WPS5266
Policy Research Working Paper 5266
Within-School Tracking in South Korea
An Analysis Using Pisa 2003
Kevin Macdonald
Harry Anthony Patrinos
The World Bank
Human Development Network
Education Team
April 2010
Policy Research Working Paper 5266
Abstract
The 2003 PISA Korea sample is used to examine the females. No evidence of an association between males and
association between within-school ability tracking and tracking is detected. While this association for females
mathematics achievement. Estimates of a variety of cannot be interpreted as a causal effect, the presence of
econometric models reveal that tracking is positively a measurable association indicates the need for further
associated with mathematics achievement among females research on tracking in Korea with a particular focus on
and that this association declines for higher achieving gender differences.
This paper--a product of the Education Team, Human Development Network--is part of a larger effort in the department
to analyze the determinants of learning. Policy Research Working Papers are also posted on the Web at http://econ.
worldbank.org. The author may be contacted at hpatrinos@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
WITHIN-SCHOOL TRACKING IN SOUTH KOREA
AN ANALYSIS USING PISA 2003
Kevin Macdonald1 and Harry Anthony Patrinos2
1
Consultant, Human Development Network Education Team, World Bank;
kadmacdonald1@worldbank.org
2
Lead Education Economist, Human Development Network Education Team, World Bank
(corresponding author) hpatrinos@worldbank.org
The opinions expressed in this paper are that of the authors alone and should not be attributed to that of the
World Bank Group.
1. Introduction
Understanding the relationship between learning achievement and tracking is especially
relevant to Korea due to its so-called equalization or leveling policy where, from 1974
onward, different areas began to assign students to upper secondary schools using a
lottery system instead of by academic performance3 (Kim et al. 2006; Educators without
Borders 2007). As a result, areas subject to equalization can be characterized as a mixed
school system since students of different abilities attend the same schools; in the other
areas, a tracked school system exists where students in each school are more homogenous
in ability.
Some research has tried to measure the impact of this policy. For example, Kim et al.
(2006) use a difference-in-differences method and find that the effect of the policy is
negative. Kang et al. (2007) examine the impact of this policy on adult earnings and find
positive effects for low ability students and smaller effects for high ability students.
Literature on tracking generally cites two paths through which tracking affects learning
achievement (Kim et al. 2008; Duflo et al. 2008; Hanushek and Wößmann 2005). In the
first, tracking benefits students because it creates a more ability-homogenous learning
environment which allows teachers and schools to choose pedagogy better suited to a
higher proportion of students. In the second, tracking inhibits low achieving students who
would otherwise benefit from exposure to high achieving peers while their high achieving
peers remain unaffected.
Consequently, recent empirical literature on tracking attempts to estimate the magnitude
of peer effects. Some recent estimates, as presented in Ammermeuller and Pischke
(2006), are small: an increase in peer composition of one standard deviation generally
results in an increase in achievement between 0.05 to 0.11 standard deviations. The
principle empirical challenge in this literature is distinguishing peer effects, the effect that
a student's peers have on his or her achievement, from correlated effects, the effect that
unobserved factors have on both the student and his or her peers. Correlated effects stem
from a number of sources including an unobserved characteristic of the teacher or
endogeneity in the selection of the peer group such as better students attending better
schools. Several different strategies have been adopted to overcome this identification
problem. For example, Ammermeuller and Pischke (2006) rely on random assignment of
teachers and students to classes; Gibbons and Telhaj (2006) take advantage of random
variation of primary students' assignments to secondary schools; Schneeweis and Winter-
Ebmer (2005) use a fixed effects model to focus on peer effects within schools where
class composition is generally random, and Fertig (2002) uses an instrumental variables
approach.
Kang (2006) examines peer effects in the context of South Korea, also using random
student assignment and instrumental variables. He finds higher ability peers have a causal
and positive impact on the achievement of a student. Additionally, he finds that a low
3
Initially the policy's official name was the "Equalization of High School Policy" (Educators without
Borders 2007).
2
achieving student tends to interact more closely with other low achieving students while a
high achieving student tends to interact more closely with other high achieving students;
this complicates the connection between peer effects and ability tracking: exposure to
high achieving students may benefit a low achiever, but he or she would be hindered by
exposure to his or her low achieving peers.
The proceeding analysis also provides a Korea-specific contribution by examining the
2003 Korea PISA sample. This paper examines the association between mathematics
achievement and within-school tracking where schools assign students into groups
depending on their ability. Particularly, this paper focuses on how this association differs
between males and females.
In the following sections, estimates of linear regression models present the association
between learning achievement and tracking and reveal a statistically significant
association for females, no statistically significant difference for males, and a statistically
significant difference in association between genders. Using PISA's categorical measure
of achievement, its mathematics proficiency levels, multinomial logit estimates show,
among females, a statistically significant decline in the association between tracking and
the odds of being in one proficiency level relative to the previous for higher levels of
proficiency. Finally, comparisons of the standard deviation of achievement between
males and females in schools with tracking and not with tracking, as well as estimates of
conditional quantile regressions, reveal no evidence that tracking associates with
inequities in achievement.
However, none of the proceeding results should be interpreted as causal. The cross-
sectional nature of the PISA dataset, in conjunction with unobserved factors, prevents
establishing a counterfactual: we can not estimate the achievement of a student in a
school with tracking had he or she been in a school without tracking. Furthermore, grade
10 students compose almost the entire sample, and the PISA examination occurred in
June, 2003; since grade 10 is the first year of high school, students have only been in the
observed school for three months; consequently, students have been exposed to tracking
or non-tracking for a maximum of three months although likely less since midterm exams
which are used to determine a student's ability are often held in late April. While we find
statistically significant associations, they likely reflect other factors that are correlated
with tracking but not observable. However, these associations are certainly interesting
and expose a need for more in-depth, empirical research on tracking in Korea.
3
2. Data
The Programme for International Student Assessment (PISA) is the Organization for
Economic Cooperation and Development's (OECD) international student assessment
targeted to 15 year olds in grade 7 or higher, and it has been conducted every three years
since 2000. In addition to testing students' ability in mathematics, science, and reading,
PISA also collects background data about each student, his or her family, and his or her
school. Schools are the primary sampling unit in PISA, and they are selected by one or
more sampling frames or explicit strata. In Korea, there are several strata which divide
the sample into general and vocational schools and by metropolitan, urban, and rural
areas. For this paper, only observations from the general school strata and for grade 10
students were included.
Both the 2003 and 2006 PISA school questionnaires include questions about tracking
within school; however, in 2003, the question specifies tracking among mathematics
classes while in 2006, the questions specifies any subject. In order to clearly estimate the
association between tracking and learning achievement, this paper uses the 2003 dataset
and focuses on mathematics achievement. The school tracking question for 2003 is drawn
from the principal's questionnaires:
Schools sometimes organize instruction differently for students with different abilities
and interests in Mathematics. Which of the following options describe what your school
does for 15-year-old students in Mathematics classes? (question 16)
The options included (a) Mathematics classes study similar content, but at different levels
of difficulty; (b) Different classes study different content or sets of Mathematics topics
that have different levels of difficulty; (c) Students are grouped by ability within their
Mathematics classes; (d) In Mathematics classes, teachers use a pedagogy suitable for
students with heterogeneous abilities (i.e. students are not grouped by ability). For each
option, a principal could choose either "for all classes," "for some classes" or "not for
any classes."
The three different types of tracking captured by parts (a) through (c) of question 16 all
occur in Korea. The Ministry of Education encourages schools to divide and instruct
students in three cohorts based on ability, although some schools divide students into two
cohorts. Additionally, many schools will divide students by ability only for a portion of
the weekly instruction and maintain mixed classes for the remainder in response to
parents and students wanting homogeneous assessment of students. Table 1 outlines how
school principals responded to the question:
4
Table 1: School Responses to Question 16
Given the varying types of tracking in Korea, part (c) seems to capture the notion of
tracking which most closely corresponds to the current literature on tracking and peer
effects. This question is the only one to emphasize ability as the method to divide
students, but its interpretation could potentially be problematic: for example, one could
reasonably interpret this as students within each mathematics class are grouped by ability
or as students among mathematics class are grouped by ability. The variable
some tracking will be a binary variable equal to one if a school's response to part (c) is
"for some classes" or "for all classes" and zero if the response is "not for any classes".
Note that this is a school level variable, and it does not tell us how or whether a particular
student in the PISA sample may have been tracked.
Like other major student assessments such as the Trends in International Mathematics
and Science Study (TIMSS) and the Progress in International Reading Literacy Study
(PIRLS), PISA treats a student's achievement as an unobservable random variable with a
distribution conditioned on his or her performance on a standardized test as well as
information about his or her background (OECD 2003). Consequently, PISA does not
provide a single estimate of achievement, but rather, for each subject, five random draws
from the latent variable's conditional distribution called plausible values. These random
draws are then incorporated into the estimation of statistics which are functions of
achievement such as means and regression coefficients.
Additionally, PISA categorizes ranges of achievement according to the typical
proficiencies displayed by students in those ranges; these are called proficiency levels
(OECD 2007). Mathematics and science achievement each are categorized into six
proficiency levels while reading achievement is categorized into five. Since proficiency
levels stem from achievement, for each subject, each student has five plausible
proficiency levels.
5
3. Stochastic Model
We assume that the observations of the PISA's school, student and family background
variables do not exactly determine the corresponding levels of student achievement, but
rather that they give us more information about what these achievement levels could be.
In this sense, the vector of achievements for the sampled group of students, y, is a random
variable conditionally distributed by the set of background variable observations, matrix
x, as expressed by the following stochastic model:
(1) y | x ~ f (y, x)
Furthermore, we assume that the conditional mean of the distribution function f has the
following property:
(2) E[y | x] = x
where is a column vector of regression coefficients comprised of one parameter for
each background variable in x. Given the setup of (1) and (2), each regression coefficient
can be interpreted as the change in a student's expected achievement associated with a
marginal change in the value of the coefficient's corresponding variable; since (2) is an
assumption about the conditional distribution function, f, and not derived from a
cognitive production function or any framework implying causation, the regression
coefficients are not interpreted as marginal effects.
For analyzing how background variables associate to the dispersion of the conditional
distribution, f, we assume that the 20th, 40th, 60th and 80th conditional quantiles of y | x are
linear functions of the background variables, x.
(3) prob{yi xi q } = q q {0.2, 0.4, ..., 0.8}, i I
where I is the set of sampled students, yi and xi are student i's achievement and
background variable observations, respectively, and q is a column vector of qth quantile
regression coefficients with one parameter for each background variable. Analogous to
the linear regression coefficients, , each qth quantile regression coefficient of q can be
interpreted as the change in the qth quantile of a student's distribution of achievement
associated with a marginal change in the corresponding background variable. In other
words, while the regular regression coefficients measure how variables associate with the
mean of a student's distribution of possible achievements given his or her background
variables, the qth quantile regression coefficients measure how variables associate with
the qth quantile of a student's distribution of possible achievements given his or her
background variables. Examining how these coefficients change for different quantiles
describes how variables associate with the dispersion of the conditional distribution; a
variable that is, for example, positively associated with the 80th quantile and negatively
with the 20th quantile would be associated with an increase in this dispersion.
6
In order to use PISA's categorical measure of achievement, its proficiency levels, we
assume that the probability of a particular student's proficiency level, pi, is conditionally
distributed on xi by a multinomial logistic function:
exp{ j xi }
(4) prob{pi = j | xi} = K
j {2, ..., K}
1 exp{ k xi }
k 0
where K is the number of proficiency levels and j is the column vector of multinomial
logit coefficients with one parameter for each background variable. (4) implies that
prob{ pi j | xi }
j j 1 xi j {2, ..., K}
(4/) ln
prob{ pi j -1 | xi }
or, in other words, that the association between a marginal change in any particular
background variable and the log change in the odds of being in proficiency level j relative
to j 1 is the corresponding component in the vector equal to j - j-1.
Estimating (4/) is conceptually similar to dividing the sample into subsamples comprised
of consecutive pairs of proficiency levels and then estimating logit models for each
subsample. If the association between the odds of being in the next proficiency level and
variables such as some tracking are stronger for lower achieving students than higher
achieving students, estimations of (4/) will capture this. Additionally, statistical tests can
reveal whether these association change for higher achieving students versus low
achieving students.
4. Variables
In order to focus as much as possible on the association between learning achievement
and some tracking, the variation in achievement attributable to other variables needs to be
accounted for. Typical analyses of tracking and peer effects assume cognitive production
functions and use similar variables. Table 2 lists variables used in some of these recent
studies which can be generally classified into three levels: student level variables which
includes student personal characteristics as well as those of their families, class level
variables which includes characteristics of their teachers, classrooms, and peers, and
school level variables which includes characteristics of the school.
7
Table 2: Background Variables Used in Previous Studies
Similar variables compiled from the 2003 PISA dataset will be used in the proceeding
analyses and are presented below.
Since this paper is particularly interested in tracking, we want to distinguish the
association with learning achievement of tracking from that of other school-level
characteristics whether observed or unobserved. While not all school characteristics are
observable in PISA, the observed characteristics might reflect the unobserved
characteristics in some way. Consequently, this analysis estimates the correlations
between several candidate school variables and some tracking in order to identify which
school variables to include in the models. The extent to which these variables act as
proxies for unobserved school characteristics correlated with tracking determines how
isolated the resulting estimates of association between some tracking and achievement is.
Of the several candidate school variables in the PISA sample tested for correlation with
some tracking, Table 3 presents those that were statistically significant. The candidate
school variables that were tested were public versus private, grade range, proportion of
funding from different sources (5 variables), school autonomy measures (12 variables),
frequency of assessments, use of assessment data (8 variables), school size, school
community size stratum (3 variables), student teacher ratio, and the importance of a
student's academic record for admission.
8
Table 3: School Variables Correlated with Tracking
Proportion
Desc. of Association with
Variable of sample
Tracking
true (%)
Public positive 48
autonomy hiring teachers negative 33
autonomy teacher salary increases negative 90
autonomy course offering positive 96
student teacher ratio positive -
located in metropolitan stratum relative to rural positive -
Source: Korea PISA 2003
The variables measuring autonomy over hiring teachers and teacher salary increases are
positively correlated with each other and negatively correlated with tracking. Since
autonomy over hiring teachers displays more variation, it can serve as a proxy for
autonomy over salary increases and any other unobserved characteristics that both might
reflect. Autonomy over course offering has very little variation since 96 percent of
schools reported this characteristic; this variable was tested for correlation with
achievement, and the results were not statistically significant; for this reason, it will be
excluded from the models.
Additionally, several variables are of interest in the Korean context. Whether a particular
school is subject to the equalization policy or not can not be observed in the 2003 PISA
sample, but the importance a school places on a student's academic record for his or her
admission can be observed. Consequently, this variable is included. Also, some schools
are co-educational and some are strictly male or female. Schools report the number of
female students and the number of male students which can be used to construct a binary
variable of whether the school is co-ed or not. Table 4 lists all the variables used in this
analysis with some descriptive statistics.
9
Table 4: Summary Statistics of Achievement and its Covariates
10
5. Mathematics Achievement and Tracking
Estimation of our models is complicated by the plausible value estimates of mathematics
achievement as well as the presence of intra-cluster correlation and other issues related to
the complex survey design. The estimation methodology used in this paper adheres
strictly to the methodology recommended by the OECD (2005) which provides unbiased
estimators and standard errors assuming the other standard, requisite assumptions for
each model are met.
Table 5 presents three estimates of the linear regression model of (2). The first includes
only the some tracking variable; the estimate of this coefficient is equivalent to the
difference in the mean achievement of students in schools with tracking versus those in
schools without tracking. As can be seen, this estimate is positive, implying students at
tracking schools have a higher level of achievement, but it is not statistically significant
implying the difference could simply stem from sampling variation.
The second estimation includes only the school variables, and the third includes all other
variables. Only with the inclusion of student and family characteristics does the positive
difference between tracking students and non-tracking students become statistically
significant.
Being female is negatively associated with mathematics achievement which is a typical
result for many countries. Additionally, being located in an urban or metropolitan stratum
instead of a rural stratum is positively associated with achievement, even when
differences in student and background characteristics are controlled for. Having a
mother's education less than upper secondary is negatively associated with achievement.
Having a mother with more than an upper secondary education is also negatively
associated with achievement; however, Table 4 reveals that this represents a small
proportion of the sample. Finally owning books positively associates with achievement as
well.
11
Table 5: Achievement Linear Model Estimates
12
6. Gender Differences and Tracking
In order to examine whether the association between learning achievement and some
tracking differs for males and females, Table 6 presents re-estimates of the linear model
which include an interaction term for gender and some tracking.
Table 6: Achievement Linear Model Estimates with Female and Tracking Interaction
The estimated model (4) includes only a binary variable for being female. By definition,
the estimate for this coefficient is equivalent to the difference in the mean achievement of
males and females, and the constant is equivalent to the mean math achievement of
males. Average achievement for females is 21 points below the average achievement of
males.
In model (5), an interaction variable and some tracking are added to the model. By
definition, the difference between average achievement of females at tracking schools
versus those not at tracking schools is the sum of the coefficients for female and female x
some tracking. As indicated, females in tracking schools achieved, on average, 32 points
higher than those not at tracking schools.
Also, by design of model (5), the sum of the parameters for female x some tracking and
female is equivalent to the difference in mean achievement between males at tracking
schools and females at tracking schools; whereas, the coefficient on female alone is the
difference between males and females not at tracking schools. Since female x some
tracking is positive, the gender gap in achievement is lower at tracking schools.
13
Finally, model (5)'s coefficient for some tracking is the difference between males in
tracking schools versus those not in tracking schools. As can be seen, there is no
significant difference. In other words, we observe a measurable difference in
achievement between tracking and non-tracking schools only for females. Model (6)
differs from model (5) with the inclusion of controls for other school, student, and family
background variables. The conclusions drawn from this model are the same as drawn
from (5), except, now they have taken into account differences in the other background
variables. The chief conclusion of these results is that some tracking is positively
associated with mathematics achievement for females; no evidence of this exists for
males. Additionally, the association is different for males than females.
7. Low Achievers and Tracking
Low achieving students may benefit from tracking due to a homogenous learning
environment or may be inhibited by tracking due to a lack of exposure to higher
achieving peers. In the preceding estimations, a significant difference in math
achievement associated with tracking is found only among females, and this difference is
positive. While this result tends to be consistent with the connection between learning
and ability-homogeneous peers, the preceding estimations do not relate this difference to
achievement level; it is possible, for example, that tracking associates negatively for low
achievers while positively for middle and higher achievers.
Previous studies which sought to measure peer effects among low achieving students
typically have baseline data on the achievement of students in their sample (Duflo et al.
2008). For the PISA 2003 dataset, this is not the case. In order to use the PISA dataset to
examine differences in tracking's association across the distribution of achievement, the
multinomial logit model for proficiency levels of (4) is estimated. As shown in (4/), this
model allows us to estimate the odds ratio associated with some tracking for different
consecutive pairs of proficiency levels. This reflects whether this association is stronger
or weaker for lower achieving students versus higher achieving students. Table 7 presents
estimates of the proportion of general high school, grade 10 students at the various levels
of mathematics proficiency. Table 7 reveals that most students are concentrated in levels
3 through 5.
14
Table 7: Proportion of Students at Each Mathematics Proficiency Level
The standard errors of multinomial logit models increase with the number of categories in
the dependent variable; consequently, this analysis groups several proficiency levels
together. The number of categories used in this analysis is four: more than this creates
very large standard errors and fewer decreases the variation in achievement.
The proceeding table presents estimates from two multinomial logit models where the
categories below 4 are grouped as one and each proficiency level greater than or equal to
4 is assigned its own category. The subsequent results are roughly similar to merging
proficiency levels 5 and 6 and creating an additional category for level 3. Each cell of the
table presents the association between the covariate and the log of the odds for each pair
of proficiency levels as well as the odds ratio in square brackets4.
The first estimated multinomial logit model, model (7), includes only the gender variable,
the some tracking variable and their interaction. Analogous to the interpretation of model
(5), the odds of a female being in level 4 relative to being in a level less than 4 is less than
half (0.43 times) of that for males; however, for students attending a tracking school, it is
not evident that females are any more or less likely than males to be in level 4 than in a
lower level as indicated by the statistical insignificance of the sum of female and female x
some tracking. Furthermore, among females, the odds of being in level 4 relative to being
in a lower level for those in tracking is more than twice the odds for those females not in
tracking as indicated by coefficient on the sum of some tracking and female x some
tracking. The results are different, however, for higher proficiency levels. For example, it
4
Recall that an odds ratio is the change in odds which is equivalent to the change in relative probabilities.
To calculate how many times the odds of achieving one proficiency level to that of a preceding level from
the coefficient, b, calculate eb (which is presented in square brackets).
15
is not evident that females are any more or less likely than males to be in level 6 than in
level 5; among females, it is not evident that those attending a tracking school are any
more or less likely to be in level 6 than in level 5. The main result is that tracking seems
more strongly associated for lower achieving females than for higher achieving females.
Table 8: Mathematics Proficiency Level Multinomial Logit Model Estimates
Model (8) presents similar results when the control variables are included; although, the
standard errors increase due to the higher number of variables.
From Table 8 alone, however, we can not conclude that this association declines for
higher pairs of proficiency levels since the lack of significance for higher pairs may be
due only to higher sampling variation and not to a weaker association. To test whether
this association declines, table 9 presents statistical tests of the differences in the reported
coefficients across the pairs of consecutive proficiency levels.
16
Table 9: Difference in Estimates Across Initial Proficiency Level
The difference between females in tracking schools and not in tracking schools, as
measured by the sum of some tracking and some tracking x female, is statistically
different for low consecutive proficiency levels versus high ones. In other words, there is
evidence that the association between tracking and learning achievement declines for
females as their achievement increases.
For males, Table 8 reveals no statistically significant association between some tracking
and the odds of being in the next proficiency level for any proficiency level, and table 9
does not reveal any change in this association.
The sum of the parameters for female and some tracking measures the log difference in
the odds of being in the next proficiency level between males and females at tracking
schools. This difference, however, is not statistically significant for any pair of
proficiency levels nor is the change across pairs significant. The parameters for female,
however, measure the difference between males and females who are not at schools with
tracking; this difference is statistically significant only for low proficiency level pairs.
The interaction term, as presented in Table 9, exhibits a statistically significant change
for higher proficiency level pairs; in other words, the gender difference in association of
tracking declines for higher pairs.
8. Dispersion and Tracking
Besides learning outcomes, a major issue surrounding tracking is the possibility that it
may reduce equity (Kim et al. 2008). Using the PISA dataset, we can examine the
association between some tracking and the dispersion of achievement. Table 10 presents
the standard deviation of achievement between students in schools with tracking and
without for males and females. It also presents F statistics for comparisons across rows
and columns; while the standard deviation is lower for both males and females in schools
17
with some tracking, the F statistics are too low for any of these differences be statistically
significant.
Table 10: Standard Deviation Comparisons
Note: Standard errors reported in parentheses.
Source: PISA 2003 Korea, Grade 10 Males, General
School Strata
An alternative measure of how tracking associates to dispersion is to look at the
conditional distribution of achievements. As modeled in assumption (1), for any
particular student observation, his or her achievement is a random variable conditionally
distributed by his or her background variables. In addition to the background variables
that associate with this distribution's mean as in (2), these background variables may also
associate with the shape of the dispersion. For example, the conditional distribution of
achievement might be wider for students at tracking schools compared to those not at
tracking schools if tracking schools reduce inequity. To estimate whether some tracking
associates with the shape of the distribution of possible achievements for a particular
student, the following table presents results from the quantile regression model of (3).
In addition to the results for the 20th, 40th, 60th and 80th conditional quantiles, estimates of
the differences in coefficients between the 80th and 20th quantiles are also presented
(Table 11). A negative difference for a variable means that the variable is associated with
making a conditional distribution more compact while a positive difference reflects the
opposite.
18
Table 11: Quantile Regression Estimates
The interpretation of the coefficients and their sums is analogous to the interpretation
presented in the previous sections except, instead of associating with the conditional
mean, they associate with the indicated conditional quantile. For example, being female
and not in a tracking school, as measured by the coefficient on female, is negatively
associated with all four presented conditional quantiles. For females, being in a tracking
school is positively associated with all four conditional quantiles as measured by the
estimates of the sums of some tracking and some tracking x female. However, none of the
differences between the 20th and 80th conditional quantile coefficients were statistically
significant meaning we can not conclude that some tracking has any association with the
shape of each student's conditional distribution. This is consistent with tracking not
affecting equity.
One possibility is that tracking is actually related to school selection: suppose low ability
female students prefer schools with tracking. In regions not subject to equalization,
among lower ability female students, those with relatively higher ability would be more
likely to gain admission to the school they prefer (with tracking) than those with
relatively lower ability; high ability female students would be indifferent between
choosing a school with tracking versus one without. The resulting pattern in achievement
data would be similar to our results. This hypothesis is furthered by Table 12 which
19
compares math achievement levels among females between schools with tracking and
without tracking for the rural, urban, and metropolitan strata.
Table 12: Mean Achievement of Girls in Tracking versus Non-Tracking Schools
While the limited number of observations prevents us from replicating the preceding
analysis in only the urban stratum, the comparisons of mean mathematics achievement in
Table 12 reveals a significant and positive difference between tracking and non-tracking
schools only for female students in the urban stratum. In the metropolitan and rural strata,
students have little choice as to which school they attend, either schools are subject to
equalization and students are therefore assigned by lottery as in the metropolitan stratum
or schools are too far away as in the rural stratum. But in many regions in the urban
stratum, students are in regions whose schools are not subject to the equalization policy
and as a result they do have a choice (Kim et al. 2008). Consequently, we cannot rule out
that the difference in achievement associated with tracking might reflect selection
stemming from a difference in preferences.
9. Conclusions and Future Research
In the 2003 PISA Korea sample, being in a tracking school is positively associated with
mathematics achievement for female students, and, as shown by estimates of multinomial
logit models, this association declines for higher levels of achievement. For males,
however, there is no conclusive association.
But how do we interpret this association? It should not be interpreted as the "effect" on
achievement of being in a school with tracking for two reasons: first, we can not establish
the counterfactual levels of achievement for students who are in tracking had they not
been, and second, students have only been exposed to their new schools for only three
months which does not seem long enough for tracking to have an impact. More likely, the
detected association between tracking and achievement stems from other factors.
However, since we control for any school level variable that is correlated with tracking as
well as the standard school, family, and student background variables, a lot of possible
factors that these variables represent and proxy for, both observed and unobserved, can
be ruled out.
20
In the Korea PISA data, girls' schools were no more or less likely to be a school with
tracking than boys' schools or co-ed schools. Also, since we control for co-ed schools, it
is unlikely that the measured association between achievement and tracking, as well as
the gender difference in this association, reflects being at a girls school. Furthermore,
schools where a student's academic record is important for admission (our proxy for
schools subject to equalization) were no more likely to be a school with tracking than a
school where academic record was not important to admission. As a result, it is unlikely
the association between achievement and tracking reflects equalization.
Alternatively, being in a tracking school might have an immediate effect on mathematics
achievement through a student's attitude or motivation towards mathematics. It is
plausible that this effect would differ across the genders, and a follow-up analysis using
PISA 2003 could gather more evidence relating to this.
Consequently, while we can not conclude from our analysis that tracking has an effect on
student achievement, we do find a very interesting pattern in the 2003 dataset, and our
results are especially interesting due to the gender difference aspect. Given the ongoing
debate around the Korea's equalization policy, these results expose the need for more
research on tracking in Korea with an emphasis on gender differences.
References
Ammermueller, A. and J. Pischke (2006), "Peer Effects in European Primary Schools:
Evidence from PIRLS", National Bureau of Economics R Working Paper 12180,
Cambridge, MA.
Betts, J. and J. Shkolnik (2000), "The Effects of Ability Grouping on Student
Achievement and Resource Allocation in Secondary Schools", Economics of Education
Review 19 1 - 15
Duflo, E., P. Dupas, and M. Kremer (2008), "Peer Effects and the Impact of Tracking:
Evidence from a Randomized Evaluation in Kenya"
Educators without Borders (2007), "Are Korean Kids Smart or Working Hard? Some
Reasons behind Top-level achievers of Korean Students", Occasional Paper No. 1,
Educators without Borders, Seoul, Korea
Fertig, M (2003), "Educational Production, Endogenous Peer Group Formation and
Class Composition - Evidence from the PISA 2000 Study", IZA Discussion Papers, 714,
Bonn
Gibbons, S. and S. Telhaj (2005), "Peer effects and pupil attainment: Evidence from
secondary school transition", London School of Economics, mimeo.
21
Hanushek, E. and L. Wößmann (2005), "Does Educational Tracking Affect Performance
and Inequality? Differences-in-Differences Evidence Across Countries", NBER, Working
Paper 11124.
Kang, C. (2007), "Classroom Peer Effects and Academic Achievement: Quasi-
Randomization Evidence from South Korea", Journal of Urban Economics, Vol 61, No.
3, pp 458 - 495
Kang C, C. Park, and M. Lee (2007), "Effects of Ability Mixing in High School on Adult
Earnings: Quasi-Experimental Evidence from South Korea", Journal of Population
Economics, Vol. 20, No. 2, pp 269-297
Kim, T., J. Lee, and Y. Lee (2008), "Mixing versus sorting in schooling: Evidence from
the equalization policy in South Korea", Economics of Education Review
OECD (2003), PISA 2003 Technical Report, Paris: OECD
OECD (2005), PISA 2003 Data Analysis Manual, Paris: OECD
OECD (2007), PISA 2006 Science Competencies for Tomorrow's World Volume 1:
Analysis, Paris: OECD
Schneeweiss, N and R. Winter-Ebmer (2005), "Peer Effects in Austrian Schools",
Department of Economics, University of Linz, Working Paper No. 0502
Zimmer, R (2003), "A new twist in the educational tracking debate", Economics of
Education Review, 22 307 315
22