The intergenerational influence of institutions in determining equality of opportunity in Brazi

7/30/2019 The intergenerational influence of institutions in determining equality of opportunity in Brazi

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GRADUATE INSTITUTE OF INTERNATIONAL AND DEVELOPMENT STUDIES

THE INTERGENERATIONAL INFLUENCE OF INSTITUTIONS IN

DETERMINING EQUALITY OF OPPORTUNITY IN BRAZIL

A THESIS

Submitted in partial fulfillment of the requirements for the degree of

Master in International Studies (MIS)

Specialization: International Economics

by

Andrew Silva(United States)

Geneva

2012


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Abstract

This paper attempts to measure equality of opportunity in Brazil by quantifying the

determinants of child tertiary education. Child tertiary education outcomes are mod-

eled as a function of two temporally independent components: (i) influences from thepast, or family influences, and (ii) influences from the present, or societal influences.

Proxy variables are chosen for each of these temporal divisions: mothers educa-

tion represents the past, while contemporary university enrollment rates represent

the present. Equality of opportunity is determined by the relative weights of past and

present influence relatively stronger present influence amounts to greater equality

of opportunity, and vice versa. Mothers education is instrumented with several insti-

tutional measures, which not only accounts for its potential endogeneity, but results

in a model of child tertiary education outcomes based entirely upon institutional in-

dicators. The model therefore measures equality of opportunity, with respect to child

tertiary educational attainment, strictly from an institutional perspective. The model

is applied to four cohorts of children who were of university enrollment age in the

1988-2007 time period. Results indicate that equality of opportunity in Brazil has

declined over this period, and that institutional influence is increasingly operating

through spillover to second generation children.

I would like to thank my thesis advisor Jean-Louis Arcand, as well as Marc Flandreau,and Ugo Panizza for their valuable feedback on my research. I would like to thank AlainBartleman, Anna Katharina Lehmann, and Tu Chi Nguyen for providing proofreading as-sistance and additional comments. Finally, I would like to thank the Instituto Brasileirode Geografia e Estatstica for providing the household survey data, and the Instituto Na-cional de Estudos e Pesquisas Educacionais Ansio Teixeira for providing data on enroll-

ment rates.

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1 Introduction

Child outcomes, however they may be defined, are the result of a seemingly infinite spec-

trum of determinants. The variables that determine future income, or educational status,

or any of a number of other social indicators are a complex combination of characteris-

tics that, for the most part, escape our abilities of quantification. Yet, predicting child

outcomes has immense importance, especially with respect to its implications for policies

that aim to promote justice and fairness in society. High social inequality, especially in

terms of income or educational attainment, has been linked to a number of social and eco-

nomic ills, such as stagnant economic performance and political instability. Most social

policies therefore aim to promote some form of equality of opportunity: the notion that

social status attainment is due to merit and personal effort, as opposed to being predeter-

mined by historical legacy.Educational attainment is a fundamental component of social outcome. Not only is it

essential to human capital formation, in the strictest economic sense, but it is a process

by which norms and values are cultivated, and by which individuals are incorporated into

society. Most would agree that education contributes substantially to the foundations of

an individuals social development, and that it is largely the responsibility of society to

provide for its distribution in the population. The institution of education is therefore an

ideal realm of assessment for equality of opportunity. Not only is education easily quan-

tified with respect to its distribution of attainment among individuals, but its embodimentin formalized institutions (school, universities, etc.) is actively influenced through public

policy. Therefore, if one were interested in effectively promoting equality of opportunity,

it would be critical to understand the role that institutions play in determining education

outcome. This study attempts to do just that.

In this paper I propose a unique model for child tertiary education outcomes in which

its determinants are divided along the temporal dimension. I model the determinants

of outcome as either (i) a function of the past, emphasizing family influences, or (ii) a

function of the present, emphasizing societal influences. To practically implement thismodel, I choose a proxy variable to represent each of these temporal divisions: the edu-

cation level of the childs mother represents influence from the past, or historical legacy,

while university enrollment rates represent influence from the present, or contemporane-

ous inputs from society. In this simple model, equality of opportunity is measured by the

degree to which present influence outweighs past influence. The model incorporates the

role of social mobility, as it measures the correlation of educational attainment between

the mother and child, yet it is still differentiated from the broader measure of equality of

opportunity. To account for the potential endogeneity of the mothers education, I instru-

ment it using several institutional measures: a university reform law, and the schooling

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enrollment rates from the mothers generation. Instrumentation also yields the advantage

of modeling child outcomes entirely through institutional indicators, which allows me to

construct a strictly institutional perspective of equality of opportunity.

I apply this model to Brazilian household data, using the 2009 Pesquisa Nacional porAmostra de Domicilos (PNAD), a national household survey. I estimate child tertiary ed-

ucation outcomes over four cohorts of children who were of university enrollment age in

the 1988-2007 time period. My results imply that equality of opportunity has declined in

Brazil over this period in that (i) maternal education is playing an increasingly stronger

role in determining child outcomes, and (ii) university enrollment rates are playing an

increasingly weaker role. To alleviate any concerns of comparing estimated coefficients

between individual regressions, I compute an inverse opportunity ratio for each cohort,

equal to the weight ratio ofmothers education to enrollment rates. This ratio confirms

the decline in equality of opportunity. The observed trends are robust to the use of several

estimators, both with and without instrumentation, while institutional identification is ro-

bust to the use of several instrument sets. Although this result is not a positive indicator

for social equality in Brazil, instrumentation for mothers education reveals that insti-

tutions are beginning to explain a larger degree of the correlation between mother and

child education outcomes, as cohort estimation progresses through this 20 year period.

This result implies that education is operating to a larger extent through intergenerational

spillover, as opposed to having a contemporaneous influence, and could have important

implications for policies that aim to equalize opportunity for educational attainment in

Brazil.

This paper is organized as follows: Section 2 provides background on the related em-

pirical literature and the evolution of Brazilian education institutions. Section 3 presents

the identification strategy, and several variants thereof. Section 4 reviews the data. Sec-

tion 5 presents the regression results, for both linear and nonlinear estimators. Section

6 considers several specification checks, including the possibility of heterogeneous inter-

generational transmission of human capital. Section 7 briefly concludes.

2 Background

2.1 Measuring equality of opportunity and social mobility

Much of the literature that focuses on equality of opportunity draws from the formal def-

initions put forward by John Rawls, Amartya Sen and others. In the field of economics,

John Roemer is perhaps best known for suggesting a formal policy framework for estab-

lishing equality of opportunity. Roemers framework consists of modeling individual out-

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comes as a consequence ofcircumstances, over which the individual has no control, and

effort, due solely to personal agency. He divides causation into these two categories so as

to distinguish equality ofopportunity from equality ofoutcomes. The former amounts to

establishing a level playing field, in which disadvantaged individuals are compensatedfor characteristics for which society believes they should not be held accountable, while

the latter amounts to a redistribution of outcomes in which the individual takes on no per-

sonal accountability (Roemer, 1998). Therefore, inequalities resulting from differentials

in expenditures of effort are perfectly compatible with the concept of equality of opportu-

nity. Roemer suggests categorizing members of society according to their circumstances

so that opportunity-equalizing policies may be applied over types, or groups of mem-

bers with the same set of circumstances. A policy that equalizes opportunity is therefore

one that equalizes outcomes, on average, over type. Empirical work on such a formulation

is complicated by the fact that effort is at least in part determined by circumstances, and

this is addressed in various ways in the literature.

The earliest implementations of Roemers framework are put forth by a body of lit-

erature that focuses on identifying useful policy instruments for equalizing opportunity,

in which counterfactual scenarios are constructed from various hypothetical implemen-

tations of the instrument. Betts and Roemer (2004) apply Roemers formulation to U.S.

Data, using parental education and racial background as characteristics of circumstances

and adopting educational finance as a policy instrument. They find large discrepancies in

spending according to circumstances, and estimate that spending on black students would

need to be nine times that of white students to mitigate the opportunity divide. This

line of research is continued with Roemer et al. (2003) who focus on fiscal systems as

opportunity-equalizing instruments.

A second body of research focuses on measuring the actual degree of equality of

opportunity within an economy, particularly by using income and wage measurements

as proxies for outcomes. Most closely related to this study is work by Bourguignon et

al. (2003, 2007) who construct an empirical model of outcomes based directly on Roe-

mers framework. Using data from the 1996 Brazilian household survey (PNAD), theauthors attribute circumstances to measures of five exogenous variables: race, place of

birth, mothers and fathers education, and fathers occupation. They then measure the

degree of equality of opportunity by assessing how much the actual marginal wage dis-

tribution differs from a counterfactual marginal wage distribution in which circumstances

have been equalized throughout the population. Some key problems with estimating Roe-

mers framework in such a regression model are (i) effort is in itself a consequence of

circumstances, and (ii) there are likely to be many omitted variables representing effort,

leaving traces of their effects in the residual term. Lacking appropriate instrumental vari-

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ables for effort, the authors use advanced econometric techniques to estimate the possible

bias arising from ordinary least squares estimation the model. They conclude that between

10 and 37 percent of wage inequality is due to circumstances, 60 percent of which is due

to the direct influence of circumstances, with the remainder operating through individualexpenditure of effort.

Other studies emphasizing wage measurements include Cogneau and Gignoux (2005),

who provide two measures of earnings inequalities for men (aged 40-49) using four sep-

arate Brazilian household surveys collected over a two decade period. They assess how

the earnings distribution changes with respect to (i) schooling expansion, (ii) changes

in the structure of earnings (particularly, the returns to education), and (iii) changes in

educational mobility. The authors determine that educational mobility (or immobility)

explains a significant, but limited proportion of wage inequalities, and are able to iden-

tify trends in the wage distribution attributed to changes in educational provisions. In

another study that uses the same survey data as Bourguignon et al. (2007), Ferreira and

Veloso (2006) estimate the intergenerational elasticities of wage attainment between fa-

thers and their children, with emphasis given to non-linearities in mobility patterns. The

authors find heterogeneous mobility over geographical location and quantile of the wage

distribution. Particularly, they find higher wage mobility in the southeast region of Brazil,

relative to the northeast, and lower mobility among high-income whites and low-income

blacks. Bourguignon et al. (2007) provide a comprehensive review of other literature that

attempts to quantify equality of opportunity via wage inequalities.

Of particular relevance to this work is the body of literature that addresses social

mobility with respect to educational attainment. Studies of social mobility are closely

related to those of equality of opportunity, the difference being that the former tends to

emphasize one particular observable characteristic (observable over multiple generations,

such as educational attainment or wages), while the latter attempts to quantify, ideally,

all the determinants of an outcome (Bourguignon et al. 2007). Note however that social

background is often a theme common to each measure, and the two concepts overlap to

the extent that educational attainment (or wages, or whichever measure is chosen) is useddirectly as the sole determinant ofoutcome itself. The literature is rich with studies that

characterize the correlations of outcomes between generations.

dHombres and Nguyen-Hoang (2011) provide perhaps the most comprehensive cross-

country study of intergenerational mobility of education to date. They focus on tertiary

education outcome (whether or not a child completed tertiary education) as determined

by dummy variables representing primary and tertiary education of the father (with sec-

ondary education as the excluded category). Their study estimates the regression coef-

ficients of the fathers education (along with an inequality of opportunity index, com-

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puted as the average of the coefficients) for a total of 68 countries across four cohorts

from 1948 to 1978, with additional estimates aggregated by geographical region. They

determine that Latin American countries have slightly higher mobility in higher educa-

tion, relative to other regions of the world. Hertz et al. (2007) study the correlations ofeducational attainment among a smaller cross-country sample of 42 countries, but using

a more comprehensive measure of education: total years of schooling completed. Using

this broader measure they find that Latin American countries have some of the lowest rates

of educational mobility. The authors also provide an extensive review of earlier studies

on social mobility, many of which tend to emphasize a particular country or region of the

world. Chevalier et al. (2003) has compiled a large study on educational mobility across

20 countries, 15 of which are in Europe. Behrman et al. (2001) study mobility of edu-

cation in Latin America and extend their analysis by tying their results to larger societal

characteristics. They find that mobility tends to be higher in countries with higher average

years of schooling and where governments tend to spend more on education, reinforcing

the conclusions and policy implications of most other studies.

Many studies on educational mobility focus on fathers education and its correla-

tion with childrens education (including both dHombres and Nguyen-Hoang, 2011 and

Chevalier et al., 2003). Better schooling data is usually available for fathers, especially

for developing countries, while in addition many surveys only tabulate occupational indi-

cators for the primary income earner of the household, which often tends to be the father.

However, several other studies emphasize the importance of maternal education in child

outcomes. Behrman (1997) surveys the literature on maternal education, and concludes

that the mothers education is more influential than the fathers in determining social out-

comes for the following generation of children, and for society as a whole. He provides

numerous references to other works that arrive at the same conclusion. In a more recent

study that supports this claim, Currie and Moretti (2003) examine the influence of mater-

nal education on infant health, highlighting a channel of human capital transmission from

mother to child not captured by wage effects. Using an instrument for maternal education

to infer causality, they determine that higher maternal education increases infant birthweight and gestational age, and is also associated with a higher probability of parental

marriage and better prenatal care. The authors conclude that traditional wage measures

could dramatically underestimate the true returns to education.

Most closely related to this study are several papers that examine educational mobility

by instrumenting parental education with changes in compulsory schooling laws. Black

et al. (2003, 2005) study educational mobility in Norway by creating an instrument for

parental education using the Norway Primary School Reform of 1959, which extended

compulsory education from 7 to 9 years of schooling. Their instrument is unique in that

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the reform took effect across different municipalities in different years, allowing them to

take advantage of the variation in parental education across both time and locality. They

do not, however, find strong causal effects on child education when instrumenting parental

education with the reform, despite strong OLS correlations. This leads the authors to con-clude that parental education does not have an effect on child education, and that the

correlation between parents and childs education is due to either family characteristics

or inherited ability. Since they focus only on social mobility, they exclude the possi-

bility that child education could be influenced by contemporary community or regional

characteristics, such as the quality of local institutions, which could also explain some

of the correlations between parentss and childs education (they nevertheless title their

study Why the Apple Doesnt Fall Far). Norway, however, may not have been a good

candidate for such a study, as it exhibits a somewhat compressed education distribution

and features relatively high social mobility (Bjrklund et al., 2002). Furthermore, their

instrument may have been poorly chosen as it identified a reform in primary schooling,

which may have only been effective in the lower quantiles of the education distribution,

especially in a country with such relatively high average educational attainment. Their

first-stage regression estimates do show strong correlations between the instrument and

parental schooling, but they neglect to report any other instrument strength tests.

In a very similar study, Chevalier (2004) addresses educational mobility in the United

Kingdom, creating an instrument for parental education from the changes instituted by the

Education Act of 1972, which extended the minimum schooling age from 15 to 16 years

old. He does find a strong causal connection between instrumented parental education

and child education, and reports that the connection is strongest with the parent having

the same gender as the child. He also shows that parents in the lower portion of the

education distribution (those with education levels closest to the minimum requirements)

show the largest transmission of education to their children via the reform. Compared to

the study by Black et al., Chevaliers study may have been more appropriate in that the

U.K. features relatively higher inequality (compared to Norway) and focuses on a reform

in secondary schooling, which is likely to have affected a larger share of the population.This paper connects to the broad base of literature in several ways. First, it aims to

identify trends in the intergenerational correlation between mother and child education

outcomes, using instruments for maternal education when it is assumed to be endoge-

nous. This fits in closely with the literature on social mobility, particularly with the work

by Black et al. (2003, 2005) and Chevalier (2004). Secondly, this study ties into the

literature on equality of opportunity as it relies upon a formal framework to model child

outcomes, incorporating an additional institutional measure (and individual and family

characteristics as robustness checks) to provide a more complete picture of educational

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attainment than would an examination of social mobility alone. The study contributes to

the literature with a model that features a unique temporal decomposition of the determi-

nants of outcome, in which the relative weights of the determinants composes a measures

of equality of opportunity. Furthermore, through the social indicators and instrumentschosen, the model almost exclusively focuses on the role of institutions in educational

attainment a perspective that has been given little emphasis in the existing literature

on equality of opportunity. (The body of research led by Betts and Roemer, 2004 per-

haps comes the closest, with their emphasis on education finance). This study focuses on

Brazil, a country characterized by relatively high education inequality, a profile that has

yet to be addressed with respect to institutional reform instrumentation. It also appropri-

ately emphasizes a reform in higher education, which should have had a significant impact

upon schooling attainment, given the prevailing restrictions on educational resources in

the pre-reform period. I go beyond the scope of much of the existing literature by apply-

ing the model over four cohorts of children, which allows me to examine trends in the

role of institutions in determining equality of opportunity with respect to child tertiary

education outcomes.

2.2 Education in Brazil and the university reform of 1968

University enrollment in Brazil was minimal in the decades prior to the 1970s. The mod-

ern history of Brazilian higher education starts in 1931, when the Ministry of Educationwas first created under the revolutionary government of Getlio Vargas, and became the

first institution to establish a common structure for the formation of Brazilian universities.

However, higher education remained in the form of specialized training institutes for sev-

eral more decades, being comprised particularly of those with a focus on medicine, law, or

engineering. Through this time period the university system was largely an institution for

established elites. It wasnt until the 1950s that the Brazilian government took an active

interest in widespread higher education as a tool for economic development (Da Silva,

1977).The first attempt at a sweeping educational reform was the 1961 Law of Guidelines

and Fundamentals of National Education (Lei de Diretrizes e Bases da Educao Na-

cional). This reform aimed to improve education at all levels while reinforcing the dis-

tinction between primary, secondary, and higher education. However, the directive failed

to meet the expectations for which it had been formulated, especially in higher educa-

tion, where low enrollment numbers prevailed through the reform period (Heimer, 1975).

It was not until the military coup in 1964 that a strong basis for higher education was

established. Da Silva (1977) argues that as the authoritarian regime concentrated its con-

trol over property, capital, income and markets, the middle class was no longer able to

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rise in the social structure through the traditional accumulation of capital. Instead, up-

ward social mobility became more dependent on the public and private bureaucracies,

thus making higher education level training an increasingly important requisite.1 Fur-

thermore, as the regime was largely supported by the middle class, it sought to appeaseits popular base by answering to their demands for greater university access.

In 1968 the regime ushered in what is now commonly referred to as the University

Reform Law. Through a series of decrees, the university system was reformed to achieve

several principal goals: (1) increase autonomy of university institutions; (2) allow more

flexibility in institutional structure; (3) create a common set of basic courses between pro-

grams, yet (4) allow more flexibility in curriculum selection (especially with regards to

the changing needs of the economy); (5) establish full-time professorships (they had pri-

marily been part-time until then); (6) dedicate provisions to encourage rural development;

(7) expand enrollment; and (8) establish graduate education, with a strong emphasis on

research. Other provisions were made as well, but the expansion of enrollment and the

establishment of research-oriented graduate education were perhaps most relevant to the

surge in demand for university education that was soon to follow.

Klein and Schwartzman (1993) cite the reform as stimulating an extraordinary in-

crease in demand for higher education in the following years.2 On the other hand, Hauss-

man (1972) claims that the 1968 reform was a direct result of student revolts that shook

the larger Brazilian cities (and much of the Western world) at that time, out of demands for

expanded enrollment and greater financial support for higher education. Da Silva (1977)

references data on university vacancies and registered (qualified) candidates for the years

leading up to reform, and notes that over 50% of qualified candidates were turned away

due to insufficient vacancies in the years of 1966 and 1967 (vacancy shortages continued

to the end of the 1960s, but eventually rose in the 1970s). Whether the reform initiated,

or was a response to, increase in demand for higher education, it is safe to assume that the

1968 university reform indicates a dramatic turning point in Brazilian education. Table 1

outlines the aggregated enrollment figures for Brazil in pre- and post-reform years. Note

the surge in undergraduate and graduate enrollment growth around 1968.The 1968 reform provides one source of exogenous variation for parental education,

but as Brazilian educational attainment evolved asymmetrically across geographical re-

gions, a closer look at state-level indicators yields a second opportunity for identifica-

tion. Plank (1987) asserts that primary and secondary enrollment diffused much faster

through the southern states than in northern regions. To accommodate this fact, I con-

struct a second instrument for parental education by using state-level enrollment rates,

1Da Silva, 1977: 202Klein and Schwartzman, 1993: 23

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Table 1: School enrollment in Brazil

Year Primary Secondary Undergraduate Graduateenrollment growth enrollment growth enrollment growth enrollment growth

1960 1758.7 1177.4 93.2 1961 7798.7 0.046 1308.0 0.111 98.9 0.061 1962 8538.8 0.095 1464.4 0.120 107.3 0.085 1963 9299.4 0.089 1719.6 0.174 124.2 0.158 1964 10217.3 0.099 1892.7 0.101 142.4 0.147 1965 9923.2 -0.029 2154.4 0.138 155.8 0.094 1966 10695.4 0.078 2483.2 0.153 180.1 0.156 1.8 1967 11263.5 0.053 2802.0 0.128 212.9 0.182 2.4 0.3331968 11943.5 0.060 3186.0 0.137 278.3 0.307 4.4 0.8331969 12294.3 0.029 3629.4 0.139 346.8 0.246 1970 12812.0 0.042 4083.6 0.125 430.5 0.241 1971 13641.0 0.065 4641.0 0.136 557.0 0.294 7.8

1972 688.4 0.236 12.4 0.5901973 772.8 0.123 1974 937.6 0.213 17.1

Enrollment numbers are aggregate values for the entire country. Enrollment numbers are in thou-sands. Growth rates are year-over-year, and expressed as %/100 (a range of 0-1). Source: Da Silva(1977)

which takes advantage of variation in both the time and geographical dimensions. Differ-

entiated progress by region also allows me to assess the effects it may have on migration

between states. Construction of these variables is covered in more detail in the data sec-

tion (Section 4).

3 Identification

3.1 The base model

I model child tertiary educational outcomes as a linear function of maternal educational

attainment and state-level university enrollment rates:

T E = 0 +1ME+2enroll +3age + (1)

In this model the dependent variable T E is a dummy indicating the outcome of the childs

tertiary (university level) educational attainment: level 0 for no tertiary education, and

level 1 for having graduated from or being currently enrolled in an institution of higher

education. Estimation of equation (1) is therefore a linear probability model which pre-

dicts the likelihood that a child will enroll in tertiary education. The principal covariates in

the model are maternal education (ME) and university enrollment rates (enroll). Maternal

education is a 5-level categorical variable representing the education level of the childs

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mother, and is equal to: 0 for no formal education; 1 for completion of primary education;

2 for completion of secondary education; 3 for completion of tertiary education; and 4 for

completion of a post-graduate degree.

I emphasize maternal education due to the nature of the available data (there are farmore single-mother households than single-father households) and because a substantial

amount of research indicates the importance of maternal education in determining child

outcomes (see Behrman, 1997 for a comprehensive review). I neglect to include both

mothers and fathers education due to the presence of assortative mating the process by

which parents of similar education levels tend to be matched. As it is difficult to gauge

the influence of assortative mating, and as its role may change greatly over observations

and may be correlated with other unobserved characteristics, inclusion of both parents

education levels could bias estimates. Particularly, the presence of assortative mating

could overstate the true influence of parental education in determining child education,

especially in situations where its effects are strong.

University enrollment rates correspond to those of the childs state of residence when

he/she was 18 years old, and serve as an indicator of the development of education infras-

tructure (especially in a country such as Brazil, where supply could conceivably be the

enrollment constraint). Education infrastructure probably has the greatest influence over

a childs schooling decisions when he/she is of enrollment age, which is why I choose the

rate that corresponds to when the child was 18 years old. The childs age (age) is also a

necessary covariate in that it determines the appropriate enrollment rate, and controls for

the linear trend in the probability of tertiary education attainment associated with age.

As maternal education is potentially endogenous, I create an instrument for it using

Brazils 1968 University Reform Law, which made a series of structural changes to the

Brazilian university system and marked a surge in demand for higher education. The

first-stage reduced form is:

ME = 0 +1reform.m +2enroll +3age + (2)

Mothers education is instrumented with reform.m, a dummy variable that indicates

whether or not the mother was affected by the 1968 University Reform Law. The re-

form dummy is equal to 1 if the mother was at least 18 years old when the University

Reform Law took effect, and 0 otherwise. Following Borgonovi et al. (2010) I restrict

the data samples to those for which the mother was 18 years old within a window of

seven years before and after the 1968 reform. Limiting observations to an age window

around the reform controls for other macroscopic changes in society that may not be re-

lated to institutional measures. Yet, seven years is deemed large enough to still provide

efficient estimates. The significance of the size of the reform window is later assessed as

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a robustness check (Section 6).

To take advantage of the fact that educational attainment diffused asymmetrically

across the country, the model is also estimated using school enrollment rates from the

mothers generation as an instrument for maternal education:

ME = 0 +1enroll.m +2enroll +3age + (3)

The instrument enroll.m is created by matching enrollment rates (a combined measure

from primary and secondary schools) to the year in which the mother was 8 years old,

which is an estimate for the upper limit of the enrollment age. Again, as enrollment rates

are reflective of education infrastructure, the quality of such infrastructure would have

the greatest influence over schooling decisions when the child is of enrollment age. In

estimating this variation of the model, observations are not restricted to the seven yearwindow within the 1968 reform, but are instead restricted to those mothers who were 8

years old in the 1950-1980 time period (the range for which interpolated parental enroll-

ment rates were available, see Section 4). Including parents from this larger three-decade

period enhances the efficiency of the estimates and the strength of the instrument, yet

is still a generational span roughly centered around the 1968 reform, which retains the

emphasis on the institutional changes that occurred during that same period (although in

this case the institutional changes in question would have affected mothers that were, on

average, 10 years younger than those affected by the university reform).A third model is then estimated using both the 1968 reform (reform.m) and the mothers

enrollment rates (enroll.m) jointly, under the hypothesis that both instruments together

will provide the strongest identification:

ME = 0 +1reform.m +2enroll.m +3enroll +4age + (4)

Estimation with equation (4) uses the same dataset as that of equation (2), restricting

observations to those for which mothers were 18 years old within the seven year window

of the reform.Instrumenting for maternal education serves two important purposes. First, using an

exogenous instrument accounts for the potential endogeneity of maternal education in ex-

plaining child educational attainment. Particularly, a mothers education decisions could

be the result of more fundamental, yet unobservable family characteristics that also have

a direct impact on child education decisions (such as natural ability). Instrumenting for

mothers education mitigates much of the upward bias likely present in OLS estimates

due to these omitted variables. Second, instrumentation allows me to construct a model

of child outcomes based primarily on institutional indicators. By isolating the exogenous

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variation in maternal education due to university reform and school enrollment rates, I am

able to exclude unobserved family characteristics and focus on the role of institutions in

determining equality of opportunity.

Equations pairs (1) and (2), (1) and (3), and (1) and (4) are estimated first by two-stage least squares. Because the marginal effects of a linear probability model are often

too large to be interpreted as changes in probability, the models are also estimated by a

probit model that allows for instrumentation of an endogenous covariate (via maximum

likelihood). Prior to estimation, the sample population is restricted to children who were

18 years old (university enrollment age) in the 1988-2007 time period. Based on the year

in which they were 18, the sample is divided into four cohorts: 1988-1992, 1993-1997,

1998-2002, and 2003-2007. I estimate the model over the four cohorts to identify trends

in child outcomes, and therefore equality of opportunity, over this twenty year period.

The primary motivation behind such a parsimonious model is to decompose child

education outcomes into two temporally distinct components: (1) past effects, or the

influence of historical legacy, and (2) present effects, or the influence of contemporary

society. A proxy variable is chosen for each of these divisions: mothers education is

a proxy for historical legacy, while enrollment rates represent contemporary influences.

Another way to view this division is between family and society, but the interpreta-

tion is the same. The mothers education embodies a broad array of family characteristics

endowed upon the child, be they indicative of nature (for example, innate genetic abil-

ity) or nurture (other unobserved forms of human capital accumulation, such as work

ethic). These legacy effects represent the channel of the intergenerational transmission

of human capital from mother to child and its relevance to child university attainment.

University enrollment rates, on the other hand, serve as an indicator of the development

of educational institutions. They represent the degree to which contemporary society

provides access to university level education, and the role it plays in determining child

university attainment. There are perhaps still other omitted factors that influence univer-

sity attainment, and of course the true components of individual outcomes can never

be perfectly modeled. Yet, the separation between past and present is perhaps themost fundamental division we can establish among the understood determinants of child

outcome.

As the dependent variable TE is a dummy, coefficient estimates measure the contri-

bution of each covariate to the probability that a child attains university-level education.

The structure of the base model balances the determinants of outcome between past and

present forces (1 and 2, respectively), which indicates the degree of equality of op-

portunity (and social mobility) for the cohort under consideration. Under theoretically

perfect equality of opportunity, one would expect the coefficient 1 to approach zero and

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the coefficient 2 to approach unity. This would imply that the probability of a child at-

taining university-level education is directly proportional to university enrollment rates at

large, and therefore solely a product of the institutions offered by society. In other words,

the probability that a randomly selected 18 year old will enroll in university would beequal to the percentage of those of similar age enrolled in university, for a given time and

state of residence. Perfect inequality of opportunity is represented by the opposite sce-

nario, in which 1 approaches unity and 2 approaches zero, implying that child outcome

is directly proportional to the mothers outcome. In practice, these extremes are never

reached. Yet to avoid any doubts in comparing coefficients between individual regres-

sions, I also compute an inverse opportunity ratio for the final regressions, equal to the

quotient of the coefficient on mothers education over the coefficient on enrollment rates

(1/2). The ratio measures the degree to which a cohort is historically-oriented, and is

therefore an inverse measure of equality of opportunity

3.2 Further specifications

Note that child tertiary educational outcomes are not regressed directly on maternal ter-

tiary education, but are instead regressed on a broader measure of the mothers education

that includes primary and secondary schooling. University enrollment rates are too low in

the mothers generation to provide sufficient identification of maternal education through

instrumentation. However, the broader educational measure appears to be a more appro-priate predictor of child tertiary education, as there has been some inflation in educational

attainment over the last generation in Brazil (as there has been elsewhere). For example,

one may argue that completion of secondary education in 1960 may be roughly compara-

ble to completion of a university degree in 1990. The data seem to support this claim. For

the cohorts under investigation, of those children who have completed (or are enrolled

in) university-level education, only 32% of their mothers have actually completed tertiary

education themselves, while 41% of mothers have completed only secondary education,

with 25% completing only primary education (and 2% with no formal education).In addition to the base model, an extended form of each model is estimated, which

adds controls for individual and family characteristics:

T E = 0 +1ME+2enroll +3age +4X+ (5)

This serves primarily as a robustness check against the base model components. In equa-

tion (5) X is vector that includes additional controls for: adopted children (adopted);

states that were late to achieve a minimum 40% enrollment rate by 1960 ( late); a fertility

measure indicating the number of children born to the mother (no.children); an indicator

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for race (black); an indicator for gender (female); and a dummy indicating mothers who

have migrated from states with lagging enrollment (late states) to states with higher en-

rollment within the last ten years (migrant10). I hypothesize that adopted children have

a lower probability of tertiary educational attainment than natural children in that theylack the genetic component of educational transmission from the mother, which I believe

to be potentially helpful. Adopted children could also lack other forms of human capital

transmission that take place at an early stage of development, depending on their expe-

riences before adoption and the age at which they were adopted. Geographical location

could also affect the probability that a child attends university, so I add the control that

accounts for states with lagged enrollment trends. The race dummy (black) is intended

to capture an additional dimension of class background. The migrant dummy is designed

to catch the impact of families who left states with poor education opportunities for bet-

ter education (and likely economic) opportunities. The indicator could be positive in the

sense that families who take the initiative to seek out better opportunities may possess a

certain know how in obtaining better outcomes (a form of human capital), or it could

be negative in the sense that the mothers of these families are comparatively uneducated

relative to mothers in their newly adopted, more highly-educated state of residence.

4 Data

Data on individual child outcomes was derived from the 2009 Pesquisa Nacional por

Amostra de Domicilos (PNAD), a nationwide household survey conducted on an annual

basis in Brazil by the census bureau, the Instituto Brasileiro de Geografia e Estatstica

(IBGE). The survey contains data on educational attainment for both children and par-

ents, along with an abundance of individual and family characteristics, as well as the

required household information to link children with their respective parents. In some

instances multiple families reside in a single household, and in these situations only the

primary family of residence was included, as it was not possible to match parent to child

in secondary families.My analysis only focuses on children who still reside with their parents, which would

normally not be a problem for primary and secondary education, but could introduce a

selection bias for tertiary education (dHombres and Nguyen-Hoang, 2011). This may

present less of a problem with Brazilian data than with data from other countries, as

Brazilian university students may tend to reside with their parents until graduation. In a

study by Guimares and Sampaio (2007) of entrance examination scores for the Universi-

dade Federal de Pernambuco, in Brazil, the authors report that an overwhelming majority

of students (80.3%) live with their parents during their studies. In my study, of the raw

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data sample of 399,387 observations, there are 34,819 individuals of ages 18-22, of which

only 22,965 are identified as a child in the household, or 66.0%. Of those who are iden-

tified as a child in the home, 4,236 are enrolled in tertiary education, or 18.4%. Of those

who are not identified as a child in the home, only 1,023 are enrolled in tertiary educa-tion, or 8.6%. It therefore appears that limiting the selection of observations to children

who live with their parents amounts to a nonrandom selection associated with higher edu-

cational attainment (dHombres and Nguyen-Hoang, 2011 find the same phenomenon in

their data). It is unclear whether or not social mobility would be higher or lower among a

relatively higher educated population, but this is taken up as a robustness check in Section

6.

I calculate university enrollment rates strictly for the period 1988-2007 and aggregate

them at the state level. I derive enrollment percentages from raw enrollment numbers

and population statistics obtained from the Instituto Nacional de Estudos e Pesquisas

Educacionais Ansio Teixeira (INEP) and IBGE, respectively. I define enrollment rates as

the percentage of enrolled university students out of the proportion of the population aged

17-24 years old, which I estimate to be about 15% of the population, based on figures

from the IBGE (2012). This research indicates that the proportion of 17-24 year olds in

the Brazilian population remained relatively constant for the 1988-2007 period. I then

matched the derived university enrollment rates to children of who were of 18 years of

age in this 20 year period. Observations for which children did not meet this criteria were

omitted from the sample.

I obtain data on parental enrollment rates from Plank (1987), which were originally

tabulated from IBGE census data. The data are available at the state level, but only at

decade intervals in census years. Rather than eliminating observations for which no

parental enrollment data exists (which would amount to eliminating 90% of my obser-

vations), I use the available data points to linearly interpolate the intervening 9 years of

missing entries between census surveys. The interpolation is done for each decade-state

combination. Specifically, I use data points for the years 1950, 1960, 1970 and 1980

to construct a panel of interpolated enrollment rates at annual intervals for the 1950-1980period. I then construct the parental enrollment rate instruments (enroll.m for mothers, en-

roll.f for fathers) by matching the state-level enrollment rates to individual parents when

he/she was 8 years old, as this is deemed to be an age when enrollment rates at large could

have a significant impact on the probability of school attendance.

I create the reform instrument by determining whether or not the the mother of the

child had been affected by the 1968 university reform. Table 2 examines the effects of the

reform on the distribution of the mothers education at 7-year and 3-year reform windows.

The reform seems to have had a positive effect on education at all levels of attainment,

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Table 2: Distribution of mothers education before and after reform

7-year window around reform 3-year window around reformBefore After Before After

No formal schooling 19.1% 10.9% 16.3% 12.6%Primary 50.1% 44.7% 49.5% 46.1%Secondary 21.8% 31.6% 24.2% 29.7%Tertiary 8.5% 11.9% 9.4% 10.7%Post-Tertiary 0.5% 0.9% 0.5% 1.0%Observations 5,892 12,6762 3,167 5,529

Before indicates the pool of mothers who were 18 in the window period prior to the reform, whileafterindicates those who were 18 in the window period after the reform,

perhaps through spillovers from higher to lower education levels. Granted, some of thechange in the distribution of education is likely due to the prevailing trends in enrollment

growth, yet the data seem to reflect the historical changes due to the 1968 reform recorded

in Table 1 .

The dummy variable representing states with lagged schooling enrollment was also

created using data from Plank (1987), who studies the temporal and geographical evo-

lution of education in Brazil in the 20thcentury. Plank determines in which years states

reached various enrollment thresholds. I construct the dummy based on whether or not

a state had achieved at least a 40% enrollment rate by 1960, which divides the coun-

trys population roughly in half between late and early adopters. Specifically, the

early-adopting states are: Esprito Santo, Par, Rio de Janeiro, Rio Grande do Sul, Santa

Caterina, So Paulo, and Sergipe.

The 2009 PNAD also contains information on adopted children living in the house-

hold. Such children are coded in the survey as agregados, which roughly translates from

Portuguese as informally adopted children. Therefore, there are no official records in-

dicating the status of these children with the families. Their numbers are small in the

cohorts under consideration, so I do not dedicate a separate analysis to their population.

However, I do include a dummy variable indicating their status in the extended-form mod-els, which does explain a statistically significant portion of child educational attainment.

They are included in the population of children as a whole, which yields estimates that

differ by a negligible amount from estimates restricted to natural children only.

One final consideration is the correlation of the 1968 reform instrument with the

mothers age. Since cohorts are selected by the childs age, yet since mothers are se-

lected from a static window around the 1968 reform for all cohorts, younger (i.e. later)

cohorts will have higher average mothers age. The reform instrument could be rendered

less valid to the extent that the mothers age is a determinant of child education. An addi-

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tional covariate for the mothers age at the childs birth is included as a robustness check

to assess its significance in determining child education attainment (Section 6).

Table 3 outlines descriptive statistics by child cohort, particularly including informa-

tion on maternal education and maternal age at childbirth.

Table 3: Descriptive statistics by child cohort

Cohort 1988-1992 1993-1997 1998-2002 2003-2007

Child tertiary educational 21.7% 27.9% 34.8% 30.1%Maternal education

No formal schooling 15.5% 12.8% 12.6% 14.4%Primary 54.7% 48.1% 43.1% 45.9%Secondary 23.9% 29.6% 30.6% 26.9%

Tertiary 5.6% 8.9% 12.8% 11.9%Post-Tertiary 0.3% 0.6% 0.9% 1.0%

Age of mother at birthminimum 14 18 23 281st quartile 21 23 27 31median 24 26 30 333rd quartile 27 30 33 37maximum 31 36 41 46mean 23.9 26.6 30.1 34.2

States with lagged enrollment* 64.7% 64.4% 61.1% 64.1%

Black 7.21% 7.9% 7.7% 7.7%Adopted (raw count) 26 49 86 80Observations 2,010 4,289 6,481 5,784

Statistics are for observations with mothers of age 18 within the 7-year window of the reform.

*States that did not reach 40% enrollment in primary and secondary schools by 1960.

5 Results

5.1 Linear model estimates

5.1.1 OLS estimates

I first estimate the parsimonious base model given in equation (1) by ordinary least-

squares for an assessment of the absolute correlations between mothers and childs ed-

ucational outcomes. OLS estimates assume that mothers education is exogenous, and

are likely biased upward as unobserved characteristics (natural ability and other unmea-

surable forms of human capital) are omitted from the model. Table 4 presents the OLS

estimates for the four cohorts. Focusing on the base model, mothers education is strongly

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significant and positive for all four cohorts, with large coefficient magnitudes that increase

in time through cohorts, indicating that social mobility (and therefore equality of oppor-

tunity) is decreasing with time. A one-level increase mothers education (from secondary

to tertiary, for example) on average increases the probability of a child attaining tertiaryeducation by 19% in the first cohort (1988-1993), to as high as 26% in the final cohort

(2003-2007).

The university enrollment rates variable is also highly significant with the expected

positive sign, yet it exhibits the opposite trend of mothers education, as its coefficient

estimates decreases in magnitude as we progress to later cohorts. Note that the enrollment

rates variable is encoded as a fraction between 0 and 1 in the dataset, which explains why

its coefficients appears relatively large, yet it explains relatively less of the probability

that a child reaches tertiary education. An additional 10% enrollment of the population

(not a 10% increase of the enrollment rate itself) explains about a 9.2% increase in the

probability of a child attaining tertiary education in the first cohort, and an 11.4% increase

in the second cohort. This decreases slight to 11.1%, then to 6.8% in the third and fourth

cohorts. The trend in enrollment rates reinforces the finding that equality of opportunity

is declining in Brazil through this time period. Legacy family effects appear to be playing

an increasingly relevant role in child outcomes, while contemporary societal influences

are playing a decreasingly relevant role.

Childs age has very weak explanatory power. It is insignificant in the first two cohorts,

and significant but of a small magnitude in the latter two, where an increase by one year

of age indicates a 1-2% increase in the probability of child tertiary education attainment.

Finally, note that the quality of the regressions increases with cohort, as measured by the

adjusted R2. The better fit of the latter two cohorts could be related to the larger sample

sizes, where errors in variables could be relatively smaller.

5.1.2 Extended model covariates

OLS estimates of the extended model, as given in equation (5), are also presented in Table

4. The inclusion of additional covariates does not detract from the explanatory power of

mothers education and enrollment rates. Each retains the significance, magnitude and

sign of base model estimates, and each follows the same trend as we progress through

the cohorts. The dummy for adopted children (adopted) is significant and of the expected

negative sign in three out of four cohorts. Its magnitude is substantial, indicating that

being adopted reduces the probability that a child attains tertiary education by 15-21%.

Because adopted children lack a genetic connection with mothers, they may be relatively

disadvantaged with respect to education outcomes compared to natural children. The

dummy indicating states with lagged enrollment (late) is mostly insignificant. Both the

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Table4:Childtertia

ryeducationoutcomes:OLS

Basemodel

E

xtendedmodel

Cohort

1988-1992

1993-1997

1998-2002

2003-2007

1988-1992

1993-1997

1998-2002

2003-2007

constant

0.069

-0.0

97

-0.4

73***

-0.6

40***

-0.0

26

-0.034

-0.4

47***

-0.7

41***

(0.2

21)

(0.1

41)

(0.1

07)

0.0

83)

(0.2

23)

(0.1

43)

(0.1

11)

(0.0

85)

motherseducation

0.1

93***

0.233***

0.2

58***

0.2

57***

0.1

89***

0.22

2***

0.250***

0.2

46***

(0.0

12)

(0.0

07)

(0.0

05)

(0.0

05)

(0.0

12)

(0.0

07)

(0.0

05)

(0.0

05)

enrollmentrates

0.9

23***

1.138***

1.1

09***

0.6

77***

0.9

55***

1.23

3***

1.080***

0.6

99***

(0.2

97)

(0.2

01)

(0.1

15)

(0.0

91)

(0.3

47)

(0.2

34)

(0.1

29)

(0.0

93)

age

-0.0

04

-0.0

01

0.0

12***

0.0

22***

-0.0

02

-0.003

0.012***

0.0

26***

(0.0

06)

(0.0

04)

(0.0

04)

(0.0

04)

(0.0

06)

(0.0

04)

(0.0

04)

(0.0

04)

adopted

0.0

21

-0.1

56**

-0.1

47***

-0.2

12***

(0.0

82)

(0.0

61)

(0.0

46)

(0.0

37)

late

0.0

10

0.03

2**

0.0

03

0.0

04

(0.0

21)

(0.0

15)

(0.0

12)

(0.0

11)

no.children

-0.0

11

-0.02

5***

-0.0

25***

-0.0

21***

(0.0

07)

(0.0

05)

(0.0

04)

(0.0

03)

black

-0.0

16

-0.08

1***

-0.0

84***

-0.0

60***

(0.0

32)

(0.0

21)

(0.0

18)

(0.0

18)

female

0.1

11***

0.13

0***

0.112***

0.1

00***

(0.0

17)

(0.0

12)

(0.0

10)

(0.0

10)

migrant10

-0.1

37

-0.1

40**

-0.0

22

-0.1

22**

(0.1

53)

(0.0

59)

(0.0

80)

(0.0

59)

Observations

2,010

4,2

89

6,4

81

5,7

84

2,0

10

4,2

89

6,4

81

5,7

84

AdjustedR2

0.144

0.2

05

0.2

67

0.2

85

0.1

63

0.2

34

0.2

92

0.3

14

EstimationofEquation(1)(basemodel)andEquation(5)(extendedmodel).OLSestimateswerealsocalculatedforthelarger

datasetthatincludesm

otherswhowere8yearsoldfrom1950-1980(forestimationofEquation(3

)),yettheyexhibitednegligible

differencesfromthese

estimates,andthereforearenotincluded.

Standarderrorsinparentheses

.*prob

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The intergenerational influence of institutions in determining equality of opportunity in Brazi