Pre-print. Forthcoming: PLoS ONE Global trends in lifespan inequality: 1950-2015. Iñaki Permanyer 1 Nathalie Scholl 2 Abstract Using data from the UN World Population Prospects, we document global trends in lifespan inequality from 1950 until 2015. Our findings indicate that (i) there has been a sustained decline in overall lifespan inequality, (ii) adult lifespan variability has also declined, but some plateaus and trend reversals have been identified, (iii) lifespan inequality among the elderly has increased virtually everywhere, (iv) most of the world variability in age-at-death can be attributed within-country variability. Such changes have occurred against a backdrop of generalized longevity increases. Our analyses suggest that the world seems to be facing a new challenge: the emergence of diverging trends in longevity and age-at-death inequality among the elderly around the globe – particularly in high-income areas. As larger fractions of the world population survive to more advanced ages, it will be necessary that national and international health planners recognize the growing heterogeneity that characterizes older populations. Keywords: lifespan inequality; global disparities; longevity; young, adult and elderly mortality 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: inaki.permanyer@uab.es. 2 Centre d’Estudis Demogràfics. E-mail: nscholl@ced.uab.es. 1 Pre-print. Forthcoming: PLoS ONE 1. Introduction Living long and healthy lives is among the most highly valued and universal human goals, so the unparalleled longevity gains recorded all over the world during the last decades is a cause for celebration. While a huge body of scholarship has shed considerable light on the ‘efficiency part’ of the process (i.e. the global, regional and country trajectories in life expectancy over time are very well documented [1 – 2]), much less is known about the ‘equality part’. Since mortality can arguably be considered as the ultimate measure of health, lifespan inequalities should be seen as the most fundamental manifestations of health disparities. Indeed, the existence of very unequal length of life distributions might go beyond purely natural causes and could be indicative of an unfair state of affairs in which some population groups might be disadvantaged or discriminated against. For this reason, the study of lifespan variability has attracted a great deal of attention from demographers and other social scientists, particularly during the last decade or so [3 – 15]. Studies on lifespan disparities usually focus their attention on differences occurring either between or within countries. The former approach typically compares the average health performance among a cross-section of countries (most often by comparing the corresponding life expectancies) and aims at understanding why population health is better in some countries than in others [16 – 18]. In contrast, the latter approach explores the lifespan differences that might exist among the individuals within a given country. Surprisingly, the study of global lifespan inequality (henceforth referred to as GLI) – that is: the study of variations in individuals’ lifespan both within and between all world countries (henceforth WLI and BLI, respectively) – is largely underdeveloped; so far, it has only been analyzed in a couple of studies either using one or two cross- sections in time ([4], [19]). Despite its importance, our understanding of how the 2 Pre-print. Forthcoming: PLoS ONE different types of inequalities are articulated into a coherent whole and how their relationship evolves as the demographic transition unfolds is still in its infancy – an issue we aim to address in this paper. For the first time, we document the joint evolution in within country, between country and global lifespan inequality during the period spanning from 1950 to 2015, and we investigate in detail the relationship between these trends and the advances in longevity that are sweeping the world. There are many reasons to be interested in the study of global trends in length of life inequality. First, from a practical perspective we now have the possibility to do so. Not long ago, the set of life tables needed to conduct comparative analyses across and within world countries for long time periods was very difficult to access for researchers. Second, from an ethical perspective, if all human beings are entitled to equal rights, egalitarian concerns should apply equally at the national and global levels (e.g. should we tolerate individual’s lifespan prospects to be determined by their country of birth?). Third, the study of global inequalities allows us to see how the world has changed – often in fundamental ways – and to study the hotly debated consequences of economic globalization or other global phenomena affecting the living conditions of all human beings. Last but not least, exploring how age-at-death differentials jointly evolve within and between countries can throw considerable light on our understanding of human mortality processes and improve the quality of national and international public health policies. An analysis of global lifespan inequality must necessarily take into consideration the unprecedented demographic transformations undergone by the world and its regions since the 1950s. On the one hand, the unfolding of the demographic and epidemiological transitions during more than six decades have dramatically changed world countries’ population structures. While the prevalence of infant mortality was 3 Pre-print. Forthcoming: PLoS ONE particularly high among most world countries in the mid-20th century, nowadays childhood and reproductive-age mortality have shrunk considerably, thus moving age- at-death distributions to more advanced ages. On the other hand, country-specific life expectancies and the corresponding population shares (which in turn are affected by differential population growth trajectories) strongly influence global trends in lifespan inequality. To gauge the specific effect that such structural changes have had on lifespan variability across and within countries we incorporate the following analytical strategies. First, we study lifespan variability not only across the entire age range, but also across adult and more advanced age ranges. For convenience, the last two ranges comprise the ages above 15 and above 65, respectively (similar age thresholds have been used in many conceptually related papers [4 – 5], [19]); the substantive findings of the paper remain unaffected by the choice of alternative thresholds). As suggested in previous studies, there are good reasons to separate childhood, adult and elderly mortality [3 – 5], [19]. Second, we resort to well-known and newly developed inequality decomposition techniques that allow going beyond purely descriptive results and analyze what factors are the most important drivers of lifespan dispersion and its evolution over time. Inter alia, we run several counterfactual analyses to identify the influence that countries’ relative population size, longevity and within country lifespan inequality have had on the dynamics of global lifespan inequality. The empirical analysis relies on the latest version of United Nations’ World Population Prospects (WPP) for the period from 1950 to 2015. The huge geographic coverage of the database (195 countries) allows performing global, regional and country-level analyses over time. Based on this data source, this paper aims to (i) document levels and trends in longevity and lifespan inequality for overall, adult and elderly mortality in the world and its regions; (ii) decompose global lifespan inequality in its within- and 4 Pre-print. Forthcoming: PLoS ONE between-country components and assess what the corresponding contributions are; and (iii) examine the main potential sources of lifespan inequality within and across countries. 1.1 Longevity and lifespan variation Classical health transition theories suggest that longevity increases go in tandem with a transformation of the mortality distribution characterized by a concentration of deaths around the modal age at death, with both the mean and modal age at death increasing [20 – 21]. In this line, the so-called ‘mortality compression’ or ‘rectangularization hypothesis’ popularized by Fries [22] postulates that as the epidemiological transition unfolds, the human survival curves gradually adopts a rectangular shape as life expectancy at birth increases and approaches an upper limit of the human lifespan. In the limit, the survival curve would become fully rectangular and all deaths would occur at the same age. While some studies suggest that the maximum lifespan of humans is fixed and is unlikely to increase over time [23], most empirical evidence has shown no evidence of an upper bound to life expectancy, which continues to increase unabated [2], [24]. The progressive rectangularization of the survival curve has been observed in several high-income countries [25 – 26]. In the majority of cases, increasing longevity is associated with low lifespan disparities when one considers the entire range of ages at death [6]. Yet, several studies have noted that restricting our attention to selected age ranges, the relationship between longevity and lifespan variability weakens, and even reverses. For the US, [27] found that while the relationship between life expectancy and lifespan inequality across the entire age range was negative, the relationship turned positive when the age at death distribution was bottom-truncated at the age of 60. [28 – 5 Pre-print. Forthcoming: PLoS ONE 29] and [5] found similar patterns for other highly industrialized countries. In the same context, [3] found stagnating – rather than the expected declining – trends in lifespan variability when bottom truncating the lifespan distribution at the age of 10. While the selection of specific age ranges in the study of mortality compression has been criticized on grounds of arbitrariness ([29], page 187), several authors suggest that studying variability measures conditional upon survival to a certain age (i.e. exploring the so- called ‘conditional’ age-at-death distributions) is a promising avenue of research that can reveal unexpected patterns in adult mortality that are otherwise concealed by unconditional measures [5], [21]. As longevity increases and larger fractions of the population survive to more advanced ages, it becomes important to go beyond the analysis of mortality across the entire age range and focus our attention on some of its subsets. Rather than sticking to a particular age range, in this paper we document global trends in overall, adult and elderly lifespan variability. Current evidence on global length of life inequality and its between- and within-country subcomponents is still incomplete. In general, unconditional length of life inequality within countries has tended to decrease as longevity increases [4], [6]. Yet, [5] report increases in lifespan variability among the elderly within a group of high-income countries. As regards between-country variation, some cross-national studies report worldwide convergence in life expectancy levels between the 1950s and the late 1980s [18], [30]. Unfortunately, the spread of HIV/AIDS in Africa and the collapse of Communism contributed to reverse this favorable trend. Lastly, the evidence on global trends in lifespan inequality is particularly scarce. Using life tables from 180 countries, [19] shows that the world inequality in length of life diminished between 1970 and 2000. In line with the previous two studies, his findings suggest that between-country inequality increased between the two points of time – a matter of concern for public 6 Pre-print. Forthcoming: PLoS ONE health planners. One of the main aims of this paper is to expand the scope of the previous studies by giving a detailed account of the global trends in lifespan inequality for the world and its regions during the last 65 years. In our analysis, we will explore both unconditional and conditional age-at-death distributions. 2. Data The main data source employed in this paper is the UN World Population Prospects’ (WPP) abridged life tables, recording the number of deaths for age groups in 5-year intervals (with separate data for infants (age group 0-1) as well as an open-ended 100+ interval) for the 1950-2015 time span, again over 5-year periods. We aggregate our estimates for both sexes, but data is also available separately for females and males (see the discussion section). The life tables information is complemented with countries’ population size (also available from UN’s WPP), which is needed to calculate the between-country component of global lifespan inequality. In our analysis we use life tables from 195 countries over 13 5-year time periods (from 1950-55 until 2010-15), yielding a total of 2535 country-period observations. To facilitate the presentation of our results, we aggregate the data at different levels employing the standard United Nations’ regional classification of countries (in the Supplementary Material section we show the countries included in each of these regions). Due to the marked impact of the HIV-Aids epidemic on length-of-life distributions, we create a separate category for Sub-Saharan African countries which have had a HIV prevalence of more than 3%. While there is excellent data on mortality by age group for high-income countries, data are generally more sparse and less reliable for developing countries. Nevertheless, the UN population division has assembled a broad data set of country life tables and 7 Pre-print. Forthcoming: PLoS ONE provides a detailed account of the data sources used in the construction of each countries’ set of mortality estimates (see https://esa.un.org/unpd/wpp/DataSources/). Although the use of model life tables is unavoidable for constructing complete data series for all developing countries, all missing country-year combinations are estimated via indirect methods based on real data. Therefore, while the accuracy of individual inequality estimates might not be perfect for every country in every year, we have strong reasons to believe that the broad picture that emerges from them is a faithful portrait of reality. As indicated along this paper, our empirical findings square well with those from other renowned studies, and the estimates we obtain from the UN WPP are highly correlated with the estimates derived from other reputable data sources, like the Human Mortality Database (HMD). 3. Methods 3.1 Measuring lifespan inequality Currently, there is an unsettled debate on whether lifespan inequality should be measured using absolute or relative measures (sometimes also referred to as ‘additive’ and ‘proportional’ measures, respectively). While there is a long tradition in using relative inequality measures (partly driven by their massive use among economists because of their ability to compare income distributions expressed in different currencies), there is no theoretical reason why one should disregard the use of absolute ones when exploring differences in length of life. The choice between absolute and relative measures can be problematic when assessing trends because the corresponding results do not necessarily coincide – an issue that is partly attributable to the explicit dependence of relative measures to the values of the mean, which tend to change over time. Very often, relative measures might show declines because the mean has 8 Pre-print. Forthcoming: PLoS ONE increased, while absolute measures might remain unaffected – a technical point that should be taken into consideration when interpreting the results. Since the choice between both kinds of measures is purely normative [31] and no clear consensus seems to be in place, in this paper we use both absolute and relative inequality measures. In the last few years, several measures have been proposed to measure lifespan variability (see [32] for an excellent review of the most widely used measures). We have selected specific inequality indices based on their popularity and their decomposability properties, which, as we show below, are very useful for the purposes of this paper. The first measure we consider is the Theil index, which is a relative measure defined as: 𝜔𝜔 1 𝛼𝛼𝑥𝑥 𝛼𝛼𝑥𝑥 𝑇𝑇𝑎𝑎 = � 𝑑𝑑𝑥𝑥 � � 𝑙𝑙𝑙𝑙𝑙𝑙 � � [𝐸𝐸𝐸𝐸1] 𝑙𝑙𝑎𝑎 𝜇𝜇𝑎𝑎 𝜇𝜇𝑎𝑎 𝑥𝑥=𝑎𝑎 where 𝑎𝑎 and 𝜔𝜔 are the youngest and oldest age intervals taken from the life table, 𝑙𝑙𝑎𝑎 is the radix of the population, 𝜇𝜇𝑎𝑎 is the average age at death of the population, and 𝑑𝑑𝑥𝑥 and 𝛼𝛼𝑥𝑥 are the life table number of deaths and the average age at death in the age interval 𝑥𝑥 to 𝑥𝑥 + 5, respectively. When 𝑎𝑎 = 0 we are including the entire lifespan distribution and when 𝑎𝑎 = 15 we disregard mortality under 15 and focus on adult mortality only. Since both approaches have been used in the literature (see [4], [19]), we calculate inequality statistics both for the unconditional and conditional distributions. In addition, we also investigate lifespan inequality trends when 𝑎𝑎 = 65, that is: length of life inequality among the population beyond the standard retirement age – an analysis that, so far, has only been conducted in a reduced group of high-income countries (see [5]). Another of the inequality indices we will consider in the paper is the variance. Using the same notation as before it is defined as: 9 Pre-print. Forthcoming: PLoS ONE 𝜔𝜔 1 𝑉𝑉𝑎𝑎 = � 𝑑𝑑𝑥𝑥 (𝛼𝛼𝑥𝑥 − 𝜇𝜇𝑎𝑎 )2 [𝐸𝐸𝐸𝐸2] 𝑙𝑙𝑎𝑎 𝑥𝑥=𝑎𝑎 Unlike the Theil index, the variance is an absolute inequality measure. Again, we will report the values of this inequality measure for 𝑎𝑎 = 0, 𝑎𝑎 = 15 and 𝑎𝑎 = 65. As a robustness check, in a Supplementary Material section we complement our analysis showing the results arising from other well-known inequality measures, like the Gini index or the coefficient of variation. 3.2. Inequality decompositions The reason why we have chosen the inequality indices shown in equations [EQ1], [EQ2] is that they are amenable to interesting decompositions that can throw some light on the factors behind lifespan variability dynamics. The Theil index and the variance are known for their additive decomposability property. This means that global lifespan inequality (i.e. variations in age at death around the whole world) can be broken down in two clearly interpretable components: the inequality observed within countries and the one capturing the differences in average attainment between countries. More formally, additively decomposable inequality measures can be written as 𝐼𝐼 = 𝐼𝐼𝐵𝐵 + 𝐼𝐼𝑊𝑊 [𝐸𝐸𝐸𝐸3] In the last equation, 𝐼𝐼𝐵𝐵 represents the inequality that would be observed in a hypothetical distribution (sometimes referred to as ‘smoothed distribution’) where the age at death of each individual corresponds to the average age at death in the corresponding country (i.e. eliminating within-country variations). The second term is a weighted average of lifespan inequality within countries. The decomposition formula [EQ3] can be applied irrespective of the choice of the age range (i.e. both for 10 Pre-print. Forthcoming: PLoS ONE conditional and unconditional lifespan distributions – see the Supplementary Material section for a full development of this equation). 3.3. Lifespan variation counterfactuals As shown in the Supplementary Material section, global lifespan inequality is a function of three factors: (i) population shares (𝑠𝑠), (ii) longevity (𝜇𝜇), and (iii) lifespan variability (𝐼𝐼) in the different world countries. To simplify notation and explicitly indicate the dependency of lifespan inequality on these three factors, we will schematically rewrite equation [EQ3] as 𝐼𝐼𝑡𝑡 = 𝑓𝑓({𝒔𝒔𝑡𝑡 }, {𝝁𝝁𝑡𝑡 }, {𝑰𝑰𝑡𝑡 }) [𝐸𝐸𝐸𝐸4] where the bold letters indicate the country-wise vectors of population shares, longevity and within-country inequality, respectively, the subscript ‘𝑡𝑡’ now refers to the time period and 𝑓𝑓 is a function (in the Supplementary Material section, we show the specific functional form that equation [EQ4] adopts when applied to the cases of the Theil index and the variance). Given the transformations undergone by these three components around the world during the last decades, it is interesting to gauge their relative importance in assessing changes in overall lifespan inequality over time. To address this issue we use a set of counterfactual analyses. We ask what would have happened to total lifespan inequality in time period ‘2’ if we held constant one of the three quantities that appear in the inequality index at its earlier (time period ‘1’) value and allowed the other two to take their later (time period ‘2’) value. In this way, we generate a counterfactual level of lifespan inequality in time period ‘2’ and by comparing this with observed inequality in time period ‘2’ we can assess the impact of change in the quantity we kept fixed at time ‘1’ levels on inequality. In this way, we generate the following counterfactual inequalities: 11 Pre-print. Forthcoming: PLoS ONE 𝐶𝐶1 = 𝑓𝑓({𝒔𝒔1 }, {𝝁𝝁2 }, {𝑰𝑰2 }) [𝐸𝐸𝐸𝐸5] 𝐶𝐶2 = 𝑓𝑓({𝒔𝒔2 }, {𝝁𝝁1 }, {𝑰𝑰2 }) [𝐸𝐸𝐸𝐸6] 𝐶𝐶3 = 𝑓𝑓({𝒔𝒔2 }, {𝝁𝝁2 }, {𝑰𝑰1 }) [𝐸𝐸𝐸𝐸7] Hence, 𝐶𝐶1 indicates the level of lifespan inequality we would observe in time ‘2’ if the population shares of each country had remained at its time ‘1’ levels (i.e. in case there were no population growth). The second counterfactual measures the level of inequality we would observe in time ‘2’ in case the longevity in each country had not changed over time. Lastly, 𝐶𝐶3 measures the inequality we would observe in time ‘2’ if within- country lifespan variation had remained at its time ‘1’ levels. Comparing the values of the counterfactuals 𝐶𝐶1 , 𝐶𝐶2 , 𝐶𝐶3 with the observed inequality levels (i.e. 𝐼𝐼1 = 𝑓𝑓({𝒔𝒔1 }, {𝝁𝝁1 }, {𝑰𝑰1 }) and 𝐼𝐼2 = 𝑓𝑓({𝒔𝒔2 }, {𝝁𝝁2 }, {𝑰𝑰2 }) we can estimate which of the three factors might have been more decisive in driving lifespan inequality changes over time. Clearly, the counterfactuals shown in equations [EQ5] to [EQ7] can be computed both for conditional and unconditional lifespan distributions. 4. Empirical Findings 4.1 Regional trends In the different panels of Figure 1 we show the evolution of length of life distributions between 1950-55 and 2010-15 for the world as a whole and for its different regions. Two major changes have occurred when moving from the mid-20th century to the present date. First, all distributions have clearly shifted to the right, thus indicating a lengthening of lifespan across all regions and for the world as a whole. Second, the shape of the age-at-death distributions has changed dramatically during the last decades. Back in the 1950s, age-at-death distributions were twin-peaked, with a local/global 12 Pre-print. Forthcoming: PLoS ONE maximum for the first age bracket and another local/global maximum at an adult age varying across regions. With the unfolding of the epidemiological and demographic transitions, infant mortality has decreased dramatically, thus gradually shifting the age at death distributions towards the right and increasingly concentrating deaths around their modal age. While these trends generally apply to all regions, we observe lots of heterogeneity across them. After World War II, the child mortality peak of the age-at- death distributions was higher than the adult mortality peak in all world regions except for the group of high-income countries – where child mortality levels were already very low in the 1950s. In the following decades, improvements in the age-at-death distributions can be observed across the board, but the pace of change has not been the same everywhere. In particular, we observe some stagnation around the 1990s for Central Asia and in the HIV-stricken countries of Sub-Saharan Africa. 13 Pre-print. Forthcoming: PLoS ONE In the light of the aforementioned transformations, what is the extent of longevity and lifespan inequality of the age-at-death distributions shown in Figure 1? The results, presented in Table 1, show several patterns that are worth pointing out. As regards unconditional lifespan distributions, global and regional life expectancies at birth have tended to increase monotonically all over the world (see the first group of columns in Table 1). The group of high-income countries has always had the highest longevity (regional 𝑒𝑒0 of 65 in 1950-55 up to 78.6 in 2010-15). At the other extreme, Sub-Saharan Africa is the region with lowest life expectancy all over the period (except in 1950-55, when South Asia was the region with the lowest regional 𝑒𝑒0 ). In tandem with these 14 Pre-print. Forthcoming: PLoS ONE increases in longevity, we also observe monotonic declines in unconditional lifespan inequality at all moments and in all places (no matter what inequality measure we choose) – a finding that aligns well with conceptually related studies [6]. Given the strong relationship between life expectancy at birth and unconditional lifespan inequality, it is not surprising to find the group of high-income countries and Sub- Saharan Africa as the regions with lowest and highest length of life inequality all over the studied period. 15 Pre-print. Forthcoming: PLoS ONE Pop. Full lifespan Ages 15+ Ages 65+ Region Year (mio.) 𝑒𝑒0 Theil Var 𝜇𝜇15 Theil Var 𝜇𝜇65 Theil Var 1950-55 732.7 44.6 0.298 854.0 59.4 0.049 308.4 74.6 0.0036 40.9 1970-75 1137.1 60.6 0.141 672.4 68.6 0.027 228.5 77.1 0.0041 49.3 EAP 1990-95 1659.3 68.8 0.077 473.4 73.0 0.021 199.7 78.9 0.0045 56.8 2010-15 2005.0 74.2 0.038 299.3 75.8 0.018 186.2 80.6 0.0050 65.2 1950-55 18.1 55.0 0.215 869.4 66.7 0.037 295.0 77.9 0.0051 62.6 1970-75 34.4 62.4 0.149 753.7 70.9 0.030 268.5 79.5 0.0055 70.6 CA 1990-95 51.2 65.3 0.107 597.8 71.0 0.028 254.2 79.4 0.0053 67.8 2010-15 63.9 70.0 0.057 388.4 72.6 0.023 217.3 79.4 0.0051 65.1 1950-55 854.0 65.0 0.105 576.3 70.6 0.027 235.3 78.4 0.0045 55.4 1970-75 1046.1 71.1 0.049 350.9 73.2 0.022 212.8 79.6 0.0048 60.6 HIC 1990-95 1184.9 74.3 0.036 305.1 75.5 0.022 226.4 81.5 0.0053 69.7 2010-15 1275.7 78.6 0.026 256.7 79.2 0.019 214.8 84.1 0.0053 74.8 1950-55 168.7 52.0 0.243 900.1 64.8 0.043 323.4 77.3 0.0044 52.6 1970-75 288.1 61.6 0.146 728.1 69.7 0.032 273.7 78.8 0.0048 60.6 LAC 1990-95 448.5 68.8 0.078 500.3 72.5 0.029 265.5 80.3 0.0053 69.2 2010-15 603.4 74.8 0.050 403.5 76.8 0.026 266.1 83.1 0.0061 84.4 1950-55 92.5 43.4 0.387 1058.1 63.5 0.046 327.5 76.5 0.0039 46.2 1970-75 155.3 55.2 0.228 921.4 68.2 0.034 279.4 77.9 0.0043 52.7 MENA 1990-95 261.2 66.7 0.097 559.7 72.1 0.025 226.6 79.0 0.0044 55.1 2010-15 383.8 72.5 0.050 361.3 74.9 0.021 203.4 80.4 0.0046 59.5 1950-55 477.0 37.2 0.411 880.3 55.4 0.065 367.7 75.0 0.0038 43.8 1970-75 715.3 49.6 0.274 931.9 64.3 0.041 303.0 76.6 0.0044 52.0 SA 1990-95 1151.0 59.8 0.156 734.2 68.6 0.031 260.1 77.7 0.0047 57.2 2010-15 1652.3 68.2 0.083 512.4 72.5 0.026 240.4 79.6 0.0054 68.4 1950-55 122.8 37.3 0.428 927.5 56.9 0.064 372.8 74.9 0.0034 39.0 SSH- 1970-75 193.5 46.2 0.301 928.7 61.4 0.053 354.2 76.1 0.0039 45.6 HIV 1990-95 334.5 49.7 0.250 878.3 62.2 0.052 360.1 76.8 0.0041 49.2 2010-15 558.1 58.1 0.149 708.5 65.3 0.046 348.1 78.0 0.0044 54.5 1950-55 58.6 35.8 0.453 922.5 56.4 0.065 373.7 74.8 0.0034 38.6 1970-75 92.0 43.3 0.346 961.9 60.4 0.057 368.3 76.1 0.0039 45.3 SSA 1990-95 161.8 49.5 0.266 926.8 63.3 0.051 359.7 77.1 0.0041 49.5 2010-15 290.5 59.2 0.152 730.4 67.1 0.041 325.6 78.2 0.0044 54.2 Table 1. Regional indicators of longevity and lifespan inequality for unconditional and conditional age-at-death distributions. EAP=East Asia & Pacific, CA= Central Asia, HIC=High-income countries, LAC=Latin America & Caribbean, MENA=Middle East & North Africa, SA=South Asia, SSH-HIV=Sub-Saharan Africa High HIV, SSA=Other Sub-Saharan African countries. Source: Authors’ elaboration based on UN WPP data. Shifting our attention to adult mortality (see the second group of columns in Table 1), we find relatively similar trends. Average length of life above age 15 (𝜇𝜇15 ) tends to 16 Pre-print. Forthcoming: PLoS ONE increase virtually in all places at all times, but not as fast as life expectancy at birth. Like in the previous case, the groups of high-income and Sub-Saharan African countries are the regions with highest and lowest levels of 𝜇𝜇15 , respectively. Simultaneously, we observe generalized declines in adult lifespan variability – albeit at a much slower pace than the declines in overall lifespan inequality. There are some exceptions to this generally favorable trend in Central Asia and the high-income group around the 1990s (arguably as a consequence of the collapse of the Eastern bloc countries included in these regions), and in the HIV-stricken Sub-Saharan African countries. For the last group we observe some stagnation in the lifespan inequality declines around the 1990s and a slight inconsistency in the trends reported by the Theil index and the variance. The regional trends in overall and adult lifespan inequality reported in Table 1 cohere roughly with the findings reported by [19] in Figure 3. Lastly, the trends in elderly mortality are notably different (see the third group of columns in Table 1). As expected, average length of life above 65 (𝜇𝜇65 ) continues to increase in the world and most of its regions, but some regions increase faster than others. Interestingly, lifespan inequality among the elderly tends to increase over time for the world and all its regions (except in Central Asia): no matter what inequality indicator we use, we observe unequivocal increases in length of live variability in the older ages. Curiously, in contrast to the other lifespan inequality indicators shown in Table 1, the levels of lifespan inequality among the elderly across regions are relatively similar. In the 1950s, the group of high-income countries and Central Asia were the region with largest elder lifespan inequality, but in 2010 inequality was largest in Latin America and the Caribbean. These findings – which cohere with the results of [5] in the context of high-income countries – are extremely interesting for several reasons that will be discussed later. 17 Pre-print. Forthcoming: PLoS ONE 4.2. Within countries lifespan inequality (WLI) In our previous analysis we have explored the regional trends in longevity and lifespan inequality. What can be said about the experience of individual countries? In Figure 2 we show a 3×2 scatterplot matrix comparing longevity levels (horizontal axes) against the corresponding lifespan inequality indicators (vertical axes) using data from all world countries between 1950-55 and 2010-15. The scatterplots in the first, second and third rows are based on unconditional, above 15 and above 65 age-at-death distributions, respectively. The scatterplots on the first and second columns measure lifespan inequality using the Theil index and the variance, respectively. In all cases, we superimpose the regional trends for comparative purposes. In general, the trends shown in Figure 2 go in line with the ones presented in Table 1. Like in previous studies [4], [19], we observe a strong negative correlation between life expectancy at birth and unconditional lifespan inequality (see first row in Figure 2). As the epidemiologic transition unfolds, longevity increases in tandem with decreases in lifespan inequality. Interestingly, all regions seem to follow a very similar path of demographic convergence, although we observe more cross-country heterogeneity when using absolute measures than relative ones. Inspecting the relationship between longevity and adult mortality (i.e. disregarding under 15 mortality) a different picture arises (see second row in Figure 2). In this case, there is also a generally negative relationship between the two variables, but it is much weaker and the variability across countries and regions is substantially larger than before. Indeed, it is possible to identify several countries and regions where the inequality declines stall and are followed by extended plateaus (this is the case for High- income countries or Latin America and the Caribbean). Once again, there is more between-country and between-region variability using absolute inequality measures than 18 Pre-print. Forthcoming: PLoS ONE using relative ones. Lastly, examining the relationship between countries’ longevity and lifespan inequality among the elderly, we observe diverging trends across the board (see third row in Figure 2): as world countries’ longevity increases, the variability in age-at- death distributions among the elderly increases as well. The validity of this interesting result does not depend on the choice of inequality measure. 4.3. Between country and global lifespan inequalities (BLI and GLI) What can we say about the trends in global lifespan inequality? To what extent are these trends determined by length of life differences within and between countries? What are the contributions of the intra- and inter-country disparities to GLI? Figure 3 plots the 19 Pre-print. Forthcoming: PLoS ONE trends in GLI and its within- and between-country components between 1950-55 and 2010-15 (the values upon which this Figure is based are shown in the Supplementary Material section). In the first row, we show the results corresponding to the entire age- at-death distributions, while the second and third rows show the results for the distributions bottom-truncated at 15 and 65, respectively. When considering unconditional age-at-death distributions, lifespan inequality has clearly declined over time – a result that does not depend on the choice of inequality measure. After six decades, GLI levels have shrunk dramatically from 0.26 to 0.06 for the Theil index and from 911.5 to 444.1 for the variance. Interestingly, most of the variation in lifespan across world citizens can be attributed to differences occurring within countries. The contribution of the between-country component for the Theil index goes from 11% in 1950-55 to 7.6% in 2010-15 (for the variance, it declines from 16% to 10.7%). The values of GLI for the adult population are declining as well, but much less than in the previous case. The Theil index (resp. the variance) declines from 0.046 to 0.025 (resp. from 333.2 to 244.7). In both cases, we observe a clear decline between 1950-55 and 1980-85 followed by a long inequality plateau. In the case of the variance, we even observe some slight increases at the turn of the millennium. These results suggest that the expected global compression in adult mortality has stagnated during the last 30-35 years approximately. Again, the contribution of the between-country component is relatively minor (around 6-12% for the Theil and 6-13% for the variance). Between- country inequality in adult mortality decreased between 1950-55 and 1970-75, increased between 1970-75 and 2000-05 and declined again from 2000-05 until 2010-15. As regards the levels of GLI for age-at-death distributions above 65, we observe the opposite trend. During the last six decades, lifespan inequality among the world elderly has increased from 0.0044 to 0.0055 for the Theil index and from 52.6 to 72 for the 20 Pre-print. Forthcoming: PLoS ONE variance. Once again, these global differences can be mainly attributed to the disparities occurring within countries. The within-country component of global lifespan inequality among the elder has been increasing during the whole period, while the between- country component has declined between 1950-55 and 1970-75 and started increasing unabated from 1970-75 until 2010-15. 4.4. Counterfactual analysis During the last six decades, the world has undergone major socio-demographic transformations. Both the population size and the rate of increase of longevity have varied considerably across countries. In addition, the shape of lifespan distributions changed substantially over time. In this swiftly changing context, it is important to 21 Pre-print. Forthcoming: PLoS ONE evaluate what of these explanatory factors have been more decisive in driving changes to GLI levels. For that purpose, we have run several counterfactual analyses. Using equations [4]-[7], we compare the real trends of GLI with the ones that would have been observed had some of its subcomponents (countries’ population shares, longevity and lifespan variability) remained constant over time. Table 2 reports such counterfactual trends, both for the Theil index and the variance and for conditional and unconditional age-at-death distributions. 22 Pre-print. Forthcoming: PLoS ONE Panel A: Theil counterfactuals Year 1950- 1960- 1970- 1980- 1990- 2000- 2010- 55 65 75 85 95 05 15 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 0.2629 0.2183 0.1571 0.1216 0.1028 0.0827 0.0629 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 0.2153 0.1504 0.1126 0.0922 0.0713 0.0520 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 0.2126 0.1443 0.1071 0.0878 0.0684 0.0497 𝐶𝐶3 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑇𝑇𝑤𝑤 ) 0.2664 0.2693 0.2782 0.2881 0.2970 0.3036 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 (15+) 0.0466 0.0407 0.0316 0.029 0.0277 0.0275 0.0249 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 0.0403 0.0307 0.0277 0.0263 0.0254 0.0225 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 0.0400 0.0305 0.0277 0.0264 0.0258 0.0227 𝐶𝐶3 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑇𝑇𝑤𝑤 ) 0.0464 0.0454 0.0467 0.0479 0.0497 0.0500 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 (65+) 0.0044 0.0046 0.0046 0.0047 0.005 0.0052 0.0055 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 0.0046 0.0047 0.0049 0.0051 0.0053 0.0056 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 0.0046 0.0047 0.0049 0.0051 0.0052 0.0055 𝐶𝐶3 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑇𝑇𝑤𝑤 ) 0.0044 0.0041 0.0041 0.0041 0.0042 0.0042 Panel B: Variance counterfactuals Year 1950- 1960- 1970- 1980- 1990- 2000- 2010- 55 65 75 85 95 05 15 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 911.5 860.8 744.9 650.3 593.0 525.5 444.1 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 856.3 727.8 621.3 555.0 478.1 392.9 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 862.9 794.4 709.5 655.2 588.6 526.1 𝐶𝐶3 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑉𝑉𝑤𝑤 ) 912.7 870.1 867.5 872.4 879.6 868.9 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 (15+) 333.2 309.6 264.4 254.6 251.5 257.9 244.7 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 307.7 260.5 248.1 245.1 246.4 231.2 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 314.6 289.5 278.6 273.7 272.2 265.2 𝐶𝐶3 (𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑉𝑉𝑤𝑤 ) 330.1 312.6 317.4 322.9 335.2 333.3 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 (65+) 52.6 55.2 56.5 59.1 63.0 67.0 72.0 𝐶𝐶1 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) 55.5 57.9 61.7 66.1 69.9 74.9 𝐶𝐶2 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜇𝜇) 54.8 58.8 61.0 64.2 67.3 71.2 𝐶𝐶3 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑉𝑉𝑤𝑤 ) 52.8 48.6 48.4 48.6 49.2 50.1 Table 2. Counterfactual analyses for the Theil index (Panel A) and the variance (Panel B). Source: Authors’ elaboration based on UN WPP data. Considering the entire age range, we can conclude that within-country inequality is the strongest determinant of the observed declines in GLI (see counterfactual 𝐶𝐶3 ). Had within-country inequality remained at its 1950-55 levels, GLI levels would have been much higher than the observed ones (i.e. from the “true” 0.0629 for the Theil in 2010- 15 up to 0.3036, and from the “true” 444.1 for the variance in 2010-15 up to 868.9). At the other extreme, had population shares remained at their 1950-55 levels, global 23 Pre-print. Forthcoming: PLoS ONE lifespan inequality would be slightly smaller as it is today (see counterfactual 𝐶𝐶1 ). Hence, even if population growth per se has contributed to widen the global lifespan distribution, its effect has been quantitatively small. Somewhere in between, we observe that the effect of longevity on GLI depends on the choice of inequality measure. For the Theil index, changes in longevity have slightly deterred further declines in GLI (i.e. fixing longevity at its 1950-55 levels, GLI would have reached 0.049 rather than the observed 0.06), while the opposite effect is found for the variance (see counterfactual 𝐶𝐶2 ). The counterfactual analyses applied to the age-at-death distributions bottom-truncated at the age of 15 are qualitatively very similar to the previous ones (see central rows in the two panels of Table 2). Lastly, the results for the distributions truncated at 65 suggest that neither population growth nor longevity changes have had an important effect in driving GLI trends. Once again, lifespan inequality trends within countries seems to be the major factor behind the observed GLI trends. Had within country inequality levels remained fixed at their 1950-55 levels, GLI levels among the elderly would have barely changed during the last sixty years. Summing up, the empirical evidence presented here suggests that the changes in global lifespan inequality have been mainly driven by changes in within-country lifespan variability and, to a much lesser extent, by longevity trends across countries. Population growth has played a minor role in this process. 5. Discussion and concluding remarks In this paper, we document for the first time global trends in lifespan inequality from the 1950s to the present day. Our findings indicate that the extent of worldwide lifespan variability depends largely on the range of ages we are taking into account. When considering the entire age-at-death distributions, we observe a sustained decline in 24 Pre-print. Forthcoming: PLoS ONE lifespan variability in the world and its regions between 1950-55 and 2010-15. Such concentration in the age-at-death distributions goes hand in hand with generalized increases in life expectancy at birth – a finding that squares well with related findings reported in previous studies [4], [6], [19]. When the focus shifts to adult mortality (i.e. considering ages above 15), we also observe declines in global lifespan variability, but the evidence is not as compelling as before. While there are clear signs of sustained decline between 1950-55 and 1970-75, from the last year onwards we observe the emergence of inequality plateaus and even trend reversals not only in some specific regions like the Eastern European countries, the HIV-stricken countries of Sub-Saharan Africa and in Latin America and the Caribbean, but also in the world as a whole. These results are in line with the findings of [3] reporting adult lifespan inequality plateaus for a selected group of highly industrialized countries. Most of these changes have taken place in spite of the generalized increases in longevity among the adult population. Lastly, focusing our attention on mortality trends among the elderly (i.e. ages above 65), we observe increases in lifespan inequality across all countries, regions, and in the world as a whole (with Latin American and high-income countries exhibiting the highest levels of inequality). Again, such changes have occurred against a backdrop of generalized mortality reductions. While such increase in elderly lifespan inequality should be expected in a context of increasing longevity, it is nonetheless important to document what countries or regions are spearheading the process and which ones are lagging behind. Decomposing global lifespan inequality levels in its within- and between-country components, we observe that most of the world variability in ages at death can be explained by differences occurring within countries. Depending on the inequality measure and the period we choose, the within-country component explains around 85% 25 Pre-print. Forthcoming: PLoS ONE and 95% of the total variation ([4] and [19] report analogous contributions within that range). This suggests that traditional narratives in global health disparities focusing on international variations in life expectancy (e.g. [18], [30]) neglect the major source of lifespan inequality: the one that takes place within countries. This is precisely the component that has experienced the most dramatic changes during the last six decades. Indeed, our counterfactual analyses suggest that the observed changes in global lifespan inequality can be largely attributable to the changes in within-country lifespan distributions, while the contribution of increasing longevity and differential population growth have played a relatively minor role. While the between-country component is relatively small, it does not mean it is irrelevant. Even if between-country inequality in life expectancies at birth declined unabated from 1950-55 onwards, the cross-national inequality in the mean age at death among adults (i.e. deaths occurring beyond the age of 15) declined between 1950-55 and 1970-75, increased between 1970-75 and 2000- 05, but resumed its downward trend until 2010-15. The description given in [19] for the period between 1970 and 2000 (identifying the rising between-country inequality in adult length-of-life) fits well with our findings, which provide a longer and more nuanced time perspective of the recent trends in international health inequality (during the last decade, between-country inequality in adult lifespan has resumed a declining trajectory). Lastly, between-country inequality in the mean age at death among the elderly declined between 1950-55 and 1970-75 but started increasing from the last period until the present day – a 40-year divergence pattern across countries. The increase in lifespan variability among the elderly was previously investigated in a selected group of highly industrialized countries [5]. According to the authors of that study, the systematic increases in longevity alter the health profile of survivors in fundamental ways: advances in medicine, socio-economic conditions and public health 26 Pre-print. Forthcoming: PLoS ONE planning have facilitated that frailer individuals reach more advanced ages, thus increasing the heterogeneity in health profiles among the elderly. As shown in this paper, it turns out that such mechanisms might have been operating not only in high- income settings, but also across all world countries and regions (irrespective of their stage in the demographic or epidemiological transitions). 5.1. Sex-specific results As done in conceptually related studies (e.g. [19]), the empirical results presented in this paper document lifespan inequality trends for the population as a whole (i.e. using both- sexes life tables). Yet, it is well known that (a) women tend to survive to older ages than men, and (b) age-at-death distributions tend to exhibit greater variability among men ([4], [14]). However, calculating our indicators for women and men separately, we observe that sex-specific trends in lifespan inequality follow the same general patterns we have identified in this study for the general population. For the sake of simplicity, we have preferred to avoid the duplicity of tables and graphs leading to the same qualitative conclusions (for the interested reader, the sex-specific results are available upon request). 5.2. Sources of lifespan inequality What factors might be driving these remarkable trends in lifespan inequality? As regards the determinants of international health inequalities (i.e. differences in longevity between countries), researchers have advanced several explanations. In an attempt to overcome the limitations of Omran’s epidemiological transition theory ([33]), [34 – 35] put forward the framework of ‘divergence-convergence cycles’. According to these authors, health transitions can be seen as a succession of cycles composed of divergence periods (generated by revolutionary health innovations, like eradication of 27 Pre-print. Forthcoming: PLoS ONE infectious diseases, or the cardiovascular revolution), followed by the convergence that ensues when laggard countries adapt and catch up with the forerunners. Indeed, the non- monotonic trends observed in adult and elderly lifespan inequality between countries (see middle and bottom panels in Figure 3) fit well with that description. Very often, the diffusion of knowledge and the adoption of new technologies are listed among the key drivers of international health convergence. Yet, the evolution of such cycles can be suddenly interrupted when socio-economic, political or other external shocks disrupt them for any reason. In this regard, the collapse of the Eastern Block and the spread of HIV/AIDS among Sub-Saharan African countries have been held responsible for the global increase in international health disparities around the 1990s [30]. Lastly, socio- economic differentials can be another key factor that might explain longevity variations across countries. In this line, the increasing cross-country disparities in elderly longevity might be partially explained by countries’ unequal access to increasingly expensive technologies that further prolong the lifespan of elderly populations. As shown before, most of global lifespan inequality changes have taken place within countries. The fundamental factor that has contributed to reduce countries’ lifespan variability is the reduction in infant mortality. This decrease has been extensively documented elsewhere [36 – 37] and can be largely attributed to the use of cheap and widely available treatments, like the use of oral rehydration and antibiotics. Among adults and the elderly, within-country disparities in lifespan are often associated with the existence of socio-economic gradients. The positive association between socio- economic status (SES) and adult health and survival is well-established [38 – 39]. To illustrate, higher-educated individuals are, through their higher income, more able to afford food, clothing and accommodation, have jobs that entail fewer health risks, are more engaged in healthy life styles and better informed to use health services and new 28 Pre-print. Forthcoming: PLoS ONE medical treatments [40 – 41]. In this regard, a collection of case studies in high-income settings suggests a clear patterning of longevity and lifespan variability within countries’ SES groups along the following lines. On the one hand, researchers have often found diverging longevity trends across SES groups, with the socially advantaged ones benefiting more than the rest ([42 – 47]; see left panel in Figure 4). On the other hand, a handful of studies suggest that (i) there is a negative gradient between SES and lifespan inequality (i.e. lower socio-economic groups tend to have higher levels of lifespan inequality), and (ii) the gradient becomes steeper over time because of the decrease (resp. increase) in lifespan variability among high (resp. low) SES groups (e.g. [10 – 11], [48 – 49]; see right panel in Figure 4). Overall, these findings suggest the emergence of divergent health dynamics across SES groups within national borders (at least in the context of high-income countries). Whether or not these diverging patterns are taking place as well in middle- and low-income countries is a matter for future research. 5.3. Limitations and conclusions 29 Pre-print. Forthcoming: PLoS ONE The analysis presented in this paper have some limitations. First, all our findings are based on the worldwide life tables provided by the UN Population Division, some of which are based on estimated data. The indirect methods that are usually employed to estimate life tables based on incomplete information might over-smooth the corresponding age-at-death distributions – a potential source of downward bias for our lifespan inequality estimates. While we acknowledge that such bias might affect our estimates of lifespan inequality levels to a certain extent, we content that it is less likely that it affects lifespan inequality trends, which are the main subject of interest in this paper. In addition, comparing lifespan inequality levels for those countries simultaneously included in the UN database and in the Human Mortality Database shows an extremely high level of correlation (see Supplementary Material section). Second, the UN life tables are constructed up to age 100, while the HMD life tables include ages up to 110, an issue that might downwardly bias our lifespan inequality estimates. Once again, robustness checks presented in the Supplementary Material section show that this source of bias is negligibly small. Lastly, our counterfactual lifespan inequality analyses might look somewhat crude at first sight. Using ceteris- paribus-like arguments, they simply assume that some of the three components in our inequality measures can be kept fixed while allowing the others to change over time as they actually did, as if they were completely independent entities. Despite this limitation, such techniques are very useful to derive first-order approximations of complex phenomena that otherwise would be very difficult to model – a factor that explains their popularity in demographic studies (e.g. [30], [50 – 51]). Despite those limitations, the results presented in this paper confirm that the study of health inequalities should not be limited to the analysis of differences in life expectancy across countries. Since most lifespan variability takes place within countries, focusing 30 Pre-print. Forthcoming: PLoS ONE on the trends of central longevity indicators alone one disregards the major source of variability, thus potentially arriving at overly simplistic conclusions. During the last decades, much progress has been made in increasing longevity while reducing age-at- death variability across the full lifespan and, to a lesser extent, across adult ages. 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(2018), “Longevity and lifespan variation by educational attainment in Spain: 1960-2015”, Paper presented at the European Population Conference 2018, Brussels. 50. Breen, R. and Andersen, S. (2012), “Educational assortative mating and income inequality in Denmark”, Demography, 49(3): 867-887. 51. Permanyer, I., García, J. and Esteve, A. (2013) “The impact of educational homogamy on isolated illiteracy levels”, Demography 50(6):2209– 2225. Supplementary Material Countries’ regional classification (United Nations) East Asia & Pacific: Brunei Darussalam, Cambodia, China, Fiji, French Polynesia, Guam, Indonesia, Kiribati, Korea (North), Korea (South), Lao PDR, Macao, SAR China, Malaysia, Micronesia, Federated States of, Mongolia, Myanmar, New Caledonia, Papua New Guinea, Philippines, Samoa, Singapore, Solomon Islands, Thailand, Timor-Leste, Tonga, Vanuatu, Viet Nam. Central Asia: Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, Uzbekistan. High Income: Albania, Australia, Austria, Belarus, Belgium, Bosnia and Herzegovina, Bulgaria, Canada, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Latvia, Lithuania, Luxembourg, Macedonia, Republic of, Moldova, Montenegro, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Russian Federation, Serbia, Slovakia, 37 Pre-print. Forthcoming: PLoS ONE Slovenia, Spain, Sweden, Switzerland, Ukraine, United Kingdom, United States of America. Latin America & Caribbean Antigua and Barbuda, Argentina, Aruba, Bahamas, Barbados, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, French Guiana, Grenada, Guadeloupe, Guatemala, Guyana, Haiti, Honduras, Jamaica, Martinique, Mexico, Nicaragua, Panama, Paraguay, Peru, Puerto Rico, Saint Lucia, Saint Vincent and Grenadines, Suriname, Trinidad and Tobago, Uruguay, Venezuela (Bolivarian Republic), Virgin Islands. Middle East & North Africa Algeria, Armenia, Azerbaijan, Bahrain, Egypt, Georgia, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Palestinian Territory, Qatar, Saudi Arabia, Syrian Arab Republic (Syria), Tunisia, Turkey, United Arab Emirates, Yemen. South Asia: Afghanistan, Bangladesh, Bhutan, India, Iran, Islamic Republic of, Maldives, Nepal, Pakistan, Sri Lanka. Sub-Saharan Africa: Angola, Benin, Cape Verde, Chad, Comoros, Congo (Brazzaville), Congo, (Kinshasa), Cote d'Ivoire, Djibouti, Eritrea, Gambia, Guinea, Madagascar, Mali, Mauritania, Mauritius, Mayotte, Niger, Reunion, Sao Tome and Principe, Senegal, Seychelles, Sierra Leone, Somalia, United Republic of Tanzania. Sub-Saharan Africa High HIV: Botswana, Burkina Faso, Burundi, Cameroon, Central African Republic, Equatorial Guinea, Ethiopia, Gabon, Ghana, Guinea-Bissau, Kenya, Lesotho, Liberia, Malawi, Mozambique, Namibia, Nigeria, Rwanda, South Africa, South Sudan, Swaziland, Togo, Uganda, Zambia, Zimbabwe. Decomposition of Global Lifespan Inequality The following table shows the levels and trends of global lifespan inequality and its decomposition in between-country and within-country inequality (Figure 3 is based upon these numbers). Theil decomposition of GLI Year 1950- 1960- 1970- 1980- 1990- 2000- 2010- 55 65 75 85 95 05 15 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 0.2629 0.2183 0.1571 0.1216 0.1028 0.0827 0.0629 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑤𝑤 0.2341 0.1947 0.1449 0.1126 0.0950 0.0756 0.0581 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑏𝑏 0.0288 0.0236 0.0122 0.0090 0.0078 0.0072 0.0048 38 Pre-print. Forthcoming: PLoS ONE %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 10.9 10.8 7.7 7.4 7.6 8.6 7.6 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 (15+) 0.0466 0.0407 0.0316 0.0290 0.0277 0.0275 0.0249 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑤𝑤 0.0410 0.0362 0.0298 0.0273 0.0259 0.0249 0.0229 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑏𝑏 0.0056 0.0045 0.0018 0.0018 0.0019 0.0026 0.0020 %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 12.0 11.0 5.7 6.1 6.7 9.5 8.0 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒 (65+) 0.0044 0.0046 0.0046 0.0047 0.0050 0.0052 0.0055 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑤𝑤 0.0041 0.0042 0.0044 0.0045 0.0047 0.0048 0.0051 𝑇𝑇ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑏𝑏 0.0003 0.0004 0.0002 0.0002 0.0003 0.0003 0.0004 %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 7.6 7.8 3.8 4.7 5.5 6.6 7.6 Variance decomposition of GLI Year 1950- 1960- 1970- 1980- 1990- 2000- 2010- 55 65 75 85 95 05 15 𝑉𝑉𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 911.5 860.8 744.9 650.3 593 525.5 444.1 𝑉𝑉𝑉𝑉𝑉𝑉𝑤𝑤 766.6 722.4 659.6 578.9 528 461 396.6 𝑉𝑉𝑉𝑉𝑉𝑉𝑏𝑏 144.9 138.4 85.3 71.4 65.0 64.5 47.5 %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 15.9 16.1 11.5 11.0 11.0 12.3 10.7 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 (15+) 333.2 309.6 264.4 254.6 251.5 257.9 244.7 𝑉𝑉𝑉𝑉𝑉𝑉𝑤𝑤 288.4 271.1 247.4 237.2 232.7 230.7 222.9 𝑉𝑉𝑉𝑉𝑉𝑉𝑏𝑏 44.8 38.5 17.0 17.4 18.8 27.2 21.8 %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 13.4 12.4 6.4 6.8 7.5 10.5 8.9 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 (65+) 52.6 55.2 56.5 59.1 63.0 67.0 72.0 𝑉𝑉𝑉𝑉𝑉𝑉𝑤𝑤 48.7 51.0 54.3 56.3 59.5 62.6 66.5 𝑉𝑉𝑉𝑉𝑉𝑉𝑏𝑏 4.0 4.3 2.2 2.8 3.5 4.4 5.5 %𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑏𝑏𝑏𝑏𝑏𝑏. ) 7.5 7.7 3.9 4.8 5.5 6.6 7.6 Table S1. Theil and variance decompositions of Global Lifespan Inequality over time for the full age-at-death distribution, the deaths above 15 and above 65. Source: Authors’ elaboration based on UN WPP data. Computing the counterfactuals. In order to compute the counterfactuals shown in equations [EQ5], [EQ6] and [EQ7], we need to write the Theil index and the variance in an appropriate form that explicitly shows the dependency of these measures on the following three factors: (i) population shares (𝑠𝑠𝑐𝑐 ), (ii) longevity (𝜇𝜇𝑐𝑐 ), and (iii) lifespan variability (𝐼𝐼𝑐𝑐 ). We start with the Theil index. Assuming we have a list of 𝑛𝑛 countries (indexed by 𝑐𝑐), it is well-known that the Theil index at time 𝑡𝑡 can be written as 𝑛𝑛 𝑛𝑛 𝜇𝜇𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 𝑇𝑇𝑡𝑡 = � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑙𝑙𝑙𝑙 � � + � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑇𝑇 [𝐸𝐸𝐸𝐸𝐸𝐸1] 𝜇𝜇𝑡𝑡 𝜇𝜇𝑡𝑡 𝜇𝜇𝑡𝑡 𝑐𝑐,𝑡𝑡 𝑐𝑐=1 𝑐𝑐=1 The first part in equation [EQA1] is the between-country component (which is obtained assuming all individuals in each country die at the same age, so there is no within- country variation) and the second one is the within- country component (which is a weighted sum of the within-country inequalities). Observing that global average age at death is equal to the population-weighted sum of country-specific average age at 39 Pre-print. Forthcoming: PLoS ONE deaths, 𝜇𝜇𝑡𝑡 = ∑𝑛𝑛𝑐𝑐=1 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 the additive decomposition of the Theil index (shown in [EQA1]) for time ‘𝑡𝑡’ can be rewritten as: 𝑛𝑛 𝑛𝑛 𝜇𝜇𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 𝑇𝑇𝑡𝑡 = � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑛𝑛 𝑙𝑙𝑙𝑙 � 𝑛𝑛 � + � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑛𝑛 𝑇𝑇 [𝐸𝐸𝐸𝐸𝐸𝐸2] ∑𝑐𝑐=1 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 ∑𝑐𝑐=1 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 ∑𝑐𝑐=1 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 𝑐𝑐,𝑡𝑡 𝑐𝑐=1 𝑐𝑐=1 In equation [EQA2] we explicitly see how the Theil index in time ‘𝑡𝑡’ can be written as a function of countries’ population shares (𝑠𝑠𝑐𝑐,𝑡𝑡 ), longevity (𝜇𝜇𝑐𝑐,𝑡𝑡 ), and lifespan variability (𝑇𝑇𝑐𝑐,𝑡𝑡 ). As regards the variance, it is also well-known that it can be written as 𝑛𝑛 𝑛𝑛 2 𝑉𝑉𝑡𝑡 = � 𝑠𝑠𝑐𝑐,𝑡𝑡 �𝜇𝜇𝑐𝑐,𝑡𝑡 − 𝜇𝜇𝑡𝑡 � + � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑉𝑉𝑐𝑐,𝑡𝑡 [𝐸𝐸𝐸𝐸𝐸𝐸3] 𝑐𝑐=1 𝑐𝑐=1 This is the additive decomposition of the variance. The first part in equation [EQA3] is the between-country component and the second one is the within- country component (which is a weighted sum of the within-country inequalities). After simple algebraic manipulations, the last equation can be written as 𝑛𝑛 𝑛𝑛 2 𝑉𝑉𝑡𝑡 = � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 − 𝜇𝜇𝑡𝑡2 + � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑉𝑉𝑐𝑐,𝑡𝑡 [𝐸𝐸𝐸𝐸𝐸𝐸4] 𝑐𝑐=1 𝑐𝑐=1 Once again, since 𝜇𝜇𝑡𝑡 = ∑𝑛𝑛𝑐𝑐=1 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 , we can finally rewrite the variance in time 𝑡𝑡 as 𝑛𝑛 𝑛𝑛 2 𝑛𝑛 2 𝑉𝑉𝑡𝑡 = � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 − �� 𝑠𝑠𝑐𝑐,𝑡𝑡 𝜇𝜇𝑐𝑐,𝑡𝑡 � + � 𝑠𝑠𝑐𝑐,𝑡𝑡 𝑉𝑉𝑐𝑐,𝑡𝑡 [𝐸𝐸𝐸𝐸𝐴𝐴5] 𝑐𝑐=1 𝑐𝑐=1 𝑐𝑐=1 This way, we have written the global variance as a function of the three ingredients we were looking for: the vector of country-specific population shares (𝑠𝑠𝑐𝑐,𝑡𝑡 ), variances (𝑉𝑉𝑐𝑐,𝑡𝑡 ) and longevity levels (𝜇𝜇𝑐𝑐,𝑡𝑡 ). Robustness checks To check the robustness of our empirical findings, we have performed different consistency tests. First, we have recalculated all our findings using well-known inequality measures other than the Theil index and the variance. Second, we have investigated whether or not the fact of working with life tables up to age 100 (rather than the value of 110 available in the HMD life tables) can downwardly bias our results. 1. Use of alternative inequality measures Are our findings robust to the choice of alternative inequality measures? To check the robustness of our empirical findings, we will use other well-known inequality measures. 40 Pre-print. Forthcoming: PLoS ONE One of them will be the family of Generalized Entropy measures GE(θ), which includes the Theil index as a particular case when 𝜃𝜃 = 1. It is defined as 𝜔𝜔 ⎧1 1 𝛼𝛼𝑥𝑥 𝜃𝜃 � 𝑑𝑑𝑥𝑥 �� � − 1� 𝑖𝑖𝑖𝑖 𝜃𝜃 ≠ 0,1 ⎪𝑙𝑙𝑎𝑎 𝜃𝜃(𝜃𝜃 − 1) 𝜇𝜇𝑎𝑎 ⎪ 𝑥𝑥=𝑎𝑎 ⎪ 𝜔𝜔 1 𝜇𝜇𝑎𝑎 GE(𝜃𝜃) = � 𝑑𝑑𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙 � � 𝑖𝑖𝑖𝑖 𝜃𝜃 = 0 [𝐸𝐸𝐸𝐸𝐸𝐸6] ⎨ 𝑙𝑙𝑎𝑎 𝛼𝛼𝑥𝑥 𝑥𝑥=𝑎𝑎 ⎪ 𝜔𝜔 ⎪ 1 𝛼𝛼𝑥𝑥 𝛼𝛼𝑥𝑥 ⎪ � 𝑑𝑑𝑥𝑥 � � 𝑙𝑙𝑙𝑙𝑙𝑙 � � 𝑖𝑖𝑖𝑖 𝜃𝜃 = 1 ⎩ 𝑙𝑙𝑎𝑎 𝜇𝜇𝑎𝑎 𝜇𝜇𝑎𝑎 𝑥𝑥=𝑎𝑎 The choice of different values of 𝜃𝜃 give more emphasis to different parts of the distribution3. In Table S2, we show the regional trends in GE(θ) when θ=0 and θ=2. In addition, Table S2 shows the regional trends in lifespan inequality when using the Gini index and the coefficient of variation, which are defined as follows: 𝜔𝜔 𝜔𝜔 1 𝐺𝐺 = 2 � � 𝑑𝑑𝑥𝑥 𝑑𝑑𝑦𝑦 �𝛼𝛼𝑥𝑥 − 𝛼𝛼𝑦𝑦 � [𝐸𝐸𝐸𝐸𝐴𝐴7] 2𝑙𝑙𝑎𝑎 𝜇𝜇𝑎𝑎 𝑥𝑥=𝑎𝑎 𝑥𝑥=𝑎𝑎 �𝑉𝑉𝑎𝑎 𝐶𝐶𝐶𝐶 = [𝐸𝐸𝐸𝐸𝐴𝐴8] 𝜇𝜇𝑎𝑎 3 Lower values of 𝜃𝜃 are associated with greater sensitivity to inequality at the lower tail of the distribution (i.e. among children and young individuals), and higher values of 𝜃𝜃 place more weight to inequality among the elderly. When 𝜃𝜃 = 0 we obtain the so-called ‘mean log deviation’ (MLD) and when 𝜃𝜃 = 2, GE(2) is ordinally equivalent to the squared coefficient of variation. 41 Full lifespan Ages 15+ Ages 65+ Region Year GE(0) GE(2) Gini CV GE(0) GE(2) Gini CV GE(0) GE(2) Gini CV 1950-55 0.7969 0.2154 0.3691 0.6564 0.0579 0.0437 0.1652 0.2955 0.0035 0.0036 0.0462 0.0850 1970-75 0.4546 0.0926 0.2221 0.4303 0.0324 0.0241 0.1183 0.2195 0.0041 0.0041 0.0507 0.0908 EAP 1990-95 0.2710 0.0507 0.1555 0.3185 0.0252 0.0187 0.1025 0.1934 0.0045 0.0045 0.0535 0.0952 2010-15 0.1199 0.0275 0.1152 0.2344 0.0213 0.0162 0.0955 0.1802 0.0050 0.0050 0.0562 0.0999 1950-55 0.4900 0.0987 0.2310 0.4442 0.0357 0.0262 0.1233 0.2289 0.0044 0.0044 0.0527 0.0940 1970-75 0.2197 0.0461 0.1526 0.3036 0.0294 0.0221 0.1132 0.2104 0.0046 0.0047 0.0542 0.0965 ECA 1990-95 0.1726 0.0414 0.1483 0.2879 0.0317 0.0242 0.1199 0.2200 0.0049 0.0049 0.0560 0.0992 2010-15 0.0972 0.0297 0.1269 0.2436 0.0285 0.0220 0.1137 0.2095 0.0053 0.0052 0.0578 0.1021 1950-55 0.3558 0.0718 0.1937 0.3790 0.0336 0.0248 0.1202 0.2228 0.0045 0.0046 0.0537 0.0955 1970-75 0.1981 0.0426 0.1458 0.2918 0.0276 0.0207 0.1093 0.2036 0.0049 0.0049 0.0558 0.0990 HIC 1990-95 0.1071 0.0282 0.1191 0.2373 0.0244 0.0184 0.1021 0.1916 0.0053 0.0053 0.0580 0.1025 2010-15 0.0635 0.0200 0.1005 0.1999 0.0201 0.0152 0.0921 0.1746 0.0054 0.0052 0.0578 0.1025 1950-55 0.7201 0.1691 0.3210 0.5815 0.0520 0.0385 0.1534 0.2773 0.0043 0.0043 0.0519 0.0931 1970-75 0.4844 0.0994 0.2333 0.4458 0.0372 0.0275 0.1272 0.2346 0.0046 0.0046 0.0540 0.0962 LAC 1990-95 0.2633 0.0559 0.1711 0.3343 0.0353 0.0261 0.1233 0.2283 0.0051 0.0052 0.0572 0.1017 2010-15 0.1492 0.0375 0.1398 0.2739 0.0323 0.0236 0.1165 0.2173 0.0061 0.0061 0.0625 0.1104 1950-55 1.1240 0.3043 0.4370 0.7802 0.0564 0.0415 0.1597 0.2880 0.0039 0.0039 0.0494 0.0888 1970-75 0.7129 0.1570 0.3039 0.5604 0.0438 0.0318 0.1371 0.2521 0.0041 0.0042 0.0510 0.0911 MENA 1990-95 0.3063 0.0600 0.1730 0.3464 0.0305 0.0222 0.1121 0.2109 0.0043 0.0044 0.0524 0.0933 2010-15 0.1647 0.0341 0.1270 0.2613 0.0240 0.0177 0.0987 0.1879 0.0045 0.0045 0.0532 0.0944 1950-55 1.0375 0.3185 0.4536 0.7982 0.0768 0.0607 0.1990 0.3485 0.0038 0.0039 0.0484 0.0884 1970-75 0.7927 0.1913 0.3427 0.6185 0.0498 0.0369 0.1499 0.2715 0.0043 0.0045 0.0524 0.0943 SA 1990-95 0.4986 0.1051 0.2411 0.4585 0.0380 0.0278 0.1278 0.2359 0.0047 0.0048 0.0545 0.0975 2010-15 0.2819 0.0567 0.1703 0.3367 0.0312 0.0233 0.1165 0.2160 0.0054 0.0055 0.0588 0.1047 1950-55 1.0868 0.3611 0.4796 0.8498 0.0765 0.0588 0.1948 0.3430 0.0033 0.0034 0.0455 0.0828 1970-75 0.8855 0.2586 0.4067 0.7192 0.0680 0.0506 0.1784 0.3180 0.0038 0.0039 0.0489 0.0882 SSH-HIV 1990-95 0.7151 0.1900 0.3448 0.6165 0.0614 0.0450 0.1668 0.3001 0.0041 0.0041 0.0508 0.0909 2010-15 0.4383 0.1045 0.2455 0.4571 0.0502 0.0362 0.1471 0.2692 0.0044 0.0044 0.0527 0.0938 1950-55 1.0505 0.3336 0.4621 0.8168 0.0754 0.0575 0.1922 0.3392 0.0034 0.0035 0.0458 0.0834 1970-75 0.7973 0.2172 0.3707 0.6591 0.0639 0.0470 0.1710 0.3067 0.0039 0.0039 0.0492 0.0887 SSH 1990-95 0.6779 0.1781 0.3343 0.5968 0.0622 0.0466 0.1708 0.3052 0.0041 0.0042 0.0509 0.0913 2010-15 0.4174 0.1050 0.2497 0.4583 0.0552 0.0408 0.1584 0.2857 0.0044 0.0045 0.0531 0.0946 Table S2. Lifespan inequality using different indicators across world regions between 1950-55 and 2010-15. Source: Authors’ elaboration based on UN WPP data. 42 The results shown in Table S2 indicate that our findings are highly robust when using other inequality indices. Even if the inequality levels inevitably change when using alternative measures, the differences across regions and over time are preserved. No matter what inequality index we use, we observe generalized declines in age-at-death inequality for the complete lifespan, weaker declines (and even some trend reversals) when focusing on adult mortality, and generalized increases among the elderly. 2. Upper limit of the life table To assess the robustness of our findings to the use of abridged life tables at age 100, we revisit our analysis with data from the Human Mortality Database (HMD) which contains life table up to age 110 for a limited numbers of (mostly high-income) countries. We find that, considering the full population of ages 0 to 110, the impact of lumping ages 100-110 together in a single category is very small: it amounts to less than 0.01 percent on average for all measures, with the smallest changes occurring for the Gini coefficients (which, as opposed to the other measures employed in the analysis, is not sensitive to the top-, but rather to the middle of the distribution). The largest percentage change observed across all measures, countries, and years is still only 0.5 percent and occurs for variance of the country with the highest life expectancy in the entire dataset, Japan, in the 2010-2015 time period. Naturally, if the population is restricted to older subpopulations, the impact of abridgment is larger, but still negligibly small: for the 65+ population, the changes on our inequality measures are all lower than .01 percent on average. Given that the countries in the HMD are among those with the highest life expectancies worldwide, the effects of abridging life tables at age 100 can be expected to be even smaller for less developed countries where only a very small part of the population survives above age 100 even in the more recent years. We therefore conclude that the use of abridged life tables has virtually no impact, neither qualitatively nor quantitatively, on the results obtained in this paper. 43