math gender gap: the role of culture

Math Gender Gap: The Role of Culture

Natalia Nollenberger

School of Business and Management, Queen Mary University of London

Núria Rodríguez-Planas Queens College - CUNY, and IZA

Almudena Sevilla

School of Business and Management, Queen Mary University of London IZA

July 2014

Abstract

This paper explores the role of cultural attitudes towards women in determining math educational gender gaps using the epidemiological approach. To identify whether culture matters, we estimate whether the math gender gap for each immigrant group living in a particular host country (and exposed to the same host country's laws and institutions) is explained by measures of gender equality in the parents' country of ancestry. We find that the higher the degree of gender equality in the country of ancestry the higher the performance of second-generation immigrant girls relative to boys. This result is robust to alternative specifications, measures of gender equality, and the inclusion of other human development indicators in the country of ancestry. Culture seems primarily to operate through school peer effects. Our results suggest that policies aimed at changing beliefs can prove effective at reducing the gender gap in mathematics.

Keywords: Gender Gap in Math, Immigrants, Gender Identity. JEL Codes: I21, I24, J16, Z13 ___________________________

The authors would like to express their thanks for the financial support provided by the Economic and Social Research Council (Grant Number ES/K003127/1) and the Spanish Ministry of Education and Science (Project ECO2012-34828). Correspondence to Núria Rodríguez-Planas, Queens College - CUNY, 300A Powdermaker Hall, 65-30 Kissena Blvd., Queens, New York 11367, USA. Email: [email protected]

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1. Introduction

It has been widely documented that teenage boys tend to outperform girls in math tests

in many industrialized countries.1 A recent study using longitudinal data for the US

found that by the end of fifth grade girls had fallen more than 0.2 standard deviations

behind boys, which is equivalent to 2.5 less months of schooling (Fryer and Levitt

2010). Using 2003 data from the Program for International Student Assessment (PISA)

that reports on mathematic tests scores of 15-year-old students from 40 countries, Guiso

et al. (2008) document that: "girls’ math scores average 10.5 (or 2 percent) lower score

points than those of boys, but the results vary by country: -22.6 in Turkey to 14.5 in

Iceland".2 Since mathematical ability appears to be an important determinant of field

choice for college graduates (Paglin and Rufolo 1990 and Turner and Bowen 1999) and

a significant part (between 8 and 20 percent) of the gender wage gap can be explained

by choice of major (Machin and Puhani 2003, and Black et al. 2008), understanding the

causes behind the divergence in math test scores between boys and girls is the first step

towards designing policies that aim to improve the conditions for female workers.3

Thus far the literature has focused on two broad explanations of the mathematics

gender gap: the biological versus the environment explanation. On the one hand, some

1Much of the research documenting gender gap in math scores has been based on US data. The size of the gap reported depends on the test and time-period. Some recent studies suggest that the average gender gap in math scores among teenagers has been narrowing (Hyde and Mertz 2009) while others document still large differences in the average performance of girls relative to boys (Fryer and Levitt 2010). There is a wide consensus that substantial differences persist at the top of the distribution (Ellison and Swanson 2010; Hyde and Mertz 2009) and that the fraction of males to females who score in the top 5 percent of the distribution in high school math has remained constant at two to one over the past 20 years (Xie and Shauman 2003). Ellison and Swanson (2010) document that the gender gap in secondary school math at high achievement levels is present in every US high school, although the size of the gap varies from school to school. Bedard and Cho (2010) review the existing evidence documenting gender gap in math scores in OECD countries. 2 The gender gap is calculated as the girls’ average score minus the boys’ average score, so that a negative gap means that boys over perform girls while a positive gap means that girls over perform boys. 3 Black et al. 2008 find that between 45 and 53 percent of the gender wage gap among college graduates in the US is explained by age, highest degree and major.

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scholars claim that the math gender difference is innate and rooted in biology, and exists

because of genetic (Geary 1998), hormonal (Kimura 2000), or cerebral differences

(Halpern 2000). On the other hand, several theories rely on societal factors (including

gender differential treatment by teachers, parents' differential expectations on math

achievement for girls and boys, and gender differences in expected returns to math

skills, among others) as the cause for the math gender gap (see Fryer and Levitt 2010

for a thorough literature review--page 212). An influential article in Science using data

from 40 countries finds that "girls’ underperformance in math relative to boys is

eliminated in more gender-equal cultures" suggesting the important role of the

environment behind the math gender gap (Guiso et al. 2008). Using cross-country data

from 41 countries from Trends in Mathematics and Science Studies (TIMMS), Fryer

and Levitt (2010) also find support for this hypothesis when Muslin countries or

countries with high sex-segregated education are excluded from the sample.4, 5

However, these studies fail to distinguish between the role of institutional constraints

versus culture in influencing the math gender gap. It may be that lower performance in

math from girls may be the result of having internalized what constitutes to be a girl and

behave according to a girl’s gender identity (Akerlof and Kranton 2000).6

Alternatively, girls may choose to invest less in math than boys (independent on beliefs)

because they expect lower labor market returns to math skills given the laws,

regulations and labor market institutions in their society (Albanesi and Olivetti 2009).

In this paper, we investigate the extent to which beliefs and preferences (as opposed to

4 PISA and TIMSS data differ in their measurement of math skills. While TIMMS mainly assesses what students have learned in the classroom, PISA assesses “the capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen” (OECD, 2004, p. 26). 5 Using 2009 PISA data, González de San Román and de la Rica (2012) find a similar relationship across regions within a country (Spain), which constitutes a more homogeneous institutional setting. 6 Note that girls' actions may be influenced by their own beliefs, or by those of their families or neighbours through the rewards and punishments associated with different actions.

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institutional constraints) explain the math gender gap. If beliefs and preferences about

gender roles are important, policies aiming to alter them early in life would be optimal.

If instead institutional constraints are most relevant, then policies aiming at changing

institutions in both the labor market and education system would be preferred.

To examine whether culture can explain gender differences in math test

performance, we follow the epidemiological approach fully developed in Fernández and

Fogli (2009) and reviewed in Fernández (2011).7 This approach focuses on second-

generation immigrants who are exposed to the same host country's labor markets,

regulations, laws and institutions, but are also influenced by different cultural beliefs of

their parents. To identify the effect of culture, we estimate whether the math gender gap

for each immigrant group living in a particular host country is explained by measures of

gender identity in the country of ancestry.8 For this purpose we merge 2003, 2006,

2009 and 2012 data from PISA and the 2009 World Economic Forum’s gender gap

index (GGI) which reflects economic and political opportunities, education, and well-

being for women in the country of ancestry.9 Using a data set containing 12,027

second-generation migrants from 45 different countries of ancestry and living in twelve

host countries, we show that the same pattern found by Guiso et al.'s exists between the

math gender gap of 15-year-old second-generation migrants and the measures of gender

identity in the migrants' country of ancestry. We find that the higher the degree of

7 Using the epidemiological approach, several studies have examined the effect of culture on different socio-economic outcomes: savings rates (Carroll, Rhee, and Rhee 1994), fertility and female labor force participation (Antecol 2000; Raquel Fernández and Fogli 2006, 2009; Raquel Fernández 2007); living arrangements (Giuliano 2007), the demand for social insurance (Eugster et al. 2011), preferences for a child’s sex (Almond, Edlund, and Milligan 2013), and divorce (Furtado, Marcén, and Sevilla 2013). 8 We follow Fernández and Fogli (2009) and define culture as "systematic differences in preferences and beliefs across either socially or geographically differentiated groups". 9 This is the same index used by Guiso et al. (2008) and Fryer and Levitt (2010). As we explain in the data section, we are constrained to using contemporary measures of gender equality in the ancestry country because the GGI is only first available in 2006, but even then only for a subset of countries. In the robustness section, we use alternative proxies of culture measured in the 1990s, which is closer in time to when the parents left their country of birth.

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gender equality in the country of ancestry, the higher the performance of second-

generation immigrant girls relative to boys. Our results suggest that cultural beliefs

about gender roles explain a large part of the difference in math’s performance between

girls and boys. To be precise we find that a one standard deviation increase in the

country of ancestry's GGI is associated with a decline in the math gender gap of second-

generation migrants of 15 per cent. Our results are robust to different: (1) specifications

strategies, (2) adjustments of standard errors, (3) measures of gender equality, as well as

to the inclusion of a large set of individual, parental and country of ancestry controls,

and (4) changes in sample criteria.

The effect of culture is mostly driven by immigrant girls, consistent with

stereotype threat hypothesis (Spencer, Steele, and Quinn 1999) and gender differential

responses to competitive testing environments (Niederle and Vesterlund 2010). The

effect of culture is particularly sensitive to the concentration of immigrants and girls in

the school, suggesting that schools play an important role in the transmission of culture.

In particular, we find that culture is less important in determining a second-generation

immigrant girl’s math score in schools with larger proportion of girls. This result

suggests that gender equality considerations are less important when peer pressure is

low, consistent with Fryer and Levitt's lack of finding in countries with same-sex

schools. We also find that the effect of culture increases with the proportion of

immigrants in the school, consistent with higher intergeneration transmission of culture

when ethnic social networks are stronger (Fernández and Fogli 2009; Furtado, Marcén,

and Sevilla 2013 find a similar result).

Our contribution to the math gender gap literature is threefold. First, we isolate

the role of culture from institutional constraints. Second, we shed some light on a

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causal interpretation of Guiso et al.'s, 2008, and Fryer and Levitt's, 2010, findings

showing that the same pattern exists among second-immigration immigrants. Third, we

identify schools as the most important channel through which culture may be

transmitted.

The paper is organized as follows. Sections 2 and 3 describe the empirical

strategy, and the data and sample selection, respectively. Sections 4 and 5 present the

main results and the robustness checks, respectively. After presenting evidence on the

channels through which gender identity may be transmitted in Section 6, we conclude in

Section 7.

2. Empirical Strategy

To distinguish the effect of culture from that of institutions and other environmental

factors in explaining variation in math scores between girls and boys, our empirical

approach makes use of the fact that all second-generation immigrants have been

exposed to the host country´s markets and institutions. Thus, evidence that gender

equality in the immigrant´s country of ancestry can explain math scores of second-

generation immigrants is suggestive that the preferences and beliefs of the migrant's

ancesters matter and have been transmitted to them by their parents and/or their ethnic

community. We use OLS to estimate the following baseline specification:

Eijkt=α1femalei + α2(femalei GEj)+ λj+ λk+ δ(femalei λk)+ λt+ X’ijktβ1+ (X’ijktfemalei)β2 +

εijkt (1)

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where i is the individual who was born in the country k but whose country of ancestry is

j and participates in PISA at time t.10 Eijkt indicates individual’s educational attainment

in math test scores. To identify the differences in educational attainment between sexes,

the variable femalei is a dummy equal to one if the individual is a girl and zero

otherwise.

The variable GEj is a measure of gender equality from the immigrant’s country

of ancestry, such that a higher value is associated with a more egalitarian culture. Our

coefficient of interest on the interaction between GEj and the female dummy, α2,

captures the role of gender equality in explaining the gender differences in the

educational achievement of second-generation immigrants boys and girls. A positive

and significant α2 would suggest that more egalitarian attitudes in the immigrant’s

country of ancestry are associated with a higher relative performance of second-

generation immigrant girls over boys, and thus smaller gender gap in children

educational attainment. Thus, the gender gap in math scores between a boy and a girl

from a country of ancestry j with more egalitarian gender roles (higher GEj) would be

smaller than the gender gap between a boy and a girl from a country of ancestry with

less egalitarian gender roles (lower GEj).

We also include country of ancestry fixed effects (λj) to account for

characteristics in the immigrant’s country of ancestry that may be related to gender roles

and educational achievements of second-generation immigrants. We include year fixed

effects (λt) to account for cohort differences and other time variation. In contrast to

10 Throughout the paper we will refer to the country where each individuals was born and lives (k) as their “host country”. Given that they are second-generation immigrants, the country where they were born and live is actually the host country of their parents.

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previous studies using the epidemiological approach, which focus on second-generation

immigrants living in one country (in general US or Canada), we need to include host-

country fixed effects (λk) in our specification to account for host country’s

characteristics that may be related to educational attainment. Crucially, host country’s

dummies are interacted with the female dummy to account for variation in host

country’s educational gender gaps that may arise from cross-country differentials in

cultural or institutional channels.

The vector Xijkt includes a set of individual characteristics, which may affect

educational attainment for reasons unrelated to gender equality, and their interaction

with female dummy. In our baseline specification we only include the age of the child

at the time of the exam and, following Guiso et al. (2008), a dummy indicating whether

the individual is in a grade different from the modal one in the country. Since all

additional socio-demographic characteristics that we observe at age 15 are potentially

endogenous, we do not to include them in our baseline specification (see specification 3

instead).

A second specification further includes GDP per capita (in logarithms) from the

immigrant’s country of ancestry interacted by the female dummy.11 Including the

interaction between the female dummy and the level of development of the country of

ancestry ensures that our coefficient of interest α2, is capturing the effect of gender

equality and not differences in the level of development that may affect an immigrant’s

11 The gross domestic product per capita is expressed in real terms deflated with Laspeyres price index. Source: Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 7.0, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, June 2011.

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test scores for reasons unrelated to gender equality.12 Throughout the paper we will

refer to this specification as our “preferred specification”.

Eijkt=α1femalei + α2(femalei GEj)+ α3(femalei lgdpj)+ λj+ λk+ δ1(femalei λk) + λt+

X’ijktβ1+ (X’ijktfemalei)β

2 + εijkt (2)

There are several sources of heterogeneity across individuals other than cultural

beliefs on gender roles that may affect their educational attainment. To take this into

account, a third specification additionally adds to equation (2) socio-demographic

characteristics related to the immigrant’s family and school (vector Z) and their

interaction with the female dummy. In particular we include as controls family

characteristics: mother’s and father’s highest educational attainment, an index

indicating the highest level of occupation of parents, two indexes indicating the cultural

and educational resources at home respectively and a dummy variable indicating

whether the individual spoke a different language at home. Among school's

characteristics we include: the percentage of girls enrolled at school, whether the school

is publicly or privately financed, and whether the school is in a metropolitan area or not.

Information on how these variables are defined and descriptive statistics are shown in

Appendix Tables A.1.13 Without these controls α2 may be capturing spurious

correlation between the individuals' unobserved factors and our measures of gender

equality. For example, if more educated mothers increase the test performance of girls

12 As a robustness test, we also estimate a specification in which we also control for the Human Development Index (HDI) as proxy of the level of development of the country of ancestry.

13 To avoid losing observations due to item non-response in one or several of these questions, we impute the missing values following the MICE method of multiple multivariate imputation described by Van Buuren, Boshuizen, and Knook (1999). This multiple imputation approach is more appropriate when the assumption of random distribution of non-response is dubious. The basic idea is to create a small number of copies of the data (in our case 5), each of which has the missing values suitably imputed. To each imputation we use the command mvis in Stata and control for country of ancestry, year and country of birth. Then, estimates of the parameters of interest are averaged across the 5 copies to give a single estimate and standard errors are computed according to the “Rubin rules” (Rubin 1987).

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relative to boys, and if it is less costly for a girl to perform relatively better in school if

her parents come from an egalitarian country, then the correlation captured by α2 would

be due to the correlation between parental characteristics by country of ancestry and

female education.

Eijkt=α1femalei+ α2(femalei GEj)+ α3(femalei lgdpj)+ λj+ λk+ δ1(femalei λk) + λt+

X’ijktβ1+ (X’ijktfemalei)β

2 + Z’ijktβ3+ (Z’ijktfemalei)β

4+ εijkt (3)

The fourth specification substitutes the interaction between the female dummy

and the host country fixed effects in equation (2) by the interaction between the female

dummy and gender equality (GEk) and GDP per capita (lgdpk) in the host country. In

doing so this specification accounts for the fact that immigrants from countries of

ancestry with less gender-equal culture may tend to settle in host countries with similar

gender-equal culture and institutions. If this is the case, our coefficient of interest in

equation 2 would be biased upwards as it would be capturing the effect of the host

country’s culture and institutions in addition to the effects of culture in the immigrant’s

country of ancestry.

Eijk= α1 femalei+ α2 (femalei GEj)+ α3(femalei lgdpj)+λj + λk +λt + δ1(femalei GEk)+

δ2(femalei lgdpk)+ X’ijktβ1+ (X’ijktfemalei)β

2 +εijk (4)

Because identification in our models comes from the variation of gender equality across

country of ancestry, standard errors are clustered at this level.

3. Data and Sample

Program for International Student Assessment (PISA) Data

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Our main data set uses the 2003, 2006, 2009 and 2012 student-level data from the

Program for International Student Assessment (PISA), an internationally standardized

assessment conducted by the Organization for Economic Cooperation and Development

(OECD) and administered to 15-year olds in schools every three years since 2000. In

contrast to other international assessment, such as TIMSS which focuses on assessing

what students have learned in the classroom, the purpose of PISA is to test whether

students have acquired the knowledge and skills essential for full participation in

society near the end of compulsory education. These skills include whether they can

analyze, reason, and communicate effectively. According to the OECD the PISA math

test assesses “the capacity to identify and understand the role that mathematics plays in

the world, to make well-founded judgments and to use and engage with mathematics in

ways that meet the needs of that individual’s life as a constructive, concerned and

reflective citizen” (OECD, 2004, p. 26). Else-Quest, Hyde, and Linn (2010) suggest

that PISA may be more relevant to measure the math gender gap than TIMMS because

it is a more challenging assessment. Even if we wanted to use TIMMS, the lack of

information on country of ancestry of second-immigrants prevents us from doing so.14

PISA assesses a range of relevant skills and competencies in three main

domains: mathematics, reading and science. In addition, students and school principals

also answer questionnaires to provide information about the students' backgrounds,

schools and learning experiences and about the broader school system and learning

environment. Our analysis focuses on mathematics and begins in 2003 because

questions entering the math scores are not comparable before and after that year. PISA

tests are paper and pencil tests, lasting up to two hours for each student. Participation in

14 TIMSS is an international assessment of mathematics and science learning in eighth graders, conducted on a 4-year cycle by the International Association for the Evaluation of International Achievement (IEA), in collaboration with Statistics Canada and the Educational Testing Service.

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PISA tests is voluntary for schools and students, although a minimum participation rate

of 65 percent (80 percent) of schools (students) from the original sample is required for

a country to be included in the international database. Each subject is tested using a

broad sample of tasks with differing levels of difficulty to represent a comprehensive

indicator of the continuum of students’ abilities. The PISA program presents the tests

scores standardized so that they have a mean of 500 test-score points and a standard

deviation of 100 test-score points across the OECD countries.

PISA uses imputation methods, denoted as plausible values (hereinafter PV), to

report student performance. In all of our analysis we use PV and follow the OECD

recommendations that involve estimating one regression for each set of PV (there are

five PV to each domain) and then report the arithmetic average of these estimates. In

addition, PISA sample is stratified at two stages: first, schools are randomly selected

and second, students at each school are randomly assigned to carry out the test in all

three subjects. Our results are robust to applying the Fay’s Balanced Repeated

Replicated (BRR) methodology that takes into account this two-stage sample design (as

shown in the results section).

Gender Equality Measures

To measure gender equality in an immigrant’s country of ancestry, we follow Guiso et

al. (2008) and use the Gender Gap Index and the Political Empowerment Index

(henceforth GGI, PEI, respectively) from The World Economic Forum (Hausmann,

Tyson, and Zahidi 2009). We also use female labor force participation in the

immigrant’s country of ancestry from the International Labour Organization. All these

measures are standard in the literature (Fryer and Levitt 2010; Guiso et al. 2008). The

GGI measures the relative position of women in a society taking into account the gap

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between men and women in economic opportunities, economic participation,

educational attainment, political achievements, health, and well-being. The PEI is a

sub-index from the GGI and measures the gap between men and women in political

participation based on the ratio women to men with seats in parliament, the ratio of

women to men in ministerial level and the ratio of the number of years with a woman as

head of state to the years with a man. Both indicators range from 0 to 1 and larger

values point to a better position of women in society.

As an additional robustness check, in Section 5 we show that our results are

robust to using an index of cultural attitudes towards women from the World Value

Survey (also used in Guiso et al. 2008), and the ratio of young literate females to males

(ages 15 to 24).15 Appendix Table A.2 presents a detailed description of all the gender

equality measures used in the analysis, as well as basic descriptive statistics.

Information of GGI and PEI is available beginning 2006. In such year, 115

countries were included in the indexes, in 2007 128, in 2008 130 and in 2009 134. In

order to maximize the number of countries in our sample, we focus on 2009 values for

all our gender equality indicators in the immigrant’s country of ancestry. The use of

contemporaneous measures of gender equality instead of the ones observed at the time

parents migrate is a common practice in the literature. First, it is reasonable to expect

that countries' aggregated preferences and beliefs about the role of women in society

change slowly over time. Also, as Fernández and Fogli (2009) point out, "one could

argue that the values that parents and society transmit are best reflected in what their

contemporaneous counterparts are doing in the country of ancestry". Rather than

trying to solve this debate on theoretical grounds, we take an empirical approach and 15 Unfortunately these two variables are missing for many countries, precluding us from using it as main indicators.

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also check the robustness of our results to using proxies of gender-equality measured in

the 1990s (shown in the Results Section).

Sample

Following the literature, our sample consists of second-generation immigrants who were

born and reside in a participating host country but whose parents (both of them) were

born in another country. We pool the 2003, 2006, 2009 and 2012 PISA waves so as to

have the larger variation possible in terms of both host countries and countries of

ancestry. To determine the students’ country of ancestry, we need specific information

on their parents’ country of birth. This question is not consistently asked among

participating countries. For instance, when asking about the country of origin, the US

only provided the options “United States of America” and “another country”. As a

consequence, only data from those participating countries providing detailed

information about the parents’ birth place were used in the analysis.16 Based on Blau et

al. (2013) who find that the effect of mother’s country of origin on second-generation

immigrants girls tend to be stronger than the effect of the father’s country of origin

when parents come from different countries, we assign the mother’s country of origin.17

We restrict our sample to those individuals for whom we observe gender equality

measures for both their country of ancestry and their host country, and focus our

analysis on host countries with immigrants from at least four countries of ancestry to

ensure that we do not compromise the identification in our model, which arises from

variation in the gender equality in the immigrant’s country of ancestry within a given

16These are Australia, Austria, Belgium, Denmark, Finland, Germany, Greece, Latvia, Liechtenstein, Luxembourg, New Zealand, Norway, Portugal, Switzerland and Scotland in 2003, 2006, 2009 and 2012 PISA, Argentina, Czech Republic, Israel, Netherlands and Qatar in 2009 and 2012 PISA, and China, Costa Rica and Turkey in 2012. 17In any case, 85 percent of the second-generation immigrants in our sample have parents who emigrate from the same country.

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host country.18 We also drop second-generation immigrant children whose country of

ancestry has fewer than five observations in a given host country.19 In the robustness

section we explore the robustness of our results to changes in sample criteria.

Our final sample has 12,027 second-generation migrants from 45 different

countries of ancestry and living in twelve host countries (as described in Appendix

Table A.3). Host countries are mainly OECD countries, whereas countries of ancestry

are from various continents and levels of development. Indeed, the countries of ancestry

in our sample cover all continents, with many European (24 countries) and some

transition economies (Albania, Poland, Russia and Ukraine), several countries in the

Americas (Bolivia, Brazil, Chile, Paraguay, Suriname, United States and Uruguay),

some in Asia (Bangladesh, China, India, Korea, Malaysia, Philippines, Vietnam), some

in the Middle East (Iran, Egypt and Pakistan), some in Africa (Ethiopia, Morocco and

South Africa), and some in Oceania (Australia and New Zealand). Second-generation

immigrants whose country of ancestry is Portugal, Turkey or Italy represent 47 percent

of the sample. Host countries with the highest sample of second-generation immigrants

are Australia, Switzerland and Luxembourg (immigrants living in these countries

represent 68 percent of the sample).

Descriptive Statistics

18The lack of gender equality measures for all countries implies losing the following countries of ancestry: Afghanistan, Bosnia and Herzegovina, Cape Verde, Occupied Palestine, Iraq, Lebanon, Liechtenstein, Netherlands Antilles, Somalia, Somoa and Serbia-Montenegro (4,345 observations) and the host country of Liechtenstein (or 135 observations). In any case, most of the countries of ancestry we lose are from conflictive zones, which are commonly excluded from this kind of analysis (see Fernández and Fogli 2009, and Furtado, Marcen, and Sevilla 2013). In addition, by limiting our analysis to host countries with at least four different groups of immigrants we lose 3,983 observations from the following ten host countries (Costa Rica, China, Denmark, Germany, Greece, Latvia, Norway, Portugal, Qatar and Turkey), and seven countries of ancestry (Brazil, Bulgaria, Belarus, Jordan, Egypt, Nicaragua and Yemen). 19 This is a common practice in the literature. For instance, Fernández and Fogli (2009) eliminate those countries of ancestry with fewer than 15 observations. Given that our regressions are run at the individual level, including or not these small numbers of observations does not affect our results. With this adjustment, we lose only 20 individuals and five different countries of ancestry (Colombia, Czech Republic, Denmark, Panama and Thailand).

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Table 1 presents summary statistics of our main country of ancestry's gender

equality measures for our sample of second-generation immigrants. Countries of

ancestry are ordered from highest to lowest gender gaps in math test scores measured as

the average boy’s minus the average girl’s scores. Panel A shows that there is a large

variation in the gender gap in math scores across countries of ancestry. At the bottom

10 percent of the distribution of the math gender gap by country of ancestry, second-

generation immigrant girls substantially underperform boys by 62 score points (0.6

standard deviation). Given that a difference of 40 points in PISA tests is equivalent to 1

year of schooling (OECD 2012), such a difference equivalent to about 1.5 years of

schooling. At the top 10 percent of the math gender gap distribution, second-generation

immigrant girls outperform boys by 34 scores points (0.3 standard deviation) or the

equivalent to ten months of schooling.

The average score of boys in our sample of second-generation immigrants is 491

points with a standard deviation of 110, whereas the average score of girls is 473 with a

standard deviation of 99. Thus, the difference in math score between girls and boys

across our sample is -18.29, which implies that girls underperform boys by 0.18

standard deviation, the equivalent to 5.5 months of schooling. This gender gap in math

scores is quite similar to the one observed among all second-generation immigrants and

natives living in the host countries included in our analysis, and not too distant from the

ones showed when all countries participating in PISA assessments are considered (see

Table A.4).

Panel A also shows the different measures of gender equality by country of

ancestry. The GGI takes values between zero and one and averages 0.68 with a

standard deviation of 0.06. It varies from 0.55 in Pakistan to 0.81 in Sweden. The PEI

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displays also a high variation across countries with a minimum of 0.02 in Iran and a

maximum of 0.50 in Sweden--it averages 0.16 with a 0.12 standard deviation in the

whole sample. FLFP also varies widely by country, moving from 0.16 percent in Iran

to over 78 percent in Ethiopia--the average FLFP in the sample is 49 percent with a

standard deviation of 12 percent. Panel B shows the cross-country correlation across

the difference gender equality measures. Not surprisingly, we find that these measures

are correlated. The cross-country correlation between the GGI and PEI or the GGI and

the FLFP is high, ranging between 0.78 and 0.67, while the PEI and FLFP have a cross-

correlation of 0.32.

Figure 1 plots the average math gender gap of second-generation immigrants by

country of ancestry (column 1 of Table 1) versus the three measures of gender equality:

GGI, PEI, and FLFP (columns 2 to 4 of Table 1). Overall, the raw data show that the

more gender equality in the country of ancestry the higher the relative performance in

math scores of second-generation immigrant girls with respect to boys. The correlations

range from 0.18 to 0.20 percent and are statistically significant at conventional levels

(see column 1 in Panel B of Table 1).

4. Main Results

Can Gender Equality Explain the Gender Gap in Math Scores?

Table 2 displays the coefficient on the interaction between female dummy and gender

equality measure, α2, which informs us on the effect of gender equality on the gender

gap in mathematics. Each column displays the results from estimating the different

empirical specifications, while each row displays the results from using alternative

measures of gender equality in the country of ancestry.

17

Column 1 in Table 2 shows a positive and statistically significant coefficient on

the interaction between the female dummy and gender equality measure, α2, suggesting

that the gender gap in mathematics narrows among children whose country of ancestry

is one with more egalitarian attitudes towards women. Results are qualitatively the

same in our preferred specification shown in column 2, which includes the interaction

between the female dummy and the GDP per capita of the country of ancestry as in

equation (2). The coefficient of interest, α2, remains positive and statistically

significant. In fact, this coefficient increases in most specifications with respect to the

coefficient estimated in column 1, suggesting that not taking into account differences in

the economic development of the immigrant’s country of ancestry could lead to a

downward bias in the estimated effect of gender equality and the gap in math scores.20

The magnitude of the coefficient on the interaction between female dummy and

gender equality measure, α2, suggests that gender identity may explain an important part

of the variation in the gender gap in mathematics across immigrants from different

countries of ancestry. For instance, the coefficient α2 in the first row of column 2

estimates that an increase in the level of GGI by one standard deviation is associated

with a reduction of 6.94 score points in the gender gap in mathematics, the equivalent of

a bit over 2 months of schooling. It also accounts for a 15 percent of the variation in the

gender gap across countries of ancestry.21 Alternatively, if immigrants from Turkish

descent, whose country of ancestry has a GGI of 0.58 and who present a gender gap in

math scores of -13.82 score points, were characterized by the mean gender equality

20 Guiso et al. (2008) also find that not taking into account differences in the economic development across countries leads to a downward bias of the estimate effect of gender equality in the math gap (Table S4, supporting material on-line). 21 Using values from Table 1 this effect was calculated as

. ∗ . .

.0.15

18

(GGI = 0.67), our statistical model would suggest that the mean score performance in

mathematics of second-generation Turkish girls relative to boys would increase by 10

score points, which would practically eliminate their gender gap.22

Similar results are obtained when we use the other measures of gender equality.

According to the second row in column 2 of Table 2, an increase in the level of PEI by

one standard deviation (across countries of ancestry) is associated with a reduction in

the gender gap in mathematics of 7 score points, which is a 15 percent of the variation

in gender gap across different ancestries. When we use the labor force participation rate

to measure gender equality, we continue to find that the gender gap in math scores

decreases with gender equality. The coefficient in rows 3 of column 2 indicates that an

increase in the FLFP by one standard deviation is associated with a reduction in the

gender gap in math scores of 3.8 score points, which is 8 percent of the variation in the

gender gap across ancestries.23

Guiso et al.'s (2008) estimated effect of the gender equality measures over the

gender gap in math scores is of 105.49, 29.1 or 45.0 when the GGI, PEI or FLFP indices

are used as gender equality proxy, respectively. This implies that an increase in the

level of each of these measures by one standard deviation is associated with a reduction

in the gender gap across countries between 51 and 68 percent depending on the measure

used.24 While these magnitudes represent about four times our estimates, they are not

22 This is calculated as 0.67 0.58 0.09 ∗ 115.73 10.4. 23 This is calculated as

. ∗ . .

.0.08

24 The cross-country standard deviation of the GGI, PEI and FLFP in Guiso et al. (2008)’s sample is 0.05, 0.15 and 0.09 respectively. Given the coefficients estimated by the authors, an increase of one standard deviation in the GGI (0.05) implies a reduction of 5.3 score points in the math gender gap, which represent a reduction of 68 percent of the variation in the gender gap across countries in the their sample (the cross-country standard deviation in the math gender gap is 7.74 according to our own calculation using 2003 PISA). Similarly, an increase of one standard deviation in the PEI and FLFP reduces the gap in math scores in 4.4 or 4.1 points or 56 (51) percent of the cross-

19

directly comparable in that the identification across studies is different. In their analysis

the identification comes from the variation of the level of gender equality across home

countries using both natives and immigrants' gender differences in mathematics test

scores. In contrast, in our models identification comes from the variation across country

of ancestry within host country using only second-generation immigrant children.

Having said this, we can compare our analysis to what we would have obtained using

all individuals and exploiting only the cross-country of residence variation as in Guiso

et al. (2008) with PISA 2003-2012 to get an approximation of how much of math

gender gap across countries of residence is explained by culture versus institutional

constraints. When we replicate Guiso et al. (2008) using all countries in PISA 2003,

2006, 2009 and 2012, we find that the effect of GGI over the gender gap in math scores

is of 47.92 (standard error = 0.048), implying that an increase in the level of this

measure by one standard deviation is associated with a reduction in the gender gap

across countries of 25 percent. Although this is only a back-of-the-envelope exercise it

suggests that the transmission of beliefs and preferences accounts for 60 percent of the

total effect.25

While the results from Guiso et al. (2008) suggest an important role for a

country’s culture and institutions (as opposed to biological explanations) influencing the

relative performance of girls in mathematics, our results assess the relative importance

of culture versus institutions, suggesting that the former has an important role in

country variation in gender gap in their sample. Information about standard deviations of each gender equality measure is available in their Supporting Online Material, available in (www.sciencemag.org/cgi/content/full/320/5880/1164/DC1). To make their results of FLFP comparable with ours, we divide their FLFP measure by 100 (and also their coefficient estimated).

25 If this back of the envelope analysis is restricted to only host countries included in our analysis, we find a similar result. In particular, we find that the GGI the over the gender gap in math scores is of 26.55 (standard error = 0.036), implying that an increase in the level of each of these measures by one standard deviation is associated with a reduction in the gender gap across host countries of 22 percent.

20

explaining gender differences in mathematics. It is also important to highlight that

because of our identification strategy, we only capture the effect of inter-generationally

transmitted culture as opposed to the effect of culture in the host country, thus our

estimates of the effect of culture ought to be considered as a downward bias of the total

effect of culture.

5. Robustness Checks

This section explores the robustness of these results to omitted variable bias, alternative

specifications to account among other things for the self-selection of immigrants,

clustering of the standard errors, alternative measures of gender equality, and changes in

sample criteria.

Sensitivity Analysis

One concern is that our results may be capturing educational differences in the country

of ancestry rather than differences in gender equality. If those more egalitarian

countries have also more advanced educational systems, the effect of gender equality

measures on math gender gap would be upward bias. We check this possibility in

column 3 of Table 2 by adding the interaction between the female dummy and the

Human Development Index (HDI), which includes, in addition to income (as GDP per

capita), measures of life expectancy and education (such as mean years of schooling and

expected years of schooling). As can be seen, adding this variable has little effect when

using GGI or PEI, and reduces precision when using FLFP.

As explained in section 2, without individual controls, α2 may still be capturing

spurious correlation between the individuals' unobserved factors and our measures of

21

gender equality. To explore whether omitted variable bias is an issue, results from

equation (3) are reported in columns 4 and 5 of Table 2 where family and school

characteristics are controlled for, respectively. Column 6 includes both family and

school covariates. After controlling for the immigrants' family and school

characteristics, the coefficient α2 remains positive and statistically significant.

Column 7 in Table 2 also shows that our results remain practically unchanged

when we adopt even a more flexible specification where each year fixed-effect is

interacted by the female dummy to allow different math gender gaps by cohort assessed

in different PISA waves.

Columns 8 and 9 in Table 2 evaluate to what extent our results are biased due to

self-selection of migrants into host countries which are similar in terms of gender

equality by substituting the interaction between the female dummy and host country

dummies with interactions between the female dummy and gender equality measures

and log GDP per capita in the host country. To do so, column 8 estimates equation (4).

In terms of gender equality measures, we include the GGI, the PEI, the total FLFP and

the labor force participation for women between 35 and 54 years old, which captures the

cohort of women with the same age interval as the mothers of the PISA students under

analysis. The idea behind including all these host country gender equality measures is

to capture as many dimensions of gender equality as possible in the host country. If

those immigrants from countries with less gender-equal cultures tend to also settle in

host countries with less gender-equal cultures and institutions, our coefficient of interest

may be capturing the effect of the host country laws and institutions rather than the

effect of the culture of ancestry. While the results in column 8 are smaller and less

precise than those in our preferred specification (shown in column 2), they are

22

consistent with beliefs' from the ancestry country explaining the math gender gap.

Column 9 shows that the results are also robust to adding the interaction between the

female dummy and host country’s HDI to the specification in equation (4).

As explained in Section II, all of our estimates are calculated by clustering

standard errors at the country of ancestry level. However, because of the double

stratification of the sampling design employed by PISA, column 10 of Table 2 shows a

specification that applies the Fay’s Balanced Repeated Replicated (BRR) methodology.

Again, the results are robust to this alternative adjustment of the standard errors when

we use the GGI or PEI indices, but we lose precision with the FLFP.

Alternative Measures of Gender Equality

Table 3 displays the results from estimating our main specification using alternative

measures of gender equality. Panel A tests the robustness of our results to the use of

gender equality indexes measured in the 1990s. In particular we use the proportion of

seats held by women in national parliaments in 1990-1997, and female labor

participation rates in 1990. As can be seen, the effect remains positive in both cases,

but it loses significance when using female labor force participation rates measured in

1990. Following Guiso et al. (2008), panel B checks the robustness of our results to

using two alternative proxies of gender equality in the country of ancestry, namely an

indicator elaborated from a series of questions about gender roles included in the World

Values Survey (WVS). Alternatively, panel B also shows a specification in which the

gender equality measure is captured by the gender gap in the literacy rate, which

23

constitutes a good proxy of gender inequality in the access to the educational system.26

In both cases, our main results holds and remains statistically significant. Most

importantly, the magnitude of the effect remains consistent with our main findings. In

particular, an increase by one standard deviation in each of these gender equality

measures is associated with a reduction in the gender gap in mathematics of 5.55, 3.35,

5.87 or 5.89 score points, respectively, which accounts for a 12, 7, 11 and 14 percent of

the cross country variation in the gender gap in mathematics.27

Changes in Sample Criteria

Table 4 shows that our results are not driven by the main group of immigrants (the

Portuguese) or the host country with the largest sample of immigrants (Switzerland)--

shown in panels A and B. Panel C shows that the effect remains when only one host

country is used (although the coefficient is not longer statistically significant in the case

of Switzerland). Also, the fact that our results remains when using alternative measures

only available for a smaller number of countries of ancestry as in Panel B of Table 3,

represents additional evidence that our results are not sensitive to changes in sample

criteria.

6. Cultural Transmission Mechanisms

This section looks at the transmission mechanisms of culture. We first look at whether

the effect of culture on closing the gender gap in math is due to more positive attitudes 26 Both measures are described in Appendix Table A.3. Note that these measures are not available for many of the countries of ancestry in our dataset, precluding their use in main analysis. In the case of the WVS indicator we lose nine of the 45 countries of ancestry, while with the literacy rate we lose 28 countries of ancestry. 27 Columns 3 and 4 of Table 3 display the cross-country standard deviation of each of these alternative measures and of the math gender gap used to these calculations. Bear in mind that the countries of ancestry varies depending on the measure used.

24

about the role of women in society increasing a girl’s math scores as opposed to

decreasing a boy’s. Exceeding at mathematics is not considered to be part of a girl’s

identity. Cvencek, Meltzoff, and Greenwald (2011) show, using a sample of adults and

children, that ‘Girls don’t do math’ is a widespread cultural stereotype.28 This

stereotype works in an asymmetric way, particularly affecting girls who deviate from

the norm, as opposed to boys (Spencer, Steele, and Quinn 1999). This asymmetry has

also been shown in studies looking at the impact of teacher’s gender on girls and boys

math performance. For example, Carrell, Page, and West (2010) find a differential

effect of professor’s gender on the performance of boys and girls, which can be

rationalized by girls being affected when female students are reminded about the belief

that they are not supposed to be good at math when being taught by a male teacher. In

contrast, boys are not necessarily affected when reminded that they are supposed to be

good when taught by a male teacher. Similarly, Gneezy, Niederle, and Rustichini

(2003) present experimental evidence that women’s performance in competitive

environments substantially decreases when competing against males, while the

performance of men in single-sex tournaments is not significantly different than in

mixed-sex tournaments.

Table 5 presents the results from estimating Equations (1) to (4) separately for

boys and girls. As can be seen in Panel A, the effect of gender equality in the country

of ancestry on girls’ math tests scores is always positive and statistically significant. An

increase of one standard deviation of the GGI index increases girls’ score in

mathematics by 15 points, explaining almost 25 percent of the cross-country variation in

28 Anecdotally, in 1994 Mattel created a Barbie™ doll that said, “Math is hard.”

25

girls’ test scores 29 In contrast to what we find for girls, Panel B of Table 5 shows that

the effect of culture on boys’ math test scores is smaller and not statistically significant.

These findings corroborate the asymmetric effect of culture and show that the reduction

of the gender gap found in Table 1 as a result from more egalitarian cultural attitudes

toward women comes primarily from girls performing differentially better than boys.

To explore the cultural mechanisms which prompt girls from more equal

cultures to perform differentially better at math, we look at how culture is transmitted.

First panel A in Table 6 looks at transmission mechanisms of culture within the school.

For example, Booth and Nolen (2012) and Booth (2009) show that school gender peer

effects can explain why girls in only-girls school behave more like boys taking on more

risks. They also find that college female students attending female-only classes perform

better relative to female students attending mixed-sex classes. Here we test whether the

effect of more egalitarian attitudes toward women in the country of ancestry on girls’

math scores remains after controlling for school peer effects, and whether the effect of

culture through peer effects is greater when there is a higher proportion of boys in the

school.

In panel A we look at the proportion of girls in the school (as recorded by the

school’s principal) and at schools that are single-sex (where 95 percent or more pupils

are girls).30 The GGI coefficient remains positive and significant after controlling for

school gender composition. Crucially, the effect of gender equality is not so important

for girls with a higher proportion of girls in the school, as shown by the coefficient on

29 The cross-country standard deviation of girl’s math tests scores is 61.99, so that 15 divided by 61.99 is equal to 0.242

30 See Appendix Table A 5 for definition and descriptive statistics of these variables.

26

the interaction between the GGI index and the proportion of girls in the school (panel

A.1) and the single-sex dummy (panel A.2). For example, an increase in the GGI index

by one standard deviation increases a girl’s math test scores by 16 points if attending a

co-educational school, whereas the effect almost halves to 9 points when attending a

single-sex school. This evidence is consistent with Fryer and Levitt's lack of finding in

countries with same-sex schools, and can be rationalized by the fact that in single-sex

schools girls do not fear being perceived as different and thus the cultural effect from

the beliefs that girls are worse at math than boys on girls’ performance is less important.

In line with the above literature of gender peer effects in schools, we also find that more

girls in a school and attendance to a single-sex school is associated with higher math

scores for girls.

Panel B looks at the transmission within local communities by assessing to what

extent culture is more important for second-generation immigrant girls having a greater

exposure to the cultural norms in the country of ancestry. Fernández and Fogli (2009)

show that the impact of culture appears to be greater for the descendants of those

immigrant groups that have a greater tendency to cluster in the same communities.31 In

particular, they argue that an immigrant ethnic network may be crucial for transferring

and protecting cultural beliefs, independently of the human capital externalities derived

from an immigrant’s neighborhood effects (as argued by Borjas 1995). In our context it

is natural to think of an immigrant’s network as school communities. In particular, there

is evidence that the scores of immigrant children are different depending on the

31 Although the literature generally refers to immigrant concentration from the same ethnicity, we cannot undertake the analysis by ethnicity at the school level as sample sizes are very small. Rather we use the concentration of immigrants in a given school as a proxy for the concentration of immigrants from the same ethnicity. To the extent that immigrants are different from natives in a systematic way, independently of the ethnicity, this is not a very strong assumption.

27

immigrant concentration in the school although the direction of the effect is still unclear

(see for instance Jensen and Rasmussen 2011, and Schnepf 2007). Panel B in Table 6

explores what the implications for girls’ attainment of having more immigrants in the

school are, and whether the effect of culture depends on how many immigrants there are

in the school. To that end we include the concentration of immigrants in the school and

its interaction with the culture proxy (GGI) in Panel B.32

The estimates presented in Column (2) of Panel B show that the culture

coefficient remains positive and significant after controlling for the proportion of

immigrants in the school. Interestingly, when the interaction between the GGI index and

the proportion of immigrants in the school is included in Column (3), we see that the

effect of culture is higher for those second-generation immigrant students in schools

with a higher proportion of immigrants. For example, an increase in the GGI by one

standard deviation is associated with an increase of 18 points in the math scores for girls

attending schools with a proportion of immigrants one standard deviation above the

median (46 per cent), which is 4 points higher than the increase experimented for those

girls attending schools with the mean proportion of immigrants (34 per cent). The

coefficient on the proportion of immigrants in the school is negative, suggesting that

second generation immigrant girls perform worse in math the higher the concentration

of immigrants. 33

32 We follow Schnepf (2007) and calculate the proportion of immigrants in each school from PISA. We include both, first and second-generation immigrants and use final student weights included in PISA data. Given that schools and students participating in PISA are chosen randomly, this ratio should be representative (see Appendix Table A 5). 33 It is important to take into account that immigrants (both first and second generation) living in the host countries included in our analysis have, on average, a lower score in math tests than natives: 470.56 (standard deviation 104.71) versus 490.77 (standard deviation 98.77).

28

Panel C explores transmission of gender identity from parents to children, a

channel that has been extensively documented in the literature (Bisin and Verdier 2001;

Farré and Vella 2013). Using the 1995–2011 March Current Population Survey and

1970– 2000 Census data Blau et al. (2013) find evidence of intergenerational

transmission of gender roles among the immigrant population from parents to children,

and in particular from mothers to daughters in issues related to fertility and labor force

participation.

To test to what extent the effect of cultural norms persist after controlling for

mother characteristics and whether there is a different effect of culture depending on

mother’s characteristics, we include the mother’s educational level and the mother’s

labor status and its interactions with our culture proxy in Panel C of Table 6. The

proportion of second-generation immigrant girls in our sample who have a mother

working is relatively high (81 percent), although mother’s educational level is on

average below upper secondary school. Results in Panel C of Table 6 show that the

coefficient on culture remains positive and statistically significant after controlling for

mother’s characteristics. Similarly, having a mother who works is positively associated

with higher girl’s math scores. Interestingly however, the coefficient for the interaction

between the GGI and mother’s characteristics is not statistically significant. Although

the interaction of the GGI index with the mother’s work dummy is negative, suggesting

that for those girls whose mother is working the role of culture in determining a girl’s

math scores is less important, the coefficient is not precisely estimated.

29

6. Conclusion

This paper aims to rigorously disentangle the effects of markets and institutions from

the effects of culture in determining gender differences in educational attainment in

mathematics. Second-generation immigrants live in the host country and absorb their

country of ancestry’s culture from their parents and ethnic communities, but are

exposed to the host country’s laws and institutions. We thus interpret the estimated

effect of gender equality in the country of ancestry on math scores of second-generation

immigrants as evidence of the role of culture.

We find that the higher degree of gender equality in the country of ancestry

improves the performance of second-generation immigrant girls relative to boys. In

particular, the gender gap disappears among immigrants from more gender-equal

cultures. Our results are robust to a battery of sensitivity tests. We also rule out

alternative explanations for the result such as self-selection of immigrants from

countries of ancestry with more gender-equal cultures living in host countries with

lower gender gaps in math scores. Our findings are consistent with those of Guiso et

al.'s (2008), and Fryer and Levitt's (2010), using cross-country variation in cultural

attitudes toward women. Our findings show that the same pattern exists among second-

immigration immigrants, and that previous evidence on the importance of culture was

not driven by differences in institutional factors across countries.

We also explore the mechanisms through which culture is transmitted. We first

show that the effect of culture on closing the gender gap in math is due to more positive

attitudes about the role of women in society increasing a girl’s math scores as opposed

to decreasing a boy’s. We find that whereas the effect of culture on a girl’s math test

scores is independent of whether the mother works, positive cultural views toward

30

women seem to be more important in increasing a girl’s math record if she attends a

school where the concentration of immigrants and the ratio of boys to girls are greater.

The transmission channels seem to be operating within the school and among peers, as

opposed to between mothers and daughters within the family. However, we cannot rule

out that more egalitarian parents send their children to schools with higher

concentration of immigrants and boys.

Our findings that a more gender-equal culture affects girls’ academic

achievement with respect to boys yield support to policies that alter the believes about

gender roles early in life (see for example work on the transmission of preferences from

mothers to daughters and sons (Blau et al. 2013; Farré and Vella 2013; R Fernández,

Fogli, and Olivetti 2004). Our findings may also explain why similar educational

systems may have a differential impact on the relative performance on math for girls

and boys, and point to the interplay between culture and institutions as the key factor.

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Table 1. Gender Gap in Math Scores and Gender Equality by Country of Ancestry

PANEL A

Country Math

Gender Gap GGI PEI FLFP N

1 Ukraine -174.97 0.69 0.06 0.53 5 2 Korea -78.24 0.61 0.07 0.49 46 3 Bangladesh -77.60 0.65 0.29 0.57 7 4 Macedonia -72.64 0.69 0.16 0.42 20 5 Slovenia -62.05 0.70 0.10 0.53 6 6 Uruguay -40.31 0.69 0.14 0.55 17 7 Fiji -38.99 0.64 0.06 0.39 35 8 Greece -35.53 0.67 0.09 0.44 46 9 Malaysia -35.19 0.65 0.06 0.44 34

10 United States -34.75 0.72 0.14 0.58 111 11 Croatia -31.74 0.69 0.16 0.47 77 12 Morocco -31.70 0.59 0.10 0.26 192 13 Sweden -31.38 0.81 0.50 0.59 9 14 Romania -30.52 0.68 0.04 0.48 58 15 Spain -25.55 0.73 0.37 0.51 246 16 Albania -25.51 0.66 0.04 0.50 136 17 United Kingdom -24.78 0.74 0.28 0.55 838 18 India -24.71 0.62 0.27 0.30 168 19 China -22.72 0.69 0.14 0.68 608 20 Italy -22.65 0.68 0.16 0.38 1,083 21 Poland -20.11 0.70 0.18 0.47 47 22 Russian Fed. -17.16 0.70 0.08 0.56 592 23 Belgium -15.56 0.72 0.24 0.47 159 24 Bolivia -14.36 0.67 0.15 0.63 131 25 Turkey -13.82 0.58 0.07 0.27 1,783 26 Hungary -12.50 0.69 0.11 0.43 7 27 Ethiopia -10.69 0.59 0.11 0.78 151 28 Suriname -10.39 0.67 0.16 0.40 107 29 Pakistan -9.95 0.55 0.15 0.22 36 30 Philippines -9.66 0.76 0.29 0.49 240 31 Portugal -8.53 0.70 0.16 0.56 2,846 32 South Africa -7.12 0.77 0.45 0.45 70 33 France -6.43 0.73 0.29 0.51 614 34 Viet Nam -2.95 0.68 0.12 0.73 359 35 Germany -1.75 0.74 0.31 0.53 398 36 New Zealand 2.42 0.79 0.39 0.62 376 37 Estonia 6.35 0.71 0.16 0.56 55 38 Paraguay 12.61 0.69 0.10 0.57 63 39 Australia 32.26 0.73 0.19 0.59 36 40 Austria 32.29 0.70 0.27 0.54 46 41 Chile 33.52 0.69 0.26 0.43 24 42 Slovakia 37.23 0.68 0.11 0.50 70 43 Iran 38.89 0.58 0.02 0.16 6 44 Netherlands 43.98 0.75 0.34 0.60 62 45 Brazil 180.38 0.67 0.06 0.59 7 mean -18.29 0.67 0.16 0.49 12,027 sd 47.51 0.06 0.12 0.18

PANEL B Math Gap 1 GGI 0.19* 1 PEI 0.18* 0.78* 1 FLFP 0.20* 0.67* 0.32* 1 Notes: Panel A displays the means of math gender gap and gender equality measures by country of ancestry estimated using our sample of second generation immigrants from 2003, 2006, 2009 and 2012 PISA. Countries are ordered by the gender gap in math scores. It was obtained from estimating a linear regression using the Plausible Values provided by the PISA data sets as LHS variable and a female dummy as RHS (we estimated one regression for each PV and present the average of the 5 coefficients estimated). See Appendix Table A.2 for details about gender equality measures. The last two rows of Panel A display the mean and cross-country standard deviation. Panel B display Pearson correlations between variables. *Indicates a correlation statistically significant at 95 per cent.

35

Figure 1. Gender Gap in Math Scores of Second-generation Immigrants and Gender Equality in Countries of Ancestry

Notes: The figure displays the correlation between the average math gender gap among second-generation immigrants and our three measures of gender equality in the country of ancestry. The math gender gap was obtained from estimating a linear regression using the Plausible Values provided by the PISA data sets as LHS variable and a female dummy as RHS variable. We estimated one regression for each PV for each country and present the average of the 5 coefficients estimated. We use individuals whose both parents were born in a foreign country from the 2003, 2006, 2009 and 2012 PISA datasets. Definitions and data sources of the gender equality measures are presented in Appendix Table A.2. Just for presentation purposes, Brazil and Ukraine were not included in the Figure.

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36

Table 2. Math Scores and Gender Equality

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1. GGI*Female 96.19** 115.73** 132.59** 112.24** 112.86** 109.65** 116.84** 101.15** 97.64* 115.73* [41.85] [44.85] [52.83] [53.55] [44.91] [53.88] [49.51] [45.57] [48.93] [61.28] 2. PEI*Female 55.81** 58.31** 57.58** 60.21* 57.89** 59.50* 55.16* 50.03* 49.54* 58.31* [27.00] [26.43] [25.90] [31.49] [26.02] [31.59] [27.93] [27.18] [27.71] [34.54] 3. FLFP*Female 30.29* 31.56* 30.97 34.62** 30.22* 33.86** 32.60* 22.41 20.46 31.56 [16.26] [16.99] [18.49] [16.39] [16.74] [16.16] [18.18] [14.70] [15.46] [23.49] Observations 12,027 12,027 12,027 12,027 12,027 12,027 12,027 12,027 12,027 12,027

Year FE X X X X X X X X X XCountry of ancestry FE X X X X X X X X X XHost country FE X X X X X X X X X XHost country FE*Female X X X X X X X XIndividuals' age and grade level and its interactions with Female dummy

X X X X X X X X X X

GDP (country of ancestry)*Female X X X X X X X X XHDI (country of ancestry)*Female XFamily characteristics and its interaction with female X XSchool characteristics and its interaction with female X XYear FE*Female XGender equality (host)*Female X XGDP (host)*Female X XHDI (host)*Female XSE adjusted by BRR XNotes: Results from estimating equations (1) to (4) on individuals’ math scores. Specification (1) includes year, country of ancestry and host country FE, the interaction between host country FE and female dummy, and control for individuals’ age and dummies for any students who are in a grade different from the modal one in the country and its interactions with the female dummy. Specification (2), our preferred specification, adds the GDP per capita from the country of ancestry interacted by the female dummy. Specification (3) adds the HDI interacted by the female dummy. Specifications (4), (5) and (6) include family, school characteristics or both and their interaction with the female dummy (see details in Appendix Table A.1). Specification (7) replicate specification (2) but adds the interaction between year FE and female dummy. Specification (8) replaces the interaction between the female dummy and host country FE by the interaction between the female dummy and (i) gender equality measures for the host country (see details in main text) (ii) the host country’s GDP per capita. Specification (9) also adds the interaction with the host country’s HDI. In specifications (1) to (9), standard errors are clustered at country of ancestry’s level, while specification (10) replicates specification (2) adjusting the Standard Error with the BRR methodology. * p<0.1, ** p<0.05, *** p<0.01.

37

Table 3. Alternative Measures of Gender Equality

Table 4. Sensitivity of Sample Selection

GGI*female (Baseline) 115.73**

[44.85]

N 12,027 A. Dropping the origin with more observations (Portugal)

GGI*female 110.34**

[47.57]

N 9,181

B. Dropping the host country with more observations (Switzerland) GGI*female 111.50**

[55.00]

N 9,117

C. Keeping only one host country Switzerland

GGI*female 163.12

[106.77]

N 2,910

Australia

GGI*female 199.08**

[84.98]

N 2,447

Notes: Results from estimating equation 2 (preferred specification) on individuals’ math scores using different samples of countries of ancestry (Panel A) and host countries (Panel B and C). Standard Errors are clustered at the country of ancestry level, which implies 44, 42, 8 and 14 clusters, respectively. * p<0.1, ** p<0.05, *** p<0.01.

Mean and St.Dev

Effect estimated (1)

GE measure (2)

Math Gender Gap (3)

A. Measures from 1990-1997

Parliament seats held by women (1990-97)*female 85.32*** 0.106 -18.21

[30.07] [0.065] [47.23]

N 12,007

FLFP(1990)*female 28.16 0.471 -18.29

[21.05] [0.119] [47.51]

N 12,027

B. Other measures of Gender Equality

WVS indicator*female 27.97** 2.72 -14.85

[13.27] [0.22] [51.88]

N 10,949

Gap in literacy rate*female 2.12*** 99.13 -19.10

[0.27] [2.78] [42.71]

N 6,797

Note: Column (1) displays the results from estimating equation 2 (preferred specification) on individuals’ math tests scores using alternative measures of gender equality (see Appendix Table A.2 for details and definition of each measure). Columns (2) and (3) display the mean and cross-country-of-ancestry standard deviation of each measure and the math gender gap, respectively. Standard Errors are clustered at country of ancestry level, which implies 44, 45, 36 and 17 clusters, respectively. * p<0.1, ** p<0.05, *** p<0.01.

38

Table 5. Effect of culture of ancestry on girls and boys

Panel A. Girls (1) (2) (3) (4) GGI 236.31** 253.95** 251.61** 233.36** [107.52] [107.68] [107.40] [94.66] PEI 40.83 17.08 17.15 18.22 [75.16] [77.50] [77.74] [78.02] FLFP 134.06** 136.48** 135.32** 116.01** [52.84] [51.72] [51.50] [48.38] N 6106 6106 6106 6106 Panel B. Boys GGI 157.63 154.82 154.89 140.94 [121.37] [128.56] [127.72] [119.19] PEI -15.08 -45.93 -45.68 -40.74 [79.98] [88.94] [88.32] [92.24] FLFP 95.64 101.11* 101.30* 89.97* [57.21] [52.18] [51.55] [51.50] N 5921 5921 5921 5921 Year FE X X X X Host country FE X X X GDP country of ancestry X X X Individuals' age and grade level X X X X Family and school characteristics X Host country Gender Equality and GDP

X

Notes: Results from estimating equations (1) to (4) on girls and boys’ math scores separately. Specification (1) includes year and host countries fixed-effects and individual controls. Specification (2) adds the GDP per capita of each country of ancestry. Specification (3) adds family and school characteristics and specification (4) replace host country fixed-effect for host countries’ gender equality measures and GDP per cápita. Standard errors clustered at country of ancestry level (45 clusters). * p<0.1, ** p<0.05, *** p<0.01.

39

Table 6. Mechanisms: (1) (2) (3) (4)

A. Peer transmission of culture GGI 253.95** 252.88** 334.74*** [107.55] [107.24] [111.32] Proportion of girls 14.16* 127.56** 158.52*** [7.14] [55.71] [52.67] GGI*Proportion of girls -167.58* -220.28*** [83.59] [79.58] GGI 253.95** 254.16** 265.82** [107.68] [107.83] [108.97] Single sex school 5.06 80.09* 90.47** [6.35] [44.60] [43.95] GGI*Single sex school -111.44* -129.89* [67.60] [66.41] B. Network transmission of culture GGI 253.95** 243.16** 57.00 [107.68] [103.52] [126.53] Proportion of immigrants -18.50 -366.23*** -262.80** [23.69] [131.64] [100.50] GGI*Proportion of immigrants 529.71** 358.80** [220.40] [165.34] C. Mother transmission of culture GGI 253.95** 186.82* 248.68** [107.55] [104.99] [118.40]

Mother’s education level 5.23*** -0.56 -23.04**

[1.53] [15.64] [11.48]

Mother work (=1) 14.48** 87.28** 35.23 [6.54] [40.40] [44.89] GGI*Mother’s education 8.65 39.98** [23.10] [17.13] GGI*Mother work -111.39 -35.19 [69.02] [74.34] Year FE X X X X Host Country FE X X X X Age and Difference Grade X X X X Country of Ancestry FE X

Notes: Column (1) display the results from estimating equation (2) on girls’ math scores (column 2 of Panel A in Table 5). In column (2) we also control for: the proportion of girls in the school or a dummy which takes the value of 0 if the girl attend to a single-sex school and zero otherwise (Panel A), the proportion of immigrants in the school (Panel B), or mother’s educational level and a dummy indicating whether the mother is working or not (Panel C). Column (3) we add the interaction between these controls and the GGI, whereas in Column (4) we replace the GGI for the country of ancestry fixed-effect. See Appendix Table A 5 for definition and descriptive statistics of these variables. We impute missing values in Panel A or C following the MICE method of multiple multivariate imputation. Standard errors clustered at country of ancestry level (45 clusters). * p<0.1, ** p<0.05, *** p<0.01.

40

Appendix Table A. 1 Individual-level variables: Definition and Descriptive Statistics

Name Definition Mean St. Dev. across

countries of ancestry A. Individual Characteristics Female Dummy variable equal to 1 if the individual is a girl 0.51 0.11 Age Years and months 15.77 0.07

Different grade Dummy equal to 1 if the current individual’s grade is different from the modal grade at the children age in the host country and 0 otherwise.

0.38 0.21

B. Family characteristics Mother highest level of education (MISCED)

Index constructed by the PISA program based on the highest education level of each parent. It has the following categories: (0) None; (1) ISCED 1 (primary education); (2) ISCED 2 (lower secondary); (3) ISCED Level 3B or 3C (vocational/pre-vocational upper secondary); (4) ISCED 3A (upper secondary) and/or ISCED 4 (non-tertiary post-secondary); (5) ISCED 5B (vocational tertiary); and (6) ISCED 5A, 6 (theoretically oriented tertiary and post-graduate).

3.48 0.93

Father highest level of education (FISCED)

3.77 0.82

Index of parents level of occupation (hisei)

The highest occupational level of parents (HISEI), elaborated by the PISA program, corresponds to the higher ISEI score of either parent or to the only available parent’s ISEI score. The ISEI (international socio-economic index of occupational status) score created by Ganzeboom, Graaf, and Treiman (1992) is based in the International Standard Classification of Occupation (ISCO) from ILO. This index ranges from 11 to 90, and higher values indicate higher level of occupational status.

45.43 9.37

Index of cultural possessions (cultposs)

The CULTPOSS index, is based on the students' responses to whether they had the following at home: classic literature, books of poetry and works of art. These variables are binary and the scale construction is done (by the PISA program) through IRT (item respond theory) scaling. Positive values on this index indicate higher levels of cultural possessions.

-0.30 0.35

Index of home educational resources (hedres)

The index of home educational resources (HEDRES) is based on the items measuring the existence of educational resources at home including a desk and a quiet place to study, a computer that students can use for schoolwork, educational software, books to help with students' school work, technical reference books and a dictionary. Again, These variables are binary and the scale construction is done through IRT scaling. Positive values on this index indicate higher levels of home educational resources.

-0.07 0.39

Language at home 1 if language spoken at home is different from the test language

0.37 0.25

C. School characteristics

Percentage of girls

PISA index of the proportion of girls enrolled in each school derived from school principals’ responses regarding the number of girls divided by the total of girls and boys at a school.

0.49 0.04

Private school Dummy equal to 1 if school is private and 0 otherwise.

0.18 0.09

Place of residence Dummy equal to 1 if the school is in a metropolis and 0 otherwise.

0.14 0.07

41

Table A. 2 Country-level variables: Definition and Descriptive Statistics

Name Definition Mean Cross-country-of-ancestry St.

Dev. A. Gender Equality Measures Gender Gap Index (GGI)

Synthesizes the position of women by considering economic opportunities, economic participation, educational attainment, political achievements, health and well-being. The index range between 0 and 1. Larger values point to a better position of women in society. We use the 2009 index. Source: World Economic Forum, 2009 Report.

0.67 0.06

Political Empowerment Index (PEI)

Measure women's political participation based on three components: (1) the ratio women to men with seats in parliament; (2) the ratio of women to men in ministerial level and (3) the ratio of the number of years with a women as head of state to the years with a man. Larger values point to a better position of women in society. We use the 2009 indexes. This index is also elaborated for the World Economic Forum as part of the Gender Gap Index. Source: World Economic Forum, 2009 Report.

0.16 0.12

FLFP Female Labor Force Participation, from 15 years old. We use the 2009 rates. Source: International Labour Organization.

0.49 0.12

WVS Index elaborated from data of the World Value Survey based on the following questions: (1)"When jobs are scarce, men should have more right to a job than women", (2)"A working mother can establish just as warm and secure a relationship with her children as a mother who does not work", (3)"Being a housewife is just as fulfilling as working for pay", (4)"Both the husband and wife should contribute to household income", (5)"On the whole, men make better political leaders than women do", (6)"If a woman earns more money than her husband, it's almost certain to cause problems" and (7)"A university education is more important for a boy than for a girl". For all but the first, levels of agreements had to be expressed on a scale from 1 to 4. In the first question the answers were "agree," "neither," and "disagree," to which we attributed the respective scores of 1.5, 2.5, and 3.5. We inverted the answers to questions (2) and (4), so that higher values indicate a better position of women in society. The final index is the average by country of the answers to all these questions. We use all waves, except the wave 2005-2008 because it doesn’t include most of these questions.

2.63 0.18

Literacy rate GPI The literacy rate gender parity index (GPI) is the ratio of female to male literacy rates (adults of +15years old). Source: World Bank. The index range from 0 to 100, and take the maximum value when male and females have the same literacy rate.

97.38 4.26

B. Macro Variables GDP per capita Gross Domestic Product per capita in real terms deflated

with Laspeyres price index. We average the 2003, 2006 and 2009 values. Source: Heston, A., Summers, R. and Aten, B, Penn, World Table Version 7.0, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, May 2011.

14,721 12,558

Human Development Index (HDI)

The HDI measures the level of development of a country, combining information on people’s life expectancies, adult literacy rates, gross enrollment ratios in different educational levels and the GDP. The index range from 0 to 100. Source: http://hdr.undp.org/en/statistics/hdi.

0.74 0.14

42

Table A. 3 Sample Size by Country of Ancestry and Destiny ARG AUS AUT BEL CHE CZE FIN GBR ISR LUX NLD NZL Total

1 Albania 4 132 136 2 Australia 36 36 3 Austria 46 46 4 Bangladesh 7 7 5 Belgium 159 159 6 Bolivia 131 131 7 Brazil 7 7 8 Chile 24 24 9 China 410 3 5 13 20 27 130 608

10 Croatia 77 77 11 Ethiopia 151 151 12 Estonia 55 55 13 Fiji 35 35 14 France 102 203 67 242 614 15 Germany 21 38 41 176 116 6 398 16 Greece 46 46 17 Hungary 7 7 18 India 158 5 5 168 19 Iran 6 6 20 Italy 88 739 256 1,083 21 Korea 31 15 46 22 Malaysia 34 34 23 Morocco 192 192 24 Netherlands 12 50 62 25 New Zealand 376 376 26 Pakistan 36 36 27 Paraguay 63 63 28 Philippines 240 240 29 Poland 47 47 30 Portugal 777 2,069 2,846 31 Romania 58 58 32 Russian Fed. 3 9 89 491 592 33 Slovakia 3 67 70 34 Viet Nam 291 68 359 35 Slovenia 6 6 36 South Africa 60 10 70 37 Spain 246 246 38 Suriname 107 107 39 Sweden 9 9 40 Turkey 509 440 591 21 222 1,783 41 Ukraine 5 5 42 Macedonia 20 20 43 United

Kingdom 651 14 5 168 838 44 United States 29 82 111 45 Uruguay 17 17

Total 242 2,447 775 633 2,910 154 187 68 791 2,856 565 399 12,027 Notes: Final sample of second-generation immigrants from 2003, 2006, 2009 and 2012 PISA datasets. ARG=Argentina, AUS=Australia, AUT=Austria, BEL=Belgium, CHE=Switzerland, CZE=Czech Republic, FIN=Finland, SCT=Scotland, ISR=Israel, LUX=Luxembourg, NLD=Netherlands, NZL= New Zealand.

43

Table A. 4 Gender Gap in Test Scores All Countries participating in PISA Countries included in our sample

All individuals Second-

generation immigrants

All individuals Second-

generation immigrants

Second-generation immigrants

(final sample) Math Scores (1) (2) (3) (4) (5) Boys 459.24 [104.74] 469.95 [94.60] 494.45 [101.94] 492.45 [100.27] 490.96 [109.95] Girls 446.78 [99.95] 459.77 [92.79] 478.99 [97.38] 475.13 [95.83] 472.67 [99.25] Gender Gap -12.46 -10.18 -15.46 -17.32 -18.29 Reading Scores Boys 440.81 [103.28] 453.74 [100.59] 468.92 [105.61] 468.31 [104.14] 462.54 [112.86] Girls 471.89 [97.10] 487.71 [94.74] 500.94 [98.20] 498.78 [97.72] 491.17 [103.11] Gender Gap 31.09 33.97 32.02 30.47 28.63 Notes: Author's calculations based on 2003, 2006, 2009 and 2012 PISA datasets. Mean and Standard Deviation in brackets. See Data section for details about which countries are included in our sample.

Table A 5 School and Mother characteristics used in the analysis of mechanisms over the sample of girls: Definitions and Descriptive Statistics

Name Definition Mean St. Dev. across

countries of ancestry A. School characteristics

Percentage of immigrants

Number of immigrants (either first or second-generation) divided the total individuals by school. Own calculation based on PISA samples by year, weighted by student final weight.

0.34 0.11

Percentage of girls See definition in Appendix Table A1. 0.50 0.04

Single-sex school Dummy equal to 1 if the percentage of girls in the school is higher than 95 per cent.

0.10 0.06

Mom work Dummy equal to 1 if mother work and 0 otherwise. 0.81 0.12 Mother highest level of education (MISCED)

See definition in Appendix Table A1. 3.34 1.05

math gender gap: the role of culture

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