1995
es
Corden, W. Max
Corden, W. Max
Una zona de libre comercio en el Hemisferio Occidental: posibles implicancias para América Latina
En: La liberalización del comercio en el Hemisferio Occidental - Washington, DC : BID/CEPAL, 1995 - p. 13-40
2014-01-02T14:51:16Z
hdl:11362/11593
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Determinants of educational performance
in Uruguay, 2003-2006
Cecilia Oreiro and Juan Pablo Valenzuela
Abstract
Students’ performance at the lower secondary level in Uruguay is examined on the
basis of the mathematics scores compiled by the Programme for International Student
Assessment (pisa) for 2003 and 2006. An effort is made to analyse the differences
in score distributions, to identify the variables influencing students’ performance and
to trace the trends over that period and weigh their significance. In order to do so, a
production function for educational achievement is defined and a number of different
decomposition methodologies are applied. The findings indicate that the small increase
in scores between 2003 and 2006 is the net result of differing changes, most of which
are primarily the result of an across-the-board increase in the school system’s efficiency,
especially in the case of public schools. However, this improvement is partially offset
by reduced resource endowments and, in particular, unfavourable socioeconomic and
cultural conditions in many of the students’ households. Most of the changes that are
analysed in this study are found to be of a redistributive nature.
KEYWORDS
JEL CLASSIFICATION
AUTHORS
Education, quality of education, measurement, evaluation, secondary education, public schools, private
schools, Uruguay
D39, I24, O38
Cecilia Oreiro, researcher with the Institute of Economics of the University of the Republic, Uruguay.
coreiro@iecon.ccee.edu.uy
Juan Pablo Valenzuela, researcher with the Centre for Advanced Research in Education (ciae) and the
Department of Economics of the University of Chile. jp.valenzuelab@gmail.com
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I
Introduction
This study’s objective is to analyse the status of basic
secondary education in Uruguay and to identify the
reasons for the differences observed between students’
scores on the mathematics portion of the test administered
by the Programme for International Student Assessment
(pisa) in 2003 and 2006.
Since the year 2000, the pisa test has been
administered to students aged 15 (regardless of what grade
they are in) in the member countries of the Organisation
for Economic Cooperation and Development (oecd)
and in a number of partner countries. The results can
be used to examine how students’ performance varies
depending on the grade that they are in, which provides
an indicator of how much they learn as they move up
from one grade to the next.
The study will look specifically at the mathematics
test results because this was the main focus of the 2003
assessment, which is the only one that can be used as a
comparison with the 2006 results. The objectives of this
analysis are to establish whether significant differences
exist between the pisa scores for 2003 and 2006, identify
the factors (characteristics of the students, features of
the schools or institutional variables) that account for
differences between the scores for those two years, and
determine whether such differences are attributable to
This study is based on a Master’s thesis written for the School of
Economics and Business of the University of Chile, January 2011.
The authors are grateful for the valuable assistance received from
Alejandro Sevilla.
variations in the magnitude of those factors, in how
“efficiently” they have been used, or both.
In line with Valenzuela and others (2009a), a
number of different methods for decomposing score
differentials are used, including those of Oaxaca (1973),
Blinder (1973) and Juhn, Murphy and Pierce (1993). An
analysis based on microsimulations of the type outlined
by Bourguignon, Fournier and Gurgand (1998) is also
undertaken.
The potential contribution of this study to the
economic and social development of the Latin American
countries lies in the possibility it offers to draw
conclusions about the quality of the education system
and its heterogeneity which will be useful in identifying
avenues for improvement. The pisa test can be used as a
tool for comparing progress in Latin America with the
advances being made in the developed world and with
those taking place in other countries of a similar level
of development. In addition, the use of decomposition
techniques that are not widely applied in the field of
education paves the way for a methodological approach
that can be highly useful in gaining a better understanding
of trends in educational achievement and that can be
replicated in other school systems in the region, as well
as being used for comparisons across countries.
This article is structured as follows. Background
information that provides a frame of reference for the
study is given in section II, while the methodology used
for the analysis is described in section III. Section IV
reports on the results, which are then compared in section
V. Section VI concludes.
II
Background
1.The social and economic context
Historically, Uruguay has had one of the lowest levels of
inequality and one of the lowest poverty rates in Latin
America. Until the mid-1990s, its per capita income
was rising, income distribution was fairly stable, and
poverty was on the decline (Amarante and Perazzo,
2008). In the second half of that decade, income levels
began to descend and income concentration increased
slightly, while poverty levels began to rise. In 1999, the
first signs of a recession began to appear, and by 2002
the country was in the midst of a deep economic crisis.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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All the economic variables worsened, there was a steep
drop in gdp and per capita income, income distribution
became more unequal, and poverty rates climbed sharply.
As the crisis was brewing, international emigration
increased to a striking level. The country’s negative
migration balance is estimated to have amounted to
100,000 people in 2000-2004 and to 26,000 between
2005 and 2006 (Pellegrino and Koolhaas, 2008).
A majority of the Uruguayans who emigrated were
between 20 and 29 years of age. Most were males with
an above-average level of education. In addition, a large
proportion of the emigrant population was composed of
entire family groups.
The level of economic activity in the country
began to rebound in 2003 and gathered steam in 20042006, which proved to be a period of rapid economic
growth. This recovery was not mirrored in the trend in
household income until late 2005, however, and it was
not until 2006 that significant reductions were seen in
indigence levels, the poverty rate and poverty intensity
(undp, 2008).
2.
Education in Uruguay
The compulsory basic education cycle in Uruguay is nine
years in length: six years of primary education and three
of basic secondary education. Both academic secondary
schools (liceos) and vocational schools use the same
curriculum. Academic secondary schools are run by
the Secondary Education Council (ces), while technical
schools are administered by the Council for Technical
and Vocational Education (cetp). The second cycle of
secondary education is also three years in length and leads
to a diploma known as a “diversified baccalaureate” if
the student has attended an academic secondary school,
and to a degree known as a “technical baccalaureate” if
the student has attended a vocational school. cetp also
offers basic training and basic vocational instruction, in
addition to advanced occupational training.
The economic recovery that came in the wake of the
2002 crisis was coupled with a slight rise in the privateschool enrolment rate. This increased private schools’ share
of total enrolment at that level, but the traditional pattern,
in which public schools have predominated, remained
intact (Cardozo, 2008). This growth phase came to an
end in 2004. Enrolment in secondary education fell in
2004 and 2005 and remained steady in 2006. The decline
registered in 2004 reflected lower enrolment in public
schools, whereas the number of students in vocational
and private schools rose. In 2005, enrollment also fell in
vocational schools but rose for the second year running in
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private schools. Nonetheless, the overall rate was lower
once again. The decrease in the total enrollment rate in
2003-2005 is attributable to a reduction in the number
of students completing their primary education and to
international emigration (anep, 2007a).
A comparison of the number of persons who
should have been attending school with the number of
persons who actually did attend yields a more accurate
measurement of the extent of educational coverage in
each sector. The secondary-school attendance rate for
15-year-olds in 2006 was 79.7%, which is a gain of five
percentage points over the attendance rate in 2003. This
increase is a reflection of an upturn in rural coverage,
which climbed from 51.8% to 69.2% during that time
period, while urban coverage (towns with a population
of over 5,000) held steady (anep, 2007b).
Uruguay participated in the 2003 and 2006 pisa
exams. Its students obtained some of the highest scores
in Latin America, but performed considerably less well
than students in oecd countries. Uruguay’s performance
was also one of the most uneven of all the participating
countries —far more unequal than the oecd countries
as a group and even, in 2006, more so than the other
countries of the region (anep, 2004 and 2007b).
Between 2003 and 2006, Uruguay’s average score
on the pisa mathematics test rose from 422.2 to 426.8
score points (an increase of just 1.1%, which is not
statistically significant). The question arises, however,
as to whether this change in the average score from
one period to the next might be the result of shifts in
opposite directions in different social and institutional
variables. The question as to whether given factors
are generating movements in different directions and
of different magnitudes will be explored by using
methodologies that make it possible to decompose the
effect of each relevant factor.
The pisa test results are also presented in an
ordinal classification of academic performance. For the
mathematics test, six proficiency levels are identified.
Figure 1 shows the percentage of students at each of
those levels in 2003 and 2006. As can be seen from the
graph, 49% of Uruguayan students were below level 2
in 2003 (i.e. their level of proficiency is not sufficient
to enable them to use mathematics in their daily lives).
This means that they also run a high risk of being unable
to participate fully in civic affairs or to gain entry to
many of the occupations associated with an informationand knowledge-based society. Another 48.5% were at
intermediate levels (2, 3 and 4), while only 2.6% were
rated at the top two levels (5 and 6). These last two levels
equate with highly developed mathematics skills relative
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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FIGURE 1
Percentage of students at each proficiency level, pisa mathematics test,
2003 and 2006
2003
Level 4
7.6
Level 5
2.2
2006
Level 6
0.4
Level 0
25.9
Level 3
17.1
Level 4
7.6
Level 5
2.3
Level 6
0.2
Level 0
23.8
Level 3
18.5
Level 1
23.0
Level 2
23.8
Level 2
25.2
Level 1
22.4
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
to the students’ age and identify the group of students
for which the educational system has performed the best.
A comparison of the students’ performance on the 2006
and 2003 tests shows that the percentage of students at
the lowest proficiency levels fell by 2.8%, while the
percentage at the intermediate levels rose by 2.8%;
the percentage of students at the top levels remained
virtually the same. This appears to signal an upward
progression, but such a gradual one that, if this trend
were to remain constant, it would take half a century
before no Uruguayan student was scoring at the lowest
levels of proficiency in mathematics.
III
Methodology
1.General methodology
(a) Production function
The first step in determining the methodology to
be used is to define a production function that relates
each student’s pisa score to a set of explanatory variables
(socioeconomic variables relating to the student and his
or her family, as well as school-related variables and
institutional factors):
Yit = Xit βt + εti(1)
where Yit denotes the score achieved by student i in
a given school at time t; Xit represents the observable
characteristics of the student, the school and institutional
t
factors; β corresponds to the estimated coefficients for
the various control variables;1 and εti is the error term,
which is assumed to have a standard distribution with
t
zero mean and a variance of σ ε and to be independent
of the exogenous variables of the model.
1 Because of the way in which the pisa test results are expressed, the
coefficients are estimated using five plausible values, which means that
the regressions have to be estimated five different times, after which
the mean for the estimates has to be calculated in order to arrive at
the statistical value. The variance is adjusted for each estimate and
for the whole distribution.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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The variables that were selected for use in the
statistical analysis are shown in table A.1 of the annex;2
table A.2 lists the main descriptive statistics.
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statistic with respect to the population parameter, and
the replications take account of the survey’s complex
design (which was conducted in two stages using a
stratified sample).
2.Imputation methodology
3.
Given the large percentage of data that are missing for
the pisa exam,3 a way has to be found for dealing with
the affected observations. Ammermüller (2004) states
that the usual approach is to eliminate an observation
from the regression if the value for any of the explanatory
variables is missing. This greatly reduces the number
of observations that can be used to arrive at estimates,
however.4 In addition, it generates a selection bias in the
sample if the distribution of omitted values is not random.
In line with Valenzuela and others (2009a), the
method used here consists of imputing the value of
the median for a similar subgroup (i.e. a group having
similar values for the different control variables), so that
the observations for which data are imputed belong to
fairly homogenous subgroups. The control groups used
to define these subgroups are gradually reduced so as
to eventually impute all the observations for which data
are missing.5
When working with data that display a significant
degree of variability, whether in the scores in each case or
in the values that are imputed because data are missing,
simply applying the mean values may result in the
omission of the level of uncertainty of the measurement.
This can distort the estimates of standard errors calculated
for the parameters, which is particularly a problem in
the case of effects that are near the significance limit.
The calculation of standard errors thus includes the
weightings for 80 balanced repeated replications (brrs)
in the database, with the Faye correction (0.5). These
standard errors provide the degree of variation for any
2 The
selection of variables was based on a number of prior national
and international studies, including, in particular, those of Llambí
and Perera (2008), Méndez and Zerpa (2009) and Hanushek and
Woessmann (2010).
3 For both tests, the missing data primarily concern the variables
corresponding to the schools, with the largest gaps being 4% of the
data missing in 2003 for the variable “Percentage of certified teachers”
and 3.8% of the data missing in 2006 for the variable “Shortages of
qualified mathematics teachers”.
4 Specifically, if the estimates were performed without correcting for
the missing data, 461 observations would have to be eliminated from
the 2003 sample and 377 would have to be removed from the 2006
sample (i.e. nearly 8% in each case).
5 The effectiveness of this method, measured as the percentage of
matches between the observed variable and the imputed variable for
each iteration, works out to 60%, which surpasses the scores for the
methodologies applied by Ammermüller (2004) and by Fuchs and
Woessmann (2004).
Decomposition methodology
The methodological approach used here consists of
a number of different techniques for decomposing
differences in scores: Oaxaca (1973), Blinder (1973),
Juhn, Murphy and Pierce (1993) and Bourguignon,
Fournier and Gurgand (1998).
The first two methodologies have been applied by
Valenzuela and others (2009b) and by Bellei and others
(2009) to identify the reasons for the differences in the
scores of Chilean students on the 2006 pisa mathematics
and reading tests as compared to the scores of students
in Poland, Spain and Uruguay. Valenzuela and others
(2009a) also used microsimulations to identify explanatory
factors for the improvement in 15-year-old Chilean
students’ scores on the pisa reading test between 2001
and 2006, as well as factors that could help to account
for the increased inequality of those scores. These were
the main methodological references used in this study.
(a) The Oaxaca (1973) and Blinder (1973)
decompositions
The decomposition method proposed by Oaxaca
(1973) and Blinder (1973) provides a way to decompose
differences in results for two groups of people or for
two different years. This decomposition methodology
involves three effects. One corresponds to the different
results that individuals belonging to the same group may
achieve as a consequence of their varying characteristics
(the “characteristics effect”). Another corresponds to
the differences in the level of efficiency with which
the group’s members make use of those characteristics
(the “return effect”). And, finally, there is a combined
“characteristics-return effect”.
For the years being considered (t and t’), given a
variable for the mean mathematics scores (Y) and a set
of explanatory variables, the Oaxaca-Blinder approach
makes it possible to estimate how much of the difference
between mean scores is accounted for by differences in
the explanatory variables for each year:
( )
R = E (Yt ) − E Yt’ (2)
where E(Y) represents the expected value for the pisa
mathematics scores in a given year.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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Obtaining estimators by ordinary least squares (ols)
ˆ
ˆ
and βt separately for the two samples (β’ and βt)
t
’
( )
( )
and using Xt and Xt as estimators for E Xt’ and E Xt ,
the decomposition can be expressed as:
’ˆ
ˆ
R = Yt − Yt’ = Xt − Xt ’ βt ’ + Xt’’
(3)
’ ˆ
ˆ ˆ
ˆ
β t − βt ’ + X t − X t ’ β t − β t ’
(
(
) (
)
)(
)
In this equation, Y reflects the mean score on the
mathematics text for each of the years in which the pisa
exam was administered. The first term in the equation
corresponds to the effect of the means of the control
variables, which are the explanatory variables that
have been incorporated into the production function
(see equation No. 1), i.e. the variables for students, for
schools and for institutional factors. The second term of
equation No. 3 corresponds to the effect of differences in
the coefficients associated with these observed variables
(in other words, the productivity or effectiveness of these
factors). The third term reflects the interaction between
these two effects (i.e. the characteristics-return effect).
(b) The Juhn, Murphy and Pierce (1993) decomposition
Juhn, Murphy and Pierce (1993) applied the
Oaxaca-Blinder (1973) methodology on a broader scale,
developing a methodology for decomposing changes in
the score distribution and for looking at their effects in
the various parts of the distribution.
The first requirement of the proposed methodology
is to obtain the residual εit as a function of two elements:
the percentile in which individual i is located at time t in
the residual distribution θit , and the residual distribution
function for the results in t, Ft(.). Then, to define:
εit = Ft−1
[ ]
θit
(4)
Xit
This makes it possible to estimate the score
distribution for each year and to separate out the effects
of changes in observable characteristics, returns and
residuals; to this end, various estimations are performed
for each year, and an initial estimation is performed for
the regular form of results for each year:
1
(
Rit ) = βt Xit + Ft−1
[ ]
θit
(5)
Xit
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A second estimation is then carried out for the
results of year t, while referring to the returns and
residuals for year t’:
(2
Rit ) = β’ Xit + Ft
t
’(−1)
[ ]
θit
(6)
Xit
Finally, the regular form for each year can be
estimated, but this time with reference only to the
residuals for the other year:
(3
Rit ) = βt Xit + Ft
’(−1)
[ ]
θit
(7)
Xit
This method makes it possible to decompose changes
in the inequality of the results into three components: the
“characteristics effect”: Rt( 2 ) − Ri’t( 1 ), the “return effect”:
’
’
Rit( 2 ) − Rit( 1 ) and the “characteristics-return effect”:
(
Rit
(
R’
it
(1)
) (
(2)
− Rit
(2)
– R’
it
)
(1)
− R’
it
. The remainder is a
“residual effect” that measures variations in inequality
that are not explained by any of the other three factors:
(3)
)
(1)
− R’
it
.
(c) Bourguignon, Fournier and Gurgand (1998)
decomposition
Other authors generalize the microsimulations
method, using it to understand changes in the total
distribution. This methodology was originally developed
by Almeida dos Reis and Paes de Barros (1991) in order to
analyse labour income inequality. Later, it was extended to
the analysis of income inequality and poverty on the basis
of total per capita household income. The first study to
move in this direction was that of Bourguignon, Fournier
and Gurgand (1998), who applied this methodology to
decompose changes in household income inequality for
Taiwan Province of China.
4.
Estimation of the production function and
choice of school
The decomposition begins with the estimation of the
production function (see equation 1). This function
is estimated for each year and for each type of school
(public and private) by ols. The choice between these
two types of schools for each student is also modeled
using a logit estimation.
A word of caution about the risk of selection
bias is called for here. A positive correlation between
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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the type of school and a student’s level of educational
achievement may be produced by a selection bias. This
bias may be due to the fact that a family’s choice of
school is an endogenous decision taken as a function
of its own characteristics. This possibility needs to be
borne in mind when analysing the results.6
5.
Counterfactuals for changes in student
characteristics
With this methodology, calculating the characteristics
effect entails finding the simulated result for individuals
at time t if, all else remaining constant, characteristic k
t
of vector X ki has the distribution of time t’. In line with
Valenzuela and others (2009a), different methodologies are
used depending on the types of variables involved. In the
case of dichotomous variables, we look at the unweighted
percentage of cases in which the characteristic is displayed
in period t’, and that datum is simulated in t. However,
possession of the characteristic for period t’ has to be
linked to each individual in t. In order to determine the
probability of each individual displaying the observed
characteristics, we estimate a probit regression in t’,
which gives us the probability in t that the characteristic
is exhibited, in accordance with the other conditions of t’.
Once these probabilities are placed in descending order,
we then look for the cut-off point based on the observed
percentage of individuals who have the characteristic
in t’. The categorical variables are simulated by means of
a multilogit estimation in t’ and, once again, a probability
of possession of the characteristic is assigned to each
individual in t, after which the cut-off point is located
on the basis of the observed percentage of individuals
that exhibit that characteristic in t’.
In the case of the continuous variables, this approach
involves looking at population groups constructed
on the basis of the type of school and the size of the
population centre.7 Using these groups, we look at the
minimum number of observations that match from one
period to the next in a single group and then use this
set of observations to construct quantiles for which the
mean per group and quantile can be calculated. Then,
using this mean for each year for the variable that is to
be simulated, we construct a factor —the relationship
6
One possible way of dealing with the selection bias is to use the
two-step Heckman adjustment. In order to use this method, however,
the selection model would have to contain at least one exclusion
variable, which was not possible in this study.
7 In some instances, adjustments have to be made in order to make
the simulation more precise, in which case other variables can be used
for the population groups as well, such as grade or grade repetition.
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between the mean for year t’ and the mean for
year t— that is a multiple of the simulated variable for
each subgroup in the population and quantile.
6.
Counterfactuals for changes in returns
The microsimulation of educational attainments while
introducing changes in the vector of returns (vector of
coefficients for the effectiveness of inputs) involves
determining the counterfactual results that a student would
attain at time t if, ceteris paribus, the returns to those
characteristics were to change (i.e. those corresponding
to period t’). To do so, we have to simulate the results
obtained by students at time t while incorporating the
ˆ t’
estimated parameters for those returns for period t’ β
while maintaining the same observable and unobservable
characteristics and the structure of the school selection
procedure for time t.
( )
7.
Counterfactuals for changes in school choice
The “choice effect” represents the change that occurs in
the distribution of students’ scores at time t if the structure
of the selection procedure for period t’ remains constant,
with the other conditions corresponding to period t (i.e.
the observable and unobservable characteristics and the
returns to those characteristics) being given. In order
to do this, we estimate a logit function for each year; a
value of 1(one) is assigned to the case in which a student
is enrolled in a public school.
The simulation is for a different school choice and
ˆ
incorporates the estimated parameters λ t ’ for period t’.
( )
j
The procedure for dealing with the error term for this
equation consists of calculating a residual as the value
of the observed decision (1 for enrolment in public
schools and 0 for enrolment in private ones), minus the
probability indicated by the logit estimation. A family
is deemed to prefer public schools if the probability
estimated by means of this simulation is equal to or
greater than 0.5; if the value is lower than that, it is
assumed that the family chooses a private school. Thus, a
structure of school choice for individuals in period t can
be simulated with parameters representing the structure
of school choice that correspond to period t’ while all
others refer to period t.
In this simulation, the individuals in period t can
choose a different type of school from the one they
actually attend. After simulating the individuals’ school
choice in period t, the performance corresponding to
the simulated situation is imputed to them. In those
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cases in which the result of the simulation changes the
choice of school, there is no estimated error term for
the production function, so random terms are selected
from a normal distribution for those residuals that
correspond to the actually observed decisions regarding
the type of school.
(a) Complementary factors
The complementary factors associated with the
microsimulation include, first of all, the simulation of
unobservable variables. Subgroups by type of institution
and the size of the population centre are used for
this purpose. One factor is calculated as the fraction
corresponding to the standard deviation of the residual
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for each year, by group, and this factor is then multiplied
by the residuals for the year 2003 by subgroup. This
procedure is used for the residuals of the two production
functions, by type of institution.
Then, in order to adjust the factors of expansion, a
fraction is calculated that reflects the ratio corresponding
to the population represented by the sample in 2006 of
a subgroup m (by type of school, size of the population
centre, grade and, in the case of public schools, grade
repetition), i.e. the sum of the factors of expansion for
each subgroup relative to the population represented by
the sample in 2003 for the same subgroup. The factor of
expansion for each observation of subgroup m in 2003
is then multiplied by this fraction.
IV
Results
1.Results of the Oaxaca-Blinder (1973)
decomposition
The Oaxaca-Blinder methodology makes it possible to
disaggregate the total change in scores over the period
2003-2006 into changes in characteristics and changes in
the returns to them. The total change occurring between
those two years was 4.6 points and is primarily attributable
to the “return effect”, which amounts to 11.2 points (see
table 1). The magnitude of this effect is substantial, as
well as being statistically significant, as it is quite similar
to the improvement that would be brought about by one
standard deviation increase in the socioeconomic and
cultural level of the students’ households. This means
that the characteristics’ efficiency in terms of educational
attainment was greater in 2006 than in 2003. However,
the characteristics effect is negative, which means that
they were more disadvantageous in 2006 than they were
in 2003. The characteristics-return effect is the least
influential and is negative.
When the effects are separated out among the three
groups of explanatory variables and the characteristics of
the students, their schools and institutional aspects, these
effects can be analysed in greater detail. The negative
changes linked to the decline in characteristics mainly
have to do with the student-related variables. The Index
of Economic, Social and Cultural Status (escs), which
is constructed by the pisa programme on the basis of
variables relating to the family environment, reflects the
average 1.8-drop in score points, with its mean shifting
from -0.35 to -0.51 during the period under study (see table
A.2 in the annex). While this may seem to be a somewhat
surprising development in the midst of an economic
recovery, there are various possible explanations. One
possibility is a shift in enrolment trends whereby more
students in the upper socioeconomic stratum could be
changing from public to private schools, which would
tend to depress the escs mean for public schools. In
addition, secondary-school coverage has increased,
chiefly as a result of greater attendance rates in smaller
towns. This means that a segment of the student body
that used to leave school at an earlier age (and that is
probably socioeconomically disadvantaged) is now staying
in school, which could be the reason for the trend seen
in the escs index during this period. Yet another reason
for the escs trend could be the large-scale emigration
from the country that took place during those years,
since many of the emigrants came from the middle and
upper-middle socioeconomic strata.
The change in the percentage of students in their
third, fourth and fifth years of secondary school accounts
for the 0.4, 0.5 and 0.7 reductions, respectively, in the
corresponding means. Another factor that could be
contributing to the drop in mean scores attributable to
the characteristic effect is the increase in the percentage
of students who have repeated one or more grades.
The only variable that has had a positive (although not
statistically significant) effect is the sex of the student.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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TABLE 1
Oaxaca-Blinder decomposition
Characteristics
Student-related variables
Sex (female=1)
Return
Characteristics-return
Fourth year
Fifth year
Behind grade
escs
Subtotal: student-related variables
School-related variables
Peer effect (escs)
School size
Student-teacher ratio
Shortages of teaching materials
Shortage of mathematics teachers
Percentage of certified teachers
Montevideo and its metropolitan area
Rural
Subtotal: school-related variables
Institutional variables
Selectivity
Private
Subtotal: institutional variables
Constant
Total
-3.02
(2.24)
-1.53
(1.28)
-12.96
(9.09)
-2.22*
(1.33)
-4.34
(4.11)
-0.84
(0.73)
0.00
(0.11)
0.08
(0.15)
0.10
(0.52)
0.17
(0.40)
-0.17
(0.42)
-0.39
(0.33)
-3.46
(2.78)
-24.91*
(14.74)
-0.21
(0.43)
-3.04**
(1.27)
-0.83
(0.87)
0.57
(0.60)
1.33
(1.10)
-0.64
(1.09)
1.54
(1.05)
-0.22
(0.30)
0.02
(0.12)
-0.85
(2.69)
-1.76
(6.99)
1.92
(10.11)
5.88
(10.51)
-3.50
(7.39)
-8.93
(8.38)
2.31
(3.08)
0.72
(1.07)
-0.39
(1.22)
0.32
(1.24)
-0.21
(1.10)
-0.67
(1.26)
0.77
(1.64)
-1.19
(1.21)
-0.10
(0.19)
-0.03
(0.16)
-1.27
(2.49)
-4.21
(18.23)
-1.50
(2.73)
-0.15
(0.32)
0.08
(0.17)
-0.21
(1.24)
-2.76
(2.02)
0.03
(0.21)
-0.15
(0.29)
-0.07
(0.41)
-2.96
(2.14)
-0.13
(0.37)
Third year
0.01
(0.30)
-0.40
(0.70)
-0.49
(2.35)
-0.69
(1.60)
-0.10
(0.25)
-1.78***
(0.57)
43.31
(26.65)
-4.79
(4.49)
11.23***
(3.22)
-1.84
(2.77)
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Levels of significance: *10%, **5%, ***1%
Standard errors are shown in parentheses.
Note: Values are expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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When looking at the school-related variables, we
find that the decrease in the peer effect accounts for a
three-point reduction in the characteristics effect, while
the decrease in average school size accounts for only
0.8 points of this effect. The decline in the indicator
for shortages of teaching materials and the increase in
the percentage of certified teachers account for positive
changes of 1.3 and 1.5 points, respectively. The total for
school-related variables is negative but not statistically
significant. Meanwhile, none of the institutional variables
proves to be significant; the dummy variable for selectivity
is negative, and attendance at private schools is positive.
As for the effects of changes in the efficiency of
characteristics (the return effect), the 43.3-point increase
in the constant can be accounted for by a recomposition
of the cumulative effect of each additional year of
schooling (whereby the attainment of students at lower
achievement levels improves considerably) and by
the broad increase in the school system’s coverage of
Uruguayan students overall. On the other hand, during
this period the learning gap between students who have
repeated one or more grades and those who have not
done so widened and had a negative effect equivalent
to 4.3 points.
As for the returns to school characteristics, the
overall change is chiefly accounted for by the decline
in effectiveness of the percentage of certified teachers
and the shortage of mathematics teachers. Shortages
of teaching materials, the student-teacher ratio and the
dummy variables, by school location, are positive. The
decrease in the return to institutional variables is mainly
accounted for by the 2.8-point change in the returns to
the choice of a private school.
Thus, the trend in the return effect of the constant
reflects a narrower range in the levels of educational
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attainment, which signals a major advance in educational
equity for Uruguayan students. This indicates that the
bulk of the improvement seen during this period has been
shared by all of the country’s students and especially
those who attend public schools. This increase in equity
has, however, been partially counterbalanced by the
decrease in the return to attendance at private schools
and the drop in returns to grade level.
The characteristics-return effect is negative but not
significant and is mainly accounted for by the trend in
this effect relative to the school-related variables.
2.Results of the Juhn, Murphy and Pierce
(1993) decomposition
In analysing the different effects of the Juhn, Murphy
and Pierce decomposition, table 2 shows the values for
each of the effects that were included in the study, by
decile and by the mean. The total change in the results is
positive for the first eight score deciles and negative for
the last two, with the greatest change being seen in the
second, third and fourth deciles. The characteristics effect
is negative for all the deciles of the score distribution,
but its absolute magnitude is the greatest for the bottom
decile. This result points to a regressive effect that is
related to the magnitude of the given characteristics. The
results obtained using the Oaxaca-Blinder methodology
indicate that this effect is concentrated in variables at
the individual level.
Table 2 shows that the total change in results is
positive for the first eight score deciles and negative
for the last two, with the biggest changes occurring in
the second, third and fourth deciles. The characteristics
effect is negative for all deciles of the score distribution,
but its absolute magnitude is the greatest for the bottom
TABLE 2
Juhn, Murphy and Pierce decomposition
Change: 2006-2003
Mean
Decile 1
Decile 2
Decile 3
Decile 4
Decile 5
Decile 6
Decile 7
Decile 8
Decile 9
Decile 10
4.60
3.85
7.19
7.34
7.72
6.47
6.62
5.22
2.81
-0.16
-1.13
Characteristics effect
-6.62
-13.24
-8.59
-6.94
-5.74
-6.13
-4.55
-4.48
-5.48
-7.22
-3.77
Return effect
11.23
16.48
15.04
13.40
12.54
11.05
10.72
10.18
8.56
7.90
6.48
Residual effect
1.92
3.49
2.98
2.72
2.95
2.63
2.20
1.78
1.33
0.89
-1.93
Characteristics-return effect
-1.93
-2.88
-2.24
-1.83
-2.02
-1.09
-1.75
-2.25
-1.60
-1.72
-1.90
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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decile. This means that there is a regressive impact
which is linked to the magnitude of the characteristics in
question. The results obtained using the Oaxaca-Blinder
methodology indicate that this effect is concentrated in
variables at the individual level.
As can be seen from figure 2, the return effect is
invariably greater than the total change and is positive,
although progressively less so. Table 2 also points to an
increase in scores in all the deciles due to a more efficient
use of the characteristics in question, with the higher
averages being in the first two deciles; this indicates that
the impact is progressive.
The residual effect is positive for the first nine
deciles but negative for the last one, although it is small in
magnitude in all cases. This effect reflects the change in
the distribution of unobserved variables in terms of both
their magnitude and their returns. The characteristicsreturn effect is negative in all cases and is greater in
magnitude in the middle deciles of the distribution.
The results of the application of the Juhn, Murphy
and Pierce decomposition are consistent with those
obtained with the Oaxaca-Blinder decomposition. Most
of the total difference between the 2003 and 2006 pisa
scores is attributable to the positive effect of the change
in the efficiency of factor use, while the magnitude of
the characteristics effect is associated with a negative
change that partially offsets the positive impact of the
school system’s increased efficiency. In other words,
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the difference between the 2003 and 2006 scores is
accounted for by a reduction in available resources and
a more efficient use of those resources.
The increase in efficiency signals that the country
is moving in the right direction. The reduction in
characteristics poses a major challenge for Uruguay’s
school system, however, since it must find a way of
improving the general conditions for students in the
system. This is a matter of some urgency, since the gain
in the effectiveness of the school system could have
enabled underprivileged students to move up a level in
terms of their performance on the mathematics test in
slightly more than a decade; however, the deterioration
in social and economic conditions for this segment of the
population during that same decade has had the effect
of lengthening the time needed to move up a level to
three decades.
3.Results of the Bourguignon, Fournier and
Gurgand (1998) decomposition
(a) Estimation of production functions
The first step in conducting the microsimulations
is to estimate the production functions for the 2003 and
2006 pisa tests for each type of school (see table 3).
The R2 in the estimates indicates that it is possible
to account for nearly 40% of the variance in scores in the
estimations for public schools, whereas, in the case of
FIGURE 2
Overall effects, Juhn, Murphy and Pierce decomposition
Difference between
PISA 2006 and PISA 2003 scores
20
10
0
–10
–20
1
2
3
4
5
6
7
8
9
10
Scoring decile
Return effect
Total change
Characteristics-return effect
Residual effect
Characteristics effect
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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TABLE 3
Estimation of production functions for public and private schools, 2003-2006
Public
2003
Student-related variables
Sex (female=1)
Third year
Fourth year
Fifth year
Behind grade
escs
School-related variables
Peer effect (escs)
School size
Student-teacher ratio
Shortages of teaching materials
Shortages of mathematics teachers
Percentage of certified teachers
Montevideo and its metropolitan area
Rural
Institutional variables
Private
2006
-18.13***
(3.49)
41.89***
(4.31)
110.00***
(9.45)
140.40***
(13.04)
-5.53
(8.55)
10.88***
(1.42)
14.50**
(5.93)
0.00
(0.01)
-0.11
(0.31)
-2.21
(2.50)
1.47
(2.17)
16.05
(13.99)
12.02**
(4.70)
-9.62
(8.43)
2003
-24.59***
(3.75)
34.76***
(5.61)
87.38***
(12.96)
106.50***
(14.68)
-21.56**
(10.21)
12.80***
(1.81)
15.79***
(5.51)
-0.01
(0.01)
-0.14
(0.60)
-1.39
(2.24)
-0.61
(2.59)
16.84
(11.84)
14.14***
(4.93)
-5.42
(8.55)
2006
-21.93***
(4.95)
110.40***
(39.16)
123.80***
(33.57)
148.60***
(34.99)
-10.75
(21.50)
12.78***
(4.73)
36.50**
(18.21)
0.01
(0.02)
-0.31
(1.26)
-12.07
(8.63)
4.62
(6.51)
52.14*
(27.11)
6.87
(13.17)
20.08
(24.84)
-21.31***
(5.27)
-3.49
(26.79)
23.49
(37.79)
44.73
(37.31)
-26.65
(25.42)
16.15***
(3.85)
54.98***
(10.96)
0.01
(0.02)
0.24
(0.91)
-7.01
(6.31)
1.28
(5.12)
-18.33
(16.04)
14.55
(14.64)
0.00
(0)
Selectivity
12.82
(10.32)
6.02
(8.34)
1.21
(12.18)
3.89
(10.87)
Constant
346.4***
(19.36)
390.9***
(21.09)
325.0***
(41.02)
432.9***
(45.19)
Observations
R2
4 679
0.39
3 826
0.38
1 156
0.17
1 013
0.24
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Levels of significance: *10%, **5%, ***1%
Standard errors are shown in parentheses.
Note: Values expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
private schools, the R2 is around 20%. This means that
the explanatory value of the estimates is nearly twice as
great for public schools as it is for private schools. This
is probably because of the make-up of the student bodies
in these two sectors and suggests that the proposed model
is a more accurate measurement of trends in scores in
public institutions.
Most of the coefficients for variables at the student
level are significant. The sex coefficient, which is negative
and significant in all cases, declined in magnitude over
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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the period in question for public schools and rose slightly
in the case of private schools. The magnitude of the
coefficients for grade-related variables decreased during
the period under study for both types of institutions.
In the case of private schools, the magnitude and
significance of the grade-related coefficients changed
considerably between the two years in question, since
part of the coefficient for 2006 is incorporated in the
constant, which exhibits a difference between 2003 and
2006 of over 100 points; this signals an improvement
for the control group.
Additional score points were achieved by persons
who are a grade ahead in all cases. The additional
inter-grade gain narrowed in public schools while, in
private schools, the lead in scores that students in their
fourth year of secondary school had over those in their
third year was greater in 2006 than in 2003. The effect
for those who were behind the grade associated with
their age was negative in all cases, but this coefficient
declined between the two years for students in both
types of schools. The escs coefficients for both public
and private schools rose.
Most of the school-related variables did not prove
to be significant,8 whereas the peer effect was not only
positive and significant in all cases but also increased
over the period under study, rising by nearly 50% in
private schools and by around 9% in public schools. The
escs coefficient at the individual level and the peer effect
behaved very differently in public schools than they did
in private schools. In the former, the peer effect was 1.3
times greater than the escs coefficient at the individual
level, while in the latter, it was almost 3 times greater.
These differences between the public and private sectors
generate a greater incentive for increased segregation
for private schools, since the maintenance of the entire
student body at a given socioeconomic level will make
it possible to obtain a “segregation premium”.
As for the size of the population centre, the dummy
variable associated with Montevideo had a positive and
increasing value during the period under study, while the
dummy variable for rural areas was negative for public
schools and positive for private ones. The institutional
selectivity variable declined between 2003 and 2006
8
Since some controls were used in the estimations that might have
a non-linear effect, the possibility existed that the lack of statistical
significance of some of them could be related to a linear specification.
School size and grade size were therefore tested for non-linearity, but
the results changed very little, with the exception of school size for
2006, where a downward trend is seen for schools with 800 students
or more, which are in the minority in the sample.
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for public schools and did just the opposite in the case
of private institutions.
Finally, the value of the constant was always positive
and significant, and its coefficient rose in 2006 relative
to its 2003 level.
(b) Estimation of choice of type of school
A logit function was estimated for each year, with
a value of 1 corresponding to cases in which the student
attends a public school. The results are shown in table 4.
The dummy variable for the sex of the student was
negative but not significant as an explanatory variable for
the probability of a student attending a public or private
school. The effect of being behind grade level, on the
other hand, was positive and significant in all cases for
the probability of attending a public school and negative
for the probability of attending a private one, while
the escs coefficient was negative for the probability of
attending a public educational institution.
The size of the school and the student-teacher ratio
had almost no effect on the probability that a student
TABLE 4
Logit estimation for choice of school type,
2003-2006
Sex (female=1)
Behind grade
escs
School size
Student-teacher ratio
Montevideo and its metropolitan area
Rural
Constant
Observations
F statistic
Prob F
2003
2006
-0.19
(0.15)
1.53***
(0.36)
-1.36***
(0.11)
0.00
(0.00)
0.07
(0.05)
-1.93***
(0.37)
0.41
(1.42)
1.35**
(0.68)
-0.09
(0.10)
1.10***
(0.29)
-1.44***
(0.10)
0.00
(0.00)
0.08**
(0.04)
-1.71***
(0.41)
5 835
32.95
0.00
4 381
50.18
0.00
1.29**
(0.55)
Source: Authors’ calculations based on data from the Organisation
for Economic Cooperation and Development (oecd), “pisa 2003”
and “pisa 2006” [online] http://www.pisa.oecd.org/document/51/0
,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Levels of significance: *10%, **5%, ***1%
Standard errors are shown in parentheses.
Value 1= Public education.
Note: Values expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
Prob F: p value associated with F statistic, used to test the null
hypothesis that all of the model’s coefficients are 0.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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would attend a public school. The variables related to
the size of the population centre indicate that residence
in Montevideo has a significant negative effect in terms
of the probability of attending a public school, while
residence in a rural area was not a significant factor
in 2003.9
These findings indicate that students in public schools
tend to come from poorer families, be less successful
academically and live in smaller cities or towns.
4.Results of the microsimulations
The main results of the microsimulations are
summed up in table 5. The table provides information
on the effects of changes both in the means and in
the different score deciles as a result of the difference
between the simulated distribution for each case and the
observed distribution in 2003. Table A.3, in the annex,
shows what the effects are when changes in the type of
school are the only factor that is considered.
(a) The characteristics effect
The characteristics effect, as a whole, has the
strongest positive impact of all in terms of explaining
the reasons for the overall change in pisa mathematics
scores between 2003 and 2006. On average, if schools
had had the same individual resource endowments in
9
The corresponding coefficient for 2006 is unavailable because the
sample for that year does not provide observations for private schools
in rural areas.
•
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2003 that they had in 2006, their scores would have been
9.2 points higher (see table 5).
A word of caution is called for here with regard to
the correct interpretation of this effect. The simulation
of characteristics for 2006 entails using the unweighted
percentage of cases in which a given characteristic is
displayed, in the case of the dichotomous or categorical
variables, or the unweighted mean, in the case of the
continuous variables. In addition, in calculating the
characteristics effect, the distribution measurements are
computed using the sample weighting for 2003, which,
as will be discussed in greater detail below, differs a great
deal from the weighting for 2006, since the samples
for those two years were designed very differently. An
accurate interpretation of the trend in available resources
during this period should therefore include not only the
simulation of the characteristics (weighted by the factor
of expansion for 2003), but also the weighting for the
sample for the year corresponding to the simulation. It
then becomes possible to see what happens when only
the characteristics for 2006 are simulated and then to
compare that result with the result of a simulation that
includes the sample weightings for that year and that
consequently provides a more accurate picture of the
population which is being simulated.
The characteristics effect is greater for the bottom
deciles and decreases in the upper deciles. This signals the
presence of a redistributive effect, since lower-performing
students benefit. If this effect is differentiated by type
of school in the simulations for 2006 (see table A.3 in
the annex), it turns out that the sharpest change is seen
TABLE 5
Average microsimulation results and microsimulation results by scoring decile,
2003-2006
Mean
pisa mathematics test – 2003
pisa mathematics test – 2006
Total difference in pisa mathematics score (2006-2003)
1
2
3
4
5
6
7
8
9
10
422.20 257.03 318.07 355.44 384.22 410.99 435.48 460.99 489.39 523.25 587.56
426.80 260.88 325.26 362.79 391.94 417.46 442.10 466.22 492.20 523.09 586.43
4.60
3.85
7.19
7.34
7.72
6.47
6.62
5.22
2.81
-0.16
-1.13
Characteristics effect
Weight effect
Characteristics+weight effect
Price effect
Characteristics+weight+price effect
Choice effect
Characteristics+weight+price+choice effect
Residual effect
9.24
-2.76
-2.11
7.69
7.59
-0.05
5.91
0.00
13.07
-4.31
0.50
13.24
17.40
-0.03
9.90
2.58
17.87
-5.02
0.77
12.15
16.54
0.02
10.11
1.62
15.48
-3.91
-0.11
10.37
12.63
0.04
7.61
1.09
13.40
-3.02
-1.53
9.21
10.22
-0.03
7.22
1.07
10.77
-3.06
-2.66
7.44
7.51
-0.01
6.22
0.68
8.50
-2.59
-2.76
6.91
4.42
-0.03
5.60
0.28
5.23
-2.04
-4.37
6.12
2.93
-0.01
4.08
0.05
2.98
-1.86
-6.07
4.67
0.35
-0.02
2.74
-0.92
2.43
-1.06
-4.31
3.90
0.97
-0.02
2.39
-2.03
2.85
-0.67
-0.64
2.67
2.86
-0.29
3.20
-4.38
Characteristics+weight+price+choice+residual effect
5.93
13.53
11.63
8.44
7.89
6.50
5.90
4.21
2.00
0.65
-1.18
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
Choice effect: School selection effect.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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in public schools (8.4 points) and that this accounts for
virtually all of the characteristics effect, since private
schools account for just 0.8 points.
Table A.4 (see the annex) provides a detailed look
at the characteristics effect for each variable in the model
and for the defined groups of variables, disaggregated
by type of school. As can be seen from the table, the
increase in educational resources is concentrated in the
individual variables (7 points) and relates mainly to the
number of students in their fourth year and to public
schools, as well as being greater in the upper deciles of
the distribution. The behind-grade variable also exhibits
a positive although small effect. The dummy variable
for the sex of the student, as well as the other grades and
escs, points to a negative effect in the trend of scores
on the pisa mathematics test.
The variables relating to educational institutions
account for a positive change of 2.3 score points, with
one of the most influential variables being the percentage
of certified teachers (1.6 points). The associated peer
effect shows a positive change of 0.2 points, while the
escs has a negative but nearly negligible effect at the
individual level. The student-teacher ratio, shortages of
teaching materials and the dummy variable associated
with Montevideo also have a positive effect, whereas
school size, shortages of mathematics teachers and the
dummy variable associated with rural zones exhibit a
negative effect. The same is true of the institutional
variable of selectiveness, which has a negative effect
(see table A.4).
(b) Weight effect
When the individual weights in the 2003 sample
are adjusted to reflect the 2006 population, the total
change in pisa scores amounts to a 2.8-point decline (see
table 5). This effect is explained chiefly by the change
made in the sample design. In the case of Uruguay, a
number of changes in the design of the different strata
were made between the 2003 and 2006 tests. For the
analysis of the 2003 test, 8 strata were used to define the
sample design, whereas, for the 2006 test, 16 strata were
used. There were also changes in the schools’ response
rate and in the number and types of schools that did not
apply them or that did so incorrectly (anep, 2007b). In
addition, as noted earlier, the attendance rates for the
2003 and 2006 tests differed, especially in the smaller
towns. All of these factors generate variations in the
sample weights that account for the size of the weight
effect obtained in microsimulations.
The negative weight effect is greater in the first
deciles of the distribution; this is accounted for primarily
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by the change in the weighting of public schools (see
table A.3 in the annex).
(c) The characteristics-weight effect
When the change in characteristics is combined with
the change in weights (see the third simulation in table
5), the average effect diminishes, but retains the negative
sign of the weight effect (-2.1 points). The change in this
result, which is attributable to the inter-year variability of
the sample weight and to the modification of the sample
design, appears to be an accurate reflection of the trend
in available resources during the period in question.
When this effect is analysed by decile, it can be
seen that it has a positive sign for the first two deciles
in the distribution but is negative for the other eight;
consequently, the overall effect is highly redistributive.
As is also true of the weight effect alone, the combination
of these two effects is negative for public schools and
positive for private ones.
(d) Return effect
The return effect is derived from the simulation of
the 2006 coefficients in the 2003 score distribution. As
shown in table A.5, the total effect of this component
amounts to an increase of 7.7 points and is positive
for all of the deciles of the distribution; the fact that
it is stronger in the first few deciles indicates that it is
redistributive. The sign of this effect reflects an increase
in the efficiency of these characteristics in public schools,
while it is negative for private schools (see table A.3).
Separate analyses of the return effect of each of
the variables in the production function (see table A.5)
show that the main factor is the greater effectiveness of
the constant, which amounts to 53.4 points and signals
a widespread improvement in student efficiency.
The combined effect of the variables at the
individual, school and institutional levels is negative.
This is consistent with the result obtained using the
Oaxaca-Blinder decomposition. The increase in the
efficiency of the peer effect (1.3 points) is notable,
while the effectiveness of the escs at the individual level
is lower. The bulk of the increase in the peer effect is
accounted for by private schools, as the effectiveness
of this factor in public schools declined.
Other variables at the school level that have a positive
impact on the return effect are the student-teacher ratio,
shortages of teaching materials and region-dependent
variables. The size of the school, shortages of mathematics
teachers and the percentage of teachers who are certified
all have a negative effect. The institutional variable of
academic selectivity also has a negative effect.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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The overall effect of the variables at the student
level is -36.5 points, with the public sector accounting
for the majority of this value (-22.6 points). Of the
variables at the individual level, the biggest change is
generated by the dummy variable for the fourth year of
secondary school (-22.5), which has a greater negative
impact in the higher deciles of the distribution. All the
other variables at the individual level have a negative,
although smaller, return effect. The institutional variable
of selectivity also has a negative effect.
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that it is redistributive. When the change is analysed by
type of school (see table A.3 in the annex), it is seen that
it is greater for public schools.
(g) The school choice effect
The school choice effect is negative on average
and very close to zero (0), as may be seen from table 5.
It is nearly equal for all the deciles of the distribution.
(e) The characteristics-return effect
Figure 3 illustrates the combined effect of the
change in characteristics and returns for all deciles in
the distribution. As indicated by the graph, this effect
is positive for the entire distribution and stronger for
the lower deciles.
(h) The characteristics-return-choice-weight effect
When a combined simulation of characteristics,
returns, school choice and weights is conducted, the
mean effect falls to 5.9 points (see table 5), with the
greatest decreases relative to the previous combined
simulation being in the lower deciles of the distribution
(see figure 4). In this case, the sign of this combined effect
is positive for public schools and negative for private ones.
(f) The characteristics-return-weight effect
The fifth simulation in table 5 shows the combined
effect of the simulation of characteristics, returns and
weights. In this case, the mean effect is weaker than it is
in the simulation of characteristics and returns alone (7.6
points). The combined effect is stronger for the lower
deciles in the distribution, which, here again, indicates
(i) Residual effect
The effect of simulating residuals for 2006 in
the 2003 distribution is, on average, nil (see table 5),
and this is true for both types of institutions (see table
A.3 in the annex). The residual effect varies by decile,
however, being positive in the first seven and negative
in the last three.
FIGURE 3
Combined effects, by scoring decile
30
Scores
20
10
0
–10
1
2
3
4
5
6
7
8
9
10
Scoring decile
Characteristics and return
Return
Characteristics and choice
Characteristics
Return and choice
Total change
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Choice effect: School selection effect.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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FIGURE 4
All effects, by scoring decile
30
Scores
20
10
0
–10
1
2
3
4
5
6
7
8
9
10
Scoring decile
Total change
Characteristics and return
Characteristics, return, choice and weight
Characteristics, return and choice
Characteristics, return, choice, weight and residual
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Choice effect: School selection effect.
(j) Combined effects of the microsimulations
The overall effect of the microsimulations (see the
final simulation in table 5) is a small change in the mean,
with a slight decrease in inequality. The progressive
nature of the overall change is accounted for by the
result for public schools.10 The results also show that
scores improve only in those schools, since the trend is
negative for private schools (see table A.3 in the annex).
The main area of progress is the widespread improvement
in the efficiency of resource use. This improvement is,
however, offset by a reduction in available resources.
When unobservable variables are included in the
first four simulations, it becomes possible to explain a
great deal of the inequality seen in the trend in average
scores. The overall effect is more positive in the lower
deciles and turns negative in the last two. This result is
in keeping with the progressive impact of the residual
effect obtained using the methodology developed by
Juhn, Murphy and Pierce.
The Gini inequality index, the Theil index and the
entropy index, which are generally used to analyse trends
10 If the combined effect of the microsimulations, by score decile, is
calculated separately for the different types of schools, it turns out to
be progressive for public schools and regressive for private schools.
These results are in keeping with the total change seen in scores by
type of institution.
in income distribution, are then used to look at the trend
in the size of the reduction in the inequality of the results.
As can be seen from table A.6 in the annex, the trend in
these three indicators reflects a small decline in levels
of inequality in scores on the mathematics test. This
reduction amounts to between 0.1% and 0.4% of these
indicators and is mainly attributable to the progressive
effect of the characteristics and price simulation and, in
particular, to the change in public schools. The residual
effect also has a progressive impact on the level of
inequality, although a weaker one. The combined effect
of all the simulations corresponds to a 0.8% decrease
on the Gini index and one of 0.3% on the Theil and
entropy indexes.
When all the simulations are combined, the mean
effect amounts to 5.9 points (of 4.6, which is the observed
change). The total adjustment is more precise for the
last deciles in the distribution and is less so for the first
decile (see figure 4). The 2006 sample design is more
complex and results in a sample that provides a more
exact reflection of the student population in the relevant
age group; consequently, when the weights for that year
are simulated in the 2003 sample (together with the
characteristics, returns, school choice and residuals),
they explain the changes seen in 90% of the distribution,
thereby making it possible to clearly identify the main
factors associated with the trend in each one of the
deciles of the score distribution.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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V
A comparison of the results
These three methodologies yield mutually consistent
results. They complement each other in terms of the
degree of complexity of the analysis, and each has its
own value-added.
The results obtained from the application of the
Oaxaca-Blinder methodology indicate that the total
score change is chiefly accounted for by a widespread
increase in the efficiency with which the school system
makes use of the available resources. The increase
in the return to the constant is the main explanatory
factor for this increase in efficiency. The fact that this
increase was seen across the student population –and
was especially marked in public schools– points to a
more even distribution of educational outcomes. The
improvement is primarily attributable to the economic
recovery that occurred during the period under study.
This positive effect is weakened somewhat by a lower
level of efficiency in the most important variables at
the student and school levels, however, especially in
the returns to the different grade levels.
The defined characteristics were more
disadvantageous in 2006 than in 2003, and most of
this effect is concentrated in student-related variables.
Although this marks a contrast with the economic recovery
of those years, it may be due to various factors, such
as changes in enrolment or the demographic changes
occurring in the country during that time.
The methodology developed by Juhn, Murphy
and Pierce also makes it possible to draw conclusions
about the influence exerted by the various effects on
the different deciles of the distribution and indicates
that there has been a progressive impact as a result of
the return effect.
The microsimulations provide a way of gauging
the extent of the differences existing between students
in public and private schools, and they indicate that the
change observed during the period under study was
accounted for solely by students in State-run schools.
The estimates also indicate just how sensitive the results
are to changes in the composition of the samples. The
characteristics effect is shown to be positive when the
microsimulations are run, which differs from the results
obtained with the other two decomposition techniques.
When the simulation of the sample weighting is added
in, however, the overall effect proves to be negative
and of a similar strength as that calculated earlier
using the Oaxaca-Blinder and the Juhn, Murphy and
Pierce methodologies.
VI
Conclusions
This study provides information on the differences in
the distribution of the pisa mathematics scores for 2003
and 2006 and identifies factors underlying those changes
and the trend in their effects over the period under study.
An analysis of the results obtained using three different
methodologies leads to mutually consistent conclusions
that support the statement that the country’s outcomes,
in terms of both equity and scores, are unsatisfactory.
A first conclusion is that, although the change seen
between the results for the 2003 and 2006 tests is very
small and has little impact in terms of an improvement
in Uruguayan students’ performance on the mathematics
tests, there have been underlying changes in the defined
characteristics and returns that offset one another, thereby
yielding a very small overall change. This bears out the
study’s initial hypothesis.
Secondly, the evidence suggests that the improvement
in scores in 2006 relative to 2003 is attributable to an
increase in the education system’s ability to convert
educational resources and characteristics into learning
outcomes and, in particular, to a widespread efficiency
gain in the use made of resources generated by the
economic recovery of that period. This was especially
marked in public schools, although it was partially offset
by a decrease in the efficiency of grade-related factors
at the individual level.
Thirdly, there was a reduction in resource
endowments, particularly at the student level. This
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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decrease was especially notable in terms of socioeconomic
and cultural characteristics and in the percentage of
students at the higher grades (above all in the case of
the more disadvantaged students). This indicates that
the deterioration in the family- and school-related
circumstances associated with students in the most
vulnerable groups of the population has had the effect
of making it take longer for these young people to move
up from one step to the next on the scale used by the pisa
test to measure proficiency in mathematics. If this had not
been the case, this group was projected to have reached
that objective in slightly more than a decade, whereas,
with the emergence of these two groups of factors, it
will take between 25 and 30 years to reach that goal.
Finally, the improvement in the scores on the pisa
mathematics test had a redistributive effect and was
concentrated among lower-performing students. This
finding reflects a reduction in test-score dispersion and is
accounted for by trends in the country’s public schools.
Economic growth ought to be closely related to
a substantive improvement in performance, but such
a relationship is not evident in the scores obtained by
Uruguayan students during this period. This indicates
that the deterioration in social and economic conditions
that occurred at the start of the decade brought about a
structural decrease in educational opportunities for young
students, while the benefits of the recovery will probably
not become evident until the results of the 2012 pisa
test are in. The methodologies used in this study offer
a means of undertaking an in depth analysis into the
challenges and situations faced by Uruguayan students
and of identifying ways of enabling the country to meet
its obligation to provide a satisfactory education to all of
its citizens. The data lead to the conclusion that efforts
should be focused on mobilizing educational resources
and boosting efficiency at the individual level. Policies
designed to provide more support for socioculturally
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disadvantaged students are of critical importance in
reducing the high rate of grade repetition and in seeking
ways of providing higher returns to each additional year
of schooling.
Despite the drop in the escs coefficient, the mean
score for this period rose and, although the increase was
slight overall, it was considerable in the lower-middle and
middle strata. This would appear to indicate that, following
the economic shock experienced by the country (which
hit the vulnerable groups in society the hardest, not only
in economic terms but also in terms of opportunities for
social mobility, including those afforded by education)
in 2003-2006, the potential retrogression triggered by
the crisis appears to have been reversed. Nonetheless,
formidable challenges remain to be overcome in order
to improve the school system’s overall effectiveness,
particularly since the headway that was made in 20032006 could simply be due to the recovery rather than to
increased effectiveness on the part of the school system.
If this proves to have been the case, then we may not
see further improvements in scores on future pisa tests,
as occurred in 2009.
This study paves the way for the use of these
methodologies to analyze the 2009 pisa scores as a
means of delving more deeply into the underlying reasons
for Uruguayan students’ performance on this test. The
incorporation of the more recent data will make it possible
to analyse the trends of the last few years, which have
been marked by economic growth and reforms aimed
at improving the education imparted by the country’s
schools while also making it more equitable. This type of
analysis could also be expanded to include comparisons
of the results obtained by Uruguay with those of other
countries at similar socioeconomic levels, such as Chile
or Argentina, and with the scores of countries that have
succeeded in making much greater gains, such as Poland.
(Original: Spanish)
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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ANNEX
TABLE A.1
Selected variables
Variable used
Comments
Results variable
Mathematics score
2003-2006 pisa scores, 5 plausible values for performance on the mathematics test
Student-related variables
Sex
Grade
Behind grade
Index of Economic, Social and
Cultural Status (escs)
Dummy variable for sex of student (omitted category: male)
Five dummy variables for a student’s current grade: grade 7 (first year of secondary school),
grade 8 (second year), grade 9 (third year), grade 10 (fourth year), grade 11 (fifth year)
(omitted categories: any grade other than those grades)
Dummy variable that indicates whether the student has repeated a grade (omitted category:
no repetition)
Variable developed by oecd/pisa which takes into consideration the education and occupation
of the parents and the types of products or goods in the home. Mean of 0 and standard
deviation of 1 for the oecd-country average. A higher ranking on the index indicates a higher
socioeconomic level
School-related variables
Peer effect
School size
Student-teacher ratio
Shortages of teaching materials
Shortages of qualified mathematics teachers
Percentage of certified teachers
Size of population centre
Variable that measures the average escs rank for students in the same school
Continuous variable that indicates the average number of students who are enrolled
Continuous variable that indicates the average student-teacher ratio
Variable that indicates the extent to which the school’s ability to educate its students is
undermined by shortages of suitable teaching materials: Scale ranges from 1 to 4
Variable that indicates the extent to which the school’s ability to educate its students is
undermined by shortages of qualified mathematics teachers: Scale ranges from 1 to 4
Variable that indicates the percentage of the schools’ teachers who are certified: Scale ranges
from 0 to 1
Four dummy variables that indicate the location of the school: Montevideo and the surrounding
metropolitan area, major cities elsewhere in the country, smaller cities, rural areas (omitted
categories: does not live in that population centre)
Institutional variables
Academic selectivity
Public secondary school
Private secondary school
Dummy variable that indicates whether or not a school applies selective criteria in reaching
admissions decisions (based on the school selectivity index developed by oecd/pisa (omitted
category: does not apply)
Dummy variable that indicates whether or not the school is a public secondary school (general,
military, rural or technical) (omitted category: does not correspond)
Dummy variable that indicates whether or not the school is a private secondary school (omitted
category: does not correspond)
Source: Authors’ calculations.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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TABLE A.2
Descriptive statistics, 2003-2006
Mean
2003
Standard
deviation
Range
Percentage
Student-related variables
2003
2006
2003
2006
422.20 426.80
Score on mathematics test
2006
95.22
93.37
108.93 734.41
102.58 732.04
Sex (female=1)
First year
Second year
Third year
Fourth year
Fifth year
Behind grade
escs
2003
2006
0.51
0.06
0.10
0.18
0.59
0.07
0.32
-0.35
Peer effect (escs)
School size
Student-teacher ratio
Shortages of teaching materials
Shortages of mathematics teachers
Percentage of certified teachers
Montevideo and its metropolitan area
Other major cities
Smaller cities
Population centres with fewer
than 5,000 inhabitants
0.50
0.23
0.30
0.39
0.49
0.26
0.46
1.05
0.50
0.26
0.30
0.38
0.49
0.25
0.47
1.18
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3.7
1.0
1.0
1.0
1.0
1.0
1.0
1.0
2.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-4.3
1.0
1.0
1.0
1.0
1.0
1.0
1.0
2.8
416.30
297.87
328.19
368.54
457.92
488.76
342.81
420.49
332.74
331.88
374.27
463.50
484.61
350.74
School-related variables
0.51
0.07
0.10
0.17
0.59
0.07
0.33
-0.51
440.64
412.65
406.87
376.85
443.31
412.72
423.77
396.50
-0.35 -0.51
531.12 435.16
17.79 15.86
2.86
2.53
2.43
1.89
0.53
0.60
0.48
0.46
0.32
0.32
0.11
0.13
0.09
0.09
Institutional variables
0.63
0.77
335.86 248.90
9.43
5.53
1.02
1.07
1.04
1.04
0.21
0.19
0.50
0.50
0.47
0.47
0.31
0.33
0.29
0.29
-2.3
9.0
1.9
1.0
1.0
0.0
0.0
0.0
0.0
0.0
1.3
2 535.0
65.0
4.0
4.0
1.0
1.0
1.0
1.0
1.0
-2.7
1.6
30.0 1 275.0
2.0
29.6
1.0
4.0
1.0
4.0
0.1
1.0
0.0
1.0
0.0
1.0
0.0
1.0
0.0
1.0
0.10
0.86
0.14
Selectivity
Public school
Private school
0.09
0.85
0.15
0.31
0.35
0.35
0.29
0.36
0.36
0.0
0.0
0.0
1.0
1.0
1.0
0.0
0.0
0.0
1.0
1.0
1.0
470.00 442.64
409.24 414.85
501.24 495.21
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
TABLE A.3
Results of microsimulations with changes in one type of school, 2003-2006
Average total effect
pisa mathematics test: 2003
pisa mathematics test: 2006
Total difference in pisa mathematics score
Characteristics effect
Weight effect
Characteristics + weight effect
Price effect
Characteristics + weight + price effect
Choice effect
Characteristics + weight + price + choice effect
Residual effect
Characteristics + weight + price + choice + residual effect
Changes only in:
Public
Private
4.60
9.24
-2.76
-2.11
7.69
7.59
-0.05
5.91
0.00
8.45
-3.99
-4.25
8.83
6.67
-0.05
6.52
0.00
0.80
1.22
2.17
-1.14
1.08
-0.05
-0.90
0.00
5.93
6.58
-0.93
422.20
426.80
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
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TABLE A.4
Results of the microsimulations of characteristics per scoring decile, 2003-2006
Total effect and effect by decile (X)
Changes only in:
Total
2
5
9
Public
Private
422.20
426.80
318.07
325.26
410.99
417.46
523.22
523.09
Total difference in pisa mathematics score
4.60
7.19
6.47
-0.13
Student-related variables
7.05
17.05
8.17
-1.18
6.85
0.20
-1.82
-1.99
11.94
-1.25
0.33
-0.15
2.23
-4.79
7.00
-1.05
1.95
-0.83
-2.99
-2.46
7.92
-2.19
0.06
-0.34
-4.05
-0.13
18.74
-1.46
-0.61
0.57
-1.84
-2.13
11.60
-0.76
0.33
-0.34
0.03
0.14
0.34
-0.49
0.00
0.19
2.29
-0.32
2.25
4.74
1.67
0.62
Peer effect (escs)
School size
Student-teacher ratio
Shortages of teaching materials
Shortages of mathematics teachers
Percentage of certified teachers
Montevideo and its metropolitan area
Rural
0.25
-0.02
0.16
1.00
-0.91
1.63
0.26
-0.08
-1.20
0.01
0.11
0.18
-0.76
1.98
-0.42
-0.14
0.01
-0.10
0.12
0.75
-0.98
1.64
0.42
-0.06
1.72
-0.04
0.27
1.78
-0.98
1.39
1.00
0.27
-0.28
-0.01
0.13
0.76
-0.87
1.70
0.26
-0.01
0.53
-0.01
0.03
0.24
-0.04
-0.06
0.00
-0.07
Institutional variables
-0.09
0.36
-0.25
0.14
-0.07
-0.02
Selectivity
Student-related and school-related variables
Student-related and institutional variables
School-related and institutional variables
All variables
-0.09
9.34
6.96
2.19
9.24
0.36
17.87
17.04
0.03
17.87
-0.25
10.71
8.16
1.89
10.77
0.14
2.82
-1.32
4.51
2.46
-0.07
8.52
6.78
1.59
8.45
-0.02
0.82
0.18
0.60
0.80
pisa mathematics test – 2003
pisa mathematics test – 2006
Sex (female=1)
Third year
Fourth year
Fifth year
Behind grade
escs
School-related variables
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
TABLE A. 5
Results of microsimulations of coefficients per scoring decile, 2003-2006
Total effect and effect by decile (β )
Changes only in:
Total
2
5
9
Public
Private
422.20
426.80
318.07
325.26
410.99
417.46
523.25
523.09
4.60
7.19
6.47
-0.16
Student-related variables
-36.54
-29.29
-35.38
-43.09
-22.63
-13.91
Sex (female=1)
Third year
Fourth year
Fifth year
Behind grade
escs
-2.80
-2.41
-22.50
-3.25
-5.05
-0.52
-3.33
-3.67
-11.91
-1.04
-11.62
-1.55
-3.17
-2.57
-22.54
-3.36
-4.31
-0.88
-2.09
-1.60
-32.44
-5.61
-0.47
0.66
-2.85
-1.22
-10.81
-1.99
-4.89
-0.87
0.04
-1.19
-11.69
-1.26
-0.16
0.34
pisa mathematics test – 2003
pisa mathematics test – 2006
Total difference in pisa mathematics score
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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Table A.5 (concluded)
Total effect and effect by decile (β )
Changes only in:
Total
2
5
9
Public
Private
School-related variables
-8.87
-6.77
-8.65
-10.89
-6.31
-2.56
Peer effect (escs)
School size
Student-teacher ratio
Shortages of teaching materials
Shortages of mathematics teachers
Percentage of certified teachers
Montevideo and its metropolitan area
Rural
1.29
-4.25
0.61
3.27
-5.32
-6.45
1.67
0.30
-0.84
-3.73
-0.42
2.47
-5.10
-1.50
0.79
0.71
0.39
-4.65
0.08
3.00
-5.32
-4.54
1.30
0.24
3.80
-4.40
1.96
4.09
-5.60
-11.42
2.55
0.18
-0.58
-4.24
-0.51
2.15
-4.64
0.34
0.77
0.38
1.87
-0.01
1.12
1.11
-0.68
-6.79
0.90
-0.07
Institutional variables
-0.26
-0.28
-0.37
-0.09
-0.39
0.13
-0.26
53.36
-45.67
-36.80
-9.13
-45.67
-0.28
45.28
-37.30
-29.48
-7.01
-37.30
-0.37
48.93
-44.88
-35.74
-8.99
-44.88
-0.09
64.49
-53.33
-43.34
-11.00
-53.33
-0.39
38.16
-29.33
-23.02
-6.70
-29.33
0.13
15.20
-16.34
-13.78
-2.43
-16.34
7.69
12.15
7.44
3.90
8.83
-1.14
Selectivity
Constant
Student-related and school-related variables
Student-related and institutional variables
School-related and institutional variables
All variables
Variables and constant
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: Values expanded for the entire population.
escs: Index of Economic, Social and Cultural Status.
TABLE A.6
Effect of microsimulations on distribution indicators
Changes in only one
type of school
Changes in only one
type of school
Changes in only one
type of school
Ginia
Public
Private
Theilb
Public
Private
Entropy
Public
Private
Total difference in pisa mathematics score
-0.004
-0.003
0.001
-0.001
-0.001
0.000
-0.002
-0.001
0.000
Characteristics effect
Weight effect
Characteristics+weight effect
Price effect
Characteristics+weight+price effect
Choice effect
Characteristics+weight+price+choice effect
Residual effect
Characteristics+weight+price+choice+
residual effect
-0.009
0.003
-0.001
-0.007
-0.010
0.000
-0.005
-0.002
-0.009
0.004
-0.001
-0.005
-0.009
0.002
-0.005
0.000
0.039
0.039
0.039
0.038
0.039
0.039
0.040
0.038
-0.003
0.001
0.000
-0.003
-0.004
0.000
-0.002
-0.001
-0.003
0.002
0.000
-0.002
-0.003
0.001
-0.002
0.000
0.014
0.013
0.014
0.013
0.013
0.013
0.014
0.013
-0.003
0.001
0.000
-0.003
-0.003
0.000
-0.002
-0.001
-0.003
0.002
0.000
-0.002
-0.003
0.001
-0.002
0.000
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.013
-0.008
-0.007
0.039
-0.003
-0.002
0.013
-0.003
-0.002
0.013
Source: Authors’ calculations based on data from the Organisation for Economic Cooperation and Development (oecd), “pisa 2003” and
“pisa 2006” [online] http://www.pisa.oecd.org/document/51/0,3746,en_32252351_32235731_39732595_1_1_1_1,00.html
Note: The entropy index was calculated using beta=2.
Choice effect: School selection effect.
a Gini coefficient.
b Theil index.
Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela
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2012
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Determinants of educational performance in Uruguay, 2003-2006 • Cecilia Oreiro and Juan Pablo Valenzuela