Pre-print (Forthcoming: PLoS ONE) 1 A century of change in global education variability and gender differences in education 1 2 Iñaki Permanyer, Centre d’Estudis Demogràfics 3 Diederik Boertien, Centre d’Estudis Demogràfics 4 5 6 A century of change in global education variability and gender differences in education 7 8 Abstract: This article shows how overall education variability can be decomposed in four 9 clearly interpretable components (variability among women and men, educational advantage 10 favoring women and favoring men) and documents how these components have evolved over 11 time in the world and its regions from 1950 to 2010 (with projections until 2040). Our 12 findings suggest that (i) with education expansion, education variability tends to follow an 13 inverted U-shape trajectory, (ii) the composition of education variability has been shifting 14 dramatically over time; in particular (iii) variability among men was usually higher than 15 variability among women until the turn of the millennium; from then onwards their 16 educational attainment distributions have the same degree of dispersion, and (iv) while in the 17 1950s the educational advantage of men was by far the main contributor to education 18 variability, nowadays the educational advantage of women has become the most important 19 source of variability in high- and middle-income countries. 20 21 Keywords: Education; Gender Inequality; Global Inequality 1 Corresponding author. Centre d’Estudis Demogràfics (a member of the CERCA Programme / Generalitat de Catalunya), Carrer de Ca n’Altayó, Edifici E-2, Campus de la UAB, 08193 Cerdanyola del Vallès, Spain. E- mail: ipermanyer@ced.uab.es. 1 Pre-print (Forthcoming: PLoS ONE) 22 1. Introduction 23 For a long time, a global expansion of mass schooling has been sweeping the globe. This 24 process, which has been observed in all countries around the world, has been highly 25 beneficial for an ever growing number of individuals, so this is a worthy cause for celebration 26 [1]. While a growing body of scholarship has shed considerable light on the ‘efficiency part’ 27 of the process (i.e. the country-level average education attainments are reasonably well- 28 documented), much less is known about the ways in which education is distributed across 29 individuals. With education expansion, it is likely that some sectors of the population benefit 30 disproportionately more than others, thus generating increasingly disperse education 31 distributions – a matter of great scientific interest and policy concern which, unfortunately, 32 has not received much scholarly attention and is still quite poorly understood. 33 One of the key characteristics of the education distribution that has indeed attracted the 34 attention of many scholars is the gender gap in education. During the last decades we are 35 witnessing the emergence of a “global first” phenomenon: the closing and reversal of the 36 gender gap in educational attainment. For the first time in history, in many high- and middle- 37 income countries, young women are attaining higher levels of education than young men, and 38 the same trend is expected to occur in other countries as well in the coming decades [2]. 39 While relevant and informative, the comparisons of average attainments for women and men 40 typically ignore the potential heterogeneity that might exist within those groups. Yet, 41 implicitly treating women and men as if they were homogeneous groups does not allow 42 addressing key questions about the education distribution. For instance: Is the education 43 distribution among women becoming more disperse as their average attainment surpasses that 44 of men? Is education variability among women higher than that of men? Does the reduction – 45 and eventual reversal – of the gender gap in education go hand-in-hand with less educational 46 variability overall? How are these concepts related with one another? While it seems clear 2 Pre-print (Forthcoming: PLoS ONE) 47 that (i) overall education variability, (ii) education variability among women and among men, 48 and (iii) educational advantage of men over women and of women over men are interrelated 49 with one another, no previous study has attempted to investigate and flesh out the nature of 50 that relationship. For the first time, in this paper we put together these different ingredients 51 into a coherent whole to explore how overall education variability is decomposed and relates 52 to its basic constituent parts. 53 The relevance of documenting the trends of these different distribution-related indicators 54 stems from their differential impacts on societies around the world, which are multiple and 55 might go in opposite directions. On the one hand, increasing education variability – either for 56 the population as a whole or for women and men separately – serves as a wellspring for 57 increases in inequality in many other quality of life domains (higher variability in educational 58 attainment is associated with higher dispersion in income and wages, higher job insecurity, 59 and lower economic growth, occupational mobility, physical and mental health and general 60 well-being – see [3]-[4]. On the other hand, the closing and reversal of the gender gap in 61 education in favor of women might increase female labor force participation (particularly in 62 better-paying formal-sector jobs), prolong the duration of women in the labor force (which in 63 turn could lead to more efficient economic outcomes; [5] and generate more egalitarian 64 attitudes (both in the domestic and public spheres [2], that could eventually shift the balance 65 of power towards females [6]. Symmetrically, high levels of gender inequality in favor of 66 men have long been considered to be detrimental for the economic performance of countries 67 and the well-being of their inhabitants [5]. For these reasons, it becomes important to explore 68 whether and to what extent education variability and the gender gap in education 69 simultaneously move in the same or in opposite directions – an issue that, to the best of our 70 knowledge, has not yet been investigated. 3 Pre-print (Forthcoming: PLoS ONE) 71 Summing up, this article aims to explore how overall education variability is articulated in 72 different moving parts and how these parts have jointly evolved over time in the world and its 73 regions. Such decomposition is extremely useful for scholars and policy-makers to go beyond 74 purely descriptive results and analyze what factors are the most important drivers of 75 education variability and its evolution over time. To attain our research objectives, we have 76 created a new measure of education variability specifically crafted to simultaneously meet 77 two requirements that are not met by currently existing measures. First, our measure nicely 78 decomposes overall variability in two broad components: variability within groups (including 79 variability among women and among men) and between groups (which can be further 80 decomposed in two subcomponents: the educational advantage of men over women and of 81 women over men). Second, it has been designed to handle the ordinal data we are dealing 82 with in this paper (currently, virtually all education variability measures are based on cardinal 83 information, like ‘years of schooling’). Hopefully, the new measure proposed in this paper 84 can be a useful addition to those practitioners aiming at gauging variability in the context of 85 ordinal variables. 86 The empirical analysis relies on the latest version of the Barro and Lee [7] database 87 (henceforth BL) for the period from 1950 to 2010 and on some of our own projections, 88 extending the results up to 2040. Such projections are solely intended to glimpse what might 89 be the evolution of education variability in case current trends were to continue during the 90 coming decades following a simple logistic growth curve. The huge geographic coverage of 91 the database (146 countries) allows performing both global and regional analyses over time. 92 93 2. Background and hypotheses 4 Pre-print (Forthcoming: PLoS ONE) 94 It is difficult to overestimate the importance of education for the well-being of individuals 95 across their entire life cycle. In general, highly educated individuals tend to have a better 96 command over resources, higher levels of employment and better-paid jobs, they have longer 97 and less unequal lifespans, lower risk of getting divorced, of being poor or materially 98 deprived and higher levels of subjective well-being ([8]-[12]). Indeed, education is a key 99 stratification variable in demographic behavior [13]. For these reasons, the education 100 expansion that has been sweeping the world during the last decades is a phenomenon that a 101 priori should be highly advantageous for those who benefit from it. This expansion includes 102 rising literacy rates [14] and increases in schooling enrollment rates and in completed years 103 of primary, secondary and college education [1] [7] [15]-[19]. Regarding college education, 104 by 1970, 6.4% of the world’s population aged 25-29 had obtained a college degree. Three 105 decades later, this proportion had increased to 13%, and the expected figure for 2050 is 106 29.4% [20]. 107 What do we know about global, regional and national trends in education variability and the 108 gender gap in education? Despite its relevance for many socio-demographic and economic 109 outcomes – e.g. high levels of education variability are associated with higher economic 110 dispersion and unemployment levels, lower social cohesion and higher poverty rates [4] – 111 researchers have only recently started to study how individuals’ education is distributed 112 across and within countries (e.g. [1] [3] [21]-[25]). While these studies differ in many 113 respects (e.g. they typically employ different indicators, datasets and methodological 114 approaches, and/or their geographic and temporal coverage does not necessarily coincide) 115 they all cohere with the following narrative. As mass education started to expand – 116 predominantly in favor of men – education variability began to increase. After several 117 decades, as education expansion gradually shifted the population from low to highly educated 118 categories, education dispersion reached its highest point and afterwards started declining 5 Pre-print (Forthcoming: PLoS ONE) 119 until the present day. In other words: empirical evidence seems to support the existence of a 120 Kuznets curve in education. This highly simplified narrative generally applies for the world 121 as a whole, its different regions and most of its countries (the studies by Castelló and 122 Domenech [21], Benaabdelaali et al. [22], Meschi and Scervini [23] and Jordá and Alonso 123 [25] focus on the second half of the 20th century, so they cover the downward part of the 124 inverted U-shape trajectory; the studies by Dorius [3] and Morrisson and Murtin [1] [24] use 125 data from the 19th to the 20th century, so they cover the upward and downward portions of 126 the trajectory). 127 A notable feature of the education expansion process is that it has not been gender neutral [6] 128 [26]-[27]. Despite initially favoring males, the gender gap has closed rapidly in recent years 129 and, in many countries, even reversed in favor of women [28], a trend that is expected to 130 continue over the next decades [13] [20]. In 1970, men represented 63.6% of the total college 131 educated population. This percentage decreased to 52.6% in 2000 and it is likely to reach 132 44% in 2050, with most high-income countries reaching lower levels [20]. The recent and 133 prospective sex-specific share shifts across the education ladder – usually in favor of women 134 – have attracted the attention of several researchers because of their potentially sizeable 135 impacts across the board (e.g. fertility changes, higher female labor force participation and 136 higher economic growth, or shifting power relations both in public and private domains; see 137 [2] [28]-[30]). It should be pointed out that the gender gap in education – which is currently 138 favoring women in most high- and middle-income countries – is not as large as it used to be 139 when it favored men in the initial stages of the education expansion. 140 Education variability and its components: trends and hypotheses 141 Having scarce empirical evidence to rely upon, we cannot but hypothesize what might be the 142 relationship between overall education variability (henceforth denoted as 𝑉𝑉) and its ‘basic 6 Pre-print (Forthcoming: PLoS ONE) 143 subcomponents’: variability among men (𝑉𝑉𝑚𝑚 ), variability among women (𝑉𝑉𝑓𝑓 ), and the two 144 components of the gender gap in education (i.e. educational advantage favoring men (𝐴𝐴𝑚𝑚 ) 145 and educational advantage favoring women (𝐴𝐴𝑓𝑓 ) – details given in the methods section). A 146 priori, there are many possible ways in which these subcomponents might have evolved over 147 time in a way that fits the aforementioned stylized narratives on the trends in overall 148 education variability and the gender gap in education. In this regard, Figure 1 plots what 149 might have been the hypothetical trajectories of 𝑉𝑉, 𝑉𝑉𝑚𝑚 and 𝑉𝑉𝑓𝑓 over time. In line with the 150 existing empirical evidence, overall education variability is posited to first increase and then 151 decrease. What about the education variability among men and among women? Since the 152 education expansion initially benefited men, we expect 𝑉𝑉𝑚𝑚 to increase earlier than 𝑉𝑉𝑓𝑓 . Yet, 153 since the education expansion for women took place in a shorter period of time, we expect 𝑉𝑉𝑓𝑓 154 to increase faster than 𝑉𝑉𝑚𝑚 . Based on the evidence reporting the closing and reversal of the 155 gender gap in education in favor of women we expect 𝑉𝑉𝑓𝑓 to exceed 𝑉𝑉𝑚𝑚 at some point in time 156 (denoted as 𝑡𝑡1 in Figure 1). Yet, given that it is unlikely that obstacles to access education, 157 which women experienced in the past, will be put in place for men, we do not expect the 158 differences in these two quantities to be as large as they might have been during the first 159 stages of the education expansion that predominantly benefited men (i.e. we expect the two 160 curves to remain relatively close to each other after time 𝑡𝑡1 ). Whether or not this has actually 161 been the case for the different world regions will be investigated in the empirical section of 162 the paper. 7 Pre-print (Forthcoming: PLoS ONE) 163 164 Figure 1. Schematic relationship between overall education variability (𝑉𝑉) and variability 165 among women (𝑉𝑉𝑓𝑓 ) and men (𝑉𝑉𝑚𝑚 ). Source: Authors’ elaboration. 166 167 What about the two components of the gender gap in education? As shown in the methods 168 section, 𝐴𝐴𝑚𝑚 can be interpreted as the likelihood that men are more highly educated than 169 women, and the opposite goes for 𝐴𝐴𝑓𝑓 . Based on current empirical evidence, we expect the 170 educational advantage of men vis-à-vis women ( 𝐴𝐴𝑚𝑚 ) to follow an inverted U-shape, 171 increasing first in the initial stages of education expansion and declining afterwards as the 172 expansion starts benefiting women (see Figure 2). The same evidence suggests that, as an 173 increasing proportion of women obtain higher education credentials than men, 𝐴𝐴𝑓𝑓 should 174 increase monotonically over time but with some delay with respect to the 𝐴𝐴𝑚𝑚 curve. 175 Depending on the relative position of these two curves (which is expected to vary across 176 world regions), the gender gap in education (which can be defined as the difference between 177 the previous two curves) might become smaller, eventually disappear or even reverse in favor 8 Pre-print (Forthcoming: PLoS ONE) 178 of women. If the two curves eventually cross in some point in time (denoted as 𝑡𝑡2 in Figure 179 2), the corresponding gender gap reverses and changes its sign. 180 181 Figure 2. Schematic evolution of male and female educational advantage (𝐴𝐴𝑚𝑚 , 𝐴𝐴𝑓𝑓 ) over time. 182 Source: Authors’ elaboration. 183 184 Lastly, since no previous studies have investigated the relationship between the trends in 185 education variability and the gender gap in education, we have no clear expectations of how it 186 might look like. A priori, both measures of variability might go in the same or in opposite 187 directions, depending on the time period or the world region we are looking at. Essentially, it 188 all boils down to determine the relative position of the different curves depicted in Figures 1 189 and 2, an issue that will be explored in the empirical section of the paper. 190 191 3. Data 192 Like many studies on education inequality we have used the dataset of Barro and Lee [7], 193 which is currently the largest in terms of geographic and temporal coverage. The data is 9 Pre-print (Forthcoming: PLoS ONE) 194 based on a compilation of censuses and surveys by UNESCO and provides comparable 195 information on 7 educational attainment categories (no education, primary uncompleted, 196 primary completed, secondary uncompleted, secondary completed, tertiary uncompleted and 197 tertiary completed) for 146 countries during the period 1950-2010. Whenever appropriate, 198 these categories can be reduced to 4 (no education, some primary, some secondary and some 199 tertiary). 200 We used the estimates from Barro and Lee on educational attainment for the period 1950- 201 2010 without further adjustments. At the same time, we decided to calculate our own 202 projections of future educational attainment using a similar procedure to Barro and Lee’s. 203 Calculating our own predictions allowed us to focus on the age group 30-34, instead of the 204 age group 15-64 for which the projections of Barro and Lee were calculated. Selecting this 205 age group enables us to minimize the influence of changes in the age structure within 206 countries on our estimates and at the same time will show the most recent changes in 207 educational attainment (by the age of 30-34, the vast majority of individuals have achieved 208 their highest educational attainment). Another motivation has been that some implausible 209 values were observed in the Barro and Lee projections (In some Western countries the 210 attainment of tertiary education for the age group 25-64 was predicted to decline dramatically 211 with time (e.g. Australia, Austria, Finland), which have been resolved in our predictions). 212 Projections 213 Our projections of future educational attainment are based on a logistic growth curve model 214 estimated for the period 1950-2010 that allows for country-specific time trends (random 215 slopes). The model, estimated separately for men, women, and each of the three educational 216 stages, can be expressed as follows: 10 Pre-print (Forthcoming: PLoS ONE) 𝑠𝑠𝑗𝑗𝑗𝑗 𝑙𝑙𝑙𝑙 � � = 𝛼𝛼𝑗𝑗 + 𝛽𝛽𝑗𝑗 𝑡𝑡 + 𝜇𝜇𝑗𝑗𝑗𝑗 [1] 100 − 𝑠𝑠𝑗𝑗𝑗𝑗 217 where 𝑠𝑠𝑗𝑗𝑗𝑗 is the share of the population having attended educational stage j in year t. The 218 coefficient 𝛽𝛽𝑗𝑗 in this case estimates the (linear) time trend in the (logistically transformed) 219 share of the population attending the given educational stage. The model estimates country- 220 specific constants (𝛼𝛼𝑗𝑗 ) as well as separate coefficients 𝛽𝛽𝑗𝑗 for each country (random slopes in a 221 multi-level model where the two levels are countries and years, 𝜇𝜇𝑗𝑗𝑗𝑗 constitutes the error 222 term), so that the predicted educational expansion over time is allowed to follow different 223 trajectories across countries. In this model, countries are expected to eventually approach a 224 100% attendance for primary and secondary education. It appears unrealistic to expect 225 countries to converge to a 100% attendance of tertiary education. We therefore arbitrarily set 226 a ceiling of 70% for tertiary education. As shown later, predictions using this ceiling fit the 227 data well. 228 The coefficients from these models are used to project attendance of educational stages for 229 the period 2015-2040. In order to arrive at the 7 educational categories of the historical data, 230 we multiplied attendance shares with the completion rates observed in 2010 for each given 231 country and gender (we multiplied the share of the population that is predicted to attend an 232 educational stage in year t, by ‘share completed in 2010’ / ‘share attended in 2010’). In a 233 small set of cases, predicted levels of attending secondary education exceeded predicted 234 levels of primary education attainment by a small margin. To assure that the shares of 235 educational categories eventually summed up to 1, in those cases we set attendance of 236 primary education to the level of secondary education attendance. 237 To safeguard comparability across historical time periods and projections, we decided to 238 present predicted results based on our growth models for all the time period 1950-2040. In 11 Pre-print (Forthcoming: PLoS ONE) 239 the results section we examine the fit of our predicted numbers to actual numbers, which 240 appears to be highly accurate. 241 4. Methods 242 In this paper we treat educational attainment as an ordinal variable. This is a non-trivial 243 decision with important implications that stands in sharp contrast to previous studies on 244 education variability across individuals. Studies like Castelló and Domenech [21], 245 Benaabdelaali et al. [22] or Jordá and Alonso [25] cardinalize the Barro and Lee dataset using 246 different techniques (the first two estimate the average length of each education cycle while 247 the last one fits a continuous distribution to capture ‘within-cycle variations’). Others, like 248 Meschi and Scervini [23] or Morrisson and Murtin [1] [24], work with the cardinal variable 249 ‘years of schooling’. There are several reasons why we have decided to treat education as an 250 ordinal variable. On the one hand, cardinal variables like ‘years of schooling’ can be a poor 251 proxy of the substantive type of education individuals might have received and their 252 interpretation can be biased because of (i) the country-specific duration of different education 253 cycles, and (ii) the existence of repeaters. In addition, ‘years of schooling’ is quite prone to 254 measurement error due to recall bias. On the other hand, ordinal variables are much less 255 prone to measurement error. As opposed to what happens with ‘years of schooling’, the 256 meaning of the ordinal variable categories (e.g. attaining primary, secondary or tertiary 257 education) is reasonably comparable across countries and over time. 258 The major disadvantage of using ordinal variables is that their variability cannot be 259 ascertained with well-known measures, like the standard deviation, the Gini coefficient or the 260 Theil index among many others (indeed this is the key methodological reason why education 261 variability studies have always relied on cardinal variables). One of the contributions of this 12 Pre-print (Forthcoming: PLoS ONE) 262 paper is to partially fill this gap enlarging the practitioner’s toolkit by proposing a new 263 variability measure specifically designed for ordinal variables. 264 A new measure of education variability for ordinal data 265 The tools available to assess variability are substantially reduced when working with ordinal 266 variables (the main reason being that the notion of ‘mean’ – which is crucial in the definition 267 of cardinal measures – is not meaningful in the ordinal case; see [31]. In this section we 268 propose a new measure of variability for ordinal variables that has useful decomposability 269 properties. Let 𝑘𝑘 be the generic number of education categories we will be working with (in 270 our case 𝑘𝑘 = 7) and let 𝑁𝑁 be the population size. We will denote the number of individuals in 271 the population with educational attainment 𝑖𝑖 (with 1 ≤ 𝑖𝑖 ≤ 𝑘𝑘) as 𝑁𝑁𝑖𝑖 , and 𝑝𝑝𝑖𝑖 = 𝑁𝑁𝑖𝑖 ⁄𝑁𝑁 will be 272 the corresponding population share. We define our ordinal variability measure as 𝑖𝑖=𝑘𝑘 𝑗𝑗=𝑘𝑘 𝑉𝑉(𝑝𝑝1 , ⋯ , 𝑝𝑝𝑘𝑘 ) ≔ � � 𝑝𝑝𝑖𝑖 𝑝𝑝𝑗𝑗 𝕀𝕀(𝑖𝑖, 𝑗𝑗) [2] 𝑖𝑖=1 𝑗𝑗=1 273 where 𝕀𝕀(𝑖𝑖, 𝑗𝑗) is an indicator function that takes a value of 1 whenever 𝑖𝑖 ≠ 𝑗𝑗 and 0 otherwise. 274 This measure indicates the probability that two randomly chosen individuals have different 275 education attainments. Whenever all individuals have the same educational achievement (i.e. 276 𝑝𝑝𝑖𝑖 = 1 for some category 𝑖𝑖) there is no variability, so 𝑉𝑉 = 0. For any other distribution, 𝑉𝑉 277 takes strictly positive values, and the higher the values, the more disperse the corresponding 278 education distribution is. 279 A useful feature of the ordinal variability index suggested here is that it is nicely 280 decomposable when the population is partitioned in different groups. In this paper we 281 consider the partition of the population between women and men (𝑁𝑁 𝑓𝑓 and 𝑁𝑁 𝑚𝑚 denote their 282 corresponding population sizes), but any other population partition in an arbitrary large 13 Pre-print (Forthcoming: PLoS ONE) 𝑓𝑓 283 number of groups would do as well. Let 𝑁𝑁𝑖𝑖 , 𝑁𝑁𝑖𝑖𝑚𝑚 be the number of women and men with 𝑓𝑓 𝑓𝑓 284 educational attainment 𝑖𝑖 (hence 𝑁𝑁𝑖𝑖 + 𝑁𝑁𝑖𝑖𝑚𝑚 = 𝑁𝑁𝑖𝑖 ). Their relative shares are denoted as 𝑝𝑝𝑖𝑖 , 𝑝𝑝𝑖𝑖𝑚𝑚 . 285 It is straightforward to check that our variability index can be decomposed as 286 𝑉𝑉 = 𝑠𝑠𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝑠𝑠𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝑠𝑠𝑏𝑏 �𝐴𝐴𝑓𝑓 + 𝐴𝐴𝑚𝑚 � [3] 287 where 𝑓𝑓 𝑓𝑓 𝑉𝑉𝑓𝑓 = 𝑉𝑉�𝑝𝑝1 , ⋯ , 𝑝𝑝𝑘𝑘 � [4] 𝑉𝑉𝑚𝑚 = 𝑉𝑉(𝑝𝑝1𝑚𝑚 , ⋯ , 𝑝𝑝𝑘𝑘𝑚𝑚 ) [5] 𝑖𝑖=𝑘𝑘 𝑓𝑓 𝐴𝐴𝑓𝑓 = � � 𝑝𝑝𝑖𝑖 𝑝𝑝𝑗𝑗𝑚𝑚 [6] 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 𝑖𝑖=𝑘𝑘 𝑓𝑓 𝐴𝐴𝑚𝑚 = � � 𝑝𝑝𝑖𝑖𝑚𝑚 𝑝𝑝𝑗𝑗 [7] 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 𝑠𝑠𝑓𝑓 = (𝑁𝑁 𝑓𝑓 ⁄𝑁𝑁)2 [8] 𝑠𝑠𝑚𝑚 = (𝑁𝑁 𝑚𝑚 ⁄𝑁𝑁)2 [9] 𝑠𝑠𝑏𝑏 = 2𝑁𝑁 𝑓𝑓 𝑁𝑁 𝑚𝑚 ⁄𝑁𝑁 2 [10] 288 The derivation of equation [3] is shown in Appendix A. 𝑉𝑉𝑓𝑓 and 𝑉𝑉𝑚𝑚 measure the degree of 289 education variability within the groups of women and men respectively, and 290 𝑠𝑠𝑓𝑓 , 𝑠𝑠𝑚𝑚, 𝑠𝑠𝑏𝑏 represent the relative weight of each component depending on the population size of 291 each group. The “between-group component” 𝐴𝐴𝑓𝑓 (resp. 𝐴𝐴𝑚𝑚 ) measures the probability that a 292 randomly selected woman has higher (resp. lower) educational attainment than a randomly 293 selected man. Therefore, 𝐴𝐴𝑓𝑓 and 𝐴𝐴𝑚𝑚 can be interpreted as women’s educational advantage 294 over men and vice versa. Interestingly, the ideas discussed in Herrero and Villar [32] bear 14 Pre-print (Forthcoming: PLoS ONE) 295 some similarity with the measures proposed in this paper. Yet, the objectives of the two 296 papers are entirely different: while Herrero and Villar [32] ultimate aim is to evaluate and 297 rank groups’ performance in an ordinal setting, our aim is to decompose ordinal variability in 298 four meaningful components. Finally, we define the extent of gender (in)equality in a given 299 society as 𝐺𝐺: = 𝐴𝐴𝑓𝑓 − 𝐴𝐴𝑚𝑚 , a measure ranging from −1 to 1. If 𝐺𝐺 = −1, there is no woman 300 whose educational attainment is higher than that of any man, and if 𝐺𝐺 = 1, the reverse is true. 301 When the education distributions of women and men are identical, 𝐺𝐺 = 0. This measure is 302 not monotonic: values above 0 reflect a better state of affairs for women and vice-versa. The 303 additive decomposition formula shown in [3] articulates into a coherent whole overall 304 education inequality and its four basic subcomponents. 305 306 Variability versus inequality 307 It should be noted that the index presented in equation [3] is a measure of ‘variability’ or 308 ‘dispersion’, but not of ‘inequality’. Both concepts are highly related, but there is a subtle 309 difference between them. While variability or dispersion measures like the standard deviation 310 simply describe the spread of a given distribution, inequality ones involve value judgements 311 regarding equity and can be made more sensitive to changes occurring in different parts of 312 the distribution (see [33]). Even if such sensitivity might make inequality measures more 313 appealing at first sight, other practical considerations make them less attractive. Most 314 importantly, in the ordinal setting considered in this paper existing inequality measures 315 cannot be broken down in a way analogous to equation [3]. Unlike their cardinal 316 counterparts, current measures of ordinal inequality do not admit additive decompositions 317 into a within-group and a between-group component. Since such decomposition is crucial to 15 Pre-print (Forthcoming: PLoS ONE) 318 address the research questions of this paper, we adhere to the notion of ‘variability’ when 319 documenting the ways in which education is distributed across individuals. 320 Previous studies investigating the distribution of education over time have relied as well on 321 variability / dispersion measures (e.g. Dorius [3]). For the sake of completeness, we have 322 compared our results with the ones we would obtain using the ordinal inequality measures 323 proposed by Abul Naga and Yalcin [34] and Kobus and Milos [35]. It turns out that they are 324 highly correlated (r=0.88) – details not shown here but available upon request. 325 Interestingly, the variability measure proposed in this paper has much in common with other 326 classical measures of heterogeneity defined in the context of nominal and cardinal variables 327 respectively: the ‘index of fractionalization’ and the ‘Gini coefficient’. Indeed, all three 328 measures are extremely similar because they are grounded in the same basic principle: two 329 individuals are picked at random and one inspects whether (or to what extent) they share a 330 given characteristic/attribute. The only difference between the nominal, ordinal and cardinal 331 cases is the metric that is used to assess the similarity between pairs of individuals. In the 332 nominal case one inspects whether the two individuals belong to different pre-specified 333 groups or not, in the ordinal one whether one of the corresponding attainments is superior to 334 the other or not and in the cardinal case one takes into account the distance between the 335 corresponding (cardinal) attainments. Not surprisingly, all three measures have an extremely 336 similar functional form. The fractionalization index for nominal variables can be written 337 exactly as in equation [2] and the Gini coefficient can be written as 𝑖𝑖=𝑘𝑘 𝑗𝑗=𝑘𝑘 � � 𝑝𝑝𝑖𝑖 𝑝𝑝𝑗𝑗 �(𝑦𝑦𝑖𝑖 /𝜇𝜇)−(𝑦𝑦𝑗𝑗 /𝜇𝜇)� [11] 𝑖𝑖=1 𝑗𝑗=1 16 Pre-print (Forthcoming: PLoS ONE) 338 where 𝑦𝑦𝑖𝑖 is the value of the cardinal variable one is interested in for group 𝑖𝑖 and 𝜇𝜇 is the 339 mean of the distribution. In this respect, our index 𝑉𝑉 can be thought as the ‘missing link’ 340 between the index of fractionalization and the Gini coefficient. 341 Interpreting variability decompositions 342 Equation [3] is reminiscent of well-known additive decompositions of inequality in within- 343 and between-group components for the cardinal case (e.g. like the ones used in Generalized 344 Entropy measures, like the Theil index or the Mean Log Deviation). Yet, the interpretations 345 in both cases are entirely different. In the cardinal case, the between-group component is the 346 inequality that would be observed in a hypothetical distribution where each individual had the 347 same educational attainment as the mean in his group. Yet, it does not make sense to speak 348 about the contribution of between-group variability to overall variability in the ordinal 349 context because the notion of ‘mean’ is not applicable. Instead, the term 𝑠𝑠𝑏𝑏 �𝐴𝐴𝑓𝑓 + 𝐴𝐴𝑚𝑚 � in 350 equation [3] should be interpreted as the proportion of pairwise comparisons where 351 individuals have different educational attainments involving a woman and a man. To 352 illustrate the difference between both approaches consider a hypothetical scenario where the 353 number of women and men and their educational attainments turned out to be exactly the 354 same. For the cardinal case the between-group component would go to zero because the 355 gender-specific means would be the same. In the ordinal setting proposed here, the between- 356 group component would amount to 50% because half of the education comparisons between 357 pairs of randomly selected individuals would involve a woman and a man. Indeed, in such 358 hypothetical scenario the contribution to overall variability of the four subcomponents shown 359 in [3] would be exactly the same: 25%. These fundamental differences should be taken into 360 account when interpreting the results. 361 17 Pre-print (Forthcoming: PLoS ONE) 362 5. Empirical findings 363 In this section we present our empirical findings based on the systematic exploration of the 7 364 education categories’ distributions that are reported in the Barro and Lee [7] dataset. We start 365 documenting the global education expansion during the period 1950-2040 using our model 366 predicted data (see section 3). Afterwards, we calculate the corresponding education 367 variability index (together with its four subcomponents) and the gender gap in education. We 368 report their values and trends – both globally and regionally – and quantify the contribution 369 of the different subcomponents to overall education variability. Finally, we analyze the 370 relationship between overall education variability and the gender gap in education. 371 Education expansion 372 Figure 3 presents the share of women having attended primary, secondary, and tertiary 373 education for 7 world regions as well as the predicted shares based on our models. Whereas 374 attendance to primary education was only close to being universal in Advanced Economies 375 and Eastern Europe in 1950, shares close to universality have now reached East Asia and 376 Latin America, and this pattern is expected to extend to South Asia, the Middle East and 377 Africa by 2040. Attendance to secondary education was still a minority phenomenon in all 378 world regions in 1950, but today a majority of individuals in most world regions attends 379 secondary education. In all regions but South Asia and Sub-Saharan Africa more than 90% of 380 women are expected to attend secondary education by 2040. Tertiary education was not very 381 extended in the 1950s, but almost half of the women aged 30-34 are expected to attain 382 tertiary education by 2040 in all regions but Sub-Saharan Africa, where tertiary education is 383 predicted to increase only slowly. Figures for men are similar and displayed in Appendix B. 384 For the period 1950-2010, Figure 3 shows both predicted and actual shares of attendance. The 385 fact that the two sets of shares are hardly distinguishable from each other in the graph reflects 18 Pre-print (Forthcoming: PLoS ONE) 386 the good fit of the logistic growth curve models described in section 3. Only for secondary 387 education in Eastern Europe and primary education in East Asia some differences between 388 both become visible in certain time periods. Due to this relatively neat fit between predictions 389 and reality, we believe that presenting our model-predicted results does not imply a 390 qualitatively important loss of information. 391 392 Figure 3. Women’s attendance of educational stages 1950-2040, by region, predicted and 393 actual (weighted by population size of countries). Parts in greyscale are predicted values. 394 Source: Authors’ calculations based on the BL dataset. 395 396 Evolution of overall education variability and its components 19 Pre-print (Forthcoming: PLoS ONE) 397 Figure 4 displays the development of education variability across the world and within world 398 regions based on ordinal educational categories. It also simultaneously displays the four 399 components of the variability decomposition formula shown in equation [3]. The thick solid 400 line represents overall variability V over time and roughly follows an inverted U-shaped 401 curve worldwide, congruent with the results of Dorius [3] and Morrisson and Murtin [24]. 402 Most regions individually appear to follow a part of that curve during the period under study. 403 In some regions variability used to be still relatively low in the 1950s, but dispersion 404 increased with time and educational expansion. In other regions, variability was already high 405 but has recently started to decrease slightly. This decrease is expected to continue in the 406 future, and to find its expression in a decline in educational variability worldwide. The region 407 of Eastern Europe and Central Asia seems to follow a slightly different trend. While we also 408 observe an inverted U-shaped trajectory until the 1990s, from that year onwards education 409 variability seems to take off and increase until 2010 (with further increases expected until 410 2040) – a trend that might be partly attributable to the collapse of the communist bloc and the 20 Pre-print (Forthcoming: PLoS ONE) 411 swift transition to capitalist economies. 412 413 Figure 4. Education variability and its components across time and space, 1950-2040, 414 weighted by country population size. Parts in greyscale are predicted values. Source: 415 Authors’ calculations based on the BL dataset. 416 417 In each of the panels in Figure 4 we also show education variability levels among women and 418 men (i.e. 𝑉𝑉𝑓𝑓 and 𝑉𝑉𝑚𝑚 ). The dashed curves for variability within men and women are only 419 visible during the period 1950-2000 and only for those regions with lower levels of education 420 (i.e. the regions of Sub-Saharan Africa, the Middle East and North Africa, East Asia Pacific 421 and South Asia). In those regions variability in terms of education among women was much 422 lower than variability among men in the 1950s. By the 2010s, variability among men and 21 Pre-print (Forthcoming: PLoS ONE) 423 women became very similar to overall education variability, so the three curves are 424 indistinguishable from each other in the right tails of the graphs. This means that in the past 425 women used to be a considerably more homogeneous group in terms of education compared 426 to men. Surprisingly, despite the observed reversal in the gender gap and its expected 427 persistence in the future, the groups of men and women are expected to exhibit the same level 428 of education variability during the period 2010-2040. The educational disadvantage of men 429 therefore does not seem to translate into them being a more homogeneous group in terms of 430 education compared to women – as we were originally expecting. Overall, this suggests that 431 the stylized trajectories shown in Figure 1 are a rough approximation of what has actually 432 happened with overall and gender-specific education variability in the different world 433 regions. 434 Lastly, the panels in Figure 4 also show the values of 𝐴𝐴𝑓𝑓 and 𝐴𝐴𝑚𝑚 (i.e. the likelihood that 435 women are more highly educated than men and vice-versa) over time. While the relative 436 position of these curves varies across regions, they roughly follow a similar pattern: 𝐴𝐴𝑚𝑚 437 increases first and at some point it starts declining, while 𝐴𝐴𝑓𝑓 increases unabated during the 438 whole period under consideration. Hence, the stylized trajectories shown in Figure 2 439 synthesize in a fairly accurate way the real patterns of female and male education 440 (dis)advantage observed in the world and its regions. Interestingly, we observe that in most 441 regions the two curves either cross before 2010 or are expected to do so between 2010 and 442 2040 (Sub-Saharan Africa is the only exception), thus meaning that the gender gap reversal 443 has already occurred or is expected to occur in the coming decades – an issue to which we 444 now turn. 445 446 Gender gap reversal in education 22 Pre-print (Forthcoming: PLoS ONE) 447 Figure 5 displays, for the 7 world regions as well as for the world overall, how the gender gap 448 in education has actually developed from 1950 to 2010 and how it is expected to develop 449 across time until 2040. Recall that negative values represent distributions where women are 450 likely to be less educated than men and vice versa. In line with previous research, one can 451 observe that women used to be less educated than men in the past in all world regions, but 452 this gender gap has reduced dramatically across the globe, and even reversed in the Advanced 453 Economies, Eastern Europe, and Latin America well before 2010. The gender gap in these 454 three regions must have reached its historical minimum in a period preceding 1950. The 455 evolution of the gender gap has not always been monotonic: in the regions of Sub-Saharan 456 Africa, the Middle East and North Africa, East Asia Pacific and South Asia it has initially 457 declined, attained its minimum somewhere between 1960 and 1990 and then started 458 increasing towards gender equality. By 2040, the gender gap is expected to be closed and 459 slightly reversed in almost all world regions (the only exception being Sub-Saharan Africa). 460 While at the beginning of our observation window we can clearly distinguish two clusters of 461 regions (on the one hand the Advanced Economies, Eastern Europe, and Latin America – 462 henceforth referred to as ‘forerunning regions’ – and on the other hand Sub-Saharan Africa, 463 the Middle East and North Africa, East Asia Pacific and South Asia – referred to as ‘laggard 464 regions’) by 2040 most gender gaps are expected to converge towards a slightly positive 465 value indicating some educational advantage in favor of women. Inspecting the ‘global 466 gender gap in education’ (i.e. taking the entire world as a unit of analysis), we also observe a 467 U-shaped trajectory over time. In 2010, the global gender gap was still in favor of men but 468 this is not expected to be the case anymore by 2040. This story differs from the conclusion of 469 an ever-decreasing gap in education between men and women over time once taking a 470 relative measure of educational differences (e.g. [7] Chapter 2.6). 23 Pre-print (Forthcoming: PLoS ONE) 471 472 Figure 5. Gender Gap in Education across the period 1950-2040, weighted by country 473 population size. Parts in greyscale are predicted values. Source: Authors’ calculations based 474 on the BL dataset. 475 476 Contribution of the Different Components to Overall Education Variability 477 Table 1 displays the relative contribution of each of the four components discussed in the 478 previous section to overall education variability (these are derived from decomposition 479 formula [3]). Recall that, as a reference, in a hypothetical country where the educational 480 attainment of men was identical to that of women, the percent contribution of the four 481 Region Year %C𝑉𝑉𝑓𝑓 %C𝑉𝑉𝑚𝑚 %C𝐴𝐴𝑓𝑓 %C𝐴𝐴𝑚𝑚 Advanced Economies 1950 26.8 23.2 22.8 27.2 24 Pre-print (Forthcoming: PLoS ONE) Advanced Economies 1980 24.5 25.4 23.6 26.5 Advanced Economies 2010 24.4 25.6 26.6 23.5 Advanced Economies 2040 23.7 26.2 27.2 22.8 East Asia and the Pacific 1950 16.1 32.9 13.5 37.5 East Asia and the Pacific 1980 22.8 26.6 17.2 33.4 East Asia and the Pacific 2010 24.2 25.7 24.0 26.1 East Asia and the Pacific 2040 21.7 28.2 27.2 22.8 E. Europe & Central Asia 1950 33.1 17.8 20.1 28.9 E. Europe & Central Asia 1980 25.6 24.3 24.1 26.0 E. Europe & Central Asia 2010 25.8 24.0 28.3 21.9 E. Europe & Central Asia 2040 23.8 26.1 28.1 22.1 Latin America & Carib. 1950 23.7 26.0 21.3 29.0 Latin America & Carib. 1980 25.1 24.8 23.7 26.3 Latin America & Carib. 2010 25.7 24.2 26.7 23.3 Latin America & Carib. 2040 23.4 26.0 30.0 20.6 Middle E.& North Africa 1950 12.1 37.4 11.7 38.7 Middle E.& North Africa 1980 18.6 29.6 14.6 37.2 Middle E.& North Africa 2010 23.2 26.5 21.7 28.5 Middle E.& North Africa 2040 22.9 26.7 26.6 23.7 South Asia 1950 9.9 38.9 9.0 42.2 South Asia 1980 16.0 31.8 12.0 40.2 South Asia 2010 21.7 27.4 17.5 33.5 South Asia 2040 22.3 27.7 25.0 24.9 Sub-Saharan Africa 1950 16.6 31.9 14.4 37.1 Sub-Saharan Africa 1980 21.2 27.4 16.1 35.3 Sub-Saharan Africa 2010 23.7 26.0 20.2 30.1 Sub-Saharan Africa 2040 24.7 25.2 22.3 27.8 World 1950 23.2 26.5 20.9 29.4 World 1980 23.6 26.1 20.4 29.9 World 2010 24.4 25.5 22.8 27.3 World 2040 23.1 26.9 25.9 24.1 482 483 Table 1. Variability in educational attainment by region and year for 25-29 year-olds, 484 decomposed into within and between women/men components. 𝑉𝑉: Overall variability; 𝑉𝑉𝑓𝑓 , 𝑉𝑉𝑚𝑚 : 485 Variability among women and men respectively; 𝐴𝐴𝑓𝑓 /𝐴𝐴𝑚𝑚 : Probability that a randomly 486 selected woman/man is more educated than a randomly selected man/woman; %C: Percent 487 contribution of the different components. Authors’ calculations based on Barro and Lee 488 (2013). 489 25 Pre-print (Forthcoming: PLoS ONE) 490 components shown in Table 1 would be exactly the same: 25%. As can be seen, the 491 composition of education variability has been shifting dramatically over time. Back in the 492 1950s, variability among women contributed very little to overall education variability in the 493 laggard regions (e.g. a mere contribution of 9.9% in South Asia), while the opposite was true 494 for variability among men (e.g. 38.9% in the same region). At the beginning of our 495 observation period, the educational advantage of men over women was by far the main 496 contributor to education variability in the world as a whole and in most of its regions (see last 497 column in Table 1). Sixty years later, that contribution has decreased substantially at a global 498 level. Indeed, in the forerunning regions (i.e. in most high- and middle-income countries) it 499 has become the least important contributor to education variability (i.e. 23.5%, 21.9% and 500 23.3% for the advanced economies, Eastern Europe and Latin America in 2010). 501 Concomitant with these changes, the educational advantage of women over men has become 502 an increasingly important ingredient of overall education variability (see second-to-last 503 column in Table 1). Sixty years ago, the contribution of that kind of variability to overall 504 education variability was by far the least important among the four (particularly so in the 505 poorest regions of the world, e.g. only 9% in South Asia). Nowadays, women’s educational 506 advantage is the main contributor to education variability in most high- and middle-income 507 countries (i.e. 26.6%, 28.3% and 26.7% for the advanced economies, Eastern Europe and 508 Latin America in 2010). 509 510 The relationship between gender equality and overall variability 511 What can we say about the relationship between the gender gap in education and overall 512 education variability in the midst of the aforementioned compositional changes? Have they 513 moved in the same or in opposite directions? To give a precise account of the joint levels and 26 Pre-print (Forthcoming: PLoS ONE) 514 trends of 𝑉𝑉 and 𝐺𝐺 , in Figure 6 we present a full-fledged description of how these two 515 indicators have co-varied over time for the world and its regions (the values of 𝑉𝑉 are shown 516 in the vertical axis and those of 𝐺𝐺 in the horizontal one). Putting together the world regions’ 517 experiences shown in that figure, we conclude this section presenting a broad-strokes account 518 of the joint evolution of education and gender inequality, which consists in four stages. Stage 519 I: The male-dominated education expansion brings increases in education variability and 520 drives the gender gap in education in favor of men. In this case, both measures of variability 521 temporarily go in the normatively undesirable direction, and might therefore be a period 522 where educational expansion has most externalities. Stage II: The delayed incorporation of 523 women into mass education tilts the gender gap towards the opposite direction and brings 524 further increases in education variability until it reaches its maximum. Here, both measures of 525 variability go in opposite directions and trade-offs between both policy objectives might 526 emerge. During this stage potential efforts to slow down education expansion in order to 527 prevent overall education variability from rising further could be at odds with reducing the 528 gender gap in education. Stage III: When further education expansion gradually shifts the 529 population towards the higher educational categories, education variability starts declining 530 and the gender gap goes to zero: this is the onset of a period where education expands while 531 both measures of variability decrease simultaneously. Stage IV: Further education expansion, 532 particularly in favor of women, reverses the gender gap in education while further decreasing 533 overall education variability. 534 Even if not all regions (let alone the individual countries) fit this stylized description, it 535 reasonably represents the different trajectories shown in Figure 6. For the laggard regions of 536 the Middle East and North Africa, East Asia Pacific and South Asia we can observe the 537 occurrence of stages I, II and III. Until 2010 Sub-Saharan Africa had only completed stages I 538 and II, and it is expected that by 2040 it will have entered in the third one. As regards the 27 Pre-print (Forthcoming: PLoS ONE) 539 advanced economies and Eastern Europe, we observe the occurrence of stages II, III and IV 540 during our 1950-2040 study period (in Appendix C we show how many years each region has 541 spent in each of the aforementioned stages). Lastly, the region of Latin America stands out as 542 being the only one that does not fit very well our 4-stage narrative. The initial reductions of 543 the gender gap go in tandem with increases in education variability and the posterior 544 decreases in education variability occur when the gender gap reverses in favor of women (i.e. 545 both measures tend to go in opposite directions). Whereas future educational expansion in 546 other regions is expected to simultaneously reduce both forms of heterogeneity, expansion in 547 Latin America is likely to increase the gender gap favoring women to relatively high levels. 548 549 Figure 6. Development of gender and overall variability in education over time. Parts in 550 greyscale are predicted values. Source: Authors’ calculations based on the BL dataset. 28 Pre-print (Forthcoming: PLoS ONE) 551 552 6. Summary and concluding remarks 553 In this paper, we have documented the trends in education variability for the world and its 554 regions. In addition, we have presented a new technique that allows decomposing overall 555 education variability in four clearly interpretable components: variability among women, 556 variability among men, educational advantage of men and educational advantage of women. 557 For that purpose, we have developed a new variability index adapted to the ordinal nature of 558 educational attainment, which for the first time allows articulating the aforementioned 559 components into a coherent whole. Such decomposition techniques are extremely useful to go 560 beyond mere descriptions of levels and trends. They allow pinpointing not only what are the 561 most important factors that explain current education variability levels, but also quantify their 562 contribution to changes over time. As an illustration, Figure 7 shows the decomposition of 563 education variability for three countries: Taiwan (for the year 1955), Australia (1980) and 564 Italy (2010). The three countries have very similar levels of overall education variability. Yet, 565 the decomposition of this measure yields completely different results. While in Taiwan 566 (1955) most of the variability can be attributed to the educational advantage of men over 567 women (a component explaining 31.7% of the total), the reverse happens in Italy (2010). 568 There, the educational advantage of men over women and of women over men are the least 569 and most important contributors to overall education variability, respectively (these 570 components explain 13.4% and 19.4% of the total). Somewhere in between we have the case 571 of Australia (1980), where the four components explain about the same percentage of 572 education variability. The possibility of breaking down outcome indicators into meaningful 573 and policy-relevant pieces of information can be very useful for the design, implementation 574 and evaluation of fine-tuned education programs. 29 Pre-print (Forthcoming: PLoS ONE) 575 576 Figure 7. Education variability and its decomposition in four components for Taiwan (1955), 577 Australia (1980) and Italy (2010). Source: Authors’ calculations based on the BL dataset. 578 579 Based on the Barro and Lee [7] dataset we have calculated the values of the variability index 580 and the contribution of its components for 146 countries during a period spanning almost a 581 century (1950-2040). Our findings indicate that the composition of education variability has 582 changed dramatically during the period between 1950 and 2010. In the past, women used to 583 be a much more homogeneous group compared to men in terms of education in several world 584 regions. With education expansion, variability among women quickly started to increase. We 585 expected that as the gender gap in education reversed in favor of women, the variability 586 among them would be higher than the variability among men. Surprisingly, our results show 587 that education variability among men and women is now very similar in all world regions, 588 and this is expected to remain so in the near future. Back in the 1950s, the educational 589 advantage of men over women was by far the main contributor to education variability in the 590 world as a whole and in most of its regions, while the opposite was true about the educational 591 advantage of women over men. Nowadays, men’s educational advantage has become the 30 Pre-print (Forthcoming: PLoS ONE) 592 least important contributor to education variability in several regions, while women’s 593 educational advantage is the main contributor to education variability in most high- and 594 middle-income countries. 595 Another of the issues investigated in this paper has been the relationship between education 596 variability and the gender gap in education. Our findings suggest that during the process of 597 education expansion, most world regions have gone (or are expected to go) through the 598 following consecutive phases: (I) increasing education variability and gender gap in 599 education in favor of men; (II) increasing education variability but reduction in the gender 600 gap in education; (III) reduction of education variability and the gender gap in education; and 601 (IV) stalling or slight reduction of education variability and reversal of the gender gap in 602 education in favor of women. One could speculate that when societies enter the third phase, 603 an opportunity window opens up where educational expansion might bring the additional 604 benefits of reducing both overall and gender inequality in education (i.e. a period where there 605 is no dilemma between ‘efficiency’ and both forms of ‘equality’). According to our results, 606 most world regions have experienced, are experiencing or are expected to experience a period 607 whereby both education variability and the gender gap decline simultaneously. Whether or 608 not the confluence of these phenomena is truly beneficial for the countries that experience 609 them is a matter for future research. In addition, if one assumes that large educational 610 advantages of one sex over the other are normatively undesirable, our findings suggest that in 611 the near future there might be some trade-offs between gender and overall education 612 variability, as they both seem to run in opposite directions. If further education expansion 613 contributes to further decreases in overall education variability and increases in females’ 614 educational advantage over men (a scenario that appears likely until a ceiling of tertiary 615 education attainment is reached in many countries), education planners might be facing 31 Pre-print (Forthcoming: PLoS ONE) 616 ethical dilemmas upon which it will be necessary to reflect (particularly in high-income 617 countries). 618 What should one expect for the more distant future? Will education variability continue to 619 decline and the gender gap to increasingly favor women? In line with Inglehart and Welzel 620 [36], our expectations are that as long as the modernization process continues to unfold, it 621 will facilitate cultural changes that make gender equality increasingly likely. Since we 622 speculate that gender equality has come to stay, we expect that the gender gap in education 623 will not continue increasing to attain the high levels it had in the initial stages of the male- 624 dominated education expansion, but will rather hover around gender parity levels. 625 As regards education variability there are a couple of reasons to not expect a continuation of 626 its currently downward trend for a long time. First, while the global decline in overall 627 education variability (both for women and for men) points to an increasing equalization of 628 opportunities across citizens worldwide, it is likely that new forms of education variability 629 not captured in our data might be (or already have been) replacing older ones. Indeed one can 630 suspect that the observed declines in overall education variability can be the attributed to the 631 clustering of the educational attainment distribution at its top, which might be hiding an 632 increasing diversity of superior education alternatives (like Masters and PhDs) not captured 633 in the 7 categories of Barro and Lee’s dataset. Some exploratory work carried out for the case 634 of the US using census microdata samples (not shown here but available upon request) 635 suggests that this might be indeed the case. When we enlarge the set of education categories 636 from 7 to 9 (including Masters and PhDs), the decline in overall education variability is less 637 pronounced. In the same line, a recent study by Meschi and Scervini [23] suggests that after a 638 long period of sustained decline, education inequality is turning upwards in many European 639 countries as a result of the expansion of tertiary and post-tertiary schooling. 32 Pre-print (Forthcoming: PLoS ONE) 640 Second, education variability is intimately associated with technological progress and 641 economic inequality, two forces that are unlikely to remain stable over time. Under the 642 assumption that technology is skill-biased [37], technological progress will widen inequality 643 among skill groups unless it is countered by increases in the supply of educated workers. 644 Depending on the outcome of the ‘race between education and technology’ [38] – which is 645 particularly uncertain – income and education inequality levels can vary to a great extent. 646 Along similar lines, Milanovic [39] recently suggested that the modern historical era from the 647 preindustrial through the postindustrial period is characterized by the so-called ‘Kuznets 648 waves’ of alternating increases and decreases in economic inequality, with many high-income 649 countries currently in the upward portion of the wave. In all likelihood, the ‘economic 650 Kuznets waves’ will translate into ‘education Kuznets waves’, thereby increasing education 651 variability as well. Whether or not such incipient trends will consolidate in the near future is a 652 matter for future research. 653 We conclude with a word of caution about the limits of our approach. Documenting the 654 variability and decompositions of educational attainment across world countries is an 655 important endeavor in and of itself. There is an extensive literature linking educational 656 attainment with all kinds of normatively desirable outcomes that social scientists and policy 657 makers are interested in – including, but not limited to, job opportunities, earning potential, 658 health outcomes and life satisfaction across the life cycle. Yet, educational attainment is not 659 only about quantity, but also about quality. Very often, students do not acquire the skills they 660 need by merely attending low quality schools with insufficient resources [40]. In future 661 research, it will be necessary to complement our findings with other indicators (like test 662 scores) that are better suited to capture the cognitive abilities and skills that students acquire 663 while at school. 664 33 Pre-print (Forthcoming: PLoS ONE) 665 Financial Disclosure Statement 666 The research leading to these results has received funding from the European Research 667 Council (ERC-2014-StG-637768, EQUALIZE project), the Spanish Ministry of Economy 668 and Competitiveness “Ramón y Cajal” Research Grant Program (RYC-2013-14196) and the 669 Spanish Ministry of Economy, Industry and Competitiveness, National R&D&I Plan 670 CRISFAM (CSO2015-64713-R). 671 34 Pre-print (Forthcoming: PLoS ONE) 672 References 673 [1] Morrisson C, Murtin F. The century of education. J Hum Cap 2009;3: 1-42. 674 [2] Esteve A, Schwartz CR, Van Bavel J, Permanyer I, Klesment K, García-Román J. The 675 End of Hypergamy: Global Trends and Implications. 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Derivation of Equation [3]. 761 Manipulating algebraically it is easy to show that 𝑖𝑖=𝑘𝑘 𝑗𝑗=𝑘𝑘 ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖 𝑁𝑁𝑗𝑗 ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖(𝑁𝑁𝑖𝑖𝑓𝑓 + 𝑁𝑁𝑖𝑖𝑚𝑚 )(𝑁𝑁𝑗𝑗𝑓𝑓 + 𝑁𝑁𝑗𝑗𝑚𝑚 ) 𝑉𝑉(𝑝𝑝1 , ⋯ , 𝑝𝑝𝑘𝑘 ) = � � 𝑝𝑝𝑖𝑖 𝑝𝑝𝑗𝑗 𝕀𝕀(𝑖𝑖, 𝑗𝑗) = = 𝑁𝑁 2 𝑁𝑁 2 𝑖𝑖=1 𝑗𝑗=1 ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖𝑓𝑓 𝑁𝑁𝑗𝑗𝑓𝑓 + ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖𝑚𝑚 𝑁𝑁𝑗𝑗𝑚𝑚 + ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖𝑓𝑓 𝑁𝑁𝑗𝑗𝑚𝑚 + ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖𝑚𝑚 𝑁𝑁𝑗𝑗𝑓𝑓 = 𝑁𝑁 2 2 𝑘𝑘 𝑓𝑓 𝑓𝑓 𝑁𝑁 𝑓𝑓 ∑𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖 𝑁𝑁𝑗𝑗 𝑁𝑁 𝑚𝑚 2 ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖𝑚𝑚 𝑁𝑁𝑗𝑗𝑚𝑚 =� � +� � + 𝑁𝑁 (𝑁𝑁 𝑓𝑓 )2 𝑁𝑁 (𝑁𝑁 𝑚𝑚 )2 𝑓𝑓 𝑁𝑁 𝑓𝑓 𝑁𝑁 𝑚𝑚 ∑𝑘𝑘𝑖𝑖=1 ∑𝑗𝑗≠𝑖𝑖 𝑁𝑁𝑖𝑖 𝑁𝑁𝑗𝑗𝑚𝑚 + �2 � 𝑁𝑁 2 𝑁𝑁 𝑓𝑓 𝑁𝑁 𝑚𝑚 𝑖𝑖=𝑘𝑘 𝑖𝑖=𝑘𝑘 𝑠𝑠𝑏𝑏 𝑓𝑓 𝑓𝑓 = 𝑠𝑠𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝑠𝑠𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝑓𝑓 𝑚𝑚 �� � 𝑁𝑁𝑖𝑖 𝑁𝑁𝑗𝑗𝑚𝑚 + � � 𝑁𝑁𝑖𝑖𝑚𝑚 𝑁𝑁𝑗𝑗 � 𝑁𝑁 𝑁𝑁 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 𝑖𝑖=𝑘𝑘 𝑖𝑖=𝑘𝑘 𝑓𝑓 𝑓𝑓 = 𝑠𝑠𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝑠𝑠𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝑠𝑠𝑏𝑏 �� � 𝑝𝑝𝑖𝑖 𝑝𝑝𝑗𝑗𝑚𝑚 + � � 𝑝𝑝𝑖𝑖𝑚𝑚 𝑝𝑝𝑗𝑗 � 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 𝑖𝑖=2 𝑗𝑗<𝑖𝑖 = 𝑠𝑠𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝑠𝑠𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝑠𝑠𝑏𝑏 �𝐴𝐴𝑓𝑓 + 𝐴𝐴𝑚𝑚 �. 762 This is the decomposition we were looking for. 763 764 39 Pre-print (Forthcoming: PLoS ONE) 765 Appendix B. Actual and predicted attendance of educational stages for men 1950-2040 766 767 768 Figure B1. Men’s attendance of educational stages 1950-2040, by region, predicted and 769 actual (weighted by population size of countries). Parts in greyscale are predicted values. 770 Source: Authors’ calculations based on the BL dataset. 40 Pre-print (Forthcoming: PLoS ONE) Appendix C. 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 - - - - - - - - - - - - - - - - - - 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 Advanced Economies 1 2 1 3 2 4 4 4 4 4 4 4 4 4 4 4 4 4 East Asia and the Pacific 1 1 1 2 2 2 2 2 4 4 2 4 4 4 2 4 2 4 Europe and Central Asia 2 2 1 4 4 4 4 4 2 4 2 2 2 2 4 2 2 2 Latin America and the Caribbean 2 2 2 2 3 2 2 2 2 2 2 4 2 4 3 3 3 3 Middle East and North Africa 1 1 1 1 1 1 1 2 2 2 2 4 4 4 4 4 4 4 South Asia 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 Sub-Saharan Africa 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 3 World 1 1 1 2 1 2 2 2 4 4 2 2 4 4 4 4 4 4 Education Variability and Gender Gap Increasing Gender Gap Decreasing, Education Variability Increasing Gender Gap Increasing, Education Variability Decreasing Education Variability and Gender Gap Decreasing Figure C1. Periods during which trends in education variability and the gender gap in education go in simultaneous or different directions. 41 Pre-print (Forthcoming: PLoS ONE) 1 In Figure C1 we indicate the starting and the end of the time periods in which the world and 2 its regions have either experienced (i) trade-offs among education variability and the gender 3 gap in education, (ii) increases in both types of measures, or (iii) simultaneous decreases 2. 4 During the time frame considered here all world regions (except in Latin America) have gone 5 through periods where education expansion has not been an egalitarian process, as it 6 simultaneously increased education variability and the gender gap in education. Generally, 7 this period has been longer for the laggard regions (e.g. 40 years in South Asia) and 8 considerably shorter for the forerunning ones. Analogously, all regions have experienced 9 considerable periods of time with trade-offs between overall education variability and the 10 gender gap in education (i.e. periods in which one measure could only be reduced at the 11 expense of increasing the other). At one extreme, the advanced economies have only 12 experienced such periods for relatively short time spells (15 years), while at the other 13 extreme, Latin America has experienced them almost during the entire time frame (80 years). 14 Overall, there have been many more periods in which education variability increased in 15 tandem with gender gap reductions than periods with the opposite combination. Lastly, the 16 world and all its regions have also gone through considerably long periods without 17 experiencing the efficiency-equality dilemma. While some regions are expected to pass 18 through such periods only for a decade (e.g. South Asia, between 2030 and 2040), others 19 have gone and are expected to go through them during 65 years (e.g. advanced economies, 20 between 1975 and 2040). The world taken as a whole entered such period in 1990, and is 21 expected to continue until 2040 with some small interruptions. 22 23 24 2 To generate this table, we have assumed that values of the gender gap between 0 and 0.1 (i.e. slight education advantage in favor of women) are not normatively undesirable. 42