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Author manuscript (07/09/2019)
Published in final edited version in:
Studies in Educational Evaluation. doi.org/10.1016/j.stueduc.2019.03.009
The socio-spatial dimension of educational inequality: A
comparative European analysis
Kaspar Burger
University of Minnesota, University College London
Abstract
Given recent evidence of rising levels of social segregation in European countries, this study uses
standardized data from the Program for International Student Assessment (n = 171,159; 50.5% male)
to examine the extent to which education systems in Europe are socially segregated and whether
social segregation in the school system affects achievement gaps between students of different social
origin. Results suggest that the degree of social segregation within education systems varied
substantially across countries. Furthermore, multilevel regression models indicate that the effect of
socioeconomic status on student achievement was moderately but significantly stronger in more
segregated education systems, even after controlling for alternative system-level determinants of
social inequality in student achievement. These findings provide original evidence that social
segregation in education systems may contribute to the intergenerational transmission of educational
(dis)advantage and thus serve to exacerbate wider problems of socioeconomic inequality in Europe.
Keywords
Cross-national comparison; Social segregation; Standardized assessment; European education systems;
Multilevel
This study is part of a project that has received funding from the European Union’s Horizon 2020 research and
innovation program under the Marie Skłodowska-Curie Grant Agreement No. 791804.
Correspondence should be addressed to Kaspar Burger, 1014 Social Sciences Building, Department of
Sociology, 267 19th Avenue South, University of Minnesota, Minneapolis, MN 55455, USA, E-mail:
burgerk@umn.edu
2
The Socio-Spatial Dimension of Educational Inequality: A Comparative
European Analysis
1. Introduction
In recent years, the level of social segregation in European countries has increased (Marcinczak,
Musterd, van Ham, & Tammaru, 2016). It is therefore crucial to examine whether, and to what
extent, education systems in Europe are also segregated along social lines, and whether social
segregation between schools shapes individual student achievement and social inequality in
educational outcomes.
Social segregation in education systems refers to the uneven distribution across schools
of students from different socioeconomic backgrounds (Jenkins, Micklewright, & Schnepf,
2008). Where students are highly segregated by socioeconomic origin between schools,
resources that contribute to students’ educational success—such as social, economic, and
cultural capital—are more unequally distributed (Owens, 2018; Reardon & Owens, 2014). An
unequal distribution of such resources among student populations typically leads to disparities
in educational opportunities, because schools draw on these resources informally in educating
their students (Chiu, 2015; Croxford & Paterson, 2006). For instance, schools serving
socioeconomically advantaged students receive more support from parents (Lee & Burkam,
2002). Their students come from families who tend to have higher educational expectations for
their children (Davis-Kean, 2005; Neuenschwander, Vida, Garrett, & Eccles, 2007); and these
families often have more knowledge of the education system (e.g., about its written and
unwritten rules, what and how students should learn, or what educational decisions to take;
Crosnoe & Muller, 2014; Jackson, Erikson, Goldthorpe, & Yaish, 2007). Moreover, schools
that serve advantaged students benefit from the fact that their students typically attach great
value to education and use similar forms of communication and interactions in school and in
their family environment (Lareau & Weininger, 2003). As a result, their student populations
constitute functional communities particularly conducive to learning (Lee & Bowen, 2006).
Children learn from each other, and peer achievement affects achievement growth (Hanushek,
Kain, Markman, & Rivkin, 2003; Lavy, Paserman, & Schlosser, 2012). Consequently, an
uneven distribution of students of diverse social origins within an education system may affect
not only student achievement but also social disparities in achievement.
3
So far, research on the relationship between social segregation within education systems
and social class gradients in student achievement across European countries is scarce. This is
despite researchers and policymakers increasingly acknowledging the need to address common
challenges, such as ensuring social cohesion and fairness in education, at a European level (e.g.,
Pépin, 2011).
In light of the above, this study pursues two main objectives. First, it assesses the links
between social segregation and socioeconomic gradients in student achievement within
European education systems. Second, it examines whether social segregation in these education
systems moderates the micro-level associations between socioeconomic status and educational
achievement, when controlling for further country- as well as school-, and individual-level
variables. The study thereby extends cross-national comparative research on the mechanisms
underlying “socioeconomic inequality in educational achievement,” which (for brevity) we also
refer to simply as “educational inequality.”
2. Prior research on social segregation and educational inequality
2.1. System-level links between social segregation and educational inequality
Prior research indicated a positive correlation between social segregation within education
systems and socioeconomic disparities in student achievement (Felouzis & Charmillot, 2013).
However, this research compared education systems at subnational levels in Switzerland. To
date, there is no research analyzing specifically whether, across Europe, more socially
segregated education systems are those in which student achievement is more closely linked to
socioeconomic status.
2.2. Effects of social segregation on educational inequality
Some studies sought to examine whether social segregation in education systems affects
educational inequality. McPherson and Willms (1987) found that moving from a selective to a
comprehensive secondary school system in Scotland minimized social class segregation
between schools and improved the educational achievement, in particular, of poor children. A
more recent study suggests that educational inequality was more pronounced in OECD
countries whose education systems exhibited higher levels of social segregation (Holtmann,
2016). However, this study did not control for any other country-level determinants of
educational inequality, thus making it difficult to conclude that segregation was the actual driver
of this inequality. Furthermore, evidence from the United States indicates that income
4
segregation between school districts exacerbated achievement gaps between privileged and
underprivileged students (Owens, 2018; Reardon, 2011). However, it remains unclear whether
social segregation also increases socioeconomic inequality in educational outcomes in
European countries where the levels of social segregation are estimated to be substantially
lower (Marcinczak et al., 2016; see also Sortkær, 2018).
More generally, there is relatively little cross-national comparative research on the
consequences of system-level segregation on educational inequalities. Prior research on socio-
spatial inequalities in education typically focused on school social composition effects (Borman
& Dowling, 2010; Dumay & Dupriez, 2008; Fekjær, & Birkelund, 2007; Opdenakker & van
Damme, 2007; Palardy, 2013; Rumberger & Palardy, 2005), rather than system-level
segregation effects. In fact, in a review of research, Reardon and Owens (2014) concluded that
“much of the research purporting to assess the links between segregation and student outcomes
instead measures the association between school composition and student outcomes” (p. 200).
Research on school composition effects tests the impact of segregation in only a limited sense,
under the assumption that segregation affects educational achievement and/or inequality
predominantly through school composition mechanisms, rather than through other mechanisms
such as the uneven distribution of resources and the corresponding disparities in learning
opportunities on a broader system level. Moreover, research on school composition effects does
not allow for analyzing system-wide segregation effects. Within a country, a given set of
schools may exhibit low levels of social segregation, although the degree of segregation at the
overall system level might be substantial. Cross-national comparative research allows for
distinguishing between school composition and system-wide segregation effects and thus may
provide a more comprehensive picture of the consequences of socio-spatial clustering of
students. In addition, cross-national research provides the opportunity to examine systematic
patterns of covariation between social segregation and educational inequality across countries
by taking into account potential system-level confounders. Prior research focusing on school
composition effects was conducted in diverse countries that differed not only in the overall level
of social segregation within the system, but also in other macro-level variables (e.g., Belfi et
al., 2014; Driessen, 2002; Lauen & Gaddis, 2013; Strand, 2010; Televantou et al., 2015; Van
Ewijk & Sleegers, 2010). In this research, effects of the socio-spatial clustering of students may
have been confounded with those of further, unmeasured, country-specific influences.
Specifically, this prior research may have overlooked alternative country-level explanations of
educational inequality, such as the overall level of national inequality (Chmielewski & Reardon,
2016), the economic development of a country (Yaish & Andersen, 2012), or the
5
comprehensiveness of the education system (Burger, 2016a).
1
Given that standardized cross-
national data on student achievement are now available, it is now possible to analyze effects of
social segregation within comparative designs that also consider further potential country-level
determinants of educational inequality. We develop such a design here.
3. Contribution to the literature
This study extends knowledge of social segregation and inequality in European countries
(Benito et al., 2014; Bernelius, & Vaattovaara, 2016; Böhlmark, Holmlund, & Lindahl, 2016;
Musterd, Marcińczak, van Ham, & Tammaru, 2017; Yang Hansen, & Gustafsson, 2016, in
press; Yang Hansen, Rosén, & Gustafsson, 2011). First, it uses cross-national standardized data
to analyze the link between social segregation within education systems and socioeconomic
gradients in student achievement across European countries. Second, because socioeconomic
gradients in achievement could be a consequence of further system-level influences (rather than
the result of segregation within the education system), the study investigates whether
segregation moderates these gradients when alternative system-level influences are considered.
Our strategy is to examine major system-level influences comprehensively while keeping the
models parsimonious. Thus, we concentrate on five economic and education policy dimensions
that have been identified as major system-level determinants of educational inequality in prior
research: (1) economic development, (2) population-level socioeconomic inequality, (3) annual
schooling time, (4) preschool enrollment rate, and (5) public expenditure on education.
Economic development and socioeconomic inequality have long been recognized as
potential drivers of educational inequality (Heyneman & Loxley, 1983; Jerrim & Macmillan,
2015). Specifically, research has shown that the level of economic development correlates
negatively with educational inequality because more economically developed societies tend to
be more open societies in which the importance of ascriptive (“non-merit”) factors such as
social origin for individual educational attainment gradually decreases (Ferreira & Gignoux,
2014; Gustafsson, Nilsen, & Yang Hansen, 2018; Marks, 2009; van Doorn, Pop, & Wolbers,
2011). Moreover, evidence suggests that socioeconomic inequality is related positively to
educational inequality (Campbell, Haveman, Sandefur, & Wolfe, 2005; Chmielewski &
1
A few studies used cross-national comparative designs, but they did not specifically consider country-specific
determinants of educational achievement and inequality (Alegre & Ferrer, 2010; Benito, Alegre, & Gonzàlez-
Balletbò, 2014; Yang Hansen, Gustafsson, & Rosén, 2014).
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Reardon, 2016; Kearney & Levine, 2014). One explanation for this is that schools may
reproduce or even exacerbate the inequalities that children bring with them (Downey &
Condron, 2016).
In addition, the comprehensiveness of education systems—in terms of the annual
schooling time, preschool enrollment rate, and public expenditure on education—may affect
educational inequality (Burger, 2016a; Pfeffer, 2008; Schütz, Ursprung, & Wössmann, 2008;
Stadelmann-Steffen, 2012). A longer annual schooling time can reduce educational inequality
because children from all social classes share similar learning environments at school, benefit
from similar learning opportunities, and thus make similar learning progress (Ammermüller,
2005; Schlicht, Stadelmann-Steffen, & Freitag, 2010). Preschool enrollment may equalize
educational outcomes among children because children of low socioeconomic status, who often
lag behind in their academic development, typically make greater developmental progress in
preschool programs than their more advantaged peers (Burger, 2010, 2013, 2015, 2016b;
Cebolla-Boado, Radl, & Salazar, 2017). Finally, public expenditure on education is commonly
thought to reduce educational inequality (OECD, 2012; Schütz et al., 2008). Where public
expenditure on education is low, a shift in responsibility from the public to the private sector
may occur, resulting in diverging educational opportunities among social classes, with more
advantaged families being likely to spend more on their children’s education (Schlicht et al.,
2010; Schmidt, 2004).
To identify the unique contribution of social segregation to educational inequality, the
current study distinguishes between social segregation and the above-mentioned economic and
education policy dimensions as potential country-specific sources of educational inequality.
Furthermore, it is essential to recognize that social segregation in education systems
may be related in part to educational tracking (Felouzis & Charmillot, 2013; Pfeffer, 2015), or
allocation of students to different types of schools or curricula that are vertically structured by
student performance and typically prepare students either for further academic or for vocational
programs. This is because a student’s likelihood of transitioning to a given track is to some
extent associated with family background characteristics (Brunello & Checchi, 2007; Lucas,
2001). However, associations between tracking and social segregation differ considerably
across education systems (Alegre & Ferrer, 2010; Chmielewski, 2014; Maaz, Trautwein,
Lüdtke, & Baumert, 2008). Moreover, the degree to which education systems are socially
segregated varies significantly, even among those systems that use comparable tracking regimes
(see Appendix A). For instance, several education systems display comparatively high levels
of social segregation, although they use little or no tracking, which is in part explained by the
7
fact that social segregation is often a result of choices made, whether consciously or
unconsciously, by families who tend to live in socially homogeneous school catchment areas,
or may decide to enroll their children in particular high-performing or private schools
(Lockheed, Prokic-Bruer, & Shadrova, 2015; Saporito & Sohoni, 2007). In addition, research
also suggests that de-tracking schools may lead to an increase in residential segregation (De
Fraja & Martinez Mora, 2012). Consequently, school tracking might actually have a de-
segregating effect, or at least prevent further increases in segregation. In a similar vein, a study
from Japan found that de-tracking reforms can yield unintended consequences, as they may
drive better-performing students out of public schools, and thus exacerbate the divide between
students from different socioeconomic backgrounds (Kariya & Rosenbaum, 1999). In
conclusion, these findings suggest that social segregation within education systems can affect
educational inequality independent of tracking (Esser & Relikowski, 2015; Waldinger, 2006).
Nevertheless, the educational track that a student attends should be considered in any study
designed to assess social disparities in educational outcomes. Thus, we consider whether a
student attended a general academic program (designed to give access to further academic
studies at the next educational level), or a pre-vocational or vocational program (designed to
give access to vocational studies or the labor market).
To conceptualize segregation effects, we draw on the distinction between “Type A” and
“Type B” effects (cf., Raudenbush & Willms, 1995). Type A effects refer to the effects that
school systems have on individual student achievement through both mechanisms they control
(e.g., educational resources) and mechanisms they do not control (contextual effects such as
peer influences). By contrast, Type B effects refer to the controllable effects alone (Castellano,
Rabe-Hesketh, & Skrondal, 2014). We study Type A effects of school system segregation,
which represent both controllable and uncontrollable influences on student achievement. This
allows us to assess the net effect of segregation, which corresponds to the sum of positive and
negative effects of segregation, adjusted for observable potential confounders.
It is clear that non-experimental research examining segregation effects typically cannot
exclude selection bias. Social segregation in education systems may generate disparities in
student achievement. However, achievement disparities may as well reflect preexisting
differences between students (i.e., differences not related to the exposure to socially segregated
schools). For instance, family characteristics such as social and economic resources contribute
to residential and school district choice and to children’s educational achievement, which
complicates the estimation of genuine segregation effects. Previous research from the United
States used measures of local government fragmentation prior to the observation period as
8
instruments for segregation, indicating that segregation does have a causal effect on inequalities
in educational attainment (Quillian, 2014). However, identifying robust instruments is difficult
(Owens, 2018). Here we use a comparative approach and standardized international student
assessment data to study whether social segregation within education systems moderates micro-
level associations between socioeconomic status and educational achievement under ceteris
paribus conditions—when observable country-, school-, and individual-level determinants of
student achievement are taken into account. We argue that social segregation within education
systems contributes to social disparities in educational achievement by increasing inequalities
between disadvantaged and advantaged schools. Schools draw on social, economic, and cultural
resources of families informally, and we expect that an unequal distribution of such resources
will intensify disparities in learning environments and educational opportunities, ultimately
exacerbating social inequality in student achievement. In view of the challenges that potential
selection effects present, the results of our study provide empirical evidence consistent with,
but not definitively demonstrating, a causal association between social segregation in education
systems and social inequality in educational achievement.
4. Method
4.1. Data
The data are drawn from the 2012 wave of the Program for International Student Assessment
(PISA), a cross-national comparative survey that has analyzed 15 year olds’ achievement in
mathematics, science, and reading in a three-year cycle since 2000, with a special focus on one
of these subjects in each wave, which was here mathematics. PISA uses a stratified sampling
procedure and, in the first stage, schools with 15-year-old students are selected with a
probability proportional to the size of the school (primary sampling units). In the second stage,
students are selected at random within schools. The sample used here comprises 29 European
countries with 171,159 students (50.5% male) from 7,301 schools.
2
Table 1 summarizes the
2
Thirty-one European countries participated in the 2012 PISA wave. Liechtenstein was excluded owing to its
small sample size. Italy was excluded because it contained 6.2% of schools in which fewer than 20 students
participated in the survey, but analyses including Italy yield virtually identical results and lead to the same
conclusions. It should also be noted that schools are not necessarily comparable across all countries. This is
exemplified by the fact that, in some countries, schools were defined as administrative units that can consist of
several buildings. In others, individual buildings were defined as schools. Of the 29 countries included in our
9
number of students and schools for each country. The PISA final student weights are applied
so that the sample of each country reflects the total population of 15-year-old students within
each country (see OECD, 2009b, p. 47ff.). These weights are inversely proportional to the
probability of selecting a given student into the PISA sample, which considers the probability
of selecting the school within a country as well as the individual student within a school.
Table 1
Number of schools and students in the sample.
Country
N schools
N students
Austria
191
4,251
Belgium
287
7,452
Bulgaria
187
4,952
Croatia
163
4,846
Czech Republic
297
5,072
Denmark
341
6,546
Estonia
206
4,562
Finland
311
8,447
France
226
4,178
Germany
230
3,632
Great Britain
507
11,524
Greece
188
4,816
Hungary
204
4,633
Iceland
134
3,275
Ireland
183
4,770
Latvia
211
4,071
Lithuania
216
4,278
Luxembourg
42
4,282
Netherlands
179
4,089
Norway
197
4,338
Poland
184
4,372
Portugal
195
4,933
Romania
178
4,983
Serbia
153
4,438
Slovakia
231
4,452
Slovenia
338
5,578
Spain
902
24,037
Sweden
209
4,155
Switzerland
411
10,197
Total
7,301
171,159
sample, 23 used individual schools as the primary sampling unit, whereas six used educational programs or tracks
within schools as the primary sampling units (BEL, HRV, HUN, NLD, ROU, SVN).
10
4.2. Measures
This section describes the variables used in this study. Table 2 displays the descriptive statistics
of these variables, pooled across countries; Table 3 displays the descriptive statistics of the
individual- and school-level variables for each country separately; Table 4 displays the
descriptive statistics of the dependent variable (5 plausible values) for each country.
Table 2
Descriptive statistics.
Predictor variables
Mean
SD
Min.
Max.
Individual level
Male
0.50
---
0
1
First-generation immigrant
0.05
---
0
1
Language spoken at home: same as test language
0.88
---
0
1
School grade relative to modal grade
-0.07
0.58
-3
2
Pre-vocational or vocational program (a)
0.20
---
0
1
Socioeconomic status (SES)
0.02
0.94
-5.95
3.27
School level
School type: private school (b)
0.19
---
0
1
Proportion of first-generation immigrants in school
0.05
0.04
0
1
School socioeconomic composition
-0.17
0.28
-1.11
1.24
Country level
Gross domestic product (GDP) per capita
104.15
43.00
38.00
264.00
Income inequality: Gini coefficient (c)
30.09
3.84
23.50
38.00
Annual taught time in compulsory education
816.13
103.13
555.00
1010.40
Preschool enrollment rate
93.05
6.72
69.53
99.50
Educational expenditure (as % of the GDP)
1.76
0.34
1.00
2.53
Social segregation within the education system
0.24
0.08
0.09
0.46
Dependent variable
Mean
SD
Min.
Max.
Student achievement: Plausible value 1
493.26
93.30
95.19
896.80
Student achievement: Plausible value 2
493.22
93.36
43.78
857.85
Student achievement: Plausible value 3
493.31
93.31
83.28
865.56
Student achievement: Plausible value 4
493.18
93.37
102.98
867.20
Student achievement: Plausible value 5
493.32
93.41
88.34
849.36
Note: N = 171,159. Descriptive statistics of binary and un-centered continuous variables. The continuous variables
were grand-mean centered for the analyses. (a) The reference category is “general academic program”. (b) As
opposed to public schools, private schools are funded by fees paid by parents (entirely if they are government-
independent, partially if they are government-dependent). (c) Gini coefficient of equivalized disposable income
(higher values of indicate greater inequality in disposable household income).
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4.2.1. Dependent variable. The dependent variable is student achievement, estimated using the
PISA measurement of math proficiency. In PISA, math proficiency is conceptualized as an
individual’s capacity to formulate, interpret, and deploy mathematics in a variety of contexts,
which involves the application of important mathematical concepts, knowledge, and skills to
solve everyday problems (OECD, 2013). Although math proficiency constitutes only one aspect
of student achievement, it is considered as a particularly suitable subject for comparative
purposes across educational systems, in particular because several educational systems contain
large proportions of immigrant students whose language proficiency may vary considerably
(Levels, Dronkers, & Kraaykamp, 2008). Math proficiency is also used as a proxy for student
achievement to compare with findings from previous studies (Schlicht et al., 2010; Stadelmann-
Steffen, 2012). Math proficiency is estimated in the form of five plausible values, which
represent the range of abilities that a student can be expected to have, given the student’s
responses to the PISA test items (Wu, 2005). To determine population statistics, each plausible
value is first used separately in any analysis. Using Rubin’s rule (1987), the results of these
analyses are then averaged in order to produce the final statistics (OECD, 2009a). By employing
plausible values instead of raw estimates of student achievement, we minimize the effect of
measurement error bias in the outcome variable.
4.2.2. Independent variable. The independent variable is students’ socioeconomic status (SES),
measured using an index that considers parents’ occupational status (the international
socioeconomic index of occupational status, HISEI), parents’ educational level (number of
years in education according to the international standard classification of education, ISCED),
and home possessions (a construct consisting of items assessing family wealth, cultural
possessions, educational resources, and the number of books at home). In the PISA dataset, this
is known as the index of economic, social, and cultural status (ESCS). This index is comparable
across countries, as determined by similar scale reliabilities (Cronbach’s α) across countries, as
well as through principal component analyses, performed separately for each country,
indicating that across countries the three components—parental occupational status, parental
education, and home possessions—had very similar loadings on the index of economic, social,
and cultural status, and thus correlated to a very similar degree with this index (OECD, 2014,
p. 352).
4.2.3. Central moderator variable. The key variable assumed to moderate the individual-level
relationship between SES and educational achievement is an index of social segregation within
12
national education systems (see Table 5). This index is estimated by means of intra-class
correlations of SES, using a multilevel modeling approach in line with previous studies (Ferrer-
Esteban, 2016; Goldstein & Noden, 2003; Mayer, 2002). The intra-class correlation (ICC)
measures the degree to which SES varies between, as opposed to within, schools. A high ICC
indicates high within-school similarity of students, meaning that students within a given school
are more similar in terms of SES to students within their school than to those in other schools.
The ICC can also be interpreted as the proportion of variance in SES that lies between schools.
Mathematically, it corresponds to the ratio of the school-level variance in SES to the total
variance in SES within a country. In order to partition the total variation in SES within a country
into two variance components—within schools and between schools—we use an unconditional
multilevel regression model with SES as the outcome and with a random intercept at the student
level and a random intercept at the school level, performed separately for each country. This
model is specified as
SESij = β0j + εij
(eq. 1)
with β0j = α00 + μ0j
(eq. 2)
where, at the individual level, SESij is the socioeconomic status of student i in school j, β0j is
the mean SES in school j, and εij is the deviation of the SES of student i from the school mean,
or the residual error (eq. 1). At the school level, α00 is the grand mean, and μ0j is the deviation
of the mean SES of school j from the grand mean, or the residual error (eq. 2). The variances
of the residual errors εij and μ0j are assumed to have a normal distribution with a mean of zero
and to be mutually independent. They are denoted as
and
, respectively, and are also
referred to as variance components. As noted above, the ICC corresponds to the ratio of the
school-level variance in SES to the total variance in SES within a country. Thus, it is calculated
as ρ =
/ (
+
), where
is the school-level variance and
is the individual-
level variance in SES.
The intra-class correlation of SES is a standard index of social segregation within
education systems (Agirdag, Van Avermaet, & van Houtte, 2013; Goldstein & Noden, 2003;
Modin, Karvonen, Rahkonen, & Östberg, 2015; Palardy, Rumberger, & Butler, 2015). There
are various other indices of segregation available (Duncan & Duncan, 1955; Gorard & Taylor,
2002; Hutchens, 2004; Jenkins et al., 2008; Reardon & Bischoff, 2011). However, typically,
and in contrast to the applied index, they are a function of observed proportions, such as poor
versus non-poor children in schools, and thus based on dichotomous measures (Leckie,
13
Pillinger, Jones, & Goldstein, 2012). The intra-class correlation relies on a continuous scale,
which captures the entire distribution of socioeconomic origin. This allows us to determine to
what extent students are socially dissimilar (segregated) between schools without determining
a cut-off value to differentiate students into broad socioeconomic categories. As any other index
of segregation, the intra-class correlation of SES provides an estimate of the unevenness in the
distribution of students across schools.
4.2.4. Alternative country-level influences on educational inequality. In addition to the index of
social segregation, the analysis includes the following country-level variables to evaluate their
effects on student achievement and whether they moderate the relationship between SES and
student achievement. As a measure of a country’s economic development, we consider the
gross domestic product (GDP) per capita in purchasing power standard (averaged across the
years 2003 through 2011, the period preceding the PISA assessment during which the students
attended compulsory school; data from Eurostat, 2017). As a measure of socioeconomic
inequality, we consider the level of income inequality within the population, notably the Gini
coefficient of equivalized disposable income (averaged across the years 2005 to 2012, given
the availability of data for this period; data from Eurostat, 2018).
3
To take into account the
amount of time that children spent in school annually in a given education system, we use the
annual taught time (in hours of 60 minutes), averaged across the compulsory education years
(2003—2011; data from Eurydice, 2013).
4
The preschool enrollment rate is estimated based on
data from the PISA database. It refers to the proportion of students who had been enrolled in
preschool (ISCED 0) for any given duration, in contrast to students who had never been
enrolled. Finally, we assess the public educational expenditure on compulsory education
(ISCED 1—4) as the percentage of the gross domestic product (GDP; averaged across the
period 2003—2011; data from Eurostat, 2017) (see Table 2). To avoid model overspecification,
we also perform models with only selected country-level variables, as explained in Section 6.
4.2.5. Control variables at the individual and school level. At the individual level, the analysis
controls for gender, immigrant status, language spoken at home, the school grade in which a
student is enrolled at the time of the assessment (school grade level), and whether a student
attended (0) a general academic program or (1) a pre-vocational or vocational program, because
3
Data for Serbia refer to 2013, owing to missing values for the preceding years.
4
Data for Serbia are derived from OECD (2011), data for Switzerland from UNESCO (2011).
14
these variables have a direct effect on student achievement (Burger & Walk, 2016; Schlicht et
al., 2010). At the school level, the analysis controls for school type (public vs. private), the
proportion of first-generation immigrants in school, and school socioeconomic composition
(the aggregate SES of a school’s student population) in order to account for their hypothesized
effects on student achievement. All control variables are derived from the PISA database.
15
Table 3
Descriptive statistics for the individual- and school-level variables, by country.
Country
Individual level
School level
Male
First-
generation
immigrant
Language at
home: same
as test
language
School grade
relative to
modal grade
(Pre-)
vocational
program
Socioeconomic
status (SES)
School type:
private school
Proportion of
first-generation
immigrants in
school
School
socioeconomic
composition
Mean
Mean
Mean
Mean (SD)
Mean
Mean (SD)
Mean
Mean (SD)
Mean (SD)
Austria
0.50
0.05
0.89
-0.51 (0.57)
0.37
0.11 (0.83)
0.09
0.04 (0.02)
-0.26 (0.21)
Belgium
0.50
0.08
0.78
-0.42 (0.65)
0.18
0.18 (0.91)
0.21
0.05 (0.02)
-0.14 (0.29)
Bulgaria
0.52
0.01
0.90
0.00 (0.33)
0.00
-0.23 (1.02)
0.08
0.04 (0.02)
-0.26 (0.21)
Croatia
0.50
0.04
0.99
0.20 (0.34)
0.23
-0.35 (0.85)
0.08
0.04 (0.02)
-0.29 (0.19)
Czech Republic
0.50
0.02
0.97
0.41 (0.57)
0.09
0.06 (0.76)
0.22
0.05 (0.02)
-0.13 (0.30)
Denmark
0.50
0.07
0.87
-0.18 (0.42)
0.00
0.28 (0.91)
0.27
0.05 (0.03)
-0.10 (0.30)
Estonia
0.50
0.01
0.94
-0.21 (0.45)
0.02
0.15 (0.13)
0.10
0.04 (0.02)
-0.24 (0.22)
Finland
0.51
0.08
0.83
-0.19 (0.43)
0.00
0.35 (0.83)
0.23
0.05 (0.02)
-0.12 (0.29)
France
0.49
0.05
0.92
-0.27 (0.56)
0.14
-0.02 (0.80)
0.11
0.04 (0.02)
-0.22 (0.22)
Germany
0.51
0.03
0.93
0.27 (0.67)
0.02
0.19 (0.93)
0.12
0.04 (0.02)
-0.20 (0.26)
Great Britain
0.50
0.05
0.93
0.16 (0.40)
0.98
0.24 (0.81)
0.35
0.06 (0.04)
-0.02 (0.32)
Greece
0.50
0.06
0.95
-0.05 (0.27)
0.15
-0.05 (0.99)
0.09
0.04 (0.02)
-0.27 (0.20)
Hungary
0.47
0.01
0.99
0.16 (0.54)
0.15
-0.20 (0.94)
0.09
0.04 (0.02)
-0.23 (0.22)
Iceland
0.50
0.03
0.96
0.00 (0.00)
0.00
0.78 (0.81)
0.07
0.05 (0.02)
-0.30 (0.18)
Ireland
0.49
0.04
0.95
0.46 (0.73)
0.24
0.13 (0.85)
0.09
0.04 (0.02)
-0.27 (0.20)
Latvia
0.49
0.00
0.90
-0.12 (0.45)
0.00
-0.18 (0.87)
0.09
0.04 (0.02)
-0.25 (0.21)
Lithuania
0.51
0.00
0.97
0.05 (0.43)
0.00
-0.13 (0.91)
0.10
0.04 (0.02)
-0.22 (0.22)
Luxembourg
0.51
0.17
0.14
0.27 (0.67)
0.06
0.08 (1.10)
0.10
0.06 (0.03)
-0.28 (0.15)
Netherlands
0.52
0.03
0.94
0.44 (0.57)
0.53
0.21 (0.78)
0.08
0.05 (0.02)
-0.28 (0.20)
Norway
0.51
0.05
0.92
0.00 (0.07)
0.00
0.47 (0.76)
0.09
0.05 (0.02)
-0.26 (0.21)
Poland
0.48
0.00
0.99
-0.04 (0.23)
0.00
-0.16 (0.92)
0.09
0.04 (0.02)
-0.28 (0.20)
Portugal
0.50
0.04
0.97
-0.56 (0.76)
0.16
-0.48 (1.17)
0.09
0.05 (0.02)
-0.25 (0.21)
Romania
0.49
0.00
0.98
0.00 (0.32)
0.95
-0.46 (0.93)
0.09
0.04 (0.02)
-0.28 (0.19)
Serbia
0.49
0.02
0.96
0.01 (0.16)
0.76
-0.30 (0.90)
0.08
0.04 (0.02)
-0.30 (0.19)
Slovakia
0.52
0.00
0.93
-0.46 (0.68)
0.09
-0.15 (0.92)
0.12
0.04 (0.02)
-0.22 (0.26)
Slovenia
0.54
0.03
0.93
0.02 (0.21)
0.63
-0.02 (0.85)
0.27
0.05 (0.02)
-0.10 (0.28)
Spain
0.50
0.09
0.86
-0.38 (0.64)
0.01
-0.11 (1.00)
0.35
0.07 (0.09)
-0.06 (0.37)
Sweden
0.50
0.06
0.90
-0.02 (0.23)
0.00
0.29 (0.81)
0.10
0.04 (0.02)
-0.24 (0.22)
Switzerland
0.50
0.08
0.83
-0.02 (0.53)
0.03
0.11 (0.87)
0.35
0.05 (0.04)
-0.05 (0.30)
Note: SD = Standard deviation. Descriptive statistics for pooled data across countries reported in Table 2.
16
Table 4
Descriptive statistics for the dependent variable ‘student achievement’ (5 plausible values), by country.
Country
Plausible values (PV)
PV1
PV2
PV3
PV4
PV5
Mean (SD)
Mean (SD)
Mean (SD)
Mean (SD)
Mean (SD)
Austria
507.71 (91.16)
507.53 (90.85)
507.84 (90.64)
507.76 (91.25)
508.05 (90.32)
Belgium
520.38 (101.49)
519.52 (101.13)
519.61 (101.54)
519.92 (101.48)
519.25 (101.97)
Bulgaria
442.16 (92.64)
442.38 (92.78)
442.95 (92.52)
442.70 (93.23)
442.16 (93.50)
Croatia
469.83 (86.70)
469.98 (87.52)
470.10 (88.02)
469.74 (87.50)
470.21 (87.43)
Czech Republic
519.77 (96.69)
520.76 (96.86)
520.12 (96.90)
520.32 (96.90)
519.31 (97.03)
Denmark
486.19 (86.59)
486.35 (85.71)
486.23 (86.10)
486.39 (86.70)
486.05 (86.25)
Estonia
521.81 (80.26)
522.36 (81.18)
522.48 (81.01)
522.11 (79.82)
522.95 (81.21)
Finland
507.53 (89.86)
506.94 (89.75)
506.94 (89.34)
507.16 (89.45)
507.30 (89.56)
France
499.47 (96.98)
497.73 (96.58)
498.26 (96.64)
497.97 (96.32)
498.44 (96.58)
Germany
513.93 (96.74)
513.79 (96.26)
513.55 (96.94)
514.12 (96.66)
513.97 (96.39)
Great Britain
489.65 (91.12)
489.52 (91.22)
489.55 (91.11)
489.67 (91.30)
490.24 (91.11)
Greece
453.89 (87.57)
453.23 (87.97)
453.77 (87.13)
453.07 (87.85)
453.61 (87.81)
Hungary
485.39 (91.34)
485.19 (91.38)
484.41 (91.27)
484.56 (91.01)
484.79 (90.64)
Iceland
493.15 (92.38)
492.21 (91.13)
492.62 (91.31)
493.22 (91.61)
493.43 (92.84)
Ireland
500.90 (84.51)
500.98 (84.20)
501.55 (84.51)
501.32 (84.85)
501.61 (84.78)
Latvia
495.45 (80.97)
495.70 (80.95)
495.34 (80.31)
495.68 (80.66)
495.52 (81.32)
Lithuania
478.68 (88.70)
479.12 (89.33)
479.58 (88.74)
479.45 (88.82)
479.37 (89.11)
Luxembourg
490.27 (95.33)
491.63 (95.67)
490.24 (95.31)
490.20 (96.05)
490.08 (95.05)
Netherlands
518.13 (92.60)
518.11 (92.56)
518.43 (92.58)
518.80 (92.27)
519.22 (92.18)
Norway
489.75 (89.84)
489.37 (89.45)
489.12 (90.07)
489.29 (89.68)
489.20 (90.41)
Poland
520.59 (91.15)
520.38 (90.75)
520.46 (91.15)
520.37 (91.21)
520.82 (91.23)
Portugal
484.56 (93.93)
484.89 (93.97)
485.73 (93.99)
485.34 (93.76)
485.09 (93.41)
Romania
445.78 (80.36)
444.28 (80.46)
445.48 (80.67)
445.36 (80.60)
445.53 (80.41)
Serbia
447.74 (89.43)
447.90 (90.18)
447.23 (89.75)
447.29 (89.70)
447.14 (89.99)
Slovakia
485.64 (102.24)
485.49 (101.42)
486.35 (101.85)
485.32 (100.73)
485.54 (102.06)
Slovenia
484.48 (89.50)
484.55 (89.88)
484.33 (89.95)
484.33 (90.28)
484.96 (90.15)
Spain
495.36 (88.43)
495.63 (88.67)
495.59 (88.35)
495.25 (88.43)
495.36 (88.50)
Sweden
479.15 (90.66)
478.79 (91.53)
479.40 (91.32)
479.23 (91.58)
479.62 (90.89)
Switzerland
520.67 (92.62)
521.25 (92.73)
520.94 (92.99)
520.83 (92.80)
521.15 (92.85)
Note: SD = Standard deviation.
17
4.3. Analytic strategy
First, we apply bivariate analysis to assess the extent to which social segregation is related to
social inequality in student achievement at the macro level of European education systems. In
this analysis, we calculate a country-specific index of social inequality in achievement, which
corresponds to the coefficient of an ordinary least-squares (OLS) regression predicting math
achievement as a function of SES, while controlling for gender, home language, immigrant
background, and school grade (coefficients reported in Table 5). To obtain this index, we
perform an OLS regression (for each country separately), because we focus solely on
individual-level variables, whereas in further analyses we will perform multilevel regressions,
which also include additional—school- and country-level—variables. The PISA final student
weights are applied in this regression analysis, resulting in coefficients that are representative
for each country.
Second, we perform multilevel (linear mixed-effects) models to ascertain whether social
segregation moderates individual-level associations between SES and educational achievement.
Multilevel models take into account that the data are hierarchically clustered—students in
schools, and schools in countries—meaning that the observations in the sample cannot be
considered as being independent (Snijders & Bosker, 2012). Standard (OLS) regression models
rely on the assumption of independence of the observations. With a hierarchical data structure,
this assumption is violated and hence the estimates of the standard errors of standard models
will be too small, which may lead to spuriously significant results (Hox, 2010). Multilevel
models allow for the simultaneous estimation of the direct effects of individual-, school-, and
country-level variables on student achievement, as well as to evaluate whether social
segregation within education systems strengthens the micro-level associations between social
origin and student achievement. The final model is represented as:
(eq. 3)
The educational achievement Y of a student i in school j in country k is estimated as a function
of the overall mean achievement across countries (β000), a vector of individual-level variables
(Xhijk to Xlijk) with their coefficients (βh to βl), a vector of school-level variables (Smjk to Sojk) with
their coefficients (αm to αo), and a vector of country-level variables (Cpk to Cuk) with their
coefficients (δp to δu). The model also includes a vector of cross-level interactions between the
18
individual-level variable ‘socioeconomic status’ and the country-level variables (Xlijk · Cvk),
with the respective coefficients (γv to γz). Furthermore, by including a random slope μ1jk ~ N(0,
1jk) on ‘socioeconomic status’ (Xlijk) at the school level, the model considers that the
association between socioeconomic status and student achievement differs between schools.
The random slope is determined by a fixed effect for the school average on socioeconomic
status and a random effect that defines the variance in the slopes between schools, as denoted
by the term (β010 + μ1jk) Xlijk, where β010 represents the slope on socioeconomic status (Xlijk) for
the average school and
1jk represents the between-school variance in this slope. Three random
terms are associated with the intercept and fixed effects, reflecting the remaining or residual
variation at the country level, ν0k ~ N(0,
0k), at the school level, μ0jk ~ N(0,
0jk), and at the
student level, ε0ijk ~ N(0,
0ijk). These random terms are assumed to have zero means given the
independent variables, to be drawn from normally distributed populations, and to be mutually
independent. The model allows for a correlation between the school-level variance in math
achievement (random intercept), ν0k, and the random slope on socioeconomic status at the
school level, μ1jk, thereby taking into account that any relationship between socioeconomic
status and student achievement may vary across schools. We use un-centered binary variables
and grand-mean centered continuous variables. There were no collinearity issues in the model,
with all variance inflation factors being below 2.39.
In conclusion, our aim is to exploit variation in the level of social segregation within
education systems across countries to describe systematic patterns of covariation between social
segregation and educational inequality, when observable potential confounders are considered.
Our models do not differentiate statistically between the effects of the systematic underlying
processes that lead to segregated schools (such as the intertwined residential and school choice
decisions of families and schools’ decisions regarding which students to admit), and the effects
of exposure to segregated schools (cf., Leckie et al., 2012). We argue that student achievement
and educational inequality are shaped by both such underlying processes and exposure to
segregated schools. Accordingly, the estimates of the models reported hereafter may be
interpreted as estimates of the combined influence of ‘selection’ into schools and ‘treatment’,
or exposure to socially homogeneous or heterogeneous student populations, in these schools,
under ceteris paribus conditions.
5
5
Given the cross-sectional nature of PISA, there is no direct measure of prior student achievement in the dataset.
Following prior research using PISA data, we include school grade at assessment as a rough (in fact, the only
available) proxy for prior student performance, presuming that 15 year olds who were enrolled in lower grades at
19
5. Results
Table 5 displays the index of social segregation within education systems and the index of social
inequality in achievement for each country.
The index of social segregation varies between 0.090 and 0.456. Greater values indicate
that students of a given socioeconomic-status group were found to a greater degree in distinct
schools and thus isolated from students of a different socioeconomic-status group. Levels of
social segregation were relatively low in Norway, Finland, and Sweden, whereas they were
considerably higher, for instance, in Slovakia, Hungary, and Bulgaria.
The index of social inequality in achievement is a measure of the relationship between
SES and the level of student achievement. It ranges from 15.60 in Spain to 51.67 in the Czech
Republic. That is, on average across European countries, a one-unit increase in SES was related
to a 31.48-point better achievement, or roughly a 0.31 standard-deviation improvement in
achievement. The variation in the indices of social inequality in achievement between countries
contributes to discussion on the degree to which student achievement is a result of inherited
ability, providing the basis for a predisposition to learning, and/or of socialization and
environmental influences (e.g., Nielsen, 2006). The degree of social inequality in achievement
varied considerably across countries, which implies that any predisposition derived from the
family context or otherwise cannot be the sole determinant of educational achievement.
Because country-specific differences in educational inequality cannot be ascribed to any genetic
or social inheritance, the macro environment seemed to play a decisive role in shaping this
inequality.
the time of the assessment had performed worse in previous years (Chiu, 2010; Lee, Zuze, & Ross, 2005). We
acknowledge the limitations of our approach in Section 6.
20
Table 5
Index of social segregation within the education system, index of social inequality in
educational achievement.
Country
Index of social
segregation
Index of social inequality in
achievement (SE)
Austria
0.311
33.60
(1.54)
Belgium
0.282
27.84
(1.00)
Bulgaria
0.456
38.12
(1.12)
Croatia
0.229
34.44
(1.36)
Czech Republic
0.276
51.67
(1.53)
Denmark
0.187
32.56
(1.06)
Estonia
0.197
28.76
(1.37)
Finland
0.101
28.62
(1.05)
France
0.278
34.34
(1.46)
Germany
0.277
32.09
(1.46)
Great Britain
0.182
39.26
(0.94)
Greece
0.292
32.40
(1.17)
Hungary
0.379
41.45
(1.21)
Iceland
0.150
29.34
(1.90)
Ireland
0.211
38.70
(1.30)
Latvia
0.254
30.23
(1.29)
Lithuania
0.246
33.75
(1.33)
Luxembourg
0.280
23.71
(1.10)
Netherlands
0.183
31.80
(1.64)
Norway
0.090
30.48
(1.73)
Poland
0.312
39.61
(1.32)
Portugal
0.288
19.22
(0.86)
Romania
0.401
37.20
(1.10)
Serbia
0.218
32.33
(1.40)
Slovakia
0.357
45.16
(1.47)
Slovenia
0.242
34.87
(1.30)
Spain
0.232
15.60
(0.47)
Sweden
0.139
29.48
(1.58)
Switzerland
0.146
26.24
(0.95)
Average
0.248
31.48
(0.19)
Note: Information about the indices in section 4.2.
21
The correlation between the index of social segregation within education systems and the index
of social inequality in achievement (r(27) = 0.372, p < .05) provides an estimate of the extent
to which social segregation in education systems was related to social gradients in student
achievement at the aggregate level of European education systems (see also Fig. 1). The
moderate positive relationship identified here supports theory in respect to social class
inequalities in education being more pronounced in those education systems where
socioeconomically diverse students are less evenly distributed across schools.
Figure 1. Scatterplot of the index of social segregation and the index of social
inequality in achievement. Abbreviations: AUT: Austria, BEL: Belgium, BGR:
Bulgaria, CHE: Switzerland, CZE: Czech Republic, DEU: Germany, DNK:
Denmark, ESP: Spain, EST: Estonia, FIN: Finland, FRA: France, GBR: Great
Britain, GRC: Greece, HRV: Croatia, HUN: Hungary, IRL: Ireland, ISL: Iceland,
LTU: Lithuania, LUX: Luxembourg, LVA: Latvia, NLD: Netherlands, NOR:
Norway, POL: Poland, PRT: Portugal, ROU: Romania, SRB: Serbia, SVK:
Slovakia, SVN: Slovenia, SWE: Sweden.
However, the bivariate relationship between social segregation within education systems and
social inequality in achievement does not allow us to gauge whether social segregation
moderates social inequality in educational achievement. Thus, we also estimated a series of
multilevel models to determine whether the strength of the relationship between SES and
educational achievement at the individual level varies across education systems that exhibit
22
different levels of social segregation, when potential alternative influences are considered at the
individual, school, and country levels.
The dependent variable had complete data for all of the students in the sample; however
three individual-level covariates contained missing values—school grade (0.4%), immigrant
status (2.6%), and SES (1.9%). Assuming that the probability of a missing value on these
variables was not conditional on unobserved values of these variables, given the observed
values (Rabe-Hesketh & Skrondal, 2008; Rubin, 1976), we performed multilevel analyses using
full maximum likelihood estimation, which is widely considered to provide robust estimations
if the assumed model is accurate. Furthermore, this allowed us to compare the goodness of fit
of several models through likelihood ratio tests (Muthén & Shedden, 1999; Schafer & Graham,
2002). In robustness analyses, we also replaced missing data with imputed data, computing
maximum likelihood estimates through the expectation-maximization algorithm, which allows
for estimation of parameters in a probabilistic model (Do & Batzoglou, 2008). These additional
analyses confirmed the conclusions that we draw from the analyses presented hereafter.
Table 6 summarizes the results of four increasingly complex multilevel models. The
unconditional (or null) model—with only intercepts at the individual, school, and country level,
and student achievement as the outcome—reveals that 5.6% of the variance in student
achievement was at the country level, whereas 12.7% was at the school-within-country level.
However, variance components between schools and countries can only be reasonably
interpreted when school grade level is considered, given that school grade level explains a large
proportion of the variance in student achievement. Thus, in a quasi-unconditional model (not
shown), which included school grade as the only predictor, we found that 9.9% of the variance
in student achievement was at the country level, whereas 15.3% was at the school-within-
country level. This result implies that student achievement scores varied systematically not only
at the individual level, but also between schools and countries.
23
Table 6. Multilevel models predicting student achievement.
Model 0
Model 1
Model 2
Model 3
Coefficient
(SE)
Coefficient
(SE)
Coefficient
(SE)
Coefficient
(SE)
Fixed effects
Intercept
491.94***
(4.34)
489.30***
(4.83)
491.61***
(4.64)
491.70***
(4.71)
Individual level
Male
16.67***
(0.37)
16.67***
(0.37)
16.69***
(0.37)
First-generation immigrant
-5.69***
(1.05)
-5.68***
(1.05)
-6.06***
(1.05)
Language spoken at home: same as test language
12.28***
(0.80)
12.29***
(0.80)
12.57***
(0.80)
School grade relative to modal grade
58.04***
(0.38)
58.04***
(0.38)
58.45***
(0.38)
Pre-vocational or vocational program
-70.63***
(0.75)
-70.63***
(0.75)
-71.14***
(0.75)
Socioeconomic status (SES)
25.64***
(0.53)
25.64***
(0.53)
25.89***
(0.53)
School level
School type: private school
0.52
(0.55)
0.52
(0.55)
0.53
(0.55)
Proportion of first-generation immigrants in school
-2.27
(12.13)
-2.31
(12.13)
-6.85
(12.09)
School socioeconomic composition
15.67***
(2.38)
15.67***
(2.36)
16.54***
(2.37)
Country level
Gross domestic product (GDP) per capita
-0.13
(0.14)
-0.11
(0.14)
Income inequality: Gini coefficient
-0.54
(1.45)
-0.47
(1.47)
Annual taught time in compulsory education
0.10
(0.05)
0.10
(0.05)
Preschool enrollment rate
0.57
(0.68)
0.59
(0.70)
Educational expenditure (as % of the GDP)
-5.59
(17.41)
-6.09
(17.68)
Social segregation within the education system
-57.43
(73.93)
-51.66
(75.08)
Cross-level interactions
SES x GDP per capita
-0.05***
(0.01)
SES x Income inequality
0.33***
(0.10)
SES x Annual taught time
-0.03***
(0.00)
SES x Preschool enrollment rate
0.37***
(0.05)
SES x Educational expenditure
11.70***
(0.91)
SES x Social segregation in the education system
24.35***
(5.21)
Random effects
Variance
(SD)
Variance
(SD)
Variance
(SD)
Variance
(SD)
Individual-level variance (SD)
7,977.4
(89.32)
129,723.2
(360.17)
129,723.3
(360.17)
129,481.3
(359.84)
School-level variance (SD)
644.1
(25.38)
398.6
(19.96)
398.6
(19.96)
394.4
(19.86)
Country-level variance (SD)
514.7
(22.69)
613.4
(26.15)
512.3
(22.63)
528.6
(22.99)
Random slope on SES at the school level (SD)
108.3
(10.41)
108.3
(10.41)
95.5
(9.77)
Correlation between the school-level variance (random intercept)
and the random slope on SES
0.14
0.14
0.14
Log-likelihood
-1,100,952
-1,034,846
-1,034,843
-1,034,660
Note: Unstandardized coefficients with standard errors (SE) are reported for the fixed effects. Variances with standard deviations (SD) are reported for the random effects. Maximum-likelihood
estimation was used. The significance of the coefficient estimates of the fixed effects was determined using Wald tests. To partition the variance in student achievement into three components
(at the individual, school and country level), model 0 was calculated with unweighted data. Models 1 to 3 were calculated with weighted data, as explained in section 4.1.
*** p < .001 (two-tailed tests).
24
In Model 1, we added the individual- and school-level predictors. The results of this model
corroborate findings of earlier studies regarding the statistically significant relationships
between student-level characteristics and educational achievement (Levels et al., 2008; Schlicht
et al., 2010). On average, male students outperformed female students, while immigrant
students underperformed. Moreover, students whose home language corresponded to the PISA
test language, and students who were enrolled in higher grades at school, outperformed their
peers who spoke a foreign language at home and were enrolled in lower school grades,
respectively. The relationship between students’ socioeconomic status and their educational
achievement was positive and highly significant. We modeled between-school variation in the
relationship between socioeconomic status and educational achievement by adding a random
slope on socioeconomic status at the school level. That is, because the relationship between
socioeconomic status and educational achievement varied across schools, we allowed the slope
on socioeconomic status to vary across schools. Including this random slope improved the
model fit significantly, as indicated by a likelihood ratio test based on a comparison of the log-
likelihoods of a model without a random slope and a model with a random slope, χ2 (2, N =
171,159) = 1481.5, p < .001 (see Raudenbush & Bryk, 2002, on likelihood ratio tests to compare
the fit of nested models based on model deviance statistics). At the school level, school type
(public vs. private) and the proportion of first-generation immigrants in school were not
significantly related to student achievement, whereas school socioeconomic composition was.
On average, each one-unit increase in school socioeconomic composition was associated with
a 15.67-point improvement in student achievement, controlling for student socioeconomic
status at the individual level and the other covariates in Model 1. This corresponds roughly to
an increase in achievement of a 0.16 standard deviation. Thus, the average difference in
achievement between students attending the most socioeconomically disadvantaged schools
and students attending the most advantaged schools was approximately 36.97 points, or
approximately a 0.37 standard deviation. Figure 2 further illustrates this relationship by
revealing that the school average achievement level was higher in those schools with more
privileged student populations. This finding does not allow for the conclusion that school
socioeconomic composition necessarily caused an improvement in student achievement, given
that PISA did not assess student ability prior to school entry. The higher achievement levels of
schools that draw a majority of their population from more privileged backgrounds could be a
consequence of greater student ability or of peer effects or a combination of both. Hence, Figure
2 does not provide evidence of a school composition effect (see also Pokropek, 2015), but it
does provide descriptive evidence of a positive association between school socioeconomic
25
composition and student achievement levels. Note that the box plots are based on pooled data
from all countries included in the study (countries with a greater number of participating schools
contribute more data points to the analysis; each school has equal weight).
Figure 2. Box plots of the distribution of school average achievement across schools
with varying socioeconomic compositions, divided into quintiles. The horizontal line
within the boxes shows the median. The box edges represent the 1st and the 3rd
quartile. The end of the upper whisker equals (Q3 + 1.5 * IQR), the end of the lower
whisker equals (Q1 – 1.5 * IQR). Observations outside the whiskers are plotted as
circles.
In Model 2, we added all of the country-level variables. This model shows that none of these
variables had a statistically significant direct effect on student achievement. This includes a
non-significant main effect of social segregation within the education system, suggesting that
the level of social segregation within an education system was not significantly related to the
average level of student achievement in a country.
In Model 3, we further included the cross-level interactions between SES and the
country-level variables. Although our main focus here is on the interaction between SES and
social segregation, we briefly summarize the findings regarding the other interactions in a first
step, because all of these interactions were statistically significant. They indicate that the
association between SES and student achievement was weaker in countries with a higher GDP
and a longer annual taught time; however, this association increased with income inequality,
preschool enrollment rates, and educational expenditure. The main finding of Model 3 was that
26
social segregation moderated educational inequality in that the effect of SES on student
achievement was stronger in countries with higher levels of social segregation within the
education system, even when the alternative system-level influences were considered. To assess
the contribution of the moderating effect of social segregation, we performed a likelihood ratio
test, comparing the log-likelihoods of a model that included the cross-level interaction between
socioeconomic status and social segregation, and a model without this interaction term. This
test indicated that adding the cross-level interaction to the model significantly improved the
model fit, χ2 (2, N = 171,159) = 21.7, p < .001. Figure 3 illustrates the interaction between SES
and social segregation, showing how the marginal effect of SES on student achievement
changed as the degree of social segregation within education systems did, when all of the other
variables in the model were kept constant (cf. Preacher, Curran, & Bauer, 2006). The black line
indicates that, on average, a one-unit increase in SES was associated with an increase in student
achievement of approximately 29 points in the least segregated education systems (Norway and
Finland), and of approximately 40 points in the most segregated system (Bulgaria). Expressed
in standard deviation units, an increase in SES by one standard deviation was associated with,
approximately, a 0.29 standard-deviation increase in student achievement in the least
segregated systems, and a 0.40 standard-deviation increase in student achievement in the most
segregated systems. The 95% confidence interval shows that the statistical uncertainty
associated with the coefficients increased slightly as the degree of social segregation within
education systems grew, which can be explained by the smaller number of countries that
exhibited a comparatively high degree of social segregation.
27
Figure 3. Change in the marginal effect of SES on student achievement as the
degree of social segregation within education systems increases.
The individual-, school-, and country-level variances shown in Table 6 represent the effects of
any unobserved covariates at the respective levels. In line with previous empirical studies and
theory (Dronkers, 2010; Schlicht et al., 2010), the unexplained individual-level variance
remained larger than the unexplained variances at the school and country levels. The weak
positive correlation between the school-level variance (random intercept) and the random slope
on SES at the school level (r = 0.14) indicates that the association between SES and student
achievement was slightly stronger in schools with higher levels of average student achievement;
however, differences between schools were negligible given the weak correlation.
We performed robustness tests to check for omitted variable and overspecification bias,
and for variation in the results when using subsets of countries in the analysis. First, we assessed
the sensitivity of the results to changes in model specification by entering additional, potentially
confounding, country-level covariates: (1) an indicator of whether countries used centrally
administered examinations to test student performance, (2) the proportion of schools that used
assessments in order to compare students with national performance, (3) the variance in parental
education attainment (as an inequality measure), and (4) an index of vocational specificity of
the education system (dual system)—using data from PISA, Eurostat (2015), and Bol and Van
de Werfhorst (2013). These variables were not included in the main models because of the
28
unavailability of data for some of the sampled countries. Second, we ran several models in
which we removed country-level variables because theoretically we might risk overspecifying
our model by including six country-level variables simultaneously, although statistically we did
not identify any multicollinearity issues. Third, we performed a type of cross-validation by
replicating the analysis based on reduced datasets, sequentially excluding (1) one country, or
(2) random pairs of countries (50 combinations), or (3) countries with comparatively strongly
decentralized education policies (Austria, Belgium, Germany, Hungary, Switzerland; cf.,
Schlicht et al., 2010) from each replication. All of these additional tests corroborated the results
reported here and lead to the same conclusions.
6. Discussion
Complementing prior research on correlates of socio-spatial separation of students, this study
assessed to what extent social segregation occurred within education systems in Europe, and it
examined patterns of covariation between social segregation within education systems and
social inequality in educational achievement, using a cross-national comparative design that
considered observable potential confounders at the individual, school, and country levels.
The findings indicate that schools were segregated along socioeconomic lines across
European countries, albeit to varying degrees. Although the extent of social segregation was
comparatively small in Scandinavian countries, it was substantially greater in some Central and
Eastern European countries. For instance, it was approximately five times greater in Bulgaria
than in Norway. Moreover, findings suggest that social segregation within education systems
was related to social inequality in student achievement—the higher the level of social
segregation within an education system, the stronger the aggregate-level relationship between
SES and student achievement in a country. However, social gradients in student achievement
could be the result of inequalities within society at large, or of the economic and education
policy context, rather than the consequence of social segregation within the education system.
We therefore examined whether social segregation in education systems moderates social
inequality in student achievement when such country-level influences are considered (see
Appendix B for a discussion of how the alternative country-level influences moderated
educational inequality).
We found that, ceteris paribus, the effect of SES on student achievement was
significantly stronger in education systems with higher levels of social segregation, suggesting
that social segregation within education systems may contribute to the intergenerational
29
transmission of educational (dis)advantage. This finding is in line with research from the United
States revealing that spatial inequalities created by social segregation increase achievement
gaps between advantaged and disadvantaged students (Owens, 2018). Moreover, the finding
casts doubt on the view that the consequences of school segregation are “at the limit of our
detectability” (Gorard, 2006, p. 87). Rather, the present investigation of nationally
representative samples in a cross-national design measurably points toward the fact that social
segregation may amplify inequality in educational outcomes. However, the moderating effect
of social segregation on educational inequality was relatively modest. In the least socially
segregated education systems, a one standard-deviation (SD) increase in SES was associated
with an increase in student achievement by approximately 0.29 SDs, whereas in the most
segregated systems it was associated with an increase in achievement of roughly 0.40 SDs. By
way of comparison, this 0.11-SD difference was somewhat smaller than the 0.18-SD difference
in the effect of SES on achievement that was attributable to variations in the annual taught
time—in those education systems with the least time spent on teaching per year, a 1-SD increase
in SES was associated with an increase in student achievement by 0.37 SDs, whereas in those
systems with the most time spent on teaching per year, a 1-SD increase in SES was associated
with an increase in achievement by 0.19 SDs, keeping all other covariates constant. However,
the 0.11-SD difference attributable to social segregation was larger than the roughly 0.05-SD
difference that was attributable to variations in economic development (GDP). It was also larger
than the 0.05-SD difference attributable to variations in income inequality (Gini) and the 0.06-
SD difference attributable to variations in preschool enrollment rates; finally, it was comparable
in magnitude with the 0.10-SD difference ascribable to variations in educational expenditure.
Multiple sensitivity analyses confirmed the robustness of our findings (see Section 5).
However, it must be acknowledged that estimates of segregation indices based on sample
surveys tend to be biased upward because they capture both the uneven distribution of students
across schools that results from actual segregation processes (i.e., the systematic underlying
processes of segregation such as school choice decisions and residential choices of families)
and the uneven distribution of students across schools that arises as a result of randomness.
Even if students were allocated to schools completely at random, we would measure some
unevenness in the distribution of diverse students across schools simply as a consequence of
random allocation (Leckie et al., 2012; Ransom, 2000). Consequently, differences in the index
of social segregation between countries are in part the result of sampling variability and must
therefore be interpreted with caution. However, an index of segregation that would measure
deviations from randomness, rather than deviations from evenness in the distribution of students
30
across schools (Allen, Burgess, Davidson, & Windmeijer, 2015), would lead to a highly similar
ranking of countries by school segregation, given that PISA sampled approximately the same
number of students per school across countries (we have removed Italy from our analyses
because it contained a relatively large proportion of schools in which fewer than 20 students
participated in the survey). We recognize that for countries with a large average school size the
index of social segregation between schools is expected to be smaller because larger schools
will lead to smaller socioeconomic differences between schools, and greater differences within
schools.
6
However, any measure of segregation that is based on a sample survey, such as PISA,
is subject to sampling variation, and previous research has demonstrated that the number of
schools sampled per country in the PISA survey is sufficiently large to minimize bias to
negligible levels (Jenkins et al., 2008).
It should not be disregarded that social segregation within education systems may be a
consequence of residential segregation, for instance, where particular schools are in more
affluent catchment areas, while others are found in districts with a high level of social housing
(Croxford & Paterson, 2006; Dupriez & Dumay, 2006; Ferrer-Esteban, 2016). Moreover, the
reputation of the school may well give rise to residential segregation, with property markets
responding to demand from families (Gorard, 2000; Kane, Riegg, & Staiger, 2006; Leech &
Campos, 2001). Thus, the relationship between school social segregation and residential
segregation may be theoretically conceived of as a reciprocal relationship of mutual
determination between school and housing “markets” (Taylor & Gorard, 2001). There are
currently no standardized cross-national data that could be cross-referenced at a European level
with the data on the schools from the PISA survey. Our research therefore cannot distinguish
between residential and school segregation. The essential question that it does address,
however, is whether the clustering of children along social background lines—as observed in
education systems—strengthens the relationship between social origin and educational
achievement, with the results indicating that this is the case.
Finally, and as previously mentioned, it is important to be aware that effects of social
segregation between schools on social inequality in achievement may be mediated by school
characteristics, such as academic entry requirements or overall ability levels (e.g., Harris &
Williams, 2012; Liu, Van Damme, Gielen, & Van Den Noortgate, 2015). Experimental
6
Analyses in which the countries with the largest average school sizes were excluded (LUX, NLD, ROU, GBR;
Eurydice, 2012) provided evidence of a slightly stronger interaction effect between socioeconomic status and
social segregation within education systems than was the case with the interaction effect presented here.
31
longitudinal studies would provide the opportunity to examine causal mediation effects.
However, such studies may pose significant ethical challenges and are therefore not necessarily
feasible. With this in mind, the value of the PISA data for cross-national comparative analyses
is substantial. Parallel data extending across European countries are rare. Thus, the standardized
international assessments provide unique data for analyzing educational inequalities, where
otherwise only smaller and non-representative samples were available (Hanushek &
Wössmann, 2014). These large-scale assessments allow for exploring variation that exists only
across countries. Even if the degree of social segregation may vary across areas within
countries, variation between European countries is considerable and therefore particularly
worthy of investigation (Fig. 1 and Tab. 5). In conclusion, and in the absence of longitudinal or
experimental data, the current study provides robust descriptive evidence in support of theory
that social segregation within European education systems is detrimental to equity in education.
7. Conclusion
Extending research on the geography of opportunity (Logan, Minca, & Adar, 2012), this cross-
national comparative study shows that the degree of social segregation within education
systems varied considerably across European countries. It also highlights a relationship at the
system level between social segregation and the degree of social inequality in student
achievement. The average level of student achievement in a country was not affected by the
level of social segregation within the education system. However, the effects of social origin
on student achievement were stronger in more socially segregated systems, although the
respective differences between systems were relatively small. These findings provide new
evidence of the potentially damaging effect of a socio-spatial separation of students, indicating
that socioeconomic segregation in European education systems may contribute to some extent
to the perpetuation of educational and, by extension, social disadvantage from one generation
to the next.
32
Research ethics
This study involves analysis of publicly available, de-identified data. Any information
presented here is such that study participants cannot be identified.
Conflicts of interest
None.
Appendix A
The scatter plots in Figure A.1 and Figure A.2 illustrate that the degree of social segregation in
European education systems is to some extent related to the number of years that children spent
in a tracked regime (Fig. A.1) and to the number of tracks that are implemented in a given
system (Fig. A.2). However, there is also considerable variation in the degree of social
segregation among education systems that use similar or even identical tracking regimes. Note
that the data on the tracking regimes are derived from Eurydice (2010) which provides official
information about the structure of European education systems. The Organization for Economic
Co-operation and Development (OECD, 2013) reports data that differ slightly for certain
countries (e.g., 4 tracks in Germany, 3 tracks in Hungary). Analyses based on OECD data
confirm the results presented in this article and lead to the same conclusions.
Figure A1.
Figure A2.
33
Appendix B
All cross-level interactions in our model were statistically significant, indicating that all
country-level variables moderated the individual-level relationship between socioeconomic
status and student achievement (i.e., educational inequality). First, levels of educational
inequality were lower in countries with a higher GDP. This supports the theory that social
inequality in educational outcomes declines with economic development (Marks, 2009),
suggesting that in the context of economic growth a transition occurs “from ascriptive rules of
social mobility to mobility patterns based on personal achievements and meritocratic ideas”
(van Doorn et al., 2011, p. 97). Second, income inequality was positively associated with the
degree of educational inequality, which ties in with recent findings from a study of selected
OECD countries (Chmielewski & Reardon, 2016). Although policy documents emphasize the
role of education in “breaking the link between socioeconomic background and life prospects”
(OECD, 2012, p. 18), school systems in Europe seem to face significant challenges in breaking
this link. Instead, they might even reproduce and exacerbate pre-existing family income-related
inequality between children (cf., Downey & Condron, 2016). Third, educational inequality was
weaker in countries with a longer annual taught time. This corroborates prior research whereby
a more intense schooling may diminish socioeconomic differentials in educational outcomes
(Schlicht, Stadelmann-Steffen, & Freitag, 2010). Fourth, the preschool enrollment rate was
positively associated with the degree of educational inequality. This unexpected finding might
be explained by socioeconomic differentials in the duration of preschool attendance across
Europe, with children of higher-SES families attending preschool for longer periods of time
(authors, 2016). As a consequence, a higher preschool enrollment rate may increase, rather than
decrease, social inequality in educational outcomes. Fifth, a higher level of educational
inequality was observed in countries with greater educational expenditure. This result
challenges the view that an increase in public spending on education might prevent the
occurrence of educational inequality. Instead, it suggests that public expenditure on education
may benefit in particular socioeconomically advantaged students who are potentially better able
to capitalize on public education. Finally, the degree of educational inequality was stronger in
countries with a higher level of social segregation in the education system, as explained in detail
in the article.
34
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