Educational Expansion and Inequality: an Analysis of 62 Countries

Educational expansion and inequality: An analysis of 62 countries

Shih-Keng Yen

PhD student, Department of Sociology, Texas A&M University

Abstract

This paper aims to examine the moderating effect of school expansion at the tertiary level on educational inequality, that is, the influence of family SES on children’s academic achievement, with a particular interest in the mechanisms that maintain educational inequalities and advantages when colleges and universities entrance are more universal but entry into prestigious programs becomes more competitive. By using the Programme for International

Student Assessment (PISA) of 2015 for 62 countries, the analyses of the multilevel models show that the impact of family SES, in terms of parental education, on student’s math performance increases whereas higher education expands. The results are consistent with the hypothesis of effectively maintained inequality (EMI), which asserts qualitative inequalities in education persist when tertiary education is almost accessible to everyone. This paper also suggests that net of parental education, educational resources, and financial resources, having cultural resources in the home is more effective in keeping children’s advantages in math while the competition for prestigious programs entrance is more intense in the era of higher education expansion.

Keywords: expansion of higher education, educational inequality, effectively maintained inequality (EMI), cultural resources

Introduction

The inequality in educational outcomes has attracted the attention of social scientists for decades. Educational inequality—the relationship between family socioeconomic status (SES) and children’s educational attainment or achievement—hinges not only on the level of social development (Buchmann and Hannum 2001) but also on the educational system and school expansion (Walters 2000), especially in secondary and higher education. Regarding the expansion at the tertiary level, such as universities and colleges, the attendance rate of higher education raised to 40% in the 1990s from below 20% in the 1960s in 15 developed countries

(Arum, Gamoran, and Shavit 2007). Likewise, according to the United Nations Educational,

Scientific and Cultural Organization (UNESCO), the gross tertiary school enrollment ratio in the world increased from roughly 10% in 1970 to 38% in 2017 (World Bank 2019). In light of this phenomenon, it is important to examine how the massive expansion of higher education is associated with educational inequality.

Three widely cited perspectives have been proposed by researchers to elaborate on the moderating role of the expansion of higher education on educational inequality. According to the industrialization/modernization perspective, as societies develop and education expands, family

SES have a lesser impact on children’s educational outcomes (Marks and Mooi-Reci 2016). As

Treiman (1970) stated, due to the free mass educational systems and the emphasis on academic success at the previous level of schooling instead financial capability, parental status gradually played a mild role in their children’s educational attainment in more industrialized societies.

Contrary to the industrialization/modernization perspective, hypotheses of maximally maintained inequality (MMI) and effectively maintained inequality (EMI) claim that the persistent or even increasing inequality in education by family SES while school expands. On the

2 one hand, with respect to MMI, the advantage of the upper classes is constant over time in the process of educational transition until their children attain a given level of education (Raftery and

Hout 1993). In other words, according to MMI, the association between social origin and educational outcomes may decrease only when the privileged backgrounds reach their saturation, say, close to 100%, at the certain level of schooling (Hout, Raftery, and Bell 1993).

On the other hand, in view of EMI, even though children from different family SES receive a similar educational outcome in terms of years of schooling, the qualitative inequalities still perdure due to the utilization of resources from the families, particularly those with privileged backgrounds (Lucas 2001). Specifically, parents with higher SES tend to mobilize their resources to secure their children’s advantage in education, such as entry into more selective programs or more prestigious institutions upon a certain level of education becoming universal. Compared to industrialization/modernization perspective and MMI, EMI pays more attention to the micro- rather than macro-educational immobility (Andrade and Thomsen 2017) along with the mechanisms of social reproduction. Given the expansion of higher education, these mechanisms and their effects on educational outcomes should be analyzed as well so that stratification could be understood.

In line with previous research (e.g. Pfeffer 2008), this paper employs parental education as the proxy for family SES. However, because family SES refers only to one facet of family background when estimating children’s educational outcomes (Buchmann 2002), I also use three family resources index—educational resources, financial resources, and cultural resources—to examine the mechanisms of maintaining inequalities when higher education expands. In general, this article aims to (1) investigate the effect of school expansion at the tertiary level on educational inequality, (2) test industrialization/modernization perspective as well as hypotheses

3 of MMI and EMI, and (3) shed some light on the mechanisms which may maintain educational inequality, such as the mobilization of educational, financial, and cultural resources, as college- attendance rate grows. The analysis largely relies on data from the Programme for International

Student Assessment (PISA) of 2015, an international survey focusing on 15-year-old students who are about to finish their compulsory education (OECD 2016).

In contrast to previous studies which usually examine educational inequality via estimating the highest educational attainment or years of schooling, this paper defines educational inequality as the relationship between family SES, that is, parental education and children’s math performance (see also Burger 2016). There are three advantages of using academic achievement rather than attainment to explore the interplay between school expansion and educational inequality.

First of all, educational achievement and corresponding standardized test scores are more applicable to the cross-national comparison than conventional measurements like educational attainment, because the latter is more vulnerable to educational system and labor market specific to a country. As Huang (2017) puts it, the focus on math achievement is helpful to conduct rigorous comparisons across societies than other subjects. Academic performance is also more detailed and can capture the nuanced differences among children from different SES. More importantly, compared to educational attainment which relates to schooling strategies in the process of educational transition, namely, children of the same level of performance may have different choices (Boudon 1974; Breen et al. 2009), educational achievement is not only a more direct measurement; focusing on it is also abler to sort out other effects, such as career plan or discrepancy of regional educational opportunity. Educational achievement also mediates the association between family backgrounds and educational attainment (Pia Blossfeld, Gwendolin

Blossfeld and Hans-Peter Blossfeld 2015). In addition, at least in the case of the U.S., as Alon

(2009) mentioned, when higher education expands and competition for entry into prestigious programs intensities, standardized test scores became more crucial in selecting students.

Furthermore, this study also merges tertiary enrollment ratio from the UNESCO Institute for Statistics with PISA of 2015 to estimate the degree of higher education expansion for a multitude of countries. In fact, only a few studies have actually measured the expansion of higher education on a global scale (e.g., Haim and Shavit 2013). In contrast, most of the previous research concluded that variables of birth cohort or birth year were indicators of the increased enrollment of higher education. However, neither cohort nor birth year is identical to the expansion of higher education. On the other hand, the growth of higher education institutions is usually nonlinear (Breen et al., 2009). Thus, it is hard to be captured by the proxies, such as cohort and birth year.

In sum, the results are consistent with the hypothesis of EMI. That is, the impact of family SES with regard to parental education on children’s math scores increases while higher education expands. Analyses also suggest that possessing cultural resources in the home is a more effective mechanism in maintaining educational advantages and inequalities, compared to educational and financial resources.

Expansion and educational inequality

Educational inequality can be conceptualized as the association between family SES, parents’ education in particular (Blossfeld et al. 2015; Pfeffer 2008), and children’s educational attainment or achievement. The stronger the relationship, the higher the educational inequality.

Moreover, the degree of educational inequality is by no means invariable. It depends on the features of the educational system such as school expansion, an apparent phenomenon in the past decades, either at the secondary or tertiary level of education.

However, when it comes to the topic, how educational inequality covaries with school expansion is still debatable. On the one hand, the industrialization/modernization perspective suggests a lessening effect of social origin and ascribed characteristics on individual’s educational outcomes, that is, a declining trend of educational inequality, as society industrializes and the availability of free mass educational systems increases (Treiman 1970). As noted by Treiman, “in more industrialized societies parental status should play a less important role in educational attainment than in less industrialized places.” Correspondingly, the declining trend of education inequality is also observed in Australia and several European countries (Breen et al. 2009; Marks and Mooi-Reci 2016).

On the other hand, educational expansion does not necessarily result in a more equal distribution of educational opportunities (Walters 2000). In other words, expansion does not automatically contribute to reducing educational inequality. This is because “as the number of places in higher education expands, there can be large increases in the amount of education any given group attains without any change in its relative position in the educational hierarchy

(Karen 2002).” A number of cross-national studies have indicated that educational inequality remains constant regardless of expansion. For instance, In Persistent Inequality, Blossfeld and

Shavit (1993) maintained that notwithstanding the growing enrollment rate in higher education, the influence of social origins on educational attainment had been unchanged in most of the thirteen industrialized countries they focused on. More recently, in Stratification in Higher

Education, Arum and his associates further suggests that although the increased attendance at the

6 tertiary level attenuates the impacts of father’s class and parental education on children’s transition to higher education, the relationship—or the moderating effect of educational expansion—is nonlinear: educational expansion reduced inequality only while it becomes nearly universal (Arum et al. 2007). The persistent inequality also exists in South Korea (Park 2004,

2007).

The findings mentioned above confirm the hypothesis of maximally maintained inequality (MMI) proposed by Raftery and Hout (1993). Accordingly, the tenet of MMI is that educational inequality persists until almost all children from privileged background “saturate” at a given level of education. Thus, family SES is less associated to educational transition at a particular level of education, such as at the secondary or tertiary level, if it is available to nearly all individuals from the upper and middle classes. Additionally, for MMI, the prevalence or actual enrollments is crucial to educational inequality and stratification (Hout et al. 1993). As

Hout (2007) has noted, “educational stratification works like a queue. The initial phases of educational expansion […] benefit the privileged families at the front of the queue.” Along with

Blossfeld and Shavit (1993) and Arum et al. (2007), the hypothesis of MMI is also supported in the case of Australia (Chesters and Watson 2013) and Britain (Boliver 2011).

Lucas (2001) further elaborated on MMI by proposing the hypothesis of effectively maintained inequality (EMI). As claimed by Lucas, families with a privileged background strive to assure their children’s advantage in either quantitatively or qualitatively better education by mobilizing their resources. As higher education expands and the tertiary education becomes universal, the socioeconomically advantaged turn to seek for the quantitatively similar but qualitatively superior positions for preserving their children’s vantages in the process of stratification. Thus, educational inequality is still constant regarding different qualities of

7 education, such as the prestige or selectivity level of universities. As a result, based on EMI, increasing enrollment in higher education is inconsequential to reducing qualitative inequalities in education. On the contrary, it not only maintains but also mounts the disparity in educational attainment among different socioeconomic groups because the more affluent ones are able to employ their resources to maintain their offspring’s advantages (Lucas 2009).

Some studies have clearly pointed out the lasting inequality in admission to more prestigious programs and institutions in higher education. For example, in the case of Germany,

Blossfeld et al. (2015) find that social origin is not consequential for the attainment of the degree of applied science universities—the less prestigious higher education institutions in Germany; on the contrary, children from families with tertiary education are more likely to graduate from the more prestigious traditional universities and the educational inequality have persisted at this type of transition, albeit the expansion of higher education. In addition, in the case of Britain, nevertheless quantitative inequalities in entering higher education in general declines as the upper class reaches saturation point, qualitative inequalities, that is, the chance of the enrollment in more prestigious, higher status, and traditional universities, remain unchanged between social classes when school expands (Boliver 2011). The persistent inequality in terms of the quality or the prestige level of higher education has also been indicated in other cases, such as in Denmark

(Andrade and Thomsen 2017) and other Nordic countries (Thomsen et al. 2017), in Israel

(Ayalon and Shavit 2004), in Taiwan (Smith et al. 2016), and in the U.S. (Karen 2002).

It is worthy to note that EMI is a revised rather than a competing hypothesis to MMI

(Ayalon and Shavit 2004), however. On the one hand, as Lucas (2001) has stated, “MMI and

EMI do not disagree about every aspect of schooling, for both perspectives would predict social background effects to be nontrivial at levels of education that are not universal.” More precisely,

8 when attaining a particular level of education is still selective, social origins will yet be influential. On the other hand, theorists of MMI also heed the principle of selection within a certain level of education although they do not particularly focus on that issue (Hout et al. 1993).

For example, Raftery and Hout (1993) have mentioned that the most prestigious institutions did not expand despite the whole system did. Their illustration corresponds to Andrade and

Thomsen’s (2017) assumption that most educational systems in industrialized societies have three phases of change: expansion, increased differentiation, and changes in the returns to education. Therefore, education systems may expand and differentiate simultaneously; differentiation further results in different tracks in terms of selectivity—the privileged backgrounds maintain their advantages in entering the most selective ones while the whole system is accessible to all social origins (Ayalon and Shavit 2004). Therefore, a significant proportion of the growth is absorbed by the less selective programs (Arum et al. 2007).

To date, however, very few studies have examined the mechanisms used by families to maintain their advantages in detail given prestigious institutions entrance is more competitive as the college- and university-attendance rate is on the rise. As illustrated, parental education is usually employed as the indicator of social origin or family SES due to its high correlation with children’s educational outcomes (Blossfeld et al. 2015; Pfeffer 2008; Ou and Reynolds 2008).

Parental education also has a substantial independent influence on children’s socioeconomic destination because of its ability to predict the other two measures of socioeconomic status: parental occupation and family income (Pfeffer and Hertel 2015).

However, the impact of family background on children’s educational outcomes is multidimensional; others factors like education, and cultural resources in the home, as well as family structure, social resources, and parental involvement also have their independent

9 influences (Buchmann 2002). Parents often utilize their educational, financial, and cultural resources to enhance children’s educational achievement (Lim and Gemici 2011). Accordingly, the persistent advantages of the privileged backgrounds in education may result from economic, social, and cultural differences (Gamoran 2001). As Roscigno and Ainsworth-Darnell (1999) stated, educational and cultural resources could be seen as mediating factors between social origins and education outcomes and then reproduce social inequality.

Teachman (1987), for instance, has pointed out that educational resources, including (1) a specific place to study, (2) reference books, (3) a daily newspaper, and (4) a dictionary/encyclopedia in the home, had a positive and significant impact on students’ educational attainment, controlling for other family backgrounds. It is also well known that financial resources in the home like family income are consequential to children’s academic outcomes, although higher education becomes universal (Marks and Mooi-Reci 2016). For instance, the influence of family economic circumstances increases in attaining a more selective diploma in Israel albeit higher education expansion (Ayalon and Shavit 2004). The increasing effect of family financial resources in terms of income on college destinations is shown between

1980 and 1992 in the U.S. as well (Karen 2002). Therefore, educational and financial resources in the home are non-trivial in investigating educational inequalities in the era of school expansion.

Besides educational and financial resources, it is often said that cultural resources in the home also have their leverage on children’s educational outcomes. According to De Graaf et al.

(2000), “cultural resources can be defined as familiarity with the conceptual codes that underlie a specific culture with its major artistic and normative manifestations.” From the perspective of cultural reproduction, cultural resources or cultural capital transmitted and advocated for by

10 educational systems is close to the culture of the dominant class whose children are more familiar with linguistic and cultural competence within their families due to the process of inculcating (Bourdieu 2000; Nash 2010). In other words, children possessing a substantial amount of cultural resources are not only more comfortable with the school requirements that emphasize middle-class values, but it is also easier for them to succeed in educational institutions since the resources give them access to more enrichment opportunities (Gamoran 2001). They also communicate easier with teachers and are less likely to be anxious by materials taught in school, such as art and literature (De Graaf et al. 2000). Cultural capital also takes time to cultivate and accumulate within families (Bourdieu 1986).

Empirically, by pointing out the cultural repertoire behind social class, Annette Lareau

(1989) indicated that parents of upper- and middle-class families were more likely to accumulate their children’s educational advantages by active parenting, heavily engaging in school activities, and navigating their children through the complex educational system, compared to working- class. The former usually adopts “concerted cultivation” parenting behaviors to enhance their children’s cognitive abilities and academic performances (Lareau 2002). Based on EMI, Alon

(2009) also proposes two mechanisms, exclusion and adaptation, which persists or even intensifies class inequality in the U.S. in response to the increasing competition for the prestigious institutions. More precisely, exclusion refers to setting financial and meritocratic barriers—such as emphasizing standardized test scores—in entering selective higher education institutions. Strategies of adaptation include using expensive preparatory tools and devoting considerable efforts towards children’s educational activities which not only raise upper- and middle-classes students’ academic achievement but also boost their chance to enroll into selective colleges and universities (Alon 2009).

Based on the relevant discussions, this paper aims to investigate the moderating effect of higher education expansion on educational inequality—in terms of the relationship between family SES and children’s math scores. Given higher education expands and then becomes more competitive, enhancing math scores is usually consequential to prestigious universities entrance.

Additionally, it is also reasonable to regard other family resources covariates, such as educational, financial, and cultural resources in the home, as the mechanisms of stratification and maintaining educational advantages which are not only more likely to be mobilized by parents but also endogenous in the association between parental education and children’s educational outcomes.

Data, measurement, and analysis

This article is largely relied on data from the Programme for International Student

Assessment (PISA) of 2015 to answer the research questions raised above. PISA is a cross- national survey that has been conducted by the Organization for Economic Co-operation and

Development (OECD) every three years since 2000. The dataset used here is the sixth survey consisting of representative samples of 72 countries and economies. It assessed roughly 540,000

15-year-old students in school—who were near the end of their compulsory education and at the transition to the more advanced level of education—in their literacy (reading), math, and scientific knowledge and skills; most of the tests were computer-based (OECD 2017). PISA

2015 collected students’ social and socioeconomic backgrounds in the student questionnaire as well. Therefore, it provides researchers plenty of children’s family background variables, in addition to their academic achievements.

As mentioned above, the dependent variable of children’s academic achievement is their math scores in PISA 2015. These scores are widely used as a proxy for measuring students’ educational achievement (Burger 2016). As Huang (2017) indicates, the focus on math achievement is more helpful in conducting rigorous comparisons across societies than any other subject. Like reading and science in PISA, students took a math test that consisted of different combinations from a mixture of multiple-choice questions. In other words, participants did not answer all questions. In order to enhance the accuracy of the measurement, PISA 2015 calculated ten plausible values for accounting for uncertainty and the measurement error by using multiple imputations based on information from the test items and the background context questionnaire

(OECD 2017). Therefore, the dependent variable in this paper is estimated by the average of the ten plausible math values for each student.

The main explanatory variables are parental education at the student-level and the degree of the expansion of higher education at the country level. There are also three types of family resources variables which account for students’ math achievement: (1) educational resources in the home, (2) financial resources in the home, and (3) cultural resources in the home. Parental education and the three resources variables are employed on a continuous scale. Specifically, parental education is the highest education of parents which was measured in the International

Standard Classification of Education (ISCED) categories. They are (1) None, (2) ISCED 1

(primary education), (3) ISCED 2 (lower secondary), (4) ISCED Level 3B or 3C (vocational/pre- vocational upper secondary), (5) ISCED 3A (general upper secondary) or ISCED 4 (non-tertiary post-secondary), (6) ISCED 5B (vocational tertiary), and (7) ISCED 5A or ISCED 6

(theoretically oriented tertiary and post-graduate).

Educational, financial, and cultural resources at home are estimated by the corresponding variables in PISA 2015 as well. Educational resources consist of whether having a desk to study at, a quiet place to study, a usable computer for school work, educational software, technical reference books, or a dictionary. Financial resources include whether having a personal bedroom,

Internet access, televisions, cars, rooms with a bath or shower, computers, tablets computers, or e-book readers. By cultural resources, they are measured by the variable of cultural possessions in the home, which refers to literature (e.g. Shakespeare), books of poetry, works of art, books on art, music, or design, or musical instruments (OECD 2017).

For the sample used by this paper, the correlations between parental education and educational, financial, and cultural resources in the home are 0.297, 0.382, and 0.278, respectively. The numbers indicate that parental education, a conventional indicator of family

SES, does not automatically transform to the three types of resources which may improve children’s educational outcomes, although it is moderately correlated to financial resources.

Thus, using the three resources variables, particularly educational and cultural resources, to estimate children’s educational outcomes is both theoretically and methodologically reasonable.

The explanatory variable of higher education expansion refers to the gross enrollment ratio (GER) in tertiary education at the country level, retrieved from UNESCO at the World

Bank website. The GER is measured by “number of students enrolled in a given level of education, regardless of age, expressed as a percentage of the official school-age population corresponding to the same level of education” (UNESCO 2019). Accordingly, the GER in tertiary education exceeding 100% is possible. In order to reduce the influence of fluctuation, the

GER in tertiary education is estimated by the average of the values between the years of 2010 and 2014 for most countries, if the data is available. It is a lagged variable.

Two covariates at the individual-level are held constant in the analyses: student’s gender

(girls = 1) and age. In addition, confounders at the country-level are also taken into account.

They are GNI per capita (PPP) in 2010 (retrieved from the World Bank) and freedom status in

2010 (retrieved from the Freedom House). By incorporating the two variables at the country- level into the analyses, the effects of the difference in economic and political developments can be ruled out substantially.

Eight countries and economic do not have corresponding data on the GER in tertiary education, freedom status in 2010, or GNI per capita (PPP) in 2010. They are Kosovo, Macao,

Puerto Rico, Trinidad and Tobago, B-S-J-G (China), Regions of Spain, Massachusetts (U.S.),

North Carolina (U.S.), and Buenos Aires (Argentina). Also, there are no valid cases for financial or cultural resources in the home in Albania and Thailand. Thus, these ten countries and economic are excluded from analyses. In sum, the following discussions consist of 418,352 cases from 62 countries and economies (hereinafter referred to as countries).

Since the data have a hierarchical structure, with students clustered within schools and countries, I employ multilevel models with a random intercept to observe the moderating effect of GER in tertiary education on the relationship between family SES and children’s math scores.

The three levels are students, schools, and countries. As mentioned above, student’s gender and age at the individual-level, and GNI per capita (PPP) in 2010 and freedom status in 2010 at the country-level are held constant in multilevel models. Because the influences of parental education and resources in the home may vary across social institutions and structures, their slopes are random at the country-level as well. Table 1 and Table 2 present the descriptive statistics and the information of the variable at the country level.

>>>Table 1 about here<<<

>>>Table 2 about here<<<

Results

Table 3 presents the multilevel regression models that estimate students’ math achievement by family SES at the individual level and the tertiary enrollment ratio at the country level, controlling for gender and age, as well as GNI per capita (PPP) in 2010 and freedom status in 2010. The coefficient in Mode 1 shows that children’s family SES, in terms of parents’ education, is significantly and positively related to their mathematical achievement (p < .001).

The higher the education that parents receive, the better their children perform in math. When parental education increases by one ISCED level, students’ math scores increase by about 6.74 points. As expected, parental education is consequential to their offspring’s educational outcomes.

>>>Table 3 about here<<<

Model 2 further incorporates the GER in tertiary education into analyses. As shown, the coefficient of parental education is almost unchanged (β = 6.73, p < .001) and still influential in children’s math performance. In addition, the coefficient of GER in tertiary education indicates that countries with higher tertiary enrollment ratio tend to perform better in math (β = 1.10, p

< .001), because they are typically more industrialized and modernized (Treiman 1970).

Model 3 adds the interaction term between parental education and the GER in tertiary education into analyses with a view to observing the moderating effect of higher education expansion on inequality, that is, the association between family SES and educational achievement. Accordingly, the impact of family SES on children’s math performances vary

16 across degrees of school expansion at the tertiary level. The impact of parental education on children’s math scores increases as college-attendance rate grows (β = 0.09, p < .001). Moreover, based on Model 4, after taking GNI per capita (PPP) and freedom status into account and ruling out the influences of economic and political disparities across countries, the interaction effect remains significant and positive.

Following Burger (2016) and Owens (2018), who have suggested that displaying marginal effects is helpful to interpret interaction effects (also see Brambor, Clark and Golder

2006), I plot the average marginal effects (AME) of parental education on math scores across degrees of GER in tertiary education from Model 4. The line in Figure 1 represents the AME of a one-unit increase in parental education on children’s math scores across the degrees of GER in tertiary education, along with the 95% confidence interval (CI), when all other covariates are held at their values. Since the GER in tertiary education lies between 38% and 80% for most of the 62 countries (mean = 59.36, S.D. = 20.87), the 95% CI is wider at the upper and lower ends.

Figure 1 indicates that the impact of family SES on students’ math achievement increases positively while the national tertiary enrollment ratio grows. For instance, compared to Qatar, where the GER in tertiary education is around 11.57%, the effect of parental education is almost five times stronger for South Korea’s, whose corresponding ratio is about 97.53%. By and large,

Figure 1 clearly shows the increasing inequality in education as higher education expands. Based on that, the hypothesis of EMI, which asserts the lasting qualitative inequalities in education although higher education becomes universal, is confirmed empirically. Specifically, yet higher education is almost accessible to everyone, family SES plays a more crucial role in children’s academic achievement, because entry into the prestigious institutions is more competitive

>>>Figure 1 about here<<<

As proposed above, educational, financial, and cultural resources in the home are important to children’s academic achievement as well. Possessing a substantial amount of these resources may also contribute to maintaining advantages when higher education expands and the increasing competition for selective colleges and universities. In order to examine their effects,

Table 4 presents the multilevel regression models that estimate children’s math achievement by education, financial, and cultural resources, along with their interactions with the GER in tertiary education, controlling for parental education, student’s gender and age, and the economic and political characteristics at the country-level.

>>>Table 3 about here<<<

Based on Model 1, before incorporating interaction terms into analyses, educational resources (β = 5.85, p < .001) and cultural resources (β = 7.87, p < .001) in the home have their positive effects on children’s math achievement, while parental education, family financial resources, as well as other student- and country-level covariates are held constant. The more educational and cultural resources the student’s family possesses, the better her/his performance in math would be. By comparison, while taking educational resources, cultural resources, and parental education into account, the influence of financial resources in the home on children’s math scores is limited statistically and substantially (β = —0.94, p > .05). Perhaps it is because the three family resources variables are moderately correlated to each other and holding the financial ones is necessary but not sufficient to the possession of other two family resources.

Besides, owning personal bedrooms, computers, and other equipment may be not necessarily beneficial to children’s math scores if they are used to enhance comfort and convenience for the whole family instead of offspring’s academic achievement. By and large, educational and

18 cultural resources in the home are more consequential than the financial ones to children’s math performance.

Additionally, by educational resources, its interplay with the GER in tertiary education on students’ math performance is modest (β = —0.04, p > .05), according to Model 2. The result suggests that the impact of educational resources in the home on children’s math scores decreases slightly but not significantly with the expansion of higher education. Therefore, having large quantities in educational resources may not be more effective in maintaining educational advantages in countries with higher tertiary enrollment ratio. This pattern is also illustrated in

Figure 3. Because the CIs do not contain zero, however, it is worthy to note that family educational resources still play a non-trivial role in children’s math scores, net of parental education and other two family resources, no matter how tertiary enrollment ratio changes. In other words, holding a certain amount of educational resources is usually crucial for enhancing children’s academic performance, regardless of how school expands.

>>>Figure 2 about here<<<

In contrast to educational resources, as shown in Model 3, the effect of financial resources in the home on math scores decreases significantly while the enrollment in higher education grows (β = —0.06, p < .05). Moreover, having financial resources is trivial in influencing children’s math performance (the CIs contain zero) for countries whose GER in tertiary education is lower than 70%, based on Figure 3. Rather, their effects on math scores become more negative in countries with higher tertiary enrollment ratio. The pattern is because, firstly, holding financial resources may contribute to improving living conditions for the whole family but not necessarily to children’s academic performance. On the other hand, having more financial resources such as computers or tablets may be disadvantageous for enhancing

19 children’s learning in math. Therefore, similar to educational resources, possessing a substantial amount of financial resources does not contribute to maintaining educational advantages effectively, whereas their patterns are different.

>>>Figure 3 about here<<<

For cultural resources in the home, their effects on children’s math scores vary significantly across degrees of GER in tertiary education (β = 0.12, p < .05), net of parental education and the other two resources, according to Model 4. More precisely, cultural resources in the home having a more positive impact on students’ math performance when GER in tertiary education rises. Figure 4 clearly shows this pattern. For instance, a one-unit increase in home cultural resources corresponds to roughly a 12-point math score increase in countries with a high tertiary enrollment ratio, such as the United States (92.17%), compared to only about 4-point increase in countries where higher education is in low development (e.g. in Algeria with

18.84%), when all other covariates are held at their values. In other words, while prestigious institutions entrance become more competitive, possessing large quantities of cultural resources are more beneficial to preserving educational advantages, at least in math. By comparison, the effect of cultural resources on children’s math performance is much larger than of educational and financial resources when higher education expands.

>>>Figure 4 about here<<<

In sum, the relationship between cultural resources and math scores is more sensitive to the change of the GER in tertiary education than educational and financial resources. However, this is not to say that having educational resources is not important to students’ academic achievement. As mentioned, they still play a significant role in children’s math scores, no matter

20 how tertiary enrollment ratio varies. By and large, with regard to cultural resources, they are more selective and difficult to accumulate than the other two resources. Having educational and financial resources may be fundamental but not sufficient for holding the cultural ones. More importantly, as theorists of cultural reproduction indicate, children with more cultural capital are more comfortable with schools and the educational system due to the feeling of familiarity. This feeling of familiarity may be helpful to improve students’ performance in academic when entry into more selective programs becomes fierce while higher education is nearly accessible to everyone. The results expand Alon’s (2009) assumption of adaptation by suggesting that the mobilization of cultural resources in the home is effective in preserving children’s advantages given the admission in the more prestigious programs is competitive.

However, aggregate-level contexts may contribute to individual outcomes in different ways across social groups (Owen 2018). For this article, children from dissimilar family backgrounds may perform differently in math when higher education expands. In order to present the results more concretely, I further illustrate predicted values of math scores against the

GER in tertiary education by dividing parental education into four groups rather than using it on the continuous scale. They are lower secondary education (ISCED 0, 1, and 2), upper secondary education (ISCED 3B, 3C, 3A, and 4), vocational tertiary education (ISCED 5B), as well as academic tertiary education (ISCED 5A and 6). Cultural resources in the home are also broke up into four quantiles. Figure 5 and 6 present the results.

Based on Figure 5, children from families with academic tertiary education (dashed line with triangle markers) constantly perform better in math than the other three groups (except when the GER in tertiary education less than 30%). Moreover, the gaps in math scores between academic tertiary and lower secondary, upper secondary, and vocational tertiary education

21 increase while college-going rate climbs. The results support EMI that educational inequalities, particularly in the qualitative aspect, still exist even though higher education becomes more accessible.

Figure 6 further portrays the widening gap across different amounts of cultural resources in the home as tertiary enrollment ration grows. Children from families with the most affluent cultural resources (Q4, dashed line with triangle markers) is more favorable in math, followed by those in the second top quantile (Q3, dotted line with X markers). In addition, children who possess the lowest amount of cultural resources (Q1, solid line) are substantially less advantaged than the other three groups as the GER in tertiary education rises. Besides, the disparity between the top and lowest two quantiles boosts while tertiary enrollment ratio grows. In general, having cultural resources in the home is effective in keeping educational inequalities and advantages when prestigious colleges and universities entrance become more competitive.

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Conclusion

I investigate the moderating effect of the expansion of higher education on educational inequality, that is, the relationship between children’s family SES and their academic achievement by using PISA 2015 for 62 countries. The results suggest that, as the proxy of family SES, parental education becomes more influential on children’s math scores, the measurement of academic achievement, while tertiary enrollment ration is on the rise. The gap of math scores between children from families with the highest education and the rest also increases

22 whereas the college-going rate climbs. Therefore, this paper is consistent with the hypothesis of

EMI that educational inequality, particularly the qualitative inequality, persists nevertheless higher education is universal and the enrollment is nearly saturated (Lucas 2001). Family SES contributes to maintaining inequalities and advantages in education when the competition for entry into more selective and prestigious is intense (Alon 2009).

Moreover, compared to educational and financial resources, having a substantial amount of cultural resources in the home is an efficacious mechanism in maintaining educational advantages in the era of higher education expansion, when accounting for parental education.

Perhaps it is because children’s with more cultural resources are more comfortable with the materials which are transmitted by educational systems, the tenet of the perspective of cultural reproduction (Bourdieu 2000; De Graaf et al. 2000; Nash and Lauder 2010). It also because cultural resources take more time to accumulate within families than educational and financial resources. Specifically, cultural resources may be more selective and situated at the top of the hierarchy of family backgrounds, followed by educational and financial ones. As a result, the mobilization of cultural resources is a more effective strategy of adaptation (Alon 2009) in preserving educational advantages given higher education is nearly accessible to everyone the struggling for prestigious institutions entrance is more intense.

However, mechanisms like parental involvement and parenting behavior could be incorporated into analyses in future studies to examine their impacts on maintaining advantages and inequalities in education as school expansion. Likewise, because the measure of cultural resources in the paper is more close to highbrow culture like possessing literature (e.g.

Shakespeare), books of poetry, works of art, etc., the variable of parental reading behaviors,

23 another important element of cultural capital, could be employed in analyses for societies that do not emphasize highbrow culture (De Graff et al. 2000).

Also, by using PISA of 2015, this study focuses on 15-year-old students who are about to finish their compulsory education, that is, around 9 years. However, for society such as Taiwan, the duration of compulsory education is 12 years instead of 9. By contrast, some countries have durations of compulsory education which are shorter than 9. Besides, for Taiwan, there is still a high-stake test for entry into higher education. Such factors may influence the relationship between family SES and educational achievement. Therefore, future studies could take the educational system and high-stake test into account while investigating the moderating effect of school expansion on educational inequality.

References Alon, Sigal. 2009. “The Evolution of Class Inequality in Higher Education: Competition, Exclusion, and Adaptation.” American Sociological Review, 74: 731-755. Ayalon, Hanna and Yossi Shavit. 2004. “Educational Reforms and Inequalities in Israel: The MMI Hypothesis Revisited.” Sociology of Education, 77(April): 103-120. Andrade, Stefan B. and Jens-Peter Thomsen. 2017. “Micro-Educational Reproduction.” Social Forces, 96(2): 717-750. Arum, Richard, Adam Gamoran, and Yossi Shavit. 2007. “More Inclusion than Diversion: Expansion, Differentiation, and Market Structure in Higher Education.” Pp. 1-35 in Stratification in Higher Education: A Comparative Study, edited by Yossi Shavit, Richard Arum, Adam Gamoran, and Gila Menahem. Stanford, CA: Stanford University Press. Blossfeld, Pia N., Gwendolin J. Blossfeld, and Hans-Peter Blossfeld. 2015. “Educational Expansion and Inequalities in Educational Opportunity: Long-Term Changes for East and West Germany.” European Sociological Review, 31(2): 144-160. Blossfeld, Hans-Peter and Yossi Shavit. 1993. “Persisting Barriers: Changes in Educational Opportunities in Thirteen Countries.” Pp. 1-23 in Changing Educational Attainment in Thirteen Countries, edited by Yossi Shavit and Hans-Peter Blossfeld. Boulder, CO: Westview Press. Breen, Richard, Ruud Luijkx, Walter Müller, and Reinhard Pollak. 2009. “Nonpersistent Inequality in Educational Attainment: Evidence from Eight European Countries.” American Journal of Sociology, 114(5): 1475-1521. Boliver, Vikki. 2011. “Expansion, Differentiation, and the Persistence of Social Class Inequalities in British Higher Education.” Higher Education, 61(3): 229-242. Boudon, Raymond. 1974. Education, Opportunity and Social Inequality: Changing Prospects in Western Society. New Jersey: Wiley. Bourdieu, Pierre. 1986. “The Forms of Capital.” Pp. 241-258 in Handbook of Theory and Research for the Sociology of Education, edited by John Richardson. New York: Greenwood. Bourdieu, Pierre. 2000. “Cultural Reproduction and Social Reproduction.” Pp. 150-197 in The Structure of Schooling: Readings in the Sociology of Education, edited by Richard Arum and Irenee R. Beattie. Mountain View, CA: Mayfield Publishing. Brambor, Thomas, William Roberts Clark, and Matt Golder. 2006. ‘‘Understanding Interaction Models: Improving Empirical Analyses.’’ Political Analysis, 14: 63-82. Buchmann, Claudia. 2002. “Measuring Family Background in International Studies of Education: Conceptual Issues and Methodological Challenges.” Pp. 91-115 in

Methodological Advances in Cross-National Surveys of Educational Achievement, edited by Andrew C. Porter and Adam Gamoran. Washington, DC: National Academy Press. Buchmann, Claudia and Emily Hannum. 2001. “Education and Stratification in Developing Countries: A Review of Theories and Research.” Annual Review of Sociology, 27 (2001): 77-102. Burger, Kaspar. 2016. “Intergenerational Transmission of Education in Europe: Do More Comprehensive Education Systems Reduce Social Gradients in Student Achievement?” Research in Social Stratification and Mobility, 44: 54-67. Chesters, Jenny and Louise Watson. 2013. “Understanding the Persistence of Inequality in Higher Education: Evidence from Australia.” Journal of Education Policy, 28(2): 198- 215. De Graaf, Nan Dirk, Paul M. De Graaf, and Gerbert Kraaykamp. 2000. “Parental Cultural Capital and Educational Attainment in the Netherlands: A Refinement of the Cultural Capital Perspective.” Sociology of Education, 73(2): 92-111. Gamoran, Adam. 2001. “American Schooling and Educational Inequality: A Forecast for the 21st Century.” Sociology of Education, 74(Extra Issue): 135-153. Haim, Eyal Bar and Yossi Shavit. 2013. “Expansion and Inequality of Educational Opportunity: A Comparative Study.” Research in Social Stratification and Mobility, 31: 22-31. Hout, Michael. 2007. “Maximally Maintained Inequality Revisited: Irish Educational Stratification in Comparative Perspective.” Pp. 23-40 in Changing Ireland in International Comparison, edited by Betty Hilliard and Maire NicGhiolla Phadraig. Dublin: Liffey Press. Hout, Michael, Adrian E. Raftery, and Eleanor O. Bell. 1993. “Making the Grade: Educational Stratification in the United States, 1925-1989.” Pp. 25-49 in Changing Educational Attainment in Thirteen Countries, edited by Yossi Shavit and Hans-Peter Blossfeld. Boulder, CO: Westview Press. Huang, Min-Hsiung. 2017. “Excellence without Equity in Student Mathematics Performance: The Case of Taiwan from an International Perspective.” Comparative Education Review, 61(2): 391-412. Park, Hyunjoon. 2004. “Educational Expansion and Inequality in Korea.” Research in Sociology of Education, 14: 33-58. Park, Hyunjoon. 2007. “Educational Expansion and Inequality of Opportunity for Higher Education in South Korea: Educational Expansion and Inequality of Opportunity for Higher Education.” Pp. 87-112 in Stratification in Higher Education: A Comparative Study, edited by Yossi Shavit, Richard Arum, Adam Gamoran, and Gila Menahem. Stanford, CA: Stanford University Press.

Karen, David. 2002. “Changes in Access to Higher Education in the United States: 1980-1992.” Sociology of Education, 75(3): 191-210. Lareau, Annette. 1989. Home Advantage: Social Class and Parental Intervention in Elementary Education. Lanham, Maryland: Rowman & Littlefield Publishers. Lareau, Annette. 2002. “Invisible Inequality: Social Class and Childrearing in Black Families and White Families.” American Sociological Review, 67(5): 747-776. Lim, Patrick and Sinan Gemici. 2011. Measuring the Socioeconomic Status of Australian Youth. Technical Paper. Adelaide: National Centre for Vocational Education Research. Lucas, Samuel R. 2001. “Effectively Maintained Inequality: Education Transitions, Track Mobility, and Social Background Effects.” American Journal of Sociology, 106(6): 1642- 1690. Lucas, Samuel R. 2009. “Stratification Theory, Socioeconomic Background, and Educational Attainment: A Formal Analysis.” Rationality and Society, 21(4): 459-511. Marks, Gary N. and Irma Mooi-Reci. 2016. “The Declining Influence of Family Background on Educational Attainment in Australia: The Role of Measured and Unmeasured Influences.” Social Science Research, 55: 171-185. Nash, Roy. 2010. Explaining Inequalities in School Achievement: A Realist Analysis (edited by Hugh Lauder). Burlington, VT: Ashgate Publishing Company. OECD. 2016. PISA 2015 Results (Volume I): Excellence and Equity in Education. Paris: PISA, OECD Publishing. Retrieved September 22, 2018 (http://dx.doi.org/10.1787/9789264266490-en). OECD. 2017. PISA 2015 Technical Report. Retrieved September 22, 2018 (http://www.oecd.org/pisa/sitedocument/PISA-2015-technical-report-final.pdf). Ou, Suh-Ruu and Arthur J. Reynolds. 2008. “Predictors of Educational Attainment in the Chicago Longitudinal Study.” School Psychology Quarterly, 23(2): 199-229. Owens, Ann. 2018. “Income Segregation between School Districts and Inequality in Students’ Achievement.” Sociology of Education, 91(1): 1-27. Pfeffer, Fabian T. 2008. “Persistent Inequality in Educational Attainment and its Institutional Context.” European Sociological Review, 24(5): 543-565. Pfeffer, Fabian T. and Florian R. Hertel. 2015. “How Has Educational Expansion Shaped Social Mobility Trends in the United States?” Social Forces, 91(1): 143-180. Raftery, Adrian E. and Michael Hout. 1993. “Maximally Maintained Inequality: Expansion, Reform, and Opportunity in Irish Education, 1921-75.” Sociology of Education, 66(1): 41-62.

Roscigno, Vincent J. and James W. Ainsworth-Darnell. 1999. “Race, Cultural Capital, and Educational Resources: Persistent Inequalities and Achievement Returns.” Sociology of Education, 72(3):158-178. Smith, Michael, Shu-Ling Tsai, Petr Matějů, and Min-Hsiung Huang. 2016. “Educational Expansion and Inequality in Taiwan and the Czech Republic.” Comparative Education Review, 60(2): 339-374. Teachman, Jay D. “Family Background, Educational Resources, and Educational Attainment.” American Sociological Review, 52(4): 548-557. Thomsen, Jens-Peter, Emil Bertilsson, Tobias Dalberg, Juha Hedman, and Håvard Helland. 2017. “Higher Education Participation in the Nordic Countries 1985-2010—A Comparative Perspective.” European Sociological Review, 33(1): 98-111. Treiman, Donald J. 1970. “Industrialization and Stratification.” Sociological Inquiry, 2: 207-234. UNESCO. 2019. “Gross Enrolment Ratio.” Retrieved July 6, 2019 (http://uis.unesco.org/en/glossary-term/gross-enrolment-ratio). Walters, Pamela Barnhouse. 2000. “The Limits of Growth: School Expansion and School Reform in Historical Perspective.” Pp. 241-264 in Handbook of the Sociology of Education, edited by Maureen T. Hallinan. New York: Springer. Word Bank. 2019. “School Enrollment, Tertiary (% Gross).” Retrieved July 6, 2019 (https://data.worldbank.org/indicator/SE.TER.ENRR).

Table 1. Descriptive Statistics. Variable Mean Standard Deviation Math score 452.29 96.10 Parental education None 0.02 ISCED 1 0.08 ISCED 2 0.13 ISCED 3B, C 0.05 ISCED 3A, 4 0.26 ISCED 5B 0.14 ISCED 5A, 6 0.32 Educational resources in the home -0.50 1.17 Financial resources in the home -0.82 1.53 Cultural resources in the home -0.19 0.92 GER in tertiary education 59.36 20.87 Girl 0.50 Age 15.79 0.29 GNI per capita (PPP) in 2010 30233.75 20363.30 Freedom status in 2010 4.89 1.56 Note: N = 418,352 students, 62 countries. Student variables from PISA of 2015. GER in tertiary education and GNI per capita (PPP) from the World Bank. Freedom status from the Freedom House. Data from PISA of 2015 are weighted, using the final student weight (W_FSTUWT) provided from PISA.

Table 2. Aggregate-level Variables in 62 Countries.

Country GER in tert. GNI per capita Freedom Country GER in tert. GNI per capita Freedom edu. (%) 1 capita (PPP) 2 Status 3 edu. (%) capita (PPP) status Greece 109.7 27600 1.5 Germany 62.3 6 40000 1 South Korea 97.5 30410 1.5 Bulgaria 62.0 14620 2 Finland 92.2 39300 1 Japan 60.9 35900 1.5 US 92.2 48880 1 Croatia 60.9 18690 1.5 Slovenia 85.8 27510 1 France 60.7 36730 1 Australia 85.3 37750 1 Hungary 59.4 20450 1 Spain 84.6 8704 1 UK 58.7 36170 1 Taiwan 83.7 35595 1.5 Uruguay 57.2 16110 1 Iceland 80.8 32200 1 Slovak R. 55.3 24430 1 New Zealand 79.5 29710 1 Switzerland 55.1 56090 1 Singapore 78.7 4 70250 4.5 Romania 54.1 16710 2 Denmark 78.3 43750 1 Montenegro 52.2 13540 2.5 Chile 78.3 16980 1 Costa Rica 49.9 12320 1 Austria 78.1 42400 1 Dominican R. 47.1 10520 2 Russia 77.4 19860 5.5 Lebanon 46.5 15910 4 Lithuania 76.8 19720 1 Colombia 46.5 10160 3.5 Norway 75.0 58560 1 Brazil 46.1 13830 2 Poland 72.7 20380 1 Malta 41.7 26350 1 Netherlands 72.1 44900 1 Peru 40.5 9040 2.5 Estonia 71.6 20460 1 Moldova 40.1 4150 3.5 Belgium 70.8 41350 1 Jordan 38.8 9210 5 Turkey 70.8 17300 3 FYROM 38.1 11120 3 Ireland 69.3 36150 1 Tunisia 34.8 9750 6 Sweden 68.1 42850 1 Georgia 33.3 6390 4 Israel 66.5 28280 1.5 Algeria 32.3 12580 5.5 Portugal 66.5 26420 1 Mexico 28.3 14680 2.5 Latvia 65.2 17780 1.5 Indonesia 27.1 8040 2.5 Czech R. 65.2 25550 1 Viet Nam 25.6 4150 6 Italy 64.8 34970 1.5 UAE 22.3 56060 5.5 Canada 64.2 5 39230 1 Luxembourg 18.8 61980 1 Hong Kong 63.2 48130 3.5 Qatar 11.6 109930 5.5 Note: 1 Usually the average of GER in tertiary education between 2010 and 2014. Data from the World Bank (https://data.worldbank.org/indicator/SE.TER.ENRR); 2 GNI per capita (PPP) in 2010. Data from the World Bank (https://data.worldbank.org/indicator/ny.gnp.pcap.pp.cd); 3 Freedom status in 2010. Data from the Freedom House (https://freedomhouse.org/report/freedom-world/freedom-world-2010). Reverse coding in regression models; 4 Data from Government of Singapore (https://data.gov.sg/dataset/combined-and-gross-enrolment-ratio-for-primary- secondary-tertiary-education); 5 Data from the UNESCO (http://uis.unesco.org/country/CA); 6 Data from the UNESCO (http://uis.unesco.org/en/country/de).

Table 3. Multilevel Regression Models Estimating Students’ Math Scores from Parental Education and the GER in Tertiary Education.

Variable Model 1 Model 2 Model 3 Model 4 Parental education (PEDU) 6.74*** 6.73*** 1.28 1.28 (0.53) (0.53) (1.31) (1.31) GER in tertiary education (GERT) 1.10*** 1.09*** 0.60** (0.28) (1.09) (0.27) PEDU × GERT 0.09*** 0.09*** (0.02) (0.02) Girl —11.82*** —11.82*** —11.82*** —11.82*** (0.96) (0.96) (0.96) (0.96) Age 9.25*** 9.25*** 9.25*** 9.25*** (0.90) (0.90) (0.90) (0.90) Log of GNI per capita (PPP) in 2010 30.93** (10.45) Freedom status in 2010 2.98 (4.45) Constant 289.73 223.21 223.84 —71.86 Note: N = 418,352 students, 62 countries. Standard errors appear in parentheses. *** p < .001, ** p <. 01, * p < .05. Unweighted analyses because of no country weights in PISA.

Table 4. Multilevel Regression Models Estimating Students’ Math Scores from Educational, Financial, Cultural Resources in the home, and the GER in Tertiary Education.

Variable Model 1 Model 2 Model 3 Model 4 Educational resources 5.85*** 8.09*** 5.84*** 5.85*** (0.54) (1.75) (0.54) (0.54) Financial resources —0.94 —0.94 2.86 —0.94 (0.64) (0.64) (1.60) (0.64) Cultural resources 7.87*** 7.87*** 7.87*** 0.35 (0.77) (0.77) (0.77) (3.08) GER in tertiary education 0.56* 0.56* 0.56* 0.57* (0.27) (0.27) (0.28) (0.28) Educational resources × GER in tertiary education —0.04 (0.03) Financial resources × GER in tertiary education —0.06* (0.03) Cultural resources × GER in tertiary education 0.12** (0.04) Parental education 4.86*** 4.86*** 4.86*** 4.86*** (0.46) (0.46) (0.46) (0.46) Girl —12.82*** —12.83*** —12.82*** —12.82*** (0.88) (0.88) (0.88) (0.88) Age 8.94*** 8.94*** 8.94*** 8.94*** (0.88) (0.88) (0.88) (0.88) Log of GNI per capita (PPP) in 2010 28.78** 28.78** 28.74** 28.78** (10.56) (10.56) (10.56) (10.56) Freedom status in 2010 3.25 3.25 3.26 3.25 (4.61) (4.61) (4.62) (4.61) Constant —34.11 —34.06 —33.64 —34.19 Note: N = 418,352 students, 62 countries. Standard errors appear in parentheses. *** p < .001, ** p <. 01, * p < .05. Unweighted analyses because of no country weights in PISA.

Marginal Effect of Parental Education Parental Effect of Marginal

-5 10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Figure 1. Average Marginal Effects (AME) of Parental Education on Math Scores against the GER in Tertiary Education. Estimate from Model 4 in Table 3.

Marginal Effect of Educational Resources Educational Effect of Marginal

-5 10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Figure 2. Average Marginal Effects (AME) of Educational Resources in the Home on Math Scores against the GER in Tertiary Education. Estimate from Model 2 in Table 4.

Marginal Effect of Financial Resources Financial Effect of Marginal

-5

10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Figure 3. Average Marginal Effects (AME) of Financial Resources in the Home on Math Scores against the GER in Tertiary Education. Estimate from Model 3 in Table 4.

Marginal Effect of Cultural Resources Cultural Effect of Marginal

-5 10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Figure 4. Average Marginal Effects (AME) of Cultural Resources in the Home on Math Scores against the GER in Tertiary Education. Estimate from Model 4 in Table 4.

500

480

460

Math score Math

440

420

400 10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Lower secondary Upper secondary Vocational tertiary Academic tertiary

Figure 5. Predicted Math Scores by Parental Education, the GER in Tertiary Education, and Their Interaction, Controlling for Student- and Country-Level Covariates.

500

480

460

Math score Math

440

420 10 20 30 40 50 60 70 80 90 100 110 GER in Tertiary Education (%)

Q1 Q2 Q3 Q4

Figure 6. Predicted Math Scores by Cultural Resources in the Home, the GER in Tertiary Education, and Their Interaction, Controlling for Student- and Country-Level Covariates.