Abstract
This research documents long-run trends in between-country education inequality and proposes a method for doing so that accounts for the ways in which most education variables differ from continuous variables such as income. Historical, national-level estimates of primary schooling enrollment rates and years of completed primary, secondary, and total schooling are used to identify several problems that arise when formal measures of inequality are used to estimate intercountry education convergence, including violation of the welfare, scale invariance, and anonymity principles. An alternate measurement strategy shows that the intercountry trend in the dispersion of education has followed an approximately normal curve over the past 140 years, but with considerable variation across measures of education. These results are in contradiction to previous education inequality studies, which have reported either monotonically rising or falling intercountry inequality.
Keywords
The increasing availability of comparable cross-national measures of education has contributed to a growing body of transnational education scholarship. This scholarship has, in turn, established the basic world trends in education and shed considerable light on the causes and consequences of the global expansion of mass schooling. It is now widely accepted that the Western model of mass education has been diffusing around the world for quite some time. So much so, in fact, that it has been called a world education revolution (Meyer et al. 1977). The global expansion of education includes rising literacy rates (Crafts 2002); an increase in schooling enrollment rates (Benavot and Riddle 1988; Benavot et al. 1991; Meyer, Ramirez, and Soysal 1992; Ramirez and Meyer 1980) and completed years of primary, secondary, and tertiary education (Barro and Lee 2000; Cohen and Soto 2007; Morrisson and Murtin 2009); and improvements in math and science achievements (Baker and LeTendre 2005; Sahn and Younger 2007). Worldwide gains in virtually all measures of education have been made possible by positive gains within every major world region.
What is not clearly understood, and is the primary goal of this research, is the effect of the worldwide education revolution on intercountry education inequalities. To be sure, average education levels, whether measured by literacy, enrollment rates, education attainment, or test scores, have been rising virtually everywhere (Barro and Wang 2000; Crafts 2002; Goesling and Baker 2008; Morrisson and Murtin 2009; Sahn and Younger 2007), but what this means for the cross-national distribution of education is unclear, because among the few attempts to directly estimate between-country education inequality, there is virtually no agreement about whether inequality is rising or falling.
Previous studies of international education inequality (IEI), or the uneven distribution of education among countries, paint as contentious and contradictory a picture of the magnitude and direction of education inequality as we have seen in the income inequality literature. Using Barro and Lee’s (2000) education data, Goesling and Baker (2008) found that population-weighted inequality in average total completed years of schooling declined by almost 50 percent from 1980 to 2000. Morrisson and Murtin (2009) constructed their own cross-national education database and reported falling inequality in completed years of primary, secondary, and higher education from 1870 to 2000 but rising human capital inequality over the same period. In another study, the slowest midcentury school enrollment growth rates were reported in countries with the highest and lowest initial levels of education (Meyer et al. 1977), suggesting that there was little compression in the distribution of education from the 1950s to the 1970s. One of the few studies to consider the unequal distribution of student performance found that although test scores were rising all around the world, there has been virtually no compression in the international distribution of test scores (Sahn and Younger 2007). And in perhaps the most far reaching study of intercountry education inequalities, Kenny (2005) estimated inequality in literacy, years of completed schooling, and primary and tertiary enrollment rates for most of the last half of the twentieth century using three different tests of convergence: growth-rate convergence, sigma convergence, and coefficient-of-variation convergence. Regressing education growth rates on initial education levels (growth-rate convergence), he reported declining inequality in four education outcomes. Using the standard deviation (sigma convergence) to measure education dispersion, Kenny reported rising inequality in primary and tertiary school enrollments, no change in the standard deviation of completed years of schooling, and declining intercountry literacy inequality. He also found that the coefficient of variation was smaller in the last survey year than in the first year for all four education outcomes. On the basis of this survey of studies, it seems all but impossible to establish the basic facts regarding world trends in education inequality. And it is not hard to see that establishing the basic facts about education inequality has significant bearing on a number of other domains of central importance to sociologists, developmental economists, demographers, policy makers, and, perhaps most important, ordinary people all around the world.
A large body of research on advanced industrial economies documents a robust relationship between education, wages (including current and lifetime earnings), and occupational mobility within countries (see, e.g., Card 1999; Hout 1984, 1988). Because of the strong correlation between educational attainment, earnings, and occupational mobility, it is likely that rising education inequalities within countries will contribute to rising intracountry income and occupational disparities. A similarly strong link between education and both physical and mental health, including the link between inequalities of education and health disparities (Adler and Newman 2002; Miech et al. 2011), is well documented in previous empirical studies (Long et al. 2001; Ross and Wu 1995, 1996).
The implications of between-nation differences in average levels of education (IEI), which is the focus of this article, are equally significant. National education levels, whether measured by literacy rates, enrollment rates, or attainment, are robustly correlated with other measures of human well-being such as income levels, life expectancy, and political and religious freedoms. High levels of human capital are associated with higher rates of innovation and technological adaptation (Nelson and Phelps 1966), implying that between-country education inequalities are likely to contribute to persistent and even growing inequalities in innovative domains such as the health sector, information technologies, and the like. Mulligan and Sala-i-Martin (1992) found a positive correlation between education levels and economic growth (see also Barro and Lee 2010), because higher levels of human capital accumulation contribute to greater investments in physical capital relative to a country’s gross domestic product. Nations with higher average levels of education tend to recover from economic shocks faster than those with lower human capital accumulation, suggesting that the IEI contributes to inequalities in human suffering. Thus, it is important to know the direction and magnitude of change in international health inequality, because an increase in education inequality is likely to serve as a wellspring for increases in between-nation inequality in other life domains, whereas declining inequality might promote declining between-nation inequality in these and other domains.
The central goal of this research is to measure long-run trends in education inequality across countries, regions, and the world for a relatively long period (1870 to 2010) and to expressly link change in IEI to the diffusion of mass education. A secondary goal is to identify some of the challenges associated with measuring inequality in nonpecuniary variables such as education and outline a strategy for doing so that adequately accounts for the ways in which measures of education differ from measures of income and other ratio-scaled variables. In the next section, I review terms and concepts central to inequality analysis, highlight several problems that can arise when mean-invariant inequality indexes are used to measure IEI, and propose an alternative method for studying IEI. I then describe the data and methods. In the following sections, I provide some background and descriptive, historical context for the study of IEI before modeling world trends in schooling inequality from 1870 to 2010.
Measuring International Education Inequality
There are at least three reasons why the picture of IEI appears to be so muddled. First, most previous studies of international inequality have applied a conceptualization of inequality that often incorrectly favors relative differences over absolute ones. The second reason for the lack of consensus on trends in IEI is the incorrect matching of the level of measurement (e.g., ordinal, ratio) with measure of dispersion (e.g., standard deviation, Gini coefficient). And third, many types of variables can be just as meaningfully expressed in either native scale or in an inverse scale (e.g., literacy vs. illiteracy, enrolled vs. not enrolled). All three issues merit further discussion, and I consider each in turn, but first, some of the most common types of variables used to study inequalities of education in social science research must be explicitly identified before considering how best to assess the dispersion of these types of variables.
When it comes to measuring cross-national education inequality, researchers have a much wider selection of variables to choose from than in many other types of research. In practice, data coverage often determines which measures are used in a particular study, but some of the most commonly used variables in cross-national education studies are literacy rates, net and gross enrollment rates (primary, secondary, and higher education), schooling completed (primary, secondary, higher, and total years), educational financing, and test scores (e.g., Trends in International Mathematics and Science Study). 1 Literacy has become an increasingly popular indicator of the degree to which people have the most basic skills necessary to successfully function in the contemporary world. Enrollments represent access to schooling, and schooling attainment measures quantity of schooling. Education quality can be assessed by inputs such as educational financing or by outputs such as math or science scores (Baker and LeTendre 2005; Thomas, Wang, and Fan 2000). Education variables differ from income because they are not typically measured on a ratio scale and can often be expressed in complementary form. They thus warrant a more cautious approach to the use of relative measures of dispersion in the context of inequality analysis.
Absolute versus Relative Disproportionality
A key distinction to be made in studies of dispersion is whether to model absolute or relative variation. The measurement of relative disproportionality, or the uneven distribution of Y, is typically accomplished through some form of mean standardization (Firebaugh 2003; Sala-i-Martin 1996). 2 The simplest relative measure of inequality is the coefficient of variation, which is the standard deviation divided by the mean (coefficient of variation = SD/μ). Other relative measures of inequality or ‘inequality indexes’, which facilitate the comparison of income distributions derived from different currencies, include, among others, the Gini coefficient, Theil index, and the mean log deviation. An important commonality among relative measures of inequality is that each gives greater weight to change near the bottom of the income distribution over similar gains near the top of the distribution, in keeping with the welfare principle. The unequal weighting of income gains among the rich and poor is important because it is widely agreed that the value of personal income increases the closer a person is to subsistence living. Thus, relative inequality indexes are more sensitive to small income gains among the poor than among the rich. The problem that arises from using relative measures of inequality such as the Gini coefficient to assess IEI is more clearly understood after first considering two related concepts: level of measurement and complementary scales.
Level of Measurement
Unlike income, most nonpecuniary variables are not continuous, even though they are often treated as such in research. A common feature of many nonincome variables is that they have either absolute or logical upper or lower bounds, or both, which is characteristic of levels of measurement below the ratio scale. National literacy and enrollment rates are reported as percentages of the population and range from 0 percent to 100 percent. 3 Educational attainment is typically measured in years and has a lower bound of zero and a probable population-level upper bound of about 15 years (Crafts 2002). The bounded nature of many education variables is important because boundedness affects growth rates, which in turn stands to affect the magnitude and direction of inequality trends. When countries reach the upper limits of the measurement scale in, say, literacy, the only possible gains are among lagging nations and so inequality must decline (Sutcliffe 2004). This kind of phenomenon might be considered a “saturation effect,” because as the universe of potential adopters becomes saturated, there is a dwindling supply of future adopters. Discrete variables trending toward the upper limits are subject to ceiling effects, which favor absolute and relative gains near the top of the distribution, while variables trending toward the lower bound are subject to floor effects that similarly favor small declines near the bottom of the distribution (Cornia and Menchini 2006; Dorius 2008). Thus, the limits of the measurement scale favor long-run convergence when variables are trending toward the upper bound and favor divergence for variables trending toward the lower bound.
Complementarity
A second unique feature of bounded variables is they can often be meaningfully expressed in complementary, or inverse, scale (Kenny 2005). Examples of complementary variables include literacy (Y) and illiteracy (~Y, or not Y), the share of enrolled and nonenrolled students, adult survival and mortality (Deaton 2007), and life expectancy at birth and years of lost life (Cornia and Menchini 2006). Complementary variables pose a unique challenge to inequality studies, because when a variable can be expressed in complementary form, it is possible to produce opposing inequality trends, depending on whether the mean is converging on the lower or upper bound of the measurement scale. When this occurs, complementary variables violate what is known as the anonymity principle.
To be rightly considered a measure of inequality, an index must adhere to a number of principles, including the anonymity, scale invariance, and welfare principles. The anonymity principle states that the level of inequality in a given distribution should not be affected by other characteristics of the units of analysis such as race or religion (Litchfield 1999). Similarly, the degree of inequality should be unaffected by the simple switching of how the units are labeled or coded, as long as recoding does not change the overall distribution. In terms of an income distribution, switching the incomes of any two individuals should have no effect on the observed degree of inequality, while in the context of education distribution, reversing the coding of enrollment rates from enrolled to not enrolled should similarly leave the level of inequality unchanged.
To see how this works, consider two equally sized nations composed of two groups of people, haves and have-nots. In both countries, the haves are enrolled in school and the have-nots are not enrolled. In country A, the haves account for 10 percent of the total population (the have-nots account for the remaining 90 percent), and in country B, the haves account for 90 percent of the total population. Which country is more equal? At first blush, one might be inclined to say that country A is the more equal society because 90 percent of its citizenry are enrolled in school, while only 10 percent of the citizenry of country B are enrolled, but adherence to the anonymity principle means that if enrollment slots within each country are simply switched, so that the haves are now the have-nots and the have-nots the haves, the degree of inequality should be unaffected. This is so because the shares are the same in both societies (0.90 and 0.10). We can visualize how this works using national-level enrollment data in 1910 for the world.
Figure 1 graphs kernel density estimates for the world distribution of enrolled and nonenrolled students and the average years of primary schooling and lost years of schooling with the assumption of six years as the maximum attainable years. Comparison of the two sets of distributions confirms that the dispersion of enrollments is identical to, but the inverse of, nonenrollments and that the distribution of schooling is identical and inverse to lost years of schooling. One would be hard-pressed to claim that one distribution is more equal than the other. In accordance with the anonymity principle, an appropriate measure of variance should report the same degree of inequality for both distributions, because (1) they contain the same people only with different labels, and (2) the spread of the two distributions are identical, only inverse. Importantly, standard measures of inequality violate the anonymity principle when a variable is discrete and can be expressed in complementary form.
Primary schooling rates and years in 1910
Returning now to the concept of absolute and relative inequality, let us consider what IEI would look like if relative measures of dispersion were used to gauge the degree of intercountry inequality in primary school enrollments. The population-weighted point estimates reported in Table 1 show that the world school enrollment rate rose from 15.2 percent in 1870 to 93.2 percent in 2000. Absolute change was 77.9 percentage points, but the relative growth rate was 511 percent. Even though absolute change in the world nonenrollment rate from 1870 to 2000 was an identical 77.9 percentage points, the relative decline was a much smaller 93 percent. That countries trending toward higher primary school enrollment are simultaneously trending toward lower nonenrollment is hardly a surprising finding, so let us consider the inequality trends. Both the Gini coefficient and the Theil index report declining inequality in primary school enrollment and rising inequality in the nonenrollment rate. Because the mean log deviation, the Theil index, and all other mean standardized inequality indexes were constructed to measure relative income differences, they favor small absolute gains at the bottom of the distribution over similar absolute gains near the top of the distribution. 4 Switching from enrolled to not enrolled changes the world mean, which in turn affects the relative difference between countries. This is a desirable feature when studying something such as income, but when the variable of interest is bounded or complementary, it is likely to distort between-country differences in ways that do not reflect the real value or meaning of education at either the individual or national level. To summarize, formal measures of inequality are mean standardized. Although mean standardization makes sense for continuous variables such as income, in the case of bounded variables subject to floor and ceiling effects, mean standardization is superfluous and it creates problems.
The Problem of Complements in Primary Schooling: Enrolled versus Nonenrolled
Note: Estimates are author’s population-weighted calculations.
If conventional, mean-standardized measures of inequality such as the Gini coefficient are not appropriate for studying the convergence of bounded education variables, what should be used? In keeping with previous conventions, I propose that the best measure for studying cross-national convergence in discrete variables, including binary and proportional variables, is the standard deviation (Allison 1978). Although the current study is not the first to use the standard deviation in the study of cross-national convergence (Deaton 2007; Neumayer 2004; Sala-i-Martin 1996), it is among the first to spell out the advantages of the standard deviation over standard measures of inequality for an entire class of variables. The standard deviation has several properties that make it a desirable and intuitive measure of the dispersion of education. First, the upper bound for the standard deviation will never exceed one half the scale range, and the standard deviation is 0 when the mean of Y is 0, assuming Y cannot take on negative values (Ram 1990). With a fixed range of 0 to half the range of the measurement scale, it is relatively easy to gauge both perfect equality and maximum inequality. In the case of literacy rates, maximum education inequality exists when SD = 50, and perfect equality is when SD = 0. Because the standard deviation will always range between 0 and 50 for education rates (e.g., literacy, enrollment, graduation, retention), researchers can readily make cross-variable inequality comparisons for many education variables. A second benefit of the standard deviation is that because it is reported in the same units as the measurement scale, the substantive meaning of the degree of inequality is often more intuitive than is the case with mean standardized measures. And third, research suggests that the standard deviation better fits education models than standard measures of inequality such as the Gini coefficient (Ram 1990).
The strength of the standard deviation is most apparent in the case of binary variables. Consider again two equally sized nations composed of haves and have-nots accounting for 90 percent and 10 percent of the population in each society. Earlier, the question was which of the two countries was more equal. Relying solely on conventional mean-standardized measures of inequality, the country composed of 90 percent haves would be considered the more equal society. Using the standard deviation as the measure of inequality, and consistent with the anonymity principle, one would conclude that the two societies have the same degree of inequality. The standard deviation in both countries is 0.3, because the standard deviation for a proportion is simply
The spread of the distribution is the same in both countries and is confirmed by absolute measures of dispersion such as the standard deviation. The same is true of other types of discrete variables such as years of completed schooling: The standard deviation will produce the same degree of inequality for completed years as it will for lost years. The symmetrical feature of discrete variables, including binary variables and aggregate measures based on binary outcomes, means that symmetrical measures of dispersion such as the standard deviation produce the same estimate of inequality for both Y and ~Y. 5 Scale-invariant measures of inequality are appropriate for continuous variables but, as has been illustrated, are problematic when used to make comparisons among distributions of discrete variables.
Data
The substantive goal of this research is to document long-run, worldwide trends in educational inequality which necessarily limits the number of education variables for which historical cross-national comparisons can be made. I chose to measure education inequality using primary enrollment rates and years of completed schooling partly for practical reasons—they are among the few variables that have extensive geographic and temporal coverage—and partly for methodological reasons. Because enrollment rates are based on a binary variable, it has a complementary form, that is, the nonenrollment rate. Years of education is a semicontinuous variable with an absolute lower bound but a somewhat “softer” upper bound. Measuring intercountry inequality trends for both variables illustrates the sensitively of inequality trends to different types of education scales.
Estimates and projections of primary, secondary, and total years of completed schooling for the period from 1870 to 2010 come from Cohen and Soto (2007) and Morrisson and Murtin (2009). 6 Population estimates were compiled from four sources: World Population Prospects: The 2008 Revision (United Nations 2009), the World Development Indicators database (World Bank 2009), a data set obtained from Benavot and Riddle (1988), and Angus Maddison’s (2004) The World Economy: Historical Statistics. I used observed regional growth rates to fill a limited number of missing population observations. 7
The enrollment data time series, spanning the period from 1870 to 2000, was assembled from UNESCO’s Institute for Statistics primary school enrollment data, the World Bank’s (2009) World Development Indicators database, and published estimates (Benavot and Riddle 1988; Easterlin 1981) on the basis of Mitchell’s (2003a, 2003b, 2003c) historical schooling estimates. The World Development Indicators data estimates are gross enrollments, while Benavot and Riddle’s (1988) education data are unadjusted enrollments. The difference between the two is that the denominator used to calculate the unadjusted enrollment rate is based on a constant school-age population of 5 to 14 years, while gross enrollment rates use a variable denominator based on the actual age range of primary school attendees in each country. Although calculation of the two enrollment rates is slightly different, the substantive differences in long-run, global trends are negligible (Benavot and Riddle 1988). Easterlin’s (1981) data are primary enrollments per 10,000 in the total population, rather than per 100 in the school-age population. To harmonize Easterlin’s data with the other enrollment data, I first recalibrated Easterlin’s data to enrollments per 100 in the total population and then adjusted the rate to the child population. 8
After the data were merged, I used linear mean interpolation to fill intertemporal missingness in the data (e.g., data were available for T1 and T3 but not T2). The interpolated primary school enrollment data series accounts for 93 percent of the world’s people in 1920 and still a majority of the world’s people dating back to the late 1800s. Observed primary enrollment rate data were used to calculate regional growth rates for each 10-year interval from 1870 to 2000. Assuming that countries within each region shared roughly similar growth rates, I then used the average of each of the fourteen 10-year regional growth rates over the period from 1870 to 2000 to extrapolate a similar growth rate for countries with missing data.
Background and Descriptive Analysis
It is instructive to begin this analysis of world trends in IEI by first situating the underlying patterns of change in both world and regional means within the context of the larger historical and theoretical framework that explains the global rise of mass education. World polity theorists have long argued that the worldwide diffusion of mass schooling is part of a larger package of global institutional change whereby (1) the nation-state has become an increasingly central global actor, and (2) the organization of states and national institutions are becoming more uniform in both time and geographic space (Benavot et al. 1991; Ramirez and Meyer 1980). As partial evidence for these claims, they point to the expansion of primary school enrollment rates and show that it is strongly linked to diffusion processes net of economic development and world system position (Meyer et al. 1977).
The world trend in primary schooling reported in Figure 2 confirms that primary schooling enrollments have indeed followed the hallmark S-shaped diffusion curve, with slow initial growth followed by a much steeper increase and then a leveling off in the growth rate as countries approach full enrollment. The trends in Figure 2 also suggest not only that the establishment of formal schooling systems made possible rapid gains in enrollment rates but that time in school, as measured by average years of completed schooling, has also been expanding. Inspection of regional education trends help illuminate how and why global schooling growth rates have recently begun to accelerate.
World trend in complete schooling and primary school enrollments
In 1870, mass education was largely a regional phenomenon (Figure 3). Europe, including the “offshoot” nations of Canada, the United States, New Zealand, and Australia, was the only country group with a mean enrollment rate in excess of 20 percent in 1870. As far back as the late 1800s, the mean primary school enrollment rate for this region was over 60 percent and had eclipsed 80 percent by the early 1900s. In all other world regions, 1870 enrollments were below 20 percent. Sixty years later, no other region had yet to achieve a mean enrollment rate of 50 percent. All of that changed beginning around the middle of the twentieth century, when enrollment rates surged in all world regions. By 1970, Eastern Europe, Latin America, and much of Asia had mean enrollments in excess of 80 percent. Even in the lagging nations of West Asia and North Africa, the mean enrollment rate rose by more than 50 percentage points from under 20 percent in 1940 to over 70 percent in 1990. Regional trends in completed years of education paint a similar picture: Europe holds a sizable education advantage over the other five world regions, but recent decades have witnessed substantial increases in both school enrollments and attainment.
Regional trends in education, 1870 to 2010
Historically large regional disparities in education reflect the origins and early diffusion of mass education where the early pioneers in formal schooling were the Protestant nations of northern and western Europe (Cippola 1969; Easterlin 1981; Melton 1988). The story of mass education has changed dramatically over the past century from essentially a regional, religious peculiarity rooted in the rise of Protestantism (Cippola 1969) to a worldwide phenomenon. Importantly, we are now fast approaching the time when primary schooling will be a universal fact of life virtually everywhere, a historical first in human history. What should be clear from the trend analysis of world and regional mean education levels is that the overall pattern of education expansion in each of six major world regions was slow initial growth followed by more rapid recent gains. From 1870 to 1940, total years of completed schooling increased by an average of about 0.3 years per decade, but since 1950, the rate doubled to an average of almost 0.6 years per decade. The post–World War II gains in primary and secondary schooling increased over the prewar period by 44 percent and 234 percent, respectively. The timing of the “globalization” of mass education is important because it squares with several other significant world developments during this period.
The decades immediately following the end of World War II witnessed the birth of the United Nations, which expedited two other processes, one institutional and the other ideational, that were already well under way. The first was decolonization, which gave rise to a large number of newly independent nations, many of which were eager to emulate the material successes of their former colonizers. The second was a commonly held set of beliefs about the causes of economic development that provided the ideational roadmap virtually every nation in the world would soon follow. Societal elites and ordinary people alike throughout the world shared (and continue to share) a common belief that educating individuals and societies would lead to economic and social development of the kind exemplified by rich Western nations (Thornton 2005). The congruence in developmental objectives between United Nations development agencies, political leaders in Western and non-Western nations alike, and the vast majority of the citizens of most countries around the world played an essential role in the expansion of mass education. Another significant event contributing to the expansion of mass education across every major world region has been the world polity. The proliferation of world cultural models began long before the more recent global take-off in mass education, but its influence on education inequality was aided by growth in the world polity, including governmental institutions such as the United Nations and nongovernmental organizations that shared a common objective of “developing” all of these newly created nations and peoples. The convergence of developmental goals created tremendous institutional isomorphic pressure that, in turn, guided nation-states into mimicking the institutional structures of Western nations, including education systems (Meyer et al. 1997). 9
Although each of these and other forces provide a model of mass schooling and an essential justification for the universality of education, cross-national variation in the presence and influence of the world polity (Beckfield 2003) as well as substantial variation in state resources critical to the expansion of mass education suggest that the diffusion of education, though universal, has been far from even. In the next section, I focus more explicitly on the world distribution of education and how it has varied over time.
Dispersion Analysis
Density Distributions
Density distributions are a useful tool in the analysis of inequality because they provide insights into the data that often go undetected by sole reliance on univariate statistics such as the mean or variance. Kernel density distributions, for example, help identify multimodal and other nonnormal distributional features in the data. Visual inspection of world education distributions at T1 and T n is also a simple method for assessing between-country education convergence: Compression in the spread of the distribution points to convergence, and a widening and flattening distribution suggests divergence, or rising inequality.
Figure 4 graphs three population-weighted Gaussian kernel density distributions (1870, 1950, and 2010) for each of the four education measures. The distributions of all four measures were concentrated near zero in 1870 but widened and flattened over time as education expanded. The distribution of primary enrollments gives the clearest example of how mass schooling is, in many ways, a story of worldwide diffusion. Primary schooling was scarce in 1870, and enrollment rates were concentrated near zero. By 1950, the spread of the distribution had widened to nearly the full width of the measurement scale, with some countries still near full nonenrollment and others having achieved universal enrollment. Over the next 50 years, rates increased rapidly among lagging nations and now national average enrollments are tightly concentrated near 100 percent. The distributions in the other three domains appear to be following a similar trajectory, though with significant variation in both the rate and form of diffusion. For example, the take-off in completed years of primary schooling started earlier than secondary schooling and was bimodal: The majority of nations fall into one of two dominant primary schooling clusters (in 1950, most countries were clustered around 1 or 5 years of primary schooling, and in 2010, the modal clusters were concentrated near 3.5 and 5.5 years). As recently as 1950, the world distribution of secondary education was still positively skewed, with most nations clustered around very low secondary attainment levels. By 2010, a large number of nations were clustered around 1.5 years of secondary schooling, and a much smaller cluster of leading nations had begun to cluster near full secondary schooling attainment, suggesting that secondary schooling may yet follow the sharply bimodal diffusion pattern observed in primary schooling attainment.
Worldwide change in the distribution of education
Inequality Analysis
I have argued that measures of absolute dispersion are preferred over mean-standardized measures of inequality when the purpose of the research is to compare the distributions of discrete measures of education. In Figure 5, I report trends in the standard deviation of primary school enrollments and completed years of primary, secondary, and total schooling from 1870 to 2010. I graph unweighted trends (each country treated equally) and trends that are population weighted by the size of each country’s total population. 10 In unreported analysis, I also used a child population weighting scheme, and the results were nearly identical to the total population results reported here. My discussion will focus largely on the population-weighted estimates, because the results are broadly similar regardless of whether the data are weighted by population.
Intercountry education inequality using the standard deviation, 1870 to 2010
Inequality trends in each of the four domains were sufficiently similar that several broad conclusions can be drawn regarding between-country education inequality. First, the worldwide expansion of education was decidedly uneven. By each measure, inequality rose sharply as mean levels of education rose. Second, the long-run inequality trend appears to be following an inverted U shape of first rising and then falling inequality. The pattern of rising and then falling inequality, referred to as the inequality transition (Dorius 2010; Firebaugh 2003), is unequivocal in primary schooling, and though it is too early to state with certainty, it appears that the same general pattern is unfolding in secondary and total years of completed schooling. And third, there is considerable variation in the inequality slopes and in the timing of peak inequality across the four education variables.
Primary enrollment inequality peaked in 1910 (SD = 30) before declining to just over 10 percent in 2000, meaning that over 60 percent of the world’s people now live in a society in which the primary enrollment rate is at least 83 percent (mean enrollment in 2000 = 93 percent). 11 Inequality in primary years of education reached a peak standard deviation of 2.1 in 1940 and has been declining at an even faster pace than enrollment inequality ever since. In fact, between-country inequality in both primary school indicators is lower now than at any point in the past 130 years. The high-water marks for intercountry inequality in secondary and total completed years of education were 1990 and 1980, respectively.
If we ignore the modest degree of cross-national variation in the required number of years to graduate from school and assume that every country requires six years to complete primary schooling and an additional six years to complete secondary education (and this assumption is very close to reality), then we can identified a critical distinction between trends in the mean and the standard deviation of primary and secondary years of education. The inequality transition in primary schooling was more compressed than the secondary schooling transition, but also more unequal. Secondary education inequality took almost 50 years longer to peak than primary education inequality, but it peaked about 0.4 years lower than did primary schooling, which means that although secondary education is expanding more slowly than primary education, the expansion has also been more equitable. With the world fast approaching full primary enrollment and universal primary school completion, education inequalities in the twenty-first century will largely play out in secondary and higher educational attainment (and, of course, schooling inputs, returns to education, and academic performance).
One final observation regarding world IEI trends is worth noting. The unweighted inequality trends closely paralleled the population weighted trends in all three completed years of schooling measures, and to a somewhat lesser degree in primary enrollments. In simplest form, when weighted and unweighted inequality trends sharply differ in either level or trend, it means that what is happening in very large countries is not representative of what is occurring in the average country. The opposite case is present with education inequality: What is happening in the average nation is also occurring in very large countries, which is to say that education is expanding everywhere, not just in a few large countries such as India, China, and Brazil.
We have seen that the early expansion of education was highly uneven but that the recent past witnessed a general trend toward cross-national convergence in measures of education. In concluding, it is useful to disaggregate the world education inequality trends separately by region because it points to future directions in IEI research. The same pattern of first rising and then falling between-country inequality observed at the world level is occurring at the regional level, but with some notable interregional differences (Figure 6). By three of the four measures, regional inequality was greatest in Asia, and if current trends hold, education inequality in the Middle East and North Africa will be similarly unequal. The expansion of mass education was the most equitable in Latin America and Europe. By three of the four measures, inequality peaked at the lowest levels in Latin America, with total years of completed schooling peaking at the lowest level among European countries.
Regional trends in the dispersion of education, 1870 to 2010
A comparison of education trends in Asia and Latin America is instructive. The mean levels of education in Latin America and Asia followed a parallel trajectory in all four domains, with mean education in Asia slightly lower than in Latin America at every time period (Figure 3). Inequality trends in the two regions were not nearly as uniform, as peak levels of inequality in Latin America were less than half the levels recorded in Asia. A comparison of the inequality trends across regions suggest that local factors, such as regional heterogeneity of linguistic, cultural, economic, and political context, are likely causes of interregional variation in education inequality. Latin America, for example, has a much more homogeneous religious, linguistic, and colonial heritage than either Africa or Asia, and it is likely that the higher relative degree of intraregional homogeneity in Latin America is partly responsible for the more equitable diffusion of mass education in that region than in others.
Discussion
The aim of this research was to measure long-run world trends in education inequality and to establish a method for doing so that adequately accounts for the ways in which measures of education differ from measures of income. Because many of the variables most frequently used in cross-national research are bounded and can often be expressed in complementary form, researchers must carefully consider the risks associated with using mean-standardized measures of inequality for traditional inequality analysis of education. I have argued that using the standard deviation or other, similarly nonnormalized statistics is an appropriate method for measuring world education inequality of symmetrical education variables, at least in the context of convergence analysis.
Inequality trends from 1870 to 2010 indicate that we are rapidly approaching the end of intercountry inequality in primary school enrollments and in years of completed primary schooling. Should the same patterns hold for secondary and total years of completed schooling, we can expect to see a steady decline in intercountry education inequality in both secondary and total years of completed education over the coming years. Because the contours of world education inequality were broadly similar regardless of which weighting scheme was used, we can conclude that the trends reflect both a world phenomenon (population weighted) and a national phenomenon (country weighted).
It is possible to draw at least two broad conclusions from this research. First, the global expansion of mass schooling can be accurately characterized as a worldwide education revolution (Meyer et al. 1977). Educational enrollment rates and completed years of schooling have been rising virtually everywhere for over 100 years and have more recently begun to accelerate. Even places that lagged behind the rest of the world, such as North Africa and West Asia, have experienced such large absolute gains in schooling over recent years that they are converging on and even eclipsing observed rates in other regions.
Second, the transition from low to high education led first to rising inequality and only much later to declining IEI. Much like with other forms of innovation diffusion, the onset of mass education was concentrated among a small number of innovator nations. In this case, the innovators were the Protestant countries of Europe, including offshoot nations (Cippola 1969; Easterlin 1981; Melton 1988). The spread of mass education outside of Europe led to an increase in world education inequality that began to decline only fairly recently. Ultimately, between-country inequality in access to, and quantity of, education can be expected to continue to decline so long as the worldwide education revolution continues.
World polity theorists have described the history of nations and its people as being composed of “eras of innovation and contestation and eras of consolidation and institutionalization” (Ramirez, Soysal, and Shanahan 1997; see also Bradley and Ramirez 1996; Tolbert and Zucker 1983). Within the context of education, the origins and early expansion of mass schooling represent a period of innovation and contestation that led to rising between-country inequality. In the more recent past, the world appears to have entered a period of consolidation because of the institutionalization of the Western model of mass education. The worldwide institutionalization of formal schooling, in turn, is a central reason for more recent declines in intercountry education inequalities.
A key finding of this research is that low-education nations are catching up with high-education nations in enrollment rates and completed years of schooling. This finding is a worthy cause for celebration. The very fact that secondary schooling attainment is diffusing more equitably than primary schooling is reason for cautious optimism about the future of inequalities in domains such as health and income. As the world continues to converge toward universal literacy and enrollment, however, it is likely that new forms of education inequality will replace older inequalities in both access to education and quantity of education. Already, we see sizable intercountry gaps in test scores (Sahn and Younger 2007) and spending on education. Without nimble intergovernmental policy prescriptions and continued efforts by governmental and nongovernmental agencies alike, it is probable that education outcomes, such as test scores, occupational mobility, postschooling earnings, and health disparities, will exhibit a high degree of between-country inequality in the coming years.
Footnotes
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by National Institute of Child Health and Human Development Training Grants from the Population Research Institute at Pennsylvania State University (T32 HD007514) and the Population Studies Center at the University of Michigan (T32 HD007339).