4. It should be pointed out that our definition of ‘con- tribution to the corrected gender gaps’ for the five variables counting the share of women and men in different political or economic institutions is ill- defined, so they have not been included in Table 1. For those specific variables, the average achieve- ment of women and men is (by definition) always equal to 50 percent because both achievements add up to 100 percent (e.g. 20% and 80%, or 10% and 90%.). Since this happens for all countries, the cor- rection coefficient is tautologically equal to 1 (see Appendix 1 for the technical details on the definition of α), so it makes no sense to talk about the contribu- tion of the achievement component to the corrected gender gaps (Cα).
5. This average does not include the five indicators counting the shares of women and men in different institutions for the reasons outlined in the previous note.
6. Both Spearman’s rank correlation coefficient and Kendall’s tau are standard measures of statistical association taking values between −1 and 1. The extreme values are taken in case of extreme positive or negative association, and in cases where there is no association, they take a value of 0. Spearman’s rank correlation coefficient assesses how well the relation- ship between two variables can be described using a monotonic function. Kendall’s tau assesses the simi- larity of the rankings that are derived from the values of two different indicators.
7. By definition, Kendall’s tau coefficient is the most appropriate way of assessing whether two different indicators rank alternative states of affairs in a con- sistent way. Nevertheless, reporting the values of the correlation coefficient or those of Spearman’s rank correlation coefficient does not alter our results in a substantive way.
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Appendix 1
Functional form of the corrected gender gaps
In the EIGE (2013) report, the corrected gender gaps are defined as
Γ = + ⋅ −[ ]⋅1 1 99α ( )g (3)
We are now going to show step by step how this formula can be rewritten as the function shown in equation (2). Assume that, for a given indicator, the average achievements of women and men are denoted as x and y, respectively.
Step 1. According to the EIGE (2013) report, the gender gap g is explicitly defined as
430 Journal of European Social Policy 25(4)
g x y x
x y ( , )
( ) =
+( ) −
2 1 (4)
Step 2. After basic algebraic manipulations, this can be rewritten as
g x y y x
y x ( , ) =
−
+ (5)
Step 3. It is straightforward to show that
1
2
2
2
− = +
>
+ >
= +
g x y
x
y x if y x
y
y x if x y
x y
y x
( , )
min{ , }
(6)
Step 4. According to the EIGE (2013) report, the correction coefficient α is explicitly defined as
α =
+
x y
M
2 (7)
where M is the maximum observed value of the average (x + y)/2 across countries. This way, α is bounded between 0 and 1.
Step 5. Plugging equations (6) and (7) into (3) and manipulating algebraically, one obtains the desired formula
Γ( , )
min{ , } .
min{ , }
x y x y
M c x y
= +
= + ⋅
1 99
1 (8)
where c is the normalization constant that bounds the values of Γ between 1 and 100.
Essentially, this functional form is a particular member of the class of indices used in the construc- tion of the United Nations Development Programme’s (UNDP) Gender-related Development Index (GDI). In that context, Anand and Sen (1995) introduced the following inequality-sensitive welfare index
W x y p x p yf m( , )
/( ) = +( )− − −1 1 1 1ε ε ε
(9)
where pf and pm represent the share of women and men in the population under consideration and ε⩾0 is a parameter representing the degree of ‘aversion to inequality’ (see Atkinson, 1970). For any ε > 0, W(x,y) is an average of x and y that is smaller than the classic arithmetic mean pf·x + pm·y (the larger the value of ε, the larger the difference between the two). When ε increases indefinitely, W(x,y) converges towards the minimum between x and y. Therefore, Γ(x,y) can be seen as a member of the class of inequality-sensitive welfare indices W(x,y) in the limiting case where ε→∞.