XLIV Reunión Anual

ANALES | ASOCIACION ARGENTINA DE ECONOMIA POLITICA
XLIV Reunión Anual
Noviembre de 2009
ISSN 1852-0022
ISBN ISBN 978-987-99570-7-3
MEASUREMENT OF EDUCATIONAL
INEQUALITIES IN THE ARGENTINE PUBLIC
SYSTEM
Cecilia Adrogué
MEASUREMENT OF EDUCATIONAL INEQUALITIES
IN THE ARGENTINE PUBLIC SYSTEM
Cecilia Adrogué*
August 2009
ABSTRACT
This paper is focused on the quantification of the educational inequality at the public
elementary level in Argentina using different measures. We start by presenting the
coefficient of variation of the quality of the schools which is between 0.10 and 0.25 when
0.10 is generally used as a benchmark. The Theil index is then offered to provide a
decomposition of the inequality found, since it allows separating the inequality between
and within the provinces, the governmental units ordered to finance primary education.
Last but not least, regression based measures and the concentration index are used to
search for unfair situations.
RESÚMEN
El presente trabajo realiza una medición de la disparidad educativa en la educación
primaria pública argentina utilizando distintas herramientas de medición. Al comienzo, se
presenta el coeficiente de variación para brindar una aproximación a la magnitud del
problema; su valor está entre 0.10 y 0.25, cuando suele usarse 0.10 como referencia.
Luego se utiliza el índice de Theil para descomponer la desigualdad de la calidad
educativa entre y dentro de las provincias, las encargadas de financiar la educación
primaria. Por último, se utilizan medidas derivadas de la técnica de regresiones y el
índice de concentración para identificar situaciones consideradas injustas.
*Universidad de San Andrés-Conicet. UdeSA Vito Dumas 284 (B1644BID) Buenos
Aires, Argentina. Tel (54-11) 4725-7000. E-mail: [email protected]
Keywords: Public education, inequality, Argentina
JEL Classification: I28, I29, J79.
1
1. Introduction
Though several studies have shown that there are great discrepancies among the
public schools in Argentina regarding their quality, there is not a conclusive or good measure
of how grave is such inequality, where the main problem is, and to what extent such
inequality is related to the level of income.
In Argentina, as in most of the countries and regions inside countries assignment of
children to state-financed schools is not by lottery, but through the minimal distance
principle; children are mandated to attend classes at the nearest school (Lott, 1987). At the
same time, schools‟ quality is not randomly distributed among districts either, but positively
associated to their economic wealth. Most notable are the great discrepancies that exist
even among the public schools financed by the same governmental unit. The coefficients of
variation corresponding to the quality of the schools in the provinces of Argentina range
between 10.3% and 25.5%, and an absolute standard of about 10 percent is generally used
for evaluating equity (Odden and Picus, 2000). Other studies also find intradistrict
inequalities; Roza et al. (2007) find great disparities in spending among the public schools
financed by the same district, and Iatarola and Stiefel, (2003) also find inequalities in the
provision of resources as well as a lack of equitable distribution of performance; in particular,
they analyze the district of New York City. So, assignment to neighbourhoods and schools
implies assignment to a level of school quality. This is the core of the social process of
educational segregation. Some children have access to high quality schools while others
have access only to poor quality ones. To close the vicious circle, educational policy-makers
do not fully compensate this “natural” segregation process through adequate improvements
of school quality in poorer districts.
This paper quantifies the educational equity at the elementary level in Argentina
following two of the three principles developed by Berne and Stiefel (1984)1: horizontal
equity and equality of opportunity. The horizontal equity, also defined as the equal treatment
of equals, will be analysed in order to determine the degree of inequality and to establish
whether the mayor existing disparities occur between or within the provinces. The provinces
are the Governmental units ordered to finance elementary education since 1970, when the
National Government, by Law 17.878 and Law 18.586, transferred the elementary schools to
the provinces and the Municipality of the City of Buenos Aires. This process was completed
in 1978. Though the schools were transferred to the provinces, educational equity remained
the responsibility of the National Government. As such, compensatory federal funds were
mandated in order to guarantee educational equity.
The equality of opportunity will be analyzed through the degree of association
between the school quality of public schools and the socioeconomic status of their students.
The proportion of immigrants and native students will also be considered. According to
Iatarola and Stiefel (2003), the equality of opportunity can be conceptualized in two ways. A
neutral formulation posits that equal opportunity exists if there is a lack of association
between per pupil resources and characteristics associated with historically disadvantaged
groups (Berne and Stiefel, 1984), while an affirmative action formulation posits that equal
opportunity is achieved if there is a positive association in the relationship (Roemer, 2005).
In Argentina, one of the main objectives established by the Federal Education Law (1993),
section 8, was to provide equality of educational opportunities, or, in Roemer‟s words, “to
level the playfield.” If this were the case, the differences in outcomes would be due to
differences in efforts. And those inequalities derived from different amounts of efforts would
not be considered inequitable.
1
Berne and Stiefel (1984) define three principles of educational equity: horizontal equity, vertical
equity and equality of opportunity. In the present study vertical equity or, as it is also called “unequal
treatment of unequals”, will not be analyzed due to lack of information.
2
In the following section, the different topics regarding educational equity and
measures used to evaluate it will be analyzed (review of the papers in the literature). Section
three provides a description of the database and sample, descriptive statistics as well as an
outline of the methodology that was used to construct the different indexes of school quality
and socioeconomic status. Section four presents the measures of inequality that will be used
and an explanation of why they were selected among the different existing inequality
measures. The following section provides the results and section six concludes.
2. On the measurement of schooling inequalities
Formal schooling is an important contributor to the skills of an individual and to his
human capital but it is not the only factor. “Parents, individual abilities and friends
undoubtedly contribute. Schools nonetheless have a special place because they are most
directly affected by public policies. For this reason, we frequently emphasize the role of
schools.”2 In addition, “[a]ll governments in the world assume a substantial role in providing
education for their citizens. A variety of motivations lead societies to provide such strong
support for schooling, some of which come from pure economics and others of which come
from improved political participation, [equality of opportunity related to] social justice and of
general development of society.”3
An equal opportunity policy, as Roemer (2005) defines it,
[I]s an intervention (e.g., the provision of resources by state agency) that
makes it the case that all those who expend the same degree of effort end up
with the same outcome, regardless of their circumstances. Thus, the equal
opportunity policy „levels the playfield‟, in the sense of compensating persons
for their deficits in circumstances, making it the case that, finally, only effort
counts with regard outcome achievement.4
In this sense, “[i]t is relatively non-controversial to consider an individual‟s
educational level and basic health status important factors in determining her set of
opportunities”5. In Argentina, the National Education Law (2006) states that knowledge and
education are public goods and personal and social rights guaranteed by the Government.
And as a way to guarantee equity for all the inhabitants of the Nation, it should be free, of
good quality, and available to everyone. In order to follow this objective, the government
should provide more funds to those areas less advantaged, so as to compensate for the
deficit in resources. What Iatarola and Stiefel (2003) call the affirmative action formulation, in
contrast to the neutral formulation, which requires a lack of association between resources
and historically disadvantaged groups.
Though not only quantity matters regarding education, “[m]ost empirical analyses of
human capital have concentrated solely on the quantity of schooling attained by individuals,
ignoring the quality differences. This focus contrasts sharply with policy consideration that,
with some exceptions, considers exclusively school quality issues.”6 One of these exceptions
took place some time ago in many developing countries, where a great effort was done in
order to expand schooling including the Education for All initiative, and good results were
obtained regarding years of schooling. Yet, much of this policy making tended to downplay
the issues of quality (Hanushek and Woessmann, 2007). In this line, the years of schooling
of the argentine population rose considerably after 1974. The proportion of people without
instruction or with primary incomplete represented 37% of the total population at that time,
2
Hanushek 2004, p.3.
Hanushek 2004, p.1.
4
Roemer 2005, pp. 3-4.
5
Gasparini 2002, p. 796.
6
Hanushek 2004, abstact.
3
3
on the contrary, in 2002, only 9%. As well, the population who had completed only primary
school reduced from 37% to 28%, and as a consequence, secondary schooling and
graduate schooling rose considerably, the latter, from 3% to 16%. This great increase of the
number of years of schooling was a great first step and, at present, the mayor concern is the
quality improvement so as to provide horizontal equity and equality of opportunity to all the
people, since precisely those who receive less quantity of education also receive a poor
quality one.
Therefore, “the issue of explanation of educational inequality is not just a matter of
computational procedure but can significantly affect our understanding of inequality and can
potentially guide the design of economic policy.”7 Berne and Stiefel (1984) analyze the
different alternative measures of horizontal equity, which are basically those that capture the
spread or dispersion in a distribution. In this sense, perfect equity would exist when every
pupil in the distribution receives the same object, and the horizontal equity measures assess
how far the distribution is from perfect equality. Although no list of horizontal equity
measures is exhaustive, they present a rather complete list of the measures that can be
used: Range, Restricted range, Federal range ratio, Relative mean deviation, McLoone
index, Variance, Coefficient of variation, Standard deviation of logarithms, Gini coefficient,
Theil‟s measure and Atkinson‟s index (Berne and Stiefel, 1984, pp. 19-21). A great number
of studies use the coefficient of variation as the measure to evaluate horizontal equity, Berne
and Stiefel (1994), Iatarola and Stiefel (2003), and Roza et al. (2007) among others. Murray
et al. (1998) construct four measures of the within-state distribution of education
expenditures –the Theil index, the Gini coefficient, the natural logarithm of the ratio of
spending at the 95th percentile to spending at the 5th percentile, and the coefficient of
variation. Those studies that are interested in decomposing inequality mainly use the Theil
inequality index. Ram (1995) studies the inequalities in access to education using the
population weighted Theil index to measure the amount of intercountry and intracountry
inequality of school enrolments, and Murray et al. (1998) use also the Theil index to show
the disparity in pupil spending between and within states.
In order to assert that the existing inequality is inequitable, it should be corroborated
that its main source is socially unacceptable (Gasparini, 2002). For example, inequality
among private schools may not be considered inequitable in sight of the fact that it derives
from the fees they charge, though, the same inequality among public schools may be
unacceptable, because the governmental unit that finances education should assign the
resources in such a way as to compensate for existing disparities and provide equal
treatment of equals.
In the case of Argentina, it is very relevant to disentangle whether the issue regarding
educational inequality is due to differences among the provinces (the governmental units
that support basic education), or to differences within each province. This would shed light
on the importance of each of the causes of the problem. In fact, it could be analysed whether
the main problem is one of provincial administration of the educational resources, or an
incomplete compensatory policy from the National Government. For this reason, it is very
convenient to develop a summary measure of explanation to relate overall educational
inequality to it constituent components and to address such issue, inequality decomposition
analysis applied to population subgroups should be used (Cowell and Jenkins, 1995). As
Bourguignon (1979) states, the decomposability of an inequality measure implies a sort of
additivity, so as to express it as the sum of inequality existing between subgroups of a
population and a kind of “weighted average” of the inequality within those groups, although
the “weights” used in this averaging do not necessarily sum up to one. In this sense, an
inequality measure is said to be additively decomposable if it can be expressed as the sum
of a “within group” inequality term and a “between group” inequality term (Shorrocks, 1980).
In the present case, the decomposability is a much desired property, though not any
decomposable measure is a satisfactory index. For example, the variance is not neutral with
respect to a scale change of the whole distribution, which would be a desirable property of
7
Cowell and Jenkins 1995, p 421.
4
an inequality measure. Another property that might be expected from an inequality measure
is to decrease with any transfer from rich to less rich schools (Pigou-Dalton condition or
strong principle of transfers). Bourguignon (1979) investigated all inequality measures which
are decomposable while satisfying a set of basic requirements: are continuous and
differentiable, symmetric, mean independent (also called income-homogeneous), satisfy the
symmetry axiom for population and satisfy the Pigou-Dalton condition. The continuity
requirement means that an infinitesimal change in the value of a school quality may be
expected to produce only an infinitesimal change in the inequality measure. The
differentiability condition leads to the elimination of a wide family of measures in which
school qualities enter with their rank in the whole distribution and which are not differentiable
everywhere (Gini coefficient, interquantiles mean incomes ratios, etc.). These measures are
generally not decomposable. The symmetry requirement is also called the anonymity rule.
The mean independence property implies that the measure is invariant when all school
quality indexes are multiplied by the same scalar, and in the same way, the symmetry axiom
for population, which requires that the inequality of a distribution be the same as that of the
distribution obtained by replicating any number of times each school quality, a kind of
population-zero-homogeneity.
Decomposable inequality measures will differ by the weighting systems and the two
most obvious candidates are naturally “income-weighted” and “population-weighted”
decomposable measures. Interestingly, Bourguignon found only one inequality measure
consistent with each concept of decomposability and satisfying the list of convenient
properties: the Theil Entropy coefficient (T) and the average logarithm of relative incomes
(L), which as he pointed out, is the same as Henri Theil‟s (1967, pp. 126-127) populationweighted index of inequality. Going one step further, Shorrocks (1980) points out that “when
inequality measures are used to assess the contribution of one particular factor to total
inequality, another problem arises in the different interpretations that can be given to
statements like „X per cent of inequality is due to Y‟.”8 Only when the decomposition
coefficients do not depend on the subgroup means will the ambiguities disappear. For this
reason, the most satisfactory decomposable measure, allowing total inequality to be
unambiguously split into the contribution due to differences between subgroups is the
population-weighted index of inequality, in which the decomposition coefficients are precisely
the population shares (ng/n). “[It allows] total inequality to be unambiguously split into the
contribution due to differences between subgroups and the contribution due to inequality
within each subgroup g=1,…,G, in such a way that total inequality is the sum of these G+1
contributions.”9
Finally, regarding the measurement of equality of educational opportunities, what are
mainly used are relationship measures (Berne and Stiefel, 1984) to quantify the degree of
association between characteristics that are considered illegitimate or unacceptable
(Gasparini, 2002). And though there are a great number of available measures, regression
based measures are the most common. They are popular not only because they are based
on certain statistical principles, but also because there are several possible equal
opportunity measures that can be derived from regression analysis. Berne and Stiefel (1984,
pp. 27-32) present eleven regression based relationship measures, of four types: correlation,
slopes, elasticities and adjusted relationship measures. Several studies use the regression
based analysis to search for educational inequities; among others we can find Berne and
Stiefel (1994), Iatarola and Stiefel (2003), Llach and Schumacher (2005) and Rubenstein et
al. (2007).
However, another interesting measure, called the Concentration Index (CI) can also
be applied to the case. The CI is an analytical tool that is being vastly used in Health
economics to analyze income related inequality in health and health care (Gravelle, 2001). It
is a generalization of the Gini coefficient (Lambert, 1993), and in the case of income related
inequality in education, the index is derived from the concentration curve which graphs the
8
9
Shorrocks 1980, p. 624.
Shorrocks 1980, p. 625.
5
cumulative proportion of the quality of education against the cumulative proportion of the
population ranked by income. A value of zero would mean that educational quality is equally
distributed over income in the sense that the pth percentage of the population ranked by
income has exactly the pth percentage of the school quality for any p. A negative value would
mean that educational quality is concentrated in the poor, whereas a positive value would
result if educational quality were concentrated in the rich.
In the case under study, the extent in which school quality is related to the level of
income of the students should be evaluated. A priori, a strong correlation would be
considered inequitable, though it should be analysed thoroughly. The existence of
cooperative associations could be enhancing this correlation, though their influence should
not be considered unacceptable. These associations are generally managed by parents of
students of the school and recollect funds from the students to invest them in improving the
quality of the service provided by the school. Therefore, the inequalities derived from the
existence of these associations could be assimilated to the one related to the fees private
schools charge, not a direct consequence of public intervention.
3. Data base and sample
As the main objective of the paper is to measure horizontal educational equity and
equality of educational opportunities, the information needed is referred in the first place to
the quality of the schools and in the second place, to the socioeconomic status of the
students.
Regarding the quality of the schools, as there are plenty of measures, they will be
grouped in three indicators of what can be defined as the main school resources (physical,
human and social capitals). They were constructed using a methodology that has been
applied in other studies in the field (Llach and Schumacher, 2005). The physical capital
index is divided in two sub indices, corresponding to the construction and functional
characteristics of the buildings, which includes the quality, functionality and state of repair of
the building, electricity, classrooms, furniture, library, courtyards and bathrooms; and the
quality and availability of teaching materials. The human capital index is referred to the
directors and teachers of the schools and is constructed on three main issues: professional
and school experience, qualifications and training and aptitude for the job. The first one
refers to the seniority in a particular school, the number of years in teaching, the contractual
status (full time, replacement, etc.), and the mode of access to the position. The following
one refers to the qualifications acquired via formal training and education, and the latter was
constructed on the analysis of the working methodology. Finally, the social capital refers to
the social networks that exist in the schools. It is divided in three sub indices, interaction with
the community, with the students‟ parents, and the internal organization and climate, which
include school autonomy, the relationship among the teaching staff and the relationship of
the director and teachers with the students. An additional comment regarding the different
measures of school quality is about the degree of subjectivity. Although the three of them
were constructed on the basis of the Operativo Nacional de Evaluación Educativa (National
Educational Assessment Operation) or ONEE, the different dimensions measured have
different degrees of subjectivity. That is to say, what regards the physical capital is
quantifiable and verifiable, the same as the years of experience and qualifications,
corresponding to the human capital, or the interaction with the community in the social
capital. On the other side, the aptitude for the job reflects in a great measure the
interviewees‟ opinion, and the relationship among the different members of the school is
quite affected by subjectivity.
With the aim of measuring unfairness, as mentioned in the previous section, an
indicator of the students‟ socioeconomic status is required. And, since the ONEE does not
include any question regarding the household income or consumption, the socioeconomic
status of the students had to be inferred. So as to estimate it, the answers provided about
6
the possession of durable goods, the utilization of public services, the number of family
members and the parents‟ educational level were used. Schumacher (2003) and Elbers et
al. (2003) were used as a reference for the estimation. See appendix 1 for details on the
construction of the index.
Our primary source of information on schools, teachers and students characteristics
is from the administrative records of the Argentine National Ministry of Education, specifically
the ONEE. Starting in 1994, this ONEE remained censual until the year 2000, after that
moment, a sample instead of a census began to be surveyed. Because of this we have
decided to work on the data corresponding to the year 2000, so as to have enough
information about the distribution of educational resources not only between provinces, but
also within them. In addition, the National Household Expenditure Survey (Encuesta
Nacional de Gastos de Hogares or ENGH) was selected to provide the income and
consumption patterns in order to calculate the socioeconomic status of the children in the
sample.
Argentina is a federal country organized in 24 autonomous political jurisdictions (23
provinces and the Autonomous City of Buenos Aires). Responsibility for pre-primary and
primary education has been decentralized at the provincial level since 1970- 1978. Both free
public schools and private institutions that charge fees to students supply education
(Berlinski and Galiani, 2005). Unfortunately, one of the provinces (Neuquén) did not
participate of the CENSUS, and therefore, we will work with 23 units. And, as our concern is
about the unacceptable sources of educational inequality, we will focus the study on the
public schools, due to the fact that the private ones may differ in quality because they
receive different amounts from the fees they charge.
An original database was constructed as a way to integrate the outcomes of the
survey of GBE sixth-year students with those obtained from the surveys of directors and
teachers for the same year. The three data bases were integrated using the section or
classroom as the unit of measurement. Therefore, each database entry represents a school
section and shows the characteristics and opinions of the director of the school, the
teachers‟ features and judgments and the average of the students‟ outcomes and
characteristics.
As a first approach to the inequality matter, the coefficients of variation for the three
school capitals and for the socioeconomic status can be seen in table 1.
7
Table 1: Means and Coefficients of Variation corresponding to the school capitals and
to the SES index
Obs.
SES
PhC
HC
SC
Mean
CV
Mean CV
Mean CV
Mean CV
All
Jurisdictions
11237 41.818 0.204 2.655 0.240 3.731 0.129 2.849 0.163
City of Bs.As.
Bs.As
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
Sgo.del Estero
Tucumán
Tierra del Fuego
525
3188
106
1030
384
506
180
440
245
168
208
113
586
563
219
469
276
156
100
804
361
539
71
59.366
43.464
40.866
43.867
37.288
36.211
49.753
41.215
33.719
37.006
46.711
43.220
40.390
36.248
42.608
37.380
38.743
40.215
53.314
39.776
33.150
38.532
54.918
0.065
0.126
0.133
0.130
0.220
0.258
0.135
0.158
0.264
0.183
0.113
0.106
0.160
0.226
0.183
0.204
0.164
0.146
0.068
0.196
0.250
0.157
0.074
3.335
2.493
2.392
2.892
2.461
2.419
3.039
2.594
2.251
2.411
3.333
2.492
2.889
2.464
2.714
2.586
2.662
2.781
3.094
2.817
2.339
2.611
3.347
0.167
0.255
0.216
0.210
0.239
0.239
0.170
0.225
0.237
0.213
0.165
0.238
0.208
0.203
0.183
0.212
0.176
0.215
0.140
0.215
0.228
0.188
0.103
3.860
3.675
3.412
3.924
3.535
3.631
3.811
3.434
3.543
3.555
3.650
3.611
3.862
3.637
3.576
3.864
3.901
3.937
3.702
3.910
3.602
3.875
3.542
0.112
0.130
0.112
0.104
0.131
0.133
0.109
0.135
0.119
0.122
0.116
0.132
0.131
0.129
0.125
0.118
0.110
0.102
0.109
0.113
0.163
0.117
0.105
2.876
2.876
2.641
2.962
2.646
2.765
2.755
2.709
2.664
2.621
2.909
2.552
2.979
2.862
2.789
2.828
3.009
2.946
2.577
2.916
2.757
2.902
2.390
0.159
0.172
0.176
0.134
0.175
0.156
0.159
0.165
0.152
0.194
0.131
0.195
0.153
0.149
0.146
0.160
0.121
0.144
0.185
0.153
0.161
0.147
0.220
As could be observed in table 1, there is a great disparity in the number of sections in
the jurisdictions, nonetheless the highest coefficients of variation are not only in the larger
ones like Buenos Aires province or Cordoba, but also in the smallest ones like Catamarca,
La Rioja, Jujuy and San Luis. The coefficients over 20% were highlighted, though 10% is
generally used as a benchmark (Odden and Picus, 2000).
It is quite noticeable that the capital most unequally distributed is the physical capital,
which is at the same time, the easiest to measure and to modify via a redistribution of
resources. At the same time, the jurisdictions with the highest mean of physical capital tend
to have it more equally distributed, this is the case for the City of Buenos Aires, Tierra del
Fuego, Santa Cruz, Chubut and La Pampa. The Human Capital presents a higher value in
all the jurisdictions and is more equally distributed. Santiago del Estero is the jurisdiction that
presents the highest coefficient of variation (16.3%). Regarding the Social Capital, Tierra del
Fuego, La Rioja, Jujuy and Santa Cruz are the ones that present the highest coefficients (all
over 18.5%). Finally, the coefficients of variation regarding the socioeconomic status of the
students range from 6.8% (Santa Cruz) to 26.4% (Formosa), being, in general, the poorer
ones the most unequally distributed.
4. Methodology and estimation strategy
To assess the relevance of the various factors discussed in the previous section on
educational equity, we adapt the decomposition methodology, the regression analysis and
the concentration index methodology to our case.
Regarding the decomposition methodology, the basic intuition is that, given a specific
partition (the provinces in this case) and a suitable inequality measure, overall inequality
can be written as some function of withinW
8
refer to inequalities within each province, and would reflect a bad assignment of resources
by the provincial
betweenB
inefficient or incomplete compensatory policy by the National Government, thus
f
,
W
(1)
B
In principle, this functional breakdown would permit the specification of the proportion
of inequality „accounted for‟ by between-group inequality with reference to a particular
present case, it would mean to differences between the provinces. If for a specific partition
W
0 B
(Cowell and Jenkins,
1995). A summary measure of the amount of inequality „explained‟ by differences between
the groups would be:
IB
RB
(2)
I
In order to implement such indexes, a suitable inequality measure is needed. Such
measure should at least guarantee that the decomposition is consistent for all logically
possible partitions
and if we also require that the measure be continuous and
differentiable, symmetric, mean independent (also called income-homogeneous), satisfy the
symmetry axiom for population and the strong principle of transfers the only measure is the
generalised entropy index (Cowell, 2000).
Ic y
I 0 ( y)
I1 ( y)
n
1 1
ncc 1
1
n
1
n
yi
c
1 ,c
0,1,
i 1
n
log
i 1
n
yi
yi
log
,c
yi
0,
(3)
,c 1
i 1
Expresion (3) specifies a family of inequality contour maps with given mean and
population. The parameter c indexes the members of the family and can be assigned any
real value, specifying a high positive value of c
-that is
particularly sensitive to changes in the upper tail of the distribution (Cowell, 2000). In
particular, when c=2 corresponds to the square of the coefficient of variation. I 1 is the Theil
index and I0 is the population weighted entropy index, also proposed by Theil (Shorrocks,
1980). I0 and I1 are particular family members for which the within-group component weights
sum to one, being I0 the most satisfactory decomposable measure, allowing total inequality
to be unambiguously split into the contribution due to differences between and within
subgroups (Shorrocks, 1980).
“For any partition we may in principle assign overall inequality to between group
and within-group components, but there are two logically separate and unavoidable
difficulties that have to be confronted when doing this [the cardinalisation issue and the
definition of between group inequality].”10 Regarding the first one, it is worth mentioning that
“[a]lthough inequality within a given population or group is a purely ordinal concept, the
10
Cowell and Jenkins 1995, p. 424.
9
decomposition by component subgroups is contingent upon the specific cardinalisation of
the inequality measure.”11 And regarding the latter, it is important to bear in mind that
[S]ince an inequality measure is defined on the sets of arbitrary dimensions,
the concept of inequality within any subgroup is straightforward; selecting a
measure for the whole population also provides a measure for any group in
-group inequalities into a
single number representing the withinnot self-evident. Two different meanings have been given to this concept: (...)
the between-group component can be interpreted as inequality of the group
means, (...) or inequality of the group representative [values]. (...) The second
interpretation is more demanding since it requires complete specification of a
social welfare function, not just an inequality index.12
This decomposition technique outlined was applied to the socioeconomic status
index and to the three schools‟ capitals indexes and the results are presented in the
following section.
In order to evaluate the equality of educational opportunities, multiple regression
analysis will be used to measure the extent to which characteristics of students or schools
explain variation in school capitals. As the neutral formulation of the equal opportunity
principle states, perfect equity would be defined as the absence of a relationship between
the object of study (school quality) and a certain characteristic considered illegitimate. The
most common one used is a measure of the student‟s wealth, in our case it would be the
socioeconomic status, though other characteristics may also be considered illegitimate, such
as being an immigrant or a native student. Regarding the measurement of the relationship
between the variables, two different aspects should be given particular attention. On the one
hand, the degree in which the variables move together, which could be analyzed through the
correlation existing among them or through the goodness of fit of the whole model, (the
coefficient of determination, which is also the square of the simple correlation, and indicates
how much of the variability of the dependant variable is explained by the model). And on the
other hand, the magnitude of the relationship can be assessed with the slope or the
elasticity.
The results obtained with the multiple regression technique regarding both types of
measures are presented in the following section. In particular, the coefficient of
determination of the model and the slopes of the variables considered illegitimate will be
offered.
Finally, as a complementary way to evaluate the equality of educational
opportunities, the degree of relationship between school quality and the level of income will
be analyzed with the concentration index (CI). The concentration index is an analytical tool
adopted for the measurement of socioeconomic inequalities in health (García Gomez and
Lopez Nicolas, 2004) and has a similar interpretation to the more familiar Gini index for pure
inequality. Actually, the two inequality measures differ in the fact that the ranking variable is
a measure of socioeconomic status (usually income) rather than educational quality (Gini
coefficient). The CI ranges between -1 and 1. A value of -1 would mean that educational
quality is concentrated in the poorest person, whereas a value of 1 would result if all
educational quality were concentrated in the richest person. A value of zero would mean that
educational quality is equally distributed over income in the sense that the pth percentage of
the population ranked by income has exactly the pth percentage of the school quality for any
p.
In the present case we are interested in calculating the CI for a measure of school
quality. Let yi denote a measure of quality of section i. i=1,2, …n, and Ri denote the
cumulative proportion of the population ranked by income up to the ith section (their relative
11
12
Cowell and Jenkins 1995, p. 425.
Cowell and Jenkins 1995, p. 425-6.
10
income rank). In our case the population is conformed by all the sections of the public
schools in Argentina.
The CI of school quality on income can be written in various ways, one (Wagstaff et
al., 2003) being
CI
2
n
n
y i Ri
1
(4)
i 1
Where
is the mean of y. CI, like the Gini coefficient, is a measure of relative
inequality, so that doubling school capitals leaves CI unchanged.
We consider three measures of school quality: physical, human and social capitals
and the SES index is used as the measure of socioeconomic status.
5. Results
This section reports the results of performing the decomposition described in the
previous section as well as the estimation strategy outlined. The objective is to shed light
over the quantitative relevance of the various phenomena discussed in section two, on
horizontal educational equity.
Table 2: Theil decomposition between and within jurisdictions
SES
Physical Capital
Total Theil
0.0449 100.0% Total Theil
0.0302 100.0%
Between
groups
Between
groups
11.2%
15.8%
0.0050
0.0047
Theil
Theil
88.8% Within group Theil
84.2%
Within group Theil
0.0399
0.0254
Human Capital
Total Theil
0.0088
Between
groups
0.0007
Theil
Within group Theil
0.0080
Social Capital
100.0% Total Theil
0.0143 100.0%
Between
groups
8.5%
5.0%
0.0007
Theil
91.5% Within group Theil
95.0%
0.0135
As can be observed in table 2, all the school capitals are distributed more evenly than
the socioeconomic status, which presents the highest Theil value (0.0449). This could mean
that there is a certain equalizing policy regarding educational quality. At the same time, it
should be noted that the largest inequalities are within each of the provinces, which would
suggest that a priori, it is the provincial administration rather than the National policy that is
failing. In the case of the physical capital, 84.2% is explained by differences within the
provinces, while for the human and social capitals, more than 90% corresponds to
differences inside the provinces. Therefore, improving the distribution of the school quality
within each jurisdiction is essential to get closer to the objective of horizontal educational
equity. At the same time, it is worth mentioning that, though the inequality in the physical
capital is less than the inequality in the socioeconomic status, a higher proportion is
explained by differences between the provinces (15.8% against 11.2%). Almost the same
inequality between jurisdictions existing in the SES (0.005) is replicated in the physical
capital (0.0047), this could indicate, there is not a National compensation regarding the
physical resources of the schools. In the case of human and social capitals between
inequalities represents 8.5% and 5% respectively.
11
Table 3: Theil index and the amount of school capitals in each jurisdiction
Rankings
Jurisdiction
Theil
SES
SES
Theil
PhC
PhC
Theil
HC
City of Bs.As.
23
23
21
22
15
Bs.As.
14
14
1
9
5
Catamarca
18
15
13
3
18
Córdoba
16
17
14
18
21
Corrientes
8
10
3
6
7
Chaco
3
4
4
5
4
Chubut
17
20
19
19
19
Entre Ríos
12
13
6
11
2
Formosa
1
1
5
1
12
Jujuy
13
3
12
4
10
La Pampa
19
19
20
21
14
La Rioja
20
18
2
8
6
Mendoza
9
11
9
17
3
Misiones
2
5
15
7
8
Río Negro
5
16
17
14
9
Salta
10
6
10
10
11
San Juan
7
8
18
13
17
San Luis
11
12
11
15
23
Santa Cruz
22
21
22
20
20
Santa Fé
4
9
8
16
16
Sgo.del Estero
6
2
7
2
1
Tucumán
15
7
16
12
13
Tierra del Fuego
21
22
23
23
22
Ranking Theil: 1: Most unequal 23: Most equal
Ranking capitals and SES: 1: Lowest value 23: Highest value
HC
Theil
SC
SC
16
13
1
22
3
10
15
2
5
6
12
9
17
11
7
18
20
23
14
21
8
19
4
9
5
7
21
6
14
12
8
16
2
22
3
11
17
19
10
23
20
4
15
13
18
1
16
15
5
21
6
11
9
8
7
4
18
2
22
14
12
13
23
20
3
19
10
17
1
The city of Buenos Aires presents the highest value in the SES index and at the
same time is the one where it is distributed most equally. While Formosa is the jurisdiction
with the poorest students and the most unequally distributed. A special case is Tierra del
Fuego, which presents a very high value of SES and quite equally distributed, the highest
value for physical capital and the most equally distributed, but the lowest and worst
distributed social capital. A similar situation can be seen in Santa Cruz. Though, as it has
been mentioned, this capital is to a certain extent affected by personal opinions. At the same
time, Tierra del Fuego is the youngest jurisdiction, and both provinces have the fewer
amount of schools and sections. An opposite situation can be seen in the case of San Juan
and San Luis, which present much better results for the human and social capitals than for
the physical capital and the Socioeconomic Status.
12
Graph 1: Theil index of the SES, Physical, Human and Social Capitals
0.0700
Theil SES
Theil PhC
Theil HC
Theil SC
0.0600
0.0500
0.0400
0.0300
0.0200
0.0100
Tierra del Fuego
Tucumán
Sgo.del Estero
Santa Fé
Santa Cruz
San Luis
San Juan
Salta
Río Negro
Misiones
Mendoza
La Rioja
La Pampa
Jujuy
Formosa
Entre Ríos
Chubut
Chaco
Corrientes
Córdoba
Catamarca
Bs.As. Province
City of Bs.As.
0.0000
As can be observed, in all jurisdictions except the City of Buenos Aires and La Rioja,
the Theil index of the SES is the highest one. This indicates that the quality of the schools is
more equally distributed than the socioeconomic status. At the same time, the Theil Index
corresponding to the human capital is the lowest in all the jurisdictions with the exception of
Tierra del Fuego, in which is equal to the corresponding one to the physical capital, and
Santiago del Estero where the social capital presents a lower Theil.
The quality of education plays a particular roll in determining the set of opportunities
of a person and its distribution concerns policy makers and people in general. Though it is
desirable an equal distribution of this good, inequality in its provision is not necessarily
unfair. Since only those differences in outcomes that are due to differences in unacceptable
variables would be considered unfair (Gasparini, 2002). Analysing inequality was the first
step, what should be done next is evaluate its degree of association with the factors
considered unacceptable in order to determine its unfairness, that is to say, to relate the
amount of school capitals to the SES, the presence of immigrants and native students
(variables considered illegitimate as determinants of school quality). The variables
corresponding to the presence of immigrants and of native students are dummy variables
which were constructed on the response given by the directors of the schools. They have a
value of 1 if there are immigrants or native students, 0 if there are not, and missing value if
the director did not answer the question.
13
Graph 2: Coefficients of Determination corresponding to the multiple regressions
including the three variables considered unacceptable: SES, immigrants and native
students.
0
0.05
0.1
0.15
0.2
0.25
City of Bs.As.
Bs.As. Province
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
Sgo.del Estero
Tucumán
Tierra del Fuego
Physical Capital
Human Capital
Social Capital
In some jurisdictions, as the City of Buenos Aires, the Buenos Aires Province,
Cordoba, Corrientes, Chaco, Chubut, Entre Rios, Formosa, Mendoza, San Juan, San Luis,
Santa Fe and Tucuman, the regressions corresponding to the physical capital are the ones
with the highest coefficient of determination. This would suggest that in these jurisdictions,
there is less equality of education opportunities regarding the physical capital than the other
capitals. Catamarca, Jujuy, La Pampa, La Rioja, Tierra del Fuego, Santa Cruz and Rio
Negro present the highest fit in the regression corresponding to the social capital, while
Misiones, Salta and Santiago del Estero show the highest fit in the human capital regression.
Corrientes and La Rioja present all the coefficients of determination under 0.05,
which would indicate that in all of them, there is not a strong association between the
variables considered unacceptable and the school capitals.
Table 4 presents the outputs of the regressions regarding the Equality of Educational
Opportunities.
14
Table 4: Equality of Educational Opportunities
Dependant variable: Physical Capital
Num.
of
obs.
All Jurisdictions
9198
SES pupils
Inmigrants
0.0306
-0.0851
***
***
native
†
students
-0.0380
City of Bs.As.
453 0.0435 *** -0.0169
-0.0802
Bs.As. Province
2643 0.0388 *** -0.0514 **
-0.0523
Catamarca
83 0.0269 ***
0.4712
0.0896
Córdoba
884 0.0390 *** -0.0560
0.2196
Corrientes
279 0.0125 *** -0.2463
0.3614
Chaco
411 0.0171 ***
0.1468
-0.1636 **
Chubut
144 0.0018
-0.1596
-0.2352 **
Entre Ríos
371 0.0224 *** -0.1697
-0.0490
Formosa
201 0.0253 *** -0.0174
0.0393
Jujuy
107 0.0017
0.2454 **
0.0207
La Pampa
170 0.0286 ***
0.1972
0.1946
La Rioja
82 0.0144
-0.0708
(dropped)
Mendoza
477 0.0195 *** -0.1250 *
0.2125 *
Misiones
472 0.0103 *** -0.1117
-0.1248
Río Negro
181 0.0029
0.1342
-0.0161
Salta
343 0.0160 ***
0.1955 ***
-0.0823
San Juan
221 0.0155 ***
0.1469
(dropped)
San Luis
124 0.0247 **
0.2309
(dropped)
Santa Cruz
72 0.0083
0.0610
-0.0077
Santa Fé
674 0.0231 ***
0.0915
-0.1530 *
Sgo.del Estero
294 0.0214 ***
0.6305 ***
0.0227
Tucumán
448 0.0322 *** -0.1923 **
0.3345 *
T. del Fuego
64 0.0135
-0.1792 **
(dropped)
*** Significant at 1%, ** significant at 5% and * significant at 10%.
†
The cases when the variable is dropped correspond to those in which
answered that there are native students.
Intercept
R2
F
1.4154
***
0.171
629.84
***
0.8160
0.8486
1.2473
1.2120
1.9814
1.8418
3.0494
1.7179
1.4011
2.2637
1.9899
1.9198
2.1494
2.1060
2.5745
1.9653
2.0548
1.7624
2.6752
1.9367
1.5845
1.3886
2.6819
**
***
***
***
*
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
0.117
0.131
0.131
0.139
0.041
0.112
0.094
0.069
0.174
0.045
0.070
0.017
0.056
0.034
0.015
0.076
0.071
0.072
0.009
0.109
0.169
0.158
0.095
19.76
133.08
3.97
47.27
3.89
17.14
4.84
9.06
13.83
1.63
4.13
0.67
9.26
5.49
0.92
9.25
8.29
4.70
0.21
27.38
19.60
27.81
3.19
***
***
**
***
***
***
***
***
***
***
***
***
***
***
**
***
***
***
**
none of the directors of the schools
The provinces that present coefficients of determination over 10% are Formosa,
Santiago del Estero, Tucuman, Cordoba, Buenos Aires, Catamarca, Chaco, Santa Fe and
the City of Buenos Aires. The highest slopes values of the SES and significantly different
from zero are those corresponding to Formosa, Tucuman, Cordoba, Buenos Aires Province,
Catamarca, the City of Buenos Aires and La Pampa.
The SES has a significant and positive effect on the level of physical capital in almost
all the jurisdictions with the exception of Chubut, Santa Cruz, Tierra del Fuego, Rio Negro,
Jujuy and La Rioja. This confirms that in most of the provinces there is not equality of
educational opportunities, because there is a significant relationship between the level of
physical capital and the wealth of the students, measured through the SES. The exceptions
are Jujuy, La Rioja, Rio Negro and Santa Cruz where we cannot reject that all the
coefficients corresponding to the independent variables are equal to zero (F-Statistic),
indicating that the present inequalities cannot be attributed to unacceptable reasons. In
these cases, though there is inequality, we cannot conclude that it is unfair.
Regarding the other two variables that would also be considered unacceptable as
determinants of the schools‟ capitals, the presence of immigrants and native students, the
outcomes presented in the table suggest that their presence is significant in very few
provinces and that their effect on the physical capital goes in both directions, either positive
or negative. Therefore, in most of the cases we cannot conclude that the inequality found is
unfair to immigrants or native students.
15
Dependant variable: Human Capital
All Jurisdictions
Num.
of
obs.
9198
SES pupils
0.0091
***
immigrants
-0.0326
***
Native
†
students
0.0061
City of Bs.As.
453 -0.0002
0.0707 *
0.0700
Bs.As. Province
2643 0.0119 *** 0.0158
-0.0127
Catamarca
83 -0.0089
0.3011
-0.5038
Córdoba
884 0.0117 *** -0.0293
0.0830
Corrientes
279 0.0052
0.0420
0.0225
Chaco
411 0.0121 *** -0.2591 **
0.0989 *
Chubut
144 -0.0028
0.1009
-0.0780
Entre Ríos
371 0.0019
0.2297 *
-0.3654
Formosa
201 0.0135 *** -0.1560 *
0.1954 **
Jujuy
107 0.0091
-0.2078 **
-0.0203
La Pampa
170 0.0278 *** 0.4254 ***
-0.0806
La Rioja
82 0.0093
-0.1167
(dropped)
Mendoza
477 0.0100 *** -0.0566
0.0023
Misiones
472 0.0156 *** -0.0579
-0.0428
Río Negro
181 0.0063
-0.0191
0.1796 **
Salta
343 0.0161 *** -0.0577
-0.0623
San Juan
221 0.0119 *** 0.1189
(dropped)
San Luis
124 -0.0030
0.0541
(dropped)
Santa Cruz
72 0.0126
0.1532
0.9329 **
Santa Fé
674 0.0049 **
0.0020
-0.0308
Sgo.del Estero
294 0.0315 *** 0.1167
0.6797 *
Tucumán
448 0.0121 *** -0.1838 **
0.1327
T. del Fuego
64 0.0014
-0.1866 **
(dropped)
*** Significant at 1%, ** significant at 5% and * significant at 10%.
†
The cases when the variable is dropped correspond to those in which
answered that there are native students.
Intercept
R2
F
3.3781
***
0.t0278
87.75
3.8294
3.1754
3.7544
3.4209
3.3893
3.2109
3.9693
3.3913
3.0688
3.3433
2.3536
3.2889
3.4938
3.0891
3.2930
3.3087
3.4399
4.0552
3.0021
3.7442
2.5816
3.4347
3.5850
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
0.0128
0.0219
0.0219
0.0274
0.0091
0.0631
0.0122
0.0114
0.1036
0.0619
0.1424
0.0135
0.0201
0.0779
0.0447
0.0831
0.0582
0.0042
0.0798
0.0091
0.2036
0.0344
0.0661
1.93
19.66
0.59
8.25
0.84
9.14
0.58
1.41
7.59
2.26
9.19
0.54
3.23
13.19
2.76
10.24
6.73
0.25
1.97
2.06
24.72
5.29
2.16
***
***
***
***
***
*
***
**
***
**
***
***
***
***
none of the directors of the schools
In the case of the human capital approximately half of the jurisdictions present a
coefficient of the SES positive and significantly different from zero. The presence of native
students is significant on the determination of the amount of human capital in very few
provinces. In all of them, the effect is positive, nor negative, which would have been
considered unacceptable. On the contrary, the presence of immigrants, when it is
significantly different from zero, is sometimes positive, as in the case of the City of Buenos
Aires, Entre Rios and La Pampa, and negative in the cases of Tucuman, Tierra del Fuego,
Chubut, Jujuy, Formosa and all the jurisdictions considered as a whole.
We cannot reject the equality of opportunity regarding the human capital in the
following jurisdictions: City of Buenos Aires, Catamarca, Corrientes, Chubut, Entre Rios, La
Rioja, San Luis, Santa Cruz and Santa Fe (The F-Statistic is not significantly different from
zero). Therefore, we cannot conclude that the inequality found in the human capital of these
jurisdictions is unfair.
16
Dependant variable: Social Capital
Num.
of
obs.
All Jurisdictions
9198
City of Bs.As.
Bs.As. Province
453
2643
SES pupils
0.0085
***
inmigrants
-0.0306
native
†
students
***
-0.0399
Intercept
**
0.0114 **
-0.0315
-0.0287
0.0200 ***
0.0018
-0.0295
Catamarca
83 0.0269 ***
1.1215 **
-1.7597 ***
Córdoba
884 0.0151 ***
-0.0133
0.1092
Corrientes
279 0.0032
-0.0098
0.0720
Chaco
411 0.0045 **
-0.0438
0.0194
Chubut
144 0.0070
0.0366
-0.0884
Entre Ríos
371 0.0122 ***
0.0186
-0.5188 **
Formosa
201 0.0149 ***
-0.0615
0.0666
Jujuy
107 0.0228 ***
-0.1821 *
-0.0357
La Pampa
170 0.0282 ***
0.2435 *
0.0025
La Rioja
82 0.0079
-0.3356
(dropped)
Mendoza
477 0.0134 ***
0.0529
0.2086 **
Misiones
472 0.0095 ***
-0.0178
0.0239
Río Negro
181 0.0086 **
0.1641 **
0.0596
Salta
343 0.0110 ***
-0.0549
0.0447
San Juan
221 0.0114 ***
-0.0179
(dropped)
San Luis
124 0.0030
0.0905
(dropped)
Santa Cruz
72 0.0402 ***
0.2017
0.6622
Santa Fé
674 0.0115 ***
-0.0662
0.1102 ***
Sgo.del Estero
294 0.0094 ***
0.3779 **
-0.2111
Tucumán
448 0.0137 ***
0.0541
0.0415
T. del Fuego
64 0.0335 **
-0.3071 ** (dropped)
*** Significant at 1%, ** significant at 5% and * significant at 10%.
†
The cases when the variable is dropped correspond to those in which
answered that there are native students.
R2
F
2.5299
***
0.0281
88.51
***
2.2419
2.0376
***
***
0.0162
0.0627
2.46
58.82
*
***
3.7333
2.3152
2.5724
2.6342
2.4442
2.2377
2.1463
1.8994
1.6086
2.2905
2.4637
2.5379
2.3917
2.4188
2.5977
2.7861
0.3949
2.4856
2.4607
2.3803
0.6600
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
***
0.1438
0.0472
0.0037
0.0104
0.0333
0.0540
0.1068
0.1513
0.1484
0.0362
0.0549
0.0364
0.0731
0.0304
0.0551
0.0069
0.1106
0.0479
0.0567
0.0423
0.1401
4.42
14.54
0.34
1.43
1.61
6.99
7.85
6.12
9.64
1.48
9.15
5.9
4.65
3.54
6.36
0.42
2.82
11.24
5.81
6.53
4.97
***
***
***
***
***
***
***
***
***
***
***
***
***
**
***
***
***
***
none of the directors of the schools
In the case of the social capital, the absence of equality of educational opportunities
can be confirmed in most of the jurisdictions. Catamarca is a special case, in which there
would be a negative association between the level of SES and of capital, suggesting the
existence of a pro-poor distribution.
The presence of native students is significant in very few provinces, and its impact
on the social capital is sometimes positive (Santa Fe and Mendoza), and sometimes
negative (Entre Rios, Catamarca and all the jurisdictions considered as a whole). A similar
situation is observed in the case of immigrants, in Catamarca, Santiago del Estero and Rio
Negro their presence has a positive and significant impact on the social capital, while in
Tierra del Fuego, on the contrary, the effect is negative. Tierra del Fuego is the only province
in which the presence of immigrants has a negative and significant effect on the three types
of capitals of the schools, and Santiago del Estero and La Pampa are the only ones in which
this variable has a positive effect on the three capitals (though in the case of the human
capital it is not significantly different from zero for Santiago del Estero and in the case of the
physical capital for La Pampa).
As was already mentioned, public schools quite often have cooperative associations
which are generally managed by parents of students of the school and recollect funds from
the students to invest them in improving the quality of the service provided by the school.
Their action could affect the amount of physical capital the school can buy or afford to repair,
or provide funds to hire more acknowledged teachers (human capital). Regarding the social
capital, as it is constructed taking into account the relationship between schools and parents;
it also takes into account if these cooperative associations are constituted in the school.
17
Therefore, it cannot be used to test if it is a determinant of the social capital, because we
already know it is.
Incorporating the presence of these cooperative associations in order to check their
impact on the physical and human capitals of the schools in most cases did not alter
significantly the results previously found. Three variables considered unacceptable (SES,
immigrants and native students) were tested as determinants of the school capitals, and one
considered acceptable (the presence of cooperative associations). The presence of a
cooperative association is a significant determinant of the physical capital in Río Negro,
Formosa, Mendoza and Misiones. In the case of Río Negro, it is the only element that
presents a coefficient significantly different from zero indicating that all the disparity in the
distribution of this capital would be due to acceptable sources. In fact, the model which was
not significant without incorporating this variable, now it is. In Mendoza and Misiones, though
the coefficients regarding the unacceptable factors are still significant, they are slightly
smaller than when these cooperative associations are not included, but in Formosa, the
coefficient regarding the SES, is even bigger than in the previous analysis. As regards the
Human Capital, the cooperative associations have a significant impact for the cases of
Buenos Aires Province, Formosa, San Juan, San Luis and Tucumán. In the case of San
Luis, it is the only determinant with a coefficient significantly different from zero, indicating
that the inequality in the Human Capital would be explained by acceptable factors, and
again, the model that was not significant now is. In the rest of the provinces, the results
regarding the other coefficients are mixed; in the case of Buenos Aires province, the
coefficients corresponding to unacceptable sources were reduced, on the contrary, in
Formosa and San Juan the coefficients were increased, and in the case of Tucumán, the
one corresponding to the SES was reduced, but the corresponding to the level of immigrants
was increased.
Finally, as a complementary way to evaluate the equality of educational
opportunities, the degree of relationship between school quality and the level of income will
be also analyzed with the concentration index (CI). The CI for the Socioeconomic Status is in
essence the Gini Coefficient, and the CI for the physical, human and social capitals is also
presented in Graph 3. As can be seen La Rioja is the only province that can be considered
pro-poor (-0.00235) regarding the physical capital, while Formosa is the one which presents
the most pro-rich distribution for this capital (0.05778). Concerning the human and social
capitals, Catamarca is the only jurisdiction that presents a negative value, indicating a propoor distribution (-0.004543 and -0.025323 respectively). Santiago del Estero is the most
pro-rich in what respects the human capital (0.04065) and Tierra del Fuego concerning the
social capital (0.024604).
18
Graph 3: Concentration index of the SES, Physical, Human and Social Capitals
CI SES
0.16
CI PhC
CI HC
CI SC
0.14
0.12
0.1
0.08
0.06
0.04
0.02
Tierra del Fuego
Tucumán
Sgo.del Estero
Santa Fé
Santa Cruz
San Luis
San Juan
Salta
Río Negro
Misiones
Mendoza
La Rioja
La Pampa
Jujuy
Formosa
Entre Ríos
Chubut
Chaco
Corrientes
Córdoba
Catamarca
-0.04
Bs.As. Province
-0.02
City of Bs.As.
0
With two exceptions, Catamarca and La Rioja, the CI is always positive. This
indicates that in almost all the cases, the school capitals are more concentrated among
those who have a higher socioeconomic status, confirming the lack of equality of educational
opportunities. At the same time, the CI for the SES is the highest one for all jurisdictions,
what would indicate that the schools capitals are distributed in a less pro-rich way than the
socioeconomic status. The results obtained by this methodology are very much in line with
the ones from the regressions presented above.
6. Concluding remarks
The need for empirical work on the measurement of educational inequalities in the
Argentine public system has often been stressed. This paper takes a step in that direction by
presenting different measures regarding the horizontal inequality, also known as the equal
treatment of equals, and the equality of educational opportunities, measured through the
degree of association between the school quality and the variables considered
unacceptable.
The coefficients of variation for the indicators of the school quality range between
12.9% (corresponding to the human capital) and 24% (corresponding to the physical capital)
considering all the jurisdictions, while 10% is usually considered as the benchmark.
Therefore, the presence of inequalities is not just a feeling but a fact. After having a first
approach to the problem, the following step was to try to unravel where the main problem
was. In that sense, it was studied whether it was one of provincial administration or of
inefficient compensatory policy by the national government. The decomposition of the Theil
index showed that the majority of the inequality was explained by differences within the
jurisdictions, more than 84% corresponded to it.
Then, we focused the study in the evaluation of the particular situation of each
jurisdiction. First we studied the horizontal equity with the coefficient of variation and the
Theil index. The ones that present the worst scenario are Buenos Aires province, Corrientes,
Chaco, Entre Rios and La Rioja. All these are the worst ranked in the distribution of the three
measures of school quality, either by the coefficient of variation as by the Theil index. The
19
best ones in this respect are Córdoba, Chubut, La Pampa, San Juan, San Luis and
Tucuman. It is worth mentioning that the size of the jurisdictions is quite different, but that
large and small jurisdictions are in both groups. Buenos Aires Province is the largest one
while Córdoba is the second largest one. And La Rioja and San Luis are among the smallest
jurisdictions. Next, the degree of association between the quality of the schools and those
variables considered unacceptable was studied to determine the degree of equality of
educational opportunities. In this sense, the regression analysis and the concentration index
showed that in most cases there is a positive association which indicates the lack of equality
of educational opportunities. With the exception of Santiago del Estero, the coefficient of
determination is never higher than 20%, and in most of the cases is fewer than 10%.
Formosa and Santiago del Estero present a worrisome situation. Not only they have the
poorest students, but also they have horizontal inequality and a lack of equality of
educational opportunities. Two cases that call the attention are La Rioja and La Pampa, the
first one has bad marks regarding horizontal inequality, while we cannot reject the
hypothesis of equality of educational opportunities, even more, the Concentration Index for
the Physical Capital is negative, what indicates that it is distributed in a pro-poor way. This
means that we could not find evidence that the distribution of the school quality is related to
unacceptable factors. On the contrary, La Pampa has good indicators about horizontal
equality, while the regression analysis shows that almost 15% of the distribution of the
schools capitals can be explained by unacceptable factors.
Finally, it is worth mentioning that though we could corroborate the lack of horizontal
equity and of equality of educational opportunities, even among the public schools financed
by the same jurisdiction, all the school capitals are distributed more evenly than the
socioeconomic status. This could mean that there is a certain equalizing policy regarding
educational quality.
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22
Apendix 1: The Socio Economic Index
So as to estimate the socioeconomic status of the students the answers provided
about the possession of durable goods, the utilization of public services, the number of
family members and the parents‟ educational level were used. Following Schumacher (2003)
and Elbers et al. (2003) a different data base containing the variable of interest was used so
as to estimate its distribution. With the purpose of getting the spending patron of the
households and their characteristics, the purchasing habits regarding durable goods and
public services corresponding to the households of different socioeconomic status were
studied as well as how the household head education affected it. The chosen survey was the
National Household Expenditure Survey because it has similar questions to the ones
corresponding to the ONEE as well as information regarding households‟ income and
consumption. It also has the advantage of representing the whole population of the country,
not as other commonly used surveys that only represent urban population.
After selecting the source of information and the variables to use, so as to know
which weight corresponds to each of the items, several regressions were run by region. And,
as there are multiple variables that define the socioeconomic status (dependant variable), as
it may be the household income or expenditure, per capita household income or expenditure
and their logarithms, several regressions were run and the explicative power of the model
was measured through the R2. The logarithm of the per capita household income was
selected as the dependant variable and the explanatory variables used in the regression
were those selected from the ONEE that were as well in the ENGH.
The regression equation was as follows:
ln(ingpcf) = a0 + a1(edup) + a2(edusi) + a3(edus) + a4(eduui) + a5(eduu) + a6(car) +
+a7(electricity) + a8(telephone) + a9(stove) + a10(gas) + a11(air conditioning) + +a12(hot
water) + a13(toilet) + a14(water) + a15(2 members) + a16(3 members) + +a17(4 members)
+ a18(5 members) + a19(6 members) + a20(7 members or more)
The first five explanatory variables are intended to represent, using dichotomic
variables, the maximum educational level attained by the head of the family: completed
primary (edup), incomplete secondary (edusi), completed secondary (edus), incomplete
tertiary (eduui) and completed tertiary (eduu). The subsequent nine variables represent the
possession or not of durable goods and utilities. Finally, the last six variables are referred to
the size of each household, only one of the last six variables is assigned the value “1” with
the remaining valued at “0”, depending on the number of members in the household.
Estimations of the households‟ expenditure patterns for each of the regions in the
country (GBA, NEA, NOA, Cuyo, Pampeana and Patagonia) were obtained, which means,
that a specific value was assigned to each of the coefficients for each of the regions. Later,
with the estimated coefficients, the explanatory variables were replaced by the different
vectors provided by the ONEE data base for each of the regions, and in this way, a
prediction of the logarithm of per capita household income of each student surveyed was
obtained, taking into account the expenditure pattern usual of his place of origin. Finally, the
values were rescaled without altering the relative positions in order to assign zero value to
the minimum and one hundred to the maximum. This was done by subtracting the minimum
value from each prediction, dividing by the difference between the maximum and the
minimum values and multiplying by one hundred. It is worth mentioning that the SES has an
economic dimension; it is the prediction of the logarithm of the household per capita income,
and also a cultural dimension, captured by the level of education of the household head and
the amount of members in the family. It is expected that the higher the SES of the student,
the bigger will be the financial capacity of the household to invest in the children‟s education
and there would be more cultural climate. In addition, the average SES for each section,
institution and jurisdiction was calculated.
23
Appendix 2: Figures and Tables
Figure A.1: Physical, human and social capitals and average SES per jurisdiction. The
size of the circle indicates the number of sections in the jurisdiction.
Physical capital and average SES per jurisdiction
3.6
3.4
Tierra del fuego
City of Bs.As.
La Pampa
3.2
Physical Capital
Santa Cruz
Chubut
3
Mendoza
Córdoba
2.8
Santa Fé
San Luis
2.6
San Juan
Tucumán Entre Ríos
Río Negro
Salta
Misiones
Chaco
2.4
La Rioja
Bs.As. Province
Corrientes
Jujuy
Catamarca
Sgo. Del Estero
Formosa
2.2
2
30
35
40
45
50
55
60
65
Socio Economic Status
Human capital and average SES per jurisdiction
4
San Juan
3.9
Salta
San Luis
Santa Fé
Tucumán
Mendoza
Córdoba
City of Bs.As.
Chubut, 3.810995
Human Capital
3.8
3.7
Santa Cruz
Bs.As. Province
Misiones
La Pampa
Chaco
3.6
La Rioja
Sgo. Del Estero
Río Negro
Jujuy
Formosa
Tierra del fuego
Corrientes
3.5
Entre Ríos
Catamarca
3.4
3.3
30
35
40
45
50
55
60
65
Socio Economic Status
24
Social capital and average SES per jurisdiction
3.6
3.4
Social Capital
3.2
3
San Juan
Mendoza
Tucumán
San Luis
Santa Fé
Misiones
Sgo. Del Estero
2.8
Salta
Chaco
La Pampa
City of Bs.As.
Bs.As. Province
Chubut
Entre Ríos
Formosa
Catamarca
Jujuy
2.6
Córdoba
Santa Cruz
La Rioja
2.4
Tierra del fuego
2.2
2
30
35
40
45
50
55
60
65
Socio Economic Status
Figure A.2: School capitals and average SES per section in each jurisdiction
Physical capital, fitted values of physical capital and average SES per section
Provincia de Buenos Aires
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
0
5
0
5
0
5
0
5
Ciudad de Buenos Aires
0
Tucumán
40
60
80
0
20
40
60
80
Tierra del Fuego
0
5
Santiago del Estero
20
0
20
40
60
80
0
20
40
60
80
0
20
40
60
80
(mean) NESal
CF
Fitted values
Graphs by juris
25
Human capital, fitted values of human capital and average SES per section
Provincia de Buenos Aires
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Ciudad de Buenos Aires
0
Tucumán
40
60
80
0
20
40
60
80
Tierra del Fuego
1 2 3 4 5
Santiago del Estero
20
0
20
40
60
80
0
20
40
60
80
0
20
40
60
80
(mean) NESal
CH
Fitted values
Graphs by juris
Social capital, fitted values of social capital and average SES per section
Provincia de Buenos Aires
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
Ciudad de Buenos Aires
0
Tucumán
40
60
80
0
20
40
60
80
Tierra del Fuego
0 1 2 3 4
Santiago del Estero
20
0
20
40
60
80
0
20
40
60
80
0
20
40
60
80
(mean) NESal
CS
Fitted values
Graphs by juris
26
0
.2
.4
.6
.8
1
Figure A.3: Nonparametric distribution of the schools capitals
All public schools
0
1
2
3
4
5
x
kdensity CF
kdensity CS
kdensity CH
Public schools per jurisdiction
Provincia de Buenos Aires
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
0
.5
1
1.5
0
.5
1
1.5
0
.5
1
1.5
0
.5
1
1.5
Ciudad de Buenos Aires
0
Tucumán
4
6
0
2
4
6
Tierra del Fuego
0
.5
1
1.5
Santiago del Estero
2
0
2
4
6
0
2
4
6
0
2
4
6
x
kdensity CF
kdensity CS
kdensity CH
Graphs by juris
27
0
.2
.4
.6
.8
1
Figure A.4: Concentration Index for the Physical, Human and Social Capitals.
All public schools
0
.2
.4
.6
.8
1
shrpob
shrCF
shrCH
shrCS
r45p
Table A.1: Theil index and the amount of school capitals in each jurisdiction
Absolute values
Theil
SES
City of Bs.As.
0.0115
Bs.As.
0.0386
Catamarca
0.0286
Córdoba
0.0334
Corrientes
0.0473
Chaco
0.0555
Chubut
0.0288
Entre Ríos
0.0428
Formosa
0.0584
Jujuy
0.0390
La Pampa
0.0278
La Rioja
0.0254
Mendoza
0.0462
Misiones
0.0571
Río Negro
0.0495
Salta
0.0451
San Juan
0.0478
San Luis
0.0428
Santa Cruz
0.0190
Santa Fé
0.0553
Sgo.del Estero
0.0481
Tucumán
0.0379
Tierra del Fuego 0.0201
Jurisdiction
Mean
SES
59.3904
43.3006
43.5550
44.5785
40.8298
38.8472
51.0881
42.5848
36.6196
38.8389
47.2685
44.8411
41.1075
38.8905
44.0559
38.9282
40.1969
41.5220
53.5776
40.6746
37.5507
40.0374
54.9696
Theil
PhC
0.0146
0.0344
0.0233
0.0230
0.0301
0.0301
0.0150
0.0271
0.0285
0.0234
0.0148
0.0307
0.0240
0.0214
0.0172
0.0235
0.0167
0.0234
0.0100
0.0242
0.0262
0.0182
0.0054
Mean
PhC
3.3353
2.4933
2.3919
2.8916
2.4612
2.4189
3.0389
2.5936
2.2512
2.4109
3.3328
2.4918
2.8887
2.4637
2.7135
2.5858
2.6619
2.7808
3.0941
2.8168
2.3388
2.6108
3.3467
Theil
HC
0.0068
0.0090
0.0063
0.0057
0.0089
0.0091
0.0061
0.0097
0.0072
0.0076
0.0068
0.0090
0.0093
0.0085
0.0080
0.0072
0.0066
0.0052
0.0061
0.0066
0.0137
0.0071
0.0054
Mean
HC
3.8598
3.6747
3.4118
3.9236
3.5349
3.6311
3.8110
3.4342
3.5430
3.5550
3.6501
3.6114
3.8617
3.6375
3.5761
3.8642
3.9012
3.9374
3.7015
3.9100
3.6018
3.8746
3.5417
Theil
SC
0.0140
0.0162
0.0159
0.0093
0.0161
0.0124
0.0132
0.0146
0.0118
0.0199
0.0086
0.0196
0.0134
0.0116
0.0111
0.0135
0.0078
0.0107
0.0177
0.0123
0.0132
0.0112
0.0236
Mean
SC
2.8763
2.8757
2.6412
2.9623
2.6462
2.7655
2.7548
2.7093
2.6636
2.6212
2.9091
2.5524
2.9790
2.8620
2.7892
2.8281
3.0086
2.9460
2.5774
2.9156
2.7566
2.9023
2.3903
28
Table A.2: Concentration index of the SES, Physical, Human and Social Capitals
Jurisdiction
City of Bs.As.
Bs.As.
Province
Catamarca
Córdoba
Corrientes
Chaco
Chubut
Entre Ríos
Formosa
Jujuy
La Pampa
La Rioja
Mendoza
Misiones
Río Negro
Salta
San Juan
San Luis
Santa Cruz
Santa Fé
Sgo.del Estero
Tucumán
Tierra
del
Fuego
SES
0.0368867
Physical Capital
0.031662632
Human Capital
0.000168755
Social Capital
0.014640484
0.07138859
0.05175813
0.010695707
0.024602865
0.0752369
0.07088999
0.12303326
0.14586407
0.07466859
0.08709147
0.14916162
0.1027711
0.06386703
0.05779457
0.08879394
0.12894981
0.10389302
0.11415454
0.0889905
0.07944139
0.0383473
0.11067375
0.14324267
0.08754757
0.039407212
0.046046889
0.015508766
0.038262139
0.014699457
0.03600217
0.05778317
0.011281701
0.022671505
-0.002348407
0.014890169
0.017595175
0.001979957
0.034443686
0.027037045
0.039453322
0.008142857
0.041957038
0.049109799
0.038994636
-0.004542602
0.008694903
0.00866496
0.015253156
0.0000360903
0.006289962
0.015343371
0.001274802
0.014763694
0.002352786
0.004971224
0.020430824
0.009163114
0.021500676
0.01595073
0.00631646
0.006925584
0.007085144
0.040652057
0.008563719
-0.025323007
0.019954057
0.007508357
0.008456322
0.013585936
0.02425742
0.023840534
0.021158576
0.022763337
0.012089895
0.012051411
0.018202922
0.016795531
0.01741193
0.014148603
0.011459611
0.021364249
0.019704006
0.015119131
0.016413879
0.04152146
0.007245935
0.006128526
0.024604441
29