Cristian Bellei Harvard Graduate School of Education -PEPG-05-13... · Harvard Graduate School of...
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The Private-Public School Controversy: The Case of Chile
Cristian Bellei
Harvard Graduate School of Education
PEPG 05-13
Preliminary draft Please do not cite without permission
Prepared for the PEPG conference:
"Mobilizing the Private Sector for Public Education" Co-sponsored by the World Bank
Kennedy School of Government, Harvard University, October 5-6, 2005
Introduction. Marked-oriented strategies have increasingly been proposed as an effective and
efficient way to increase both quality and equity in education. Academic and political
discussions have attempted to predict the most probable consequences that market
incentives could have on educational systems. A key issue on those analyses has been the
comparative study of the public and private schools’ effectiveness in terms of students’
academic achievement. In this paper, I critically review the research about whether
Chilean students attending private schools obtain greater learning outcomes than their
peers studying at public schools.
Chile constitutes a paradigmatic case to the public/private schools debate, and
research on its experience might shed light on such a controversy. Its nationwide school-
choice system finances both public and private subsidized schools under the same
funding system, a particular type of voucher program. Compared to the small-scale of the
majority of the U.S. voucher and school-choice programs, the Chilean situation is a
particularly attractive case to study. Paradoxically, previous research on Chilean
education has obtained very contrasting findings.
The paper begins with (I) a brief description of the Chilean education; then, it
reviews the research on both (II) systemic effects of school-choice and (III) private/public
schools’ effect. Section (IV) analyzes some key methodological issues that account for
the contrasting findings of previous research; and sections (V), (VI), (VII), (VIII) and
(IX) provide empirical evidence about the consequences of the identified methodological
limitations. A final section summarizes the main conclusions of the analysis, elaborates
some interpretative hypothesis, and states some educational policy implications.
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I. School choice and market oriented institutions in the Chilean Public Education.
For more than two decades, the Chilean educational system has operated under an
institutional design whose fundamental regulation and decision elements do not rely on
national authorities, but on the combination of family preferences (which are expressed in
their free choice of school) and (public and private) school competition for attracting
such preferences. This system was created during the 1980s within the context of large
national economic and institutional reforms, including the privatization of state
companies, the restructuration of the social security and health systems, and the opening
of the economy to international markets. The Chilean government of that time applied the
neo-liberal canon in a paradigmatic way, trying to make education a self-regulated
market. The main reforms were:
i.) Creation of a single funding system for all state “subsidized” schools, be they
public or private. The funding mechanism is a “voucher”, which consists of a monthly
payment, to every school, of a fixed fee per each student who is enrolled and regularly
attends his classes.
ii.) Promotion of competition among public and private schools. Every school
must compete to attract the families’ preferences, in order to guarantee its own funding.
To obtain public funding, all schools must be free for families. Families do not have any
restrictions to choose a school (be they public or private, near or distant from home, etc.).
Private schools are not compelled to accept any applicant: They can select their students.
Instead, public schools are compelled to admit any applicant.
iii.) Deregulation of schools institutional management. Schools that receive state
subsidy (be they public or private) must satisfy a number of minimum operational
conditions, such as having basic facilities, hiring certified teachers, and fulfilling the
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national curriculum objectives. With the exception of these “minimum standards”,
schools are permitted to be managed with all the possible freedom, which means, for
instance, the deregulation of teachers’ labor situation and wage, and the possibility for the
school owner to profit.
iv.) Decentralization of public schools administration. State schools
administration was transferred from the Ministry of Education to the local governments
(municipalities). The purpose of this measure was to establish the competition between
public and private schools as local suppliers of education.
v.) Creation of different institutional conditions for the competition among
schools. The most important ones were: Creation of a decentralized Ministry of
Education’s system of supervision; curriculum deregulation, in order for schools to create
diverse “educational offers”; creation of a national evaluation system of students’
learning (SIMCE, Spanish acronysm for Measurement of Education Quality System),
aimed at informing families about the quality of schools.
Since 1990, the Chilean governments have driven a large-scale national
educational reform, which attempts to combine the aforementioned market institutions
with state regulation and intervention. Thus, the educational policies have been oriented
to expand and deepen the market-oriented model, as well as to restrict it, through the
promotion of social equity and educational quality. The main measures were:
i.) Greater regulation of teacher labor market, through the creation of a “teacher
labor statute”. This statute recovered a significant part of the historic teachers’ privileges,
such as an ad-hoc minimum wage, rules for increasing teacher wage, wage bonus (by
seniority and training, among others), and the rigidification of the firing mechanism.
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Although all these regulations are compulsory only for municipal schools, many of them
also rule subsidized private schools.
ii.) Compensatory programs aimed at improving (public and private) schools that
serve the poorest students, and/or those students who achieve the lowest learning
outcomes. These “positive discrimination” programs consist, basically, in supplying
students and teachers with teaching and learning materials, teaching training, external
advisory, and enhancement of schools facilities.
iii.) Full coverage policies to improve the quality of education. For instance,
installation of computational laboratories, provision of school texts, teacher training,
investment in school facilities, and the extension of the students’ school day. In addition,
these policies included a curriculum reform much more prescriptive than that suggested
by the flexible norms inherited from the 80s reform.
iv.) Creation of a “price discrimination” system among subsidized private schools
(in the case of municipal schools, this system only affects high schools), which allows
schools to charge families for tuition, without loosing the state subvention, or, at most,
reducing it to a minimum amount.
v.) Strengthening of the national learning evaluation system. SIMCE results have
been used to determine the target populations of compensatory programs, as well as those
teachers who win a wage incentive, which operates as a merit-pay system. The technical
characteristics of the test were also enhanced, while its coverage was expanded to rural
schools (which had not been evaluated previously). Finally, and perhaps the most
relevant issue, the knowledge and use of SIMCE results was spread among families (the
results obtained by each schools are yearly published in the national press) as well as
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among school communities (a school-level report is sent to the principal, teachers, and
parents’ organizations).
To understand the current structure of the Chilean school system (primary and
secondary education), table 1 shows its different types of schools, classified by funding
source and property. As seen, a few more than half of the students (53%) study in public
schools (“municipal”), most of which are free. The remainder studies in private schools
(47%). In most cases (34.2% of the national enrollment) private schools are co-financed
by public funds and tuition charged to the families. Totally free private schools educate a
marginal fraction of students (3.8%), while private schools totally paid by families
represent approximately a tenth of Chilean preschool system (9%). Summing up, nearly
half of the Chilean students pay for their education. In this paper, I will only distinguish
between public, private subsidized (voucher), and private non-subsidized schools.
Table 1. Chilean schools by funding source and property (percentage of total national enrollment).
Funding source
Public (free) Mixed (co-pay) Private (tuition)
Public
Municipal
(47.7%)
Municipal with co-pay (some High
Schools) (5.3%)
-----------
53%
Ownership and administration
Private
Subsidized Private
(3.8%)
Subsidized Private with co-pay
(34.2%)
Non-subsidized Private
(9%)
47%
51.5% 39.5% 9% Source: author elaboration, based on Ministry of Education 2002.
Additionally, graph 1 shows the evolution of enrollment between 1980 and 2000.
Overall, the total enrollment remained quite stable during the first ten years of the new
system. However, this stability did not imply that each type of school kept a steady level
of enrollment: Private subsidized schools enrollment increased rapidly, especially during
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the first 5 years (1981-1986), period in which it more than doubled. Simultaneously,
municipal schools saw a systematic fall of their enrollment from 1981 and 1991. This
“transfer” from public to private schools involved more than a half million of students
(almost a fifth of the entire school system). The period that began in 1991 showed a
different trend: national enrollment increased rapidly and systematically; thus, in 2000
there were 600,000 more students than in 1991. For the first time since the creation of the
subvention system, municipal education stopped losing students, starting a slow
expansion: In a decade, it increased in approximately 200,000 students. Private
subsidized schools’ enrollment continued its expansionist trend, although less rapidly
than in the 1980’s decade: it increased by 300,000 students during this period. The
enrollment of non-subsidized private schools slowly increased throughout the entire
period, remaining as a minor part of the Chilean school population, however.
Finally, the testing system (SIMCE) has pointed out a systematic pattern: on
average, private non-subsidized schools’ students score higher than private subsidized
students, while private subsidized students’ score higher than public schools’ students.
Since the early nineties, the raw achievement gap between non-subsidized private schools
and public schools has been approximately 1.2 to 1.8 S.D. In turn, the raw test-score gap
between subsidized private schools and public schools has been about 0.3 to 0.4 S.D.
Whether or not this raw gap is produced by genuinely greater private school effectiveness
has been one of the most controversial academic and political questions in the Chilean
educational debate in the last fifteen years.
Graph 1. Evolution of the Chilean primary and secondary education enrollment by type of schools.
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Number of students by type of school. 1981 - 2000
0
250,000
500,000
750,000
1,000,000
1,250,000
1,500,000
1,750,000
2,000,000
2,250,000
2,500,000
2,750,000
3,000,000
3,250,000
3,500,000
3,750,000
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
TotalMunicipalPrivate subsidizedPrivate non-subsidized
Source : Ministry of Education 2002.
II. The research about systemic effects of school choice in Chile.
There are two competing theories (both are simultaneously academic and policy
theories) about the systemic effects of the Chilean voucher system. One states that
subsidized private schools can help to improve public schools through a competition
effect, predicting a global improvement of the Chilean education. The other theory
proposes that the (expected) positive productivity effect on private and public schools
may be canceled out by the (unexpected) negative effect of sorting (private schools
“skim” the best public students) on public schools, predicting a kind of “zero-sum game”,
with no systemic improvement. In spite of their contrasting points of view, both theories
agree that, in order to evaluate the Chilean voucher system, it is necessary to assess its
impact on both public and private schools. Unfortunately, there is very little research on
this issue.
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Gauri (1998), in a 1993-1994 survey based on a random sample of 726
households of the Santiago metropolitan area, studied the school choice process. He
created a multinomial logit model to predict what kind of students attend the different
types of schools, especially high performing publicly funded schools (both private and
public). He found that the probability of attending a school situated in the top third of
students’ learning outcomes significantly increased with the parents’ education, family
income, and other family characteristics associated with higher socioeconomic status. He
also found that the probability of studying in a high performing school significantly
increased when the student was required to take a cognitive and/or academic test as a
requirement to be admitted to the school. In other words, he found that top-performing
schools systematically applied academic admission policies to select the most talented
students. Gauri concluded that choice policies have increased both the social and the
academic stratification of the Chilean educational system. Although this study provides
valuable evidence about the current testing policies applied by schools with higher test
scores, it is not clear the extent to which these processes are associated with the voucher
system and the extent to which they have increased the stratification of the Chilean
education.
Hseih and Urquiola (2003) attempted to evaluate whether the introduction of
school choice in Chile increased the educational and socioeconomic differences between
private and public schools. The students’ outcomes they analyzed were 4th grade
mathematics and language tests scores, repetition rates, and years of schooling among 10-
15 year olds, between 1982 and 1988, at schools and commune level. They controlled for
several socioeconomic schools and commune factors. They found that communes with
higher proportion of private enrollment tended to have higher public/private test-score
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gap and repetition rate gap, as well as higher students’ SES public/private difference at
commune level. The authors also found that commune enrollment in private schools rate
was negatively associated with public test scores, after controlling for several commune
and school factors. Hseih and Urquiola interpreted these findings as an evidence of a
negative effect of private schools on public schools. Finally, at commune level, neither
the level of 1990 private enrollment nor the 1982-1990 increase in private enrollment
were associated with students’ outcomes (test scores, repetition rate, and schooling
among 10-15 year olds). In other words, they did not find evidence that private
subsidized schools yielded positive systemic effects. I think this study shows strong
evidence of the association of both private enrollment and public/private gap, but fails to
demonstrate a causal link between them.
Finally, Gallegos (2002) also attempted to estimate the impact of market
competition on public and private subsidized schools. The author used 4th grade (1994
and 1996) and 8th grade (1995 and 1997) test scores at school level (school mean of
Language and Mathematics) as the outcome variables, and controlled for the schools’
SES composition. Gallegos defined each commune as a different school-market, and
controlled for commune variables (level of urbanization, size). The study found that the
level of market competition (as measured by the proportion of private enrollment at
commune level) positively affected the school performance (statistically significant
estimates for 1994, 1995, and 1997), and that this “competition effect” was stronger for
private schools. The key limitation of this approach is that the level of private enrollment
is not an exogenous variable to students’ performance; on the contrary, there is strong
evidence that private schools tend to serve students, families, and geographical areas with
characteristics positively associated with students’ learning outcomes. In a further study,
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Gallegos (2004) attempted to overcome this limitation. He used “priest per capita” as an
instrumental variable to identify exogenous variation in private subsidized enrollment at
commune level. The paper analyzed 4th grade (2002) test scores, and controlled for
students’ mother education and school resources. The author estimated that an increase in
private enrollment by one S.D. (which is about 20 percentage points) was associated with
a 0.2 S.D. increase in students’ test scores. Catholic schools account for about 10% of the
Chilean enrollment (only a third of the total private subsidized enrollment), and Catholic
schools are precisely those private schools that existed in Chile prior to the introduction
of the market oriented model. Consequently, it is not clear that priest per capita might be
a valid instrument for private schools in Chile.
Overall, the available evidence is not sufficient to evaluate the abovementioned
theories about the systemic effects of school choice in Chile. A more productive approach
should include analyses of longitudinal educational data, analyses of institutional and
educational policy contexts, and a deeper understanding of the parents’ choice and
schools’ selection processes. Undoubtedly, this is a very difficult task. Instead, most of
the research has been focused on test-scores comparisons between private and public
schools. The rest of the paper analyses this line of inquiry.
III. Private versus Public schools’ effectiveness in Chile.
In general terms, the research on the comparison between public and private
schools’ effectiveness in Chile has evolved following three stages.
Rodriguez (1988), Aedo and Larrañaga (1994), Aedo (1997), are the best
examples of the first phase. All of them studied small (not representative) samples of
schools, and analyzed exclusively school-level data (obtained during the eighties or early
nineties), and focused on urban primary schools. These three studies concluded that -after
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controlling for school characteristics- private schools scored higher than public schools,
and that this difference was statistically significant. Unfortunately, it is not possible to
generalize these findings to the Chilean school population. Because of their lack of
representativeness, I do not include the research of this phase in my analysis.
All the available studies of the second and third phases are summarized in table 2.
The first six listed studies also analyzed exclusively school-level data, but they studied
very large, nationally representative samples; in fact, most of them used the entire,
nation-level database of schools’ test scores1. This research is also focused on primary
education (mainly 4th grade), and all of them applied Ordinary Least Squares estimates.
These six studies constitute the second phase of this kind of research. Finally, the last
four studies included in table 2 are part of a third, more sophisticated stage. These four
studies analyzed student-level test scores as the outcome variable, and also included
student-level predictors. They used the entire nation-level database, and included both
primary and secondary education. As shown, studies of the third phase applied more
sophisticated research methods: in addition to OLS estimated, they applied Hierarchical
Linear Models, and probabilistic models of choice. Although the first three studies
included in table 2 analyzed more than one year of students’ test scores, none of them is a
longitudinal analysis (these studies are only a series of cross-sectional estimates).
The studies on Chilean education have analyzed Mathematics and/or Language
test scores as the outcome variable (two of them used the Mathematics-Language average
as the outcome measure). As reported in the last column of table 2, studies using school-
level data explain a greater proportion of the test-scores variation (about 40% to 60%)
1 Vegas (2002) is an exception: her sample is only representative of the Santiago Metropolitan Area. I included this study because it is very recent (analyzed 1999 test-scores), and used a unique database on teachers’ characteristics.
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than studies using student-level information (about 10% to 20%). As known, this is a
consequence of the loss of variation caused by the aggregation of individual test-scores at
school level.
Most studies compare public schools with two categories of private schools:
voucher and non-subsidized schools, although some of them also distinguish between
Catholic voucher schools and non-religious voucher schools. As shown in table 2, there
are noticeable differences in the estimates of the private/public test score gap: while some
authors have found private school advantage (0.05 S.D. to 0.27 S.D.), others have found
public school advantage (0.06 S.D. to 0.26 S.D.), and some others have found no
statistically significant difference between them. Moreover, these differences can be
found not only between studies, but also within studies. An additional puzzling fact is
that several studies have differed in their findings even if they analyzed the same
database. In the next section, I will provide some hypothesis and new evidence to explain
those contrasting conclusions.
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Table 2. Summary of the studies about private/public test score gap in Chilean schools. Analyzed data, controlled variables and main results.
Study Level/type of analysis Control variables Year/
Grade Private/Public difference in
S.D. by Subject matter* R2
Bravo et al., 1999 School (OLS)
School SES (school average of parents’ education and family educational spending) / geographical location
[ This paper estimated 12 models for every grade and subject matter for years 1992, 1994, and 1996. In the last column of this table I only reported equivalent models that are available for all years (all of them only controlled for the mentioned variables). The additional non-reported models introduced more family characteristics (opinion about the school), and school variables (for example student/teacher ratio, number of teachers, school SES Index). In general terms, when these additional controls are included the difference between private subsidized and public schools is not statistically significant neither for language nor for mathematics, neither for 4th nor for 8th grade. In turn, the difference between private non-subsidized and public schools although reduced, remains statistically significant for both Mathematics and Language in 4th grade, but it is not statistically significant for 8th grade in both subject matters. ]
1982/4th
1983/4th
1984/4th
1988/4th
1990/4th
1992/4th
1994/4th
1996/4th
1982/8th
1983/8th
1984/8th
1989/8th
1991/8th
1993/8th
1995/8th
1997/8th
Language: Subsidized: +* 1982, ‘83, ‘84, ‘88, ‘92, ’94, ‘96 + 1990 Non-subsidized: +* ‘82, ‘84, ‘88, ‘92, ’94, ‘96 + 1983, 1990 Mathematics: Subsidized: +* 1982, ‘83, ‘84, ‘88, ‘94 + 1990, ‘92, ‘96 Non-subsidized: +* ‘82, ‘83, ‘84, ‘88, ’94, ‘96 + 1990, ‘92 Language: Subsidized: +* ‘82, ‘83, ‘84, ’89, ‘93, ‘95, ’97 + 1991 Non-subsidized: +* ‘82, ‘83, ‘84,’91, ‘95, ’97 + ’89, ‘93 Mathematics: Subsidized: +* ‘82, ‘83, ‘84, ‘93, ‘95, ’97 + 1989 - 1991 Non-subsidized: +* ‘82, ’83, ‘84, ‘97 + ‘91, ‘95 - ’89, ‘93
0.42- 0.64
0.42- 0.57
0.42- 0.59
0.43- 0.54
Gallegos, 2002 School (OLS)
School SES level (1-4) / % private subsidized enrollment at commune level
1994/4th
1996/4th
1995/8th
1997/8th
Lang/Math average: 0.08* Subsidized 0.05* Subsidized 0.14* Subsidized 0.11* Subsidized
≈0.26 -0.31
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Carnoy and McEwan, 2000
School (OLS)
Average schooling of parents (levels 1-5) / % of mothers with less/more than 8 years of schooling / School SES Index (%) / geographical location (rural/urban)/ size of the city (levels 1-5)
1990/4th
1992/4th
1994/4th
1996/4th
1990/4th
1992/4th
1994/4th
1996/4th
Language: -0.05* Non-religious Sub. 0.31* Catholic Subsidized 0.63* Non-Subsidized -0.10* Non-religious Sub. 0.23* Catholic Subsidized 0.61* Non-Subsidized -0.07* Non-religious Sub. 0.25* Catholic Subsidized 0.66* Non-Subsidized -0.07* Non-religious Sub. 0.27* Catholic Subsidized 0.38* Non-Subsidized
Mathematics: -0.04* Non-religious Sub. 0.28* Catholic Subsidized 0.67* Non-Subsidized -0.10* Non-religious Sub. 0.19* Catholic Subsidized 0.58* Non-Subsidized -0.08* Non-religious Sub. 0.17* Catholic Subsidized 0.65* Non-Subsidized -0.08* Non-religious Sub. 0.24* Catholic Subsidized 0.40* Non-Subsidized
0.60
0.63
0.64
0.54
0.55
0.55
0.56
0.47
Mizala and Romaguera, 1999
School (OLS)
School SES level (1-4) / School SES Index (%) School SES level (1-4) / School SES Index (%) / geographical location / male-female school / student/teacher ratio / school size / teacher experience / preschool level in the school
1996/4th Lang/Math average: -0.02 Subsidized 0.18* Non-Subsidized 0.03 Subsidized 0.45* Non-subsidized
0.42
Sapelli, 2003 School (OLS)
Mothers’ education (school mean and school S.D.) / geographical location
1999/4th Mathematics: 0.79* Subsidized
0.17
Vegas, 20022 School2
(OLS) School SES Index (%) / Teacher characteristics (education, years experience, high school grade, teachers’ salary) / School management (decentralization of decision making, teacher absenteeism, teachers autonomy, teachers’ satisfaction)
1999/4th Mathematics: 0.01 Non-religious Sub. 0.30* Catholic Subsidized 1.04* Non-Subsidized
0.69
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McEwan, 2001 Student
(OLS)
(OLS+ model of choice)
Gender / indigenous mother / mother and father education / family income / books at home / geographical location / % indigenous student in the classroom / mean of classroom mother education / mean of classroom father education / mean of classroom family income Gender / indigenous mother / mother and father education / family income / books at home / geographical location / % indigenous student in the classroom / mean of classroom mother education / mean of classroom father education / mean of classroom family income / selectivity variable (multinomial logit model of choice)
1997/8th Language: -0.07* Non-religious Sub. 0.09* Catholic Subsidized 0.46* Non-Subsidized
Mathematics: -0.12* Non-religious Sub. 0.12* Catholic Subsidized 0.47* Non-Subsidized
Language: -0.12 Non-religious Sub. -0.06 Catholic Subsidized 0.12 Non-Subsidized
Mathematics: -0.26 Non-religious Sub. -0.11 Catholic Subsidized 0.03 Non-Subsidized
0.08- 0.19
0.08- 0.17
0.09- 0.19
0.08- 0.17
Mizala and Romaguera, 2003
Student (OLS)
(HML
between school)
School SES (weighted mean of mother and father education, and family income) / School SES Index (%) / gender / school curriculum / length of school day / school size / teacher experience / student/teacher ratio. School SES (weighted mean of mother and father education, and family income) / male-female school / school size / teacher experience / student/teacher ratio / students with similar achievement (%) School SES*type of school interaction / students with similar achievement (%)*type of school interaction / male-female school / school size / teacher experience / student/teacher ratio
1998/10th Language: 0.27* Subsidized 0.35* Non-Subsidized
Language (school mean): 0.27* Subsidized -0.06 Non-Subsidized
Language (school mean) 1: 0.28* Subsidized 0.36* Non-Subsidized
0.26
Sapelli and Vial, 2002 Student (OLS)
Family income / mother education / father education / indigenous family Family income / mother education / father education / indigenous family / self-selection model Family income / mother education / father education / indigenous family / self-selection model
1998/10th Language (OLS): 0.19* Subsidized
-0.05 Subsidized (ATE) 0.14* Subsidized (TTE)
0.14
Mizala et al., 2004 Student (HLM
between school)
School SES (weighted mean of mother and father education, and family income)*School type interaction / geographical location / male-female school / length of school day / school size / teacher experience / student/teacher ratio / students with similar achievement (%)
1999/4th Mathematics (school mean)1: 0.04* Subsidized 0.39* Non-subsidized
Source: author elaboration. * Key: * = p < .05; + = positive private school effect; - = negative private school effect. 1 Interaction effect was added to the main effect, by using the total population mean of the respective variable. 2 Sample: 171 Santiago schools.
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In spite of those divergences among the summarized studies, it is possible to draw some
general trends about the private/public test score gap. Table 3 synthesizes the main conclusion of
every study included in table1. To elaborate this synthesis, I have taken into account the most
complete model included in the research, the most precise estimate, or the most general findings
according to the author (note: table 2 does not include all estimates of every study, but the most
comparable or consistent). As shown, five out of the ten studies concluded that private
subsidized schools score higher than public schools; four studies concluded that there is no
statistically significant difference between both kinds of schools; and one study concluded that
private subsidized schools score lower than public schools. In addition, two out of the three
studies that made that distinction estimated that Catholic subsidized schools score higher than
public schools, while one study found no statistically significant difference between them.
Finally, six out of the seven studies that included comparisons with private non-subsidized
schools found that this type of schools score higher than public schools, while one of them found
no statistically significant difference between public and private non-subsidized schools.
Table 3. Main conclusion about private school effect on test-scores in ten studies about Chilean schools.
Study Private subsidized
Catholic subsidized
Private non-subsidized
Bravo et al., 1999 = + Gallegos, 2002 + Carnoy and McEwan, 2000 - + + Mizala and Romaguera, 1999 = + Sapelli, 2003 + Vegas, 2002 = + + McEwan, 2001 = = = Mizala and Romaguera, 2003 + + Sapelli and Vial, 2002 + Mizala et al., 2004 + +
Source: author elaboration. Key: + : positive effect; - : negative effect; = : no statistically significant difference. Reference category: public schools.
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As pointed out, the size of the estimated differences varies markedly; nevertheless, it is
also possible to identify some general trends to this respect. The estimated effect size of the
private subsidized schools on students’ test-scores seems to be extremely small in 4th grade
(about 0.05 S.D.). It is important to note that, when studies have found public schools’
advantage, the estimated effect size has had similar magnitude. The very large sample size used
in those studies is a key factor to explain why so small test-score differences are found
statistically significant. Unfortunately, the available evidence on 8th and 10th grades is not
sufficient to conclude about a general pattern on these grades. On the other hand, the estimated
effect size of private non-subsidized schools on students’ achievement seems to be larger than
that of private subsidized schools (about 0.4 S.D.), although the parameter estimates are, in this
case, less accurate.
Whether or not these general findings are valid conclusions depends on the
methodological strength of the available research. In the next section, I will analyze some key
limitations of the aforesaid studies.
IV. Methodological issues in the research on Chilean public/private schools comparisons.
As described, Chilean students are not randomly assigned to their schools. As a
consequence, there are at least three factors that complicate the comparisons between public and
private schools’ performance in Chile. Firstly, the supply of private schools is not evenly
distributed among geographical areas or among social classes: private schools tend to be situated
in urban areas, as well as to serve middle and middle-high (voucher schools) and high (non-
subsidized schools) social-class students. Some studies have attempted to use instrumental
variables to overcome this limitation, but their results are arguable, because of the difficulty to
find a valid instrument for the supply of private schools (see for example Gallegos 2004).
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Secondly, each type of schools operates with different levels of resources: non-subsidized
schools charge families very high tuitions; most voucher schools charge families with variable
tuitions; and, although most public schools do not charge tuition, they receive other kinds of
public transfers. Therefore, it is difficult to control for “school resources”. This is a key
challenge for those studies focused on the cost-effectiveness of private and public schools.
Nevertheless, for this analysis, oriented to determine whether there is a private school advantage,
not why this would be the case, this is not a relevant methodological problem.
Finally –and most importantly-, the selection processes by which Chilean students are
enrolled in schools is highly complex and there is little information about them. There are no
formal restrictions for parents to choose, and so, they can select a school based on their
preferences and/or their capacity to pay the tuition. However, private schools may select their
students. The process by which Chilean schools select the best students has not been studied in-
depth, even though its existence has been reliably documented. Gauri (1988) found that, in
Santiago, 82% of non-subsidized private school students, 37% of voucher school students, and
18% municipal school students had been compelled to take a selection test in order to be
admitted to their respective schools. As stated, Gauri also found that the probability for a given
student to study in a publicly funded school (be they private or public) situated in the upper third
of the student outcome distribution (as measured by SIMCE 1992) significantly increased when
they took an admission test. CIDE–La Tercera, in 2002, surveyed the principals of the schools
that obtained the highest SIMCE-2000 scores at national level; they found that 88% of non-
subsidized private schools, 66% of voucher schools and 22% of public schools systematically
used those compulsory admission tests. Those tests -focused on basic language, reasoning,
psychomotor and social skills- were applied even to pre-school applicants. In a 2003 nationwide
18
full-coverage survey to 10th graders’ parents2, 85% of the private non-subsidized, 73% of the
voucher, and 59% of the public schools’ respondents stated that their child was selected by the
school through an admission process that included some kind of examination or minimum
academic requirement. Finally, student selection is not limited to the school admission, but it is a
continuing process, which can operate at any time of the students’ schooling. In fact, many
private schools expel those students who have low academic achievement or behavioral
problems. In these cases, the students’ selection is not based on predicted but on demonstrated
student capacities.
Consequently, selection bias affects the estimates of the public/private test-scores gap.
This has been the most difficult challenge that researchers on the Chilean case have faced.
Selection bias is a crucial problem because unobserved students’ characteristics related to
students’ performance are highly correlated to the probability of attending a private/public
school. Thus, cognitive skills, motivation, and discipline are probably the most relevant
unobserved students’ characteristics affecting the private/public school effects estimates. This
implies an additional methodological problem: controlling for family characteristics is not
sufficient to control for selection bias. Unfortunately, there is no information about students’
initial characteristics or previous test scores. Researchers have tried to control this bias by
introducing different student-level (e.g. parents’ education), and school-level controls (e.g.
students’ SES), as well as by applying different methodological tools (e.g. instrumental
variables, statistical models for selection). The findings have been highly sensitive to the type of
approach used.
Additionally, it is relevant to take into account that selection bias is not only an
individual issue, but also a collective factor affecting students’ performance. In fact, the literature
2 Author’s calculation based on SIMCE 2003 data base.
19
about the Chilean case has increasingly recognized the potential role of peer-effects on students’
learning outcomes. Peer-effect is always present in school settings, but it is possible that, in
highly segregated environments, peer-effect might play an even more influential role on
students’ performance. Researchers also vary in the way they measure and model peer-effects
(compare, for example, Sapelli 2003 with McEwan 2001).
The appropriate level of data aggregation has also been a source of divergence among
authors; while some of them apply commune-level analysis, others prefer school-, classroom-,
and student-level analysis. The recent availability of student-level data permitted to create more
complex methodological models (phase two versus phase three studies). As known, models
estimated by using student-level outcomes are more rigorous, but less accurate in predicting test-
scores. Data aggregation is also an issue linked to the control variables. While some authors
think that controlling for student-level variables (if available) suffices, others think that school
compositional effects are relevant as well, so that they should be simultaneously included.
Finally, little attention has been given to the multilevel nature of the educational data (only
Mizala and Romaguera 2003, and Mizala et al. 2004 have applied multilevel analysis). To this
respect, there is little information about between-schools and within-schools test scores variation,
and how this issue is linked to the different types of schools and the segregation patterns of
students’ distribution in Chile.
The control variables introduced into the analysis is another source of disagreement. As
shown in table 1, studies differ considerably in both the quantity and the quality of the control
variables they use. In addition, researchers assess the same phenomenon in very different ways
and scales. For example, students’ characteristics at school level has been measured as the
percentage of students whose parents have attained primary education, the school mean of
20
parents’ education, or the standard deviation of parents’ education. Finally, structural variables
(geographical location or family income) have frequently been present in the studies, but cultural
variables (like peer-effects or books at home) have been almost absent.
Lastly, little attention has been given to the exploration of possible differential
effectiveness between private and public schools. For example, Mizala and Romaguera (2004)
found an interaction effect between students SES and the type of school they attend. Other
researchers have suggested that private school effect differs according to the level of urbanity of
the city. Unfortunately, there is little research on the interaction between type of school and
grade level, student’s initial ability, subject matters, etc.
In the next five sections, I will empirically demonstrate the consequences of some of the
mentioned methodological issues. Based on this analysis, I will conclude that even the answer to
the most basic question on this topic (what are the most effective types of schools) is extremely
sensitive to methodological decisions, and –consequently- the current literature does not provide
a defendable conclusion for the public/private debate on the Chilean case.
The data I analyzed was SIMCE 2003, 10th grade evaluation. This database contains
243,151 students, who are the 95% of the total 2003 Chilean student population of the
corresponding grade. The data includes 2,117 high schools, which are the 96% of the Chilean
high schools. Individual test scores on Mathematics and Language were analyzed, and several
student-level and school level control variables were included.
Table 4 provides a description of every variable used in the analysis. In order to illustrate
some of the aforementioned methodological disagreements and to analyze whether these choices
significantly affect the estimated private school effect, I conducted several regression analyses.
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Table 4. Descriptive statistics and variable definitions. Variable Definition
Student-level variables Mathematics Standardized IRT test score (S.D.=50; mean=250) Language Standardized IRT test score (S.D.=50; mean=250) Mother’s education Years of education of the student’s mother Father education Years of education of student’s father Family income Natural LOG of student’s family income Books Number of books at student’s home, scale ranging from 0 (no books) to 5 (more
than 200 books) Gender Dummy variable for student’s gender (omitted category: woman) Repetition Dummy variable indicating whether the student has repeated a grade Selection Dummy variable indicating whether the student was selected by the school through
an admission process (e.g. tests, grades requirements) School-level variables
Mean mothers’ education School average of years of education of students’ mothers S.D. mothers’ education School standard deviation of years of education of students’ mothers Mean parents’ education School average of years of education of both students’ parents Mean books at home School average of the individual variable “books at home” Selected students Percentage (divided by 100) of students who sere selected by the school through an
admission process School SES level Series of 5 dummy variables that classifies schools in Low/Middle-
Low/Middle/Middle-High/High students’ socioeconomic status (the classification is based on mother’s and father’s years of education, family income, and proportion of at-risk students in the school)
Quintile income Quintile classification of schools based on the school average of family income LOG income Natural LOG of the school average of student’s family income S.D. families’ income School standard deviation of the students’ family income Type of school Series of three dummy variables indicating whether the school is public (omitted
category), private voucher, or private non-subsidized V. How to control for parents’ education?
There is a wide academic agreement on the relevance of parents’ education as a predictor
of students’ test scores. Thus, to the extent that public and private schools serve students with
markedly different levels of parents’ education, research focused on the private/public test score
gap needs to introduce some kind of control for this variable. This consensus is also present in
the research on the Chilean private/public school gap: all studies synthesized in table 1 included
control information on parents’ education. Nevertheless, those studies vary noticeably in the way
22
this control is introduced into the regression models. In first place, some studies use a specific
measure of parents’ education (e.g. Sapelli and Vial 2002), while others use indexes and other
kinds of composite variables as general measures of school socio-economic status (e.g. Mizala
and Romaguera 1999). Below, I will explore some of the consequences of using these indexes. In
second place, studies also differ in the level of aggregation of parents’ education variables: while
some of them measure parents’ education at student level (e.g. McEwan 2001), others introduce
school-level measures into this aspect (e.g. Carnoy and McEwan 2000). Finally, studies diverge
in the specific parents’ education variables that are introduced.
In order to show how those differences may affect the estimates of the private/public test
score gap, table 5 shows several regression models with different options, all of them present in
the research on the Chilean private/public gap.
The six models were estimated by using the same student population. Model 1 is a base-
line model: private voucher schools score about 21 test-scores higher than public schools (0.42
S.D.), and private non-subsidized schools score about 88 points higher than public schools (1.76
S.D.). Models 2 and 3 use student-level parents’ education variables (mother’s and father’s years
of schooling). As expected, controlling for mother’s education –model 2- reduce the
private/public test score gap (to 0.27 S.D. and 1.17 S.D. respectively), nevertheless this gap
remains statistically significant. Moreover, when father’s education is added –model 3- the
private school advantage is reduced only slightly and remains statistically significant for both
kinds of private schools.
Models 4, 5, and 6 also control for parents’ education, but measured at school level.
Model 4 estimates the private/public gap by controlling for the school average of mothers’ years
of education. The results are very different from those obtained by models 2 and 3: students in
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both private voucher schools and private non-subsidized schools obtain lower test-scores than
students in public schools do. As shown, although small (0.04 S.D. in both cases), the size of the
gap is statistically significant. More recently, some researchers have introduced the heterogeneity
of the student population as a different control variable for parents’ education. Model 5 uses the
school standard deviation of the mothers’ years of education as the only control variable:
interestingly, this variable per se has almost no effect on the private/public school gap. In fact,
neither the estimates nor the R2 of model 1 are different from model 5, and this control variable
has a very little effect on students’ test scores (statistically significant only at 10% level).
Table 5. How to control for parents’ education? Regression models that describe the relationship between school type and students’ Mathematics achievement, controlling for different parents’ education variables. Omitted category: Public schools.
Dependent variable: 10th grade students’ Mathematics test score, SIMCE 2003
MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6
Private voucher 20.79*** 13.36*** 11.67*** -2.03*** 20.84*** -2.34***
Private non-subsidized 87.91*** 58.66*** 50.33*** -1.83** 88.16*** -3.20***
Mother’s education 4.53*** 3.03***
Father’s education 2.50***
School mean mothers’ education 13.91*** 13.94***
School SD mothers’ education 0.68~ -3.21***
Constant 230.9*** 189.6*** 179.8*** 104.4*** 228.8*** 114.4***
R2 0.14 0.21 0.23 0.30 0.14 0.30
N (students) 180, 388 180, 388 180, 388 180, 388 180, 388 180, 388Source: author elaboration. Key: ~p<.10; *p<.05; **p<.01; ***p<.001
Finally, model 6 shows that when the school mean of mothers’ education is present in the
model, the school standard deviation of mothers’ education effect changes its sign and increases
its effect (in other words, at similar levels of school mothers’ education, more homogeneous
schools tend to score higher than more heterogeneous schools). Model 6 also shows that when
24
both school-level controls are simultaneously introduced, the negative differences between
private voucher and private non-subsidized schools, on the one hand, and the public schools
slightly increase (to 0.05 S.D. and 0.06 S.D. respectively), on the other hand.
Summarizing: The size and –more importantly- the sign of the private/public school test-
score gap are significantly affected by the way parents’ education is included in the regression
models. When regression models control for parents’ education at student-level, students in
private schools score –on average- higher than students in public schools do; on the contrary,
when parents’ education is controlled at school-level, students in public schools tend to score
higher than students in private schools.
VI. How to control for schools’ socioeconomic status?
Researchers also broadly agree that the socioeconomic characteristics of the student
population at aggregated levels (classroom or –more frequently studied- school level) are
relevant factors that significantly affect student academic achievement -holding constant the
student own socioeconomic status. There are several hypotheses about how this relationship
works. Firstly, the socioeconomic status of the student population might affect teachers’
expectations and teaching practices; secondly, it might represent a measure of the available
material and symbolic resources at school level; and thirdly, it might be a measure of peer-effects
(students might benefit from their peers’ family resources and personal abilities through their
permanent daily interaction). As stated before, public and private schools differ in the
socioeconomic status of their student populations; therefore, it is necessary to control for
schools’ socioeconomic status in order to reduce the bias of the estimates of the private/public
schools gap. As shown in table 2, almost all of the analyzed studies include at least one control
variable on this aspect (Sapelli and Vial 2002 is an exception).
25
Nevertheless, those studies also differ in this respect. First, although the majority of the
studies use school level variables, McEwan (2001) use classroom-level socioeconomic status
variables. Second, studies differ in the control variables included: mothers’ education, fathers’
education, family income, educational spending, ethnic ascendance, or some combination of
them. Third, studies also vary in the type of measurement of school’s socioeconomic status.
These differences about how to control for schools’ socioeconomic status can affect the
comparisons between private and public schools very significantly. I will illustrate this assertion
by analyzing the impact of several alternative ways to control for schools’ socioeconomic status
(all of them present in the discussed literature) on the estimated private/public test-score gap.
After reading the previous analysis about how to control for parents’ education, one
might conclude that the only relevant difference among control variables is that between student
and school level variables. However, this would be a misleading conclusion. Table 6 shows ten
regression models containing exclusively school-level measurements on students’ socioeconomic
status. These models combine six different school-level controls3. Model 1 is the base-line
model4. All the eleven regression models were estimated by using the same student population.
Model 2 to model 7 were estimated by including –in addition to the private school
categories- a single control variable each time. The introduction of these control variables
significantly increases the capacity of the models to predict students’ test scores: the proportion
of the variation explained for the models ranges from 0.14 in the base line model to 0.25-0.29 in
models with a school SES control variable added. Based on the R2 statistics, the six control
3 I did not include the most used School SES index, which is the percentage of students with “at risk” (see table 2). This index is an administrative tool used by the Ministry of Education to distribute free lunch among schools. The index is mainly based on physical health indicators; it uses only information of the first grader students, and is a self-report of the schools. All private non-subsidized and many private voucher schools have no information on this index (researchers assign 0% to these schools). I think this index is not a good measure for research purposes. 4 The parameter estimates associated with the initial private/public test-scores gap differ slightly from those reported in model 1, table 3, because of differences in sample sizes.
26
variables have similar effects on the regression models; nevertheless, their consequences on the
estimates of the private/public test scores gap are markedly different.
Model 2 controls for schools’ socioeconomic status by using a Ministry of Education
classification, which sorts schools in five socioeconomic groups (in table 6 four dummies are
incorporated; the omitted category is “Low SES”). This classification –based on mother’s and
father’s years of education, family income, and proportion of at-risk students in the school-
correspond to those used by Mizala and Romaguera (1999), and Gallegos (2002), and it is
comparable to those used by Bravo et al. (1999), Mizala and Romaguera (2003), and Mizala et
al. (2004). As expected, the introduction of this control variable dramatically reduces the positive
differences between private voucher and private non-subsidized schools, over public schools (to
0.05 S.D and 0.08 S.D. respectively), although these differences remain statistically significant.
Models 3, 4, and 5 use the same information (family income), but measured in three
different scales at school level (all of them used in the Chilean research): income quintiles, the
natural logarithm of income, and the standard deviation of income. Although these three control
variables reduce the size of the private/public gap and this gap remains statistically significant in
the three analyzed models, the size of the estimated gap is noticeably different and –more
importantly- the effect of the control variable differs by type of private school. Thus, private
voucher schools advantage over public schools ranges from 0.01 S.D. in model 3 (statistically
significant only at 5% level) to 0.14 S.D. in model 5. On the other hand, the estimated positive
difference between private non-subsidized schools and public schools ranges from 0.17 S.D. in
model 4 to 0.83 S.D. in model 3. Finally, model 8 shows that when the absolute level of family
income is present (log school mean of family income), the introduction of a variability measure
27
(standard deviation of income; see for example Sapelli 2003) has almost no effect on the private
voucher effect estimates (compare with model 4).
Models 6 and 7 introduce control variables referred to cultural capital (as opposed to
economic capital, included in the three previous models): the school mean of parents’ years of
education (similar to Carnoy and McEwan 2000, Sapelli 2003, McEwan 2001), and the school
mean of books at students’ home (similar to McEwan 2001). When parents’ education is
incorporated as a control variable, both private voucher and private non-subsidized schools score
lower than public schools, by 0.01 S.D. (statistically significant at 5% level) and 0.04 S.D.
respectively. In turn, when books at home is added as a control, only private voucher students
have lower test scores than public students (0.03 S.D.), while private non-subsidized students
score higher than public students (0.07 S.D.). Finally, when both control variables are added
simultaneously (model 9), both types of private schools obtain statistically significant lower
students’ achievement than public schools, and these differences increase slightly (private
voucher students score 0.04 S.D. lower than public students, and private non-subsidized students
score 0.08 S.D. lower than public students).
28
Table 6. How to control for School SES? Regression models that describe the relationship between school type and students’ Mathematics achievement controlling for different school SES variables. Omitted category: Public schools.
Dependent variable: 10th grade students’ Mathematics test score, SIMCE 2003
MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6 MODEL 7 MODEL 8 MODEL 9 MODEL 10 MODEL 11
Private voucher 20.38*** 2.29*** 0.52* 1.33*** 6.78*** -0.53* -1.60*** 1.53*** -2.09*** -2.59*** -1.94***
Private non-subsidized 86.72*** 3.98*** 41.42*** 8.58*** 10.78***
-1.94*** 3.54*** 4.10*** -4.04*** -11.10*** -6.99***
Middle-Low SES 10.43*** -14.64***
Middle SES 49.94*** -9.29***
Middle-High SES 81.98*** -4.83***
High SES 105.82*** -6.43***
Quintile Sch. income 22.32***
Log sch. Fam. Incom. 37.54*** 30.16*** -7.99***
SD sch. Fam. Income 35.20*** 9.20*** 7.07***
Mean sch. parents’ ed 12.98*** 7.79*** 7.64*** 7.67***
Mean books at home 49.09*** 22.18*** 24.93*** 25.20***
Constant 230.0*** 215.1*** 186.1*** 227.9*** 184.1*** 109.8*** 148.5*** 216.3*** 121.1*** 127.2*** 108.4***
R2 0.14
0.27 0.27 0.27 0.25 0.29 0.29 0.27 0.30 0.31 0.30
N (students) 238,305 238,305 238,305 238,305 238,305 238,305 238,305 238,305 238,305 238,305 238,305Source: author elaboration. Key: ~p<.10; *p<.05; **p<.01; ***p<.001
29
The last two models evaluate the impact of using simultaneously economic and cultural
capital control variables. Interestingly, while the cultural variables’ parameter estimates are very
stable (compare models 9, 10, and 11), both the school SES groups and the family income
variable estimates change not only their sizes but also their signs (compare models 2 and 10, and
models 4 and 11, respectively). Compared to model 9, the estimated private voucher schools’
effect on models 10 and 11 remains almost the same in sign and magnitude. This is suggesting
that cultural differences –as opposed to economic differences- between the student populations
are the most relevant factors to explain the observed advantage of voucher schools over public
schools. Finally, models 10 and 11 shows that the public schools’ advantage over private non-
subsidized schools increases noticeably when both kinds of control variables are included
simultaneously.
Summarizing: Despite the generalized consensus on the importance of controlling for
schools’ socioeconomic status, there are relevant differences on the ways researchers attempt to
control for this factor. Moreover, this disagreement may have dramatic effects not only on the
size of the estimated private/public schools test-scores gap, but also on the sign of this gap.
Additionally, there is evidence suggesting that economic and cultural variables play different
roles in the public/private comparisons, depending on the kind of private schools under analysis.
VII. Student-level versus School-level control variables.
Until 1997, student level data (both test scores and background information) was not
available in Chile; consequently, all studies analyzed exclusively school level outcome and
predictor variables. It is widely accepted that more accurate estimates are obtained by using
student level test-scores information; consequently, since 1997, most research on the Chilean
case has analyzed –as an outcome variable- individual test scores (there are two exceptions:
30
Sapelli 2003, and Vegas 2002). Nevertheless, researchers still disagree in what is the best level
of aggregation of control variables: thus, some studies use exclusively school level controls (e.g.
Mizala et al. 2004), others use exclusively student level controls (e.g. Sapelli and Vial 2002), and
some use both (McEwan 2001). As previously, I will analyze several multiple regression models
(see table 7) to demonstrate the consequences of this disagreement on the estimates of the
private/public test score gap.
Models 1 to 4 in table 7 use Mathematics test score as the outcome variable, while
models 5 to 8 use Language test scores. Models 1 and 5 are baseline models5. It is interesting to
note that the initial gap between both private voucher and private non-subsidized schools, and
public schools is higher in Mathematics than in Language test scores (0.38 S.D. versus 0.28 S.D.
in voucher schools, and 1.61 S.D. versus 1.07 S.D. in non-subsidized schools respectively).
A set of relevant student-level control variables was added to models 2 and 6. These
variables were selected for theoretical and methodological reasons, based on the summarized
literature, being –as a group- the variables with the greatest capacity to explain students’ test
scores. The controls include some socioeconomic background factors (mother’s years of
education, father’s years of education, the log of family income, the quantity of books at
student’s home), some indirect measures of student cognitive abilities (whether the student has
previously repeated a grade, and whether the student was admitted by the school after a selection
process), and student’s gender. All control variable parameter estimates have the expected signs
in both models. The two measures of student’s ability have especially large effects. Students who
5 The parameter estimates associated with the initial private/public test-scores gap differ slightly from those reported in previous models because of differences in the sample sizes. The objective of these analyses is not to have the more accurate private/public school gap estimates, but to demonstrate the consequences of using different control variables on the parameter estimates. Consequently, it is more crucial to maintain coherence within every analysis than between analyses. Therefore, models included in the same table are always elaborated by using the same sample of students, which is composed of the total of students with available information. As shown, the sample size is always extremely large and the parameters are estimated with high levels of accuracy.
31
have previously repeated a grade score –on average- 0.35 S.D. and 0.27 S.D. lower than students
who have not repeated a grade, in Mathematics and Language respectively. In addition, students
who were selected by the schools score 0.36 S.D. (Mathematics) and 0.24 S.D. (Language)
higher –on average- than students who were not selected through those admission processes.
Chilean public schools include significantly more students who have repeated a grade and less
non-selected students than the two kinds of private schools. Student-level control variables
dramatically reduce the gap between private and public schools in both subject matters,
nevertheless this gap remains positive and statistically significant (private voucher schools: 0.12
S.D. and 0.08 S.D.; non-subsidized private schools: 0.6 S.D. and 0.29 S.D., in Mathematics and
Language respectively).
In contrast, models 3 and 7 in table 7, use exclusively school-level control variables.
These variables were selected following the same criteria as that explained for student-level
controls. The controls include some families’ socioeconomic variables (school mean of parents’
years of education, school standard deviation of mothers’ years of education, and school mean of
books at students’ home), and the percentage of students in the school who were admitted
through a selection process.
As suggested before, school control variables have a huge effect on the estimates of the
private/public test scores gap; in fact, after controlling for these school-level factors, public
school students score higher than private school students do, in both Mathematics and Language
(private voucher score 0.12 S.D. and 0.09 S.D. lower than public schools in Mathematics and
Language respectively. The corresponding “negative” gaps for non-subsidized private schools
are 0.09 S.D. and 0.19 S.D.).
32
Table 7. Comparing student versus school level controls. Regression models that describe the relationship between school type and students’ Mathematics achievement controlling for different students’ and schools’ variables. Omitted category: Public schools.
Dependent variable: 10th grade student’s test score, SIMCE 2003
MATHEMATICS LANGUAGE
MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6 MODEL 7 MODEL 8
Private voucher 18.91*** 6.17*** -6.15*** -6.04*** 14.21*** 4.21*** -4.27*** -3.81***
Private non-subsidized 80.50*** 30.15*** -4.27*** -6.00***
53.53*** 14.50*** -9.48*** -9.19***
Mother’s education 1.69*** 0.80*** 1.57*** 0.97***
Father’s education 1.33*** 0.48*** 1.16*** 0.59***
LOG Family income 9.67*** 2.56*** 5.98*** 1.21***
Books at home 6.42*** 4.49*** 5.57*** 4.27***
Gender (Male) 8.37*** 9.74*** -6.20*** -5.25***
Student repeated at least a grade -17.24*** -14.67*** -13.23*** -11.53***
Selected student 17.82*** 3.53*** 12.01*** 2.75***
School mean parents’ education 7.49*** 5.47*** 5.38*** 3.60***
School SD mothers’ education 2.54*** 2.18*** 3.65*** 3.10***
School mean books at home 18.13*** 14.79*** 15.12*** 10.32***
% Selected students in school 36.60*** 29.64*** 23.81*** 18.95***
Constant 238.5*** 197.0*** 103.7*** 122.4*** 248.8*** 219.7*** 144.1*** 164.8***
R2 0.14 0.29 0.31 0.35
0.09 0.24 0.24 0.28
N (students) 135,516 135,516 135,516 135,516 135,516 135,516 135,516 135,516Source: author elaboration. Key: ~p<.10; *p<.05; **p<.01; ***p<.001
33
Finally, models 4 and 8 include all control variables at both student and school level.
When both types of controls are simultaneously present, school-level predictors’ parameter
estimates tend to be more stable than student-level predictors are. Especially pronounced is the
decrease in both the “family income” and the “selected student” effects. As shown in table 7, the
estimates of the private/public test-score gap calculated by these two full-models are very similar
(in sign and size) to those estimated by using exclusively school-level control variables: public
schools’ students score higher than both private voucher (0.12 S.D. and 0.08 S.D) and private
non-subsidized students (0.12 S.D. and 0.18) in both Mathematics and Language respectively.
The R2 of these full-models is slightly larger than the R2 obtained by using only one-level control
variables, suggesting that both kinds of predictors (student and school variables) are needed to
better explain students’ test scores. As a final point, although the size of both the initial and final
estimated gaps between private and public schools are different in Mathematics and Language,
they follow the same global pattern.
To synthesize: The estimates of the Chilean public/private test-score gap may be
significantly affected by the level of aggregation of the control variables included in the
regression models. Specifically, by using student-level variables, although the private school
advantage is reduced, it remains positive and statistically significant; by contrast, including
school-level controls public schools score significantly higher than both kinds of private schools.
Additionally, although both individual and school level controls are needed to obtain more
precise estimates of the public/private test score gap, there is evidence suggesting that the
available school-level controls are better predictors of students’ test scores than the available
individual-level predictors. This last idea may be paradoxical: if student-level test scores are
being predicted, it is expected that student-level variables are the most relevant factors. In order
34
to better understand this puzzle, a multi-level regression analysis is needed: the next section will
explore this path.
VIII. Between versus within schools’ test-scores variation: a multilevel approach.
Multilevel models are recommended to study students’ achievement because the basic
regression assumption that residuals are independent is not satisfied in educational settings.
There are two key reasons for that: school effectiveness (students share common educational
experiences within their schools that significantly affect their learning outcomes), and school
segregation (students enrolled in the same school share unobserved previous characteristics
which are related to their academic performance).
As showed in table 2, only Mizala and Romaguera (2003) and Mizala et al. (2004) have
applied multilevel analysis to study Chilean test-scores. They were mainly interested in testing
the presence of interaction effects between type of schools and students’ SES, and students’
abilities. The purpose of this section is different and more basic: I want to suggest that the highly
stratified nature of the Chilean school system implies an additional challenge to study the
public/private test-score gap, and –in general- to predict student-level test scores.
Table 8 contains six multilevel regression models. As known, these models permit to
separate the total variation of students’ test scores in between-schools variation and within-
schools variation. The first key finding included in table 8 is that there is a very large between-
schools variation in the Chilean education: about half of the mathematics test-scores variation
and more than a third of the Language test-scores variation occur between schools. In order to
have a point of reference about this issue, international comparisons are helpful. PISA study
(OECD-UNESCO 2003) –an international survey on students’ performance in Language,
Mathematics, and Science- found that there is a negative relationship between the national level
35
of students’ learning outcomes and the national level of between-school variation. For example,
the three countries with the highest students’ performance Finland, Canada, and New-Zealand
had between-schools variation of 12.3%, 17.6%, and 16.2% respectively; United States had 29.6
between-schools variation; in that test, Chile had one of the highest levels of between-schools
variation: 56.7%. Chilean students’ learning outcomes are highly predictable depending on the
schools they attend.
That very large between-schools variation explains why school-level predictors are so
successful to estimate Chilean students’ test-scores. Thus, models 1 and 4 incorporate
exclusively school-level variables; as shown in table 8, these variables -as a group- explain 71%
of the Mathematics and 80% of the Language total variation between-schools. Obviously, school
level-predictors cannot explain within-schools variation (this might be the case if interaction
terms between school-level and individual-level predictors were included in the model).
Consistent with the previous analyses, when school-level predictors are included, public schools
score slightly higher than private subsidized schools.
In order to explain some of the within-school variation, models 2 and 5 use exclusively
student-level control variables (note that type of school is a school-level variable). As shown, all
these variables account for an extremely small proportion of the within-school variation: 3 % in
Mathematics and 5% in Language. In other words, once within-schools variation is distinguished
it becomes apparent that the available standardized information is very insufficient to understand
the individual learning outcome, in a context where schools are highly stratified. As previously
analyzed, private school advantage only remains when individual controls are included.
36
Table 8. Multilevel regression models. Relationship between school type and students’ Mathematics and Language achievement, controlling for different students’ and schools’ variables. Omitted category: Public schools.
Dependent variable: 10th grade student’s test score, SIMCE 2003:
MATHEMATICS LANGUAGE
Initial Between schools variation 49% 37%
Initial Within schools variation 51% 63%
MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6
Private voucher -3.1* 21.3*** -4.1** -1.7~ 14.6*** -2.4**
Private non-subsidized 4.1 61.2*** 2.0 -4.3** 36.8*** -4.1**
School mean parents’ education 4.9*** 4.0*** 4.2*** 3.0***
School mean books at home 17.3*** 12.5*** 15.0*** 8.7***
% Selected students in school 39.1*** 35.8*** 25.2*** 21.6***
Mother’s education 1.0*** 0.9*** 1.2*** 1.1***
LOG Family income 1.6*** 1.6*** 1.8*** 1.3***
Books at home 4.7*** 4.6*** 4.5*** 4.4***
Gender (Male) -12.1*** 10.9*** -4.6*** -4.5***
Student repeated at least a grade -12.0*** -10.0*** -9.9***
Percentage of explained variation:
Between Schools 71.4% 54.7% 73.6% 79.7% 65.3% 81.8%
Within Schools 0% 2.6% 2.6% 0% 4.8% 4.8%Source: author elaboration. Key: ~p<.10; *p<.05; **p<.01; ***p<.001
Finally, full models 3 and 6 include both student-level and school-level predictors. As
before, public schools score higher than private schools when both kinds of controls are added.
As expected, in these final models the proportion of explained within-school variation is the
same as in models 2 and 5; nevertheless, student-level variables also contribute to explain
between-school variation: the explained proportion of this source of variation is slightly higher
than in models 1 and 3. It is important to note that the proportion of explained variation is
relative to the respective proportion of explainable between and within school variations. To
have a general picture about how the total students’ test score variation is composed, graphs 2
37
(Mathematics) and 3 (Language) separate the total variations in their four components, and
estimate their proportion relative to the grand total.
Graph 2. Graph 3.
Multilevel model: explained vs. unexplained between and w ithin schools' Mathematics test-scores variation. SIMCE 2003.
Unexplained Between-schools
13%
Explained Between-schools
36%
Explained Within-schools
1%
Unexplained Within-schools
50%
Multilevel model: explained vs. unexplained between and w ithin schools' Language test-scores variation. SIMCE 2003.
Unexplained Within-schools
60%
Explained Within-schools
3%
Explained Between-schools
30%
Unexplained Between-schools
7%
IX. Identifying the effect of student selection during the schooling process.
As mentioned in section IV, none of the analyzed studies have considered the process of
student selection that occurs at school level during the schooling process. In fact, without
specific information, it is almost impossible to distinguish between a student who moved to a
different school because of some reasons unrelated with the school (e.g. family migration) and a
student who changed the school because of school related factors (e.g. school expelled him
because of his low academic performance, his parents took him to a new school because they
were unsatisfied with the former school). In this section, I will analyze some new information
related to this issue, which has been available just in recent years in Chile. In particular, I will
use the SIMCE-2002 database, which is the latest data for 4th-grade students’ performance.
The database SIMCE-2002 contains 274,864 fourth-grade students, who represent the
95% of the total 2002 Chilean student population of the corresponding grade. The data includes
6,145 schools. As in the previous analysis, individual test scores on Mathematics and Language
38
were analyzed (the findings in both subject matters were very similar, thus I present the
Mathematics results only), and several student-level and school level control variables were
included. Table 9 provides a description of the variables included in this analysis that were
absent in the previous analysis. Complementary information (based on a parents’ survey) about
student, family and school characteristics was available for 75% of the evaluated students.
Table 9. Variable definitions: 4th grade SIMCE 2002. All not included variables are defined as in table 4. Variable Definition
Student-level variable Parent’s expectation Parents’ expectation about the future student’s educational attainment, scale
ranging from 1 (4th grade) to 8 (graduate studies) School-level variables
% repitent students in school Percentage of students in the school who have repeated at least a grade
School expels repitent students School that (according to parents) expels students who repeat a grade
% students always in this school Percentage of students who have been in the same school since 1st grade
School mean years in this school School average of years that students have studied in this school
Table 10 shows that public and voucher school students differ markedly in almost all of
the variables associated with social class origin: students in voucher schools have –on average-
more educated parents, higher family income, more books at home, and parents with higher
expectations about their educational attainment. As a consequence, about 2 out of 3 public school
students attend a school with a student population classified as mainly low or middle-low SES;
while only 1 out of 5 voucher school students attends this kind of school. This segregated pattern
is not reduced to social-class dimensions. In fact, table 10 also shows that the proportion of
students who have repeated a grade in public schools is twice as large as that of voucher
schools6. This higher proportion of repitent students in public schools can be caused by lower
quality of teaching or higher promotion standards. There is no information about these
hypotheses. Nevertheless, in the Chilean context, it is misleading to infer about school quality
39
based on the current proportion of repitent students: some schools do not admit students who
have previously repeated a grade and others expel their students who are repeating the grade.
Table 10 shows that these practices of academic selection are more frequent in voucher schools
than in public schools: while 31% of the voucher school parents affirm that their school expels
repitent students, only 14% of the public school parents do so. Consequently, this practice
accounts for some proportion of the students who have moved to a different school since 1st
grade. As shown in table 10, about 3 out of 10 of the Chilean 4th-graders did not start their
primary education in their current school, proportion that is slightly higher in voucher than in
public schools.
Table 10. Comparing public and voucher school student population. 4th grade SIMCE-2002.
Public
N=135,969
Private voucher
N=99,708
Father’s education (scale) 1.96 (high-school drop-out) 2.78 (high-school)
Mother’s education (scale) 1.88 (high-school drop-out) 2.68 (high-school)
LOG Family income (original scale: 1 to 13) 0.52 0.87
Books at home 2.89 (from 11 to 20 books) 3.71 (from 21 to 50 books)
Parent’s expectation 5.06 (high-school) 5.97 (two-year College)
Low SES 14.96% 4.76%
Middle-Low SES 48.58% 14.37%
Middle SES 32.95% 49.54%
Middle-High / High SES 3.51% 30.28%
Student has not changed school 72.96% 67.38%
Student repeated at least a grade 14.68% 8.06%
School expels repitent students 13.55% 30.68% Source: author elaboration.
In order to know whether the comparatively higher exclusion of repitent students among
voucher schools explains part of the observed voucher school advantage, table 11 contains the
6 Note that table 10 shows repetition rate at the middle of 4th grade. According to the Chilean rules, students should not repeat 1st grade; thus at that point, students could have repeated only 2nd and 3rd grades.
40
parameter estimates of six multiple regression models that relate this information with students’
test scores. Baseline model 1 shows that the raw difference between public and voucher 4th-
grade Chilean students in Mathematics achievement is 0.38 S.D. (about 19 test-score points).
Model 2 includes some basic student and school characteristics as control variables. As known,
students who have repeated a grade score significantly lower than their non-repitent peers (0.43
S.D.); additionally –as expected- students who attend a school with higher proportion of repitent
students tend to score significantly lower: a positive difference of 10 percentage points in
repitent students in the school is associated with a negative difference of 0.07 S.D. in
Mathematics test-scores. Finally, schools that expel repitent students score about 0.21 S.D.
higher than schools that do not apply this selective policy. As shown in model 2, when all these
variables are controlled, there is no difference in Mathematics test score between public and
voucher school students, on average.
Models 3 and 4, and 5 and 6 in table 11, replicates this analysis for the sub-sample of
students who have always studied in the same school and for those students who have moved to
a different school, respectively. Although the general pattern is similar in both sub-samples, there
are some suggesting findings. First, the positive association between attending a selective school
that expels repitent students and test-scores is stronger for students who have changed school
than for students who have remained in the same school (0.30 vs. 0.16 S.D. respectively).
Second, conversely, the negative association between the percentage of repitent students in the
school and student’s test scores is stronger for students who have changed school than for
students who have remained in the same school. Both results point in the same direction:
students who change school seem to be more sensitive to the selective nature of their new school.
Note that this relation is consistent with two described market dynamics: schools selecting the
41
best students and families choosing more selective schools. As shown in table 11, while there is
not statistically significant difference between public and private school students within the
population who have not changed school (model 4), among students who have changed school,
students in public schools score significantly higher than their peers in voucher schools (0.04
S.D.). These results are also coherent with the hypothesis that attributes part of the voucher
schools’ advantage to their capacity to select and attract more skilled students.
Table 11. Identifying the effect of student selection during the schooling process. Relationship between school type and Mathematics achievement. Omitted category: Public schools.
Dependent variable: 4th grade students’ Mathematics test score, SIMCE 2002
All studentsStudents who have not
changed schoolStudents who have
changed school
MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6
Private voucher 18.83*** -0.31 20.55*** 0.28 16.34*** -1.75***
Private non-subsidized 61.11*** 7.33*** 62.47*** 8.22*** 55.99*** 4.51***
Student repeated at least a grade -21.66*** -23.77*** -19.30***
% repitent students in school -0.33*** -0.26*** -0.40***
School expels repitent students 10.54*** 7.82*** 14.74***
% students always in this school 15.99*** 32.11*** 0.06
School mean years in this school 1.30*** 0.05 2.90***
Gender (Male) 5.04*** 4.94*** 5.18***
Father’s education 1.46*** 1.55*** 1.46***
Mother’s education 2.31*** 2.38*** 2.17***
LOG Family income 2.61*** 2.87*** 1.96***
Books at home 1.75*** 1.70*** 1.86***
Parent’s expectation 6.30*** 6.41*** 6.13***
Low SES -10.61*** -11.99*** -9.06***
Middle-Low SES -12.70*** -12.84*** -12.30***
Middle SES -7.54*** -7.06*** -8.23***
Constant 238.2*** 188.2*** 239.9*** 180.7*** 234.8*** 192.6***
R2 0.10 0.25 0.11 0.26 0.07 0.25
N (students) 199,112 199,112 137,181 137,181 54,895 54,895Source: author elaboration. Key: ~p<.10; *p<.05; **p<.01; ***p<.001
42
Summarizing: A significant proportion of the Chilean schools continue the process of
selecting the most able students after the admission process, by, for example, expelling students
who repeat grade. These selective practices are associated with higher students’ test scores.
Some of this gap may be the result of peer-effect. There is evidence suggesting that the level of
school selectivity is more relevant for students who changed their original schools. Finally, part
of the voucher school advantage over the public schools –as measured by students’ academic
performance- is associated with these selectivity practices applied during the schooling process.
Conclusions.
Chile is a paradigmatic case of school choice and market oriented education: private and
public schools openly compete for capturing both family preferences and public subsidies.
Consequently, there is a considerable amount of research on the systemic effects of school
choice, and on the comparison between private and public students’ learning outcomes.
Unfortunately, several data limitations and methodological divergences among researchers have
affected the validity of the findings. As a result, previous research has obtained noticeably
contrasting conclusions about these issues. This paper identified four main sources of threat to
the validity of this research. The most important one is selection bias: the parents’ school-choice
process and the schools’ students-selection process introduce severe biases that researchers have
not been able to overcome. Additionally, what the appropriate level of data aggregation and data
analysis should be, what the relevant control variables to include in the comparisons should be,
what the consequences of the multilevel nature of education are, and what kinds of interaction
effects are present, are four supplementary sources of divergences among researchers.
43
By conducting exemplary data analyses, this paper demonstrated that the discussed
methodological issues can affect not only the size but also the sign of the estimated
private/public school effect on students’ academic achievement. Based on those analyses, I
conclude that the answer to the question about whether private or public schools are the most
effective in Chile is extremely sensitive to the methodological decisions made by the researchers.
Nevertheless, my own most precise estimates (see model 4 in table 7 and model 2 in table 11)
indicate that voucher schools are not more effective than public schools, and that they may be
less effective. Although those results were based on OLS estimates, not on quasi-experimental
designs, they introduced –for the first time in the analysis about the Chilean case- some measures
of the sorting process (in both the admission and the schooling processes), in my opinion, the
most relevant source of bias in previous research comparing public and voucher schools’
effectiveness. In fact, as hypothesized, both sorting mechanisms –whether a student was
admitted by the school through a selection process and whether the school rejects repitent
students- were significant predictors of the students’ test scores and were more disseminated
among voucher schools, accounting for some proportion of their observed advantage.
The reasons why voucher schools are not more effective than public schools in Chile are
beyond the scope of this study. One hypothesis is that, although in the past voucher schools were
more effective, public schools have reacted to the competition by improving their quality, and –
consequently- they closed the previous gap. As explained, there is little –if any- evidence to
support this optimistic hypothesis. An alternative hypothesis is that the institutional design of the
Chilean educational system has structural deficiencies, because schools can improve their market
position without improving the quality of their educational service.
44
The theory underlying this last hypothesis is as follow: The competition among schools
have not caused an improvement of educational quality, because schools (mainly the private
ones) have competed to attract the best students, rather than to increase the value-added to their
educational service. In this “zero-sum game”, the increments of some schools are annulled by the
decreases of others. Additionally, parents’ choices have not necessarily been oriented by
indicators of educational quality (because of information deficiencies and parents’ use of non-
academic criteria). As a consequence, schools have not received signals towards the educational
improvement from their customers, but towards the use of status symbols and social segregation.
Finally, deregulation and free competition have also tended to increase school segregation
through a process of mutual reinforcement between schools (supply side) and families (demand
side). From the supply side, schools have responded to the incentives of the competence, by
distorting the indicators of quality by rejecting students who are less likely to succeed in school
(applying admissions tests), and those who have demonstrated low capacities (expelling them).
These sorting and re-sorting mechanisms, massively applied for two decades, have shaped the
Chilean school system in its current segregated features. From the demand point of view, middle
and high social-class families have found that schools’ social and academic selectivity provide
them a large profit of “peer effects” within schools: given the high correlation between learning
outcomes and student’s social background, when Chilean families aim at social selectivity, they
obtain academic selectivity by extension.
As discussed, the current evidence provides partial support to the latter interpretation. The
main findings of this paper are also coherent with this hypothesis. Of course, if this reasoning is
correct, it does not imply that private schools cannot be a positive partner of Chilean public
education, but it does suggest that, in order to contribute to improve educational quality and
45
equity, voucher programs must be carefully designed. In this sense, the Chilean experience
provides some relevant lessons.
Firstly, every school that receives public resources should guarantee non-discrimination
to applicant students; thus, admission tests, academic and economic requirements, and other
forms of sorting should be prohibited. Secondly, bad information can be as harmful as no-
information: if the evaluation system does not estimate the actual academic value-added by the
school, it can orient the families and the policies to a wrong direction. Thirdly, funding system,
public policies and other institutional regulations should recognize that some students (e.g. low-
income students, ethnic minorities) are more challenging to educate than others. This implies that
schools that serve more disadvantaged students should receive more resources. Fourthly, it is
overoptimistic to expect that families’ demand will improve educational quality by itself;
complementarily, some public incentives, pressures, and regulations should also be in place in
order to push schools toward genuine processes of school improvement. Finally, Chilean voucher
schools include for-profit and nonprofit institutions, and the current system does not make this
distinction at all. The legislation and educational policies should differentiate these two kinds of
schools, in order to limit the access to public funded school improvement programs and different
public resources (texts, computers, teaching materials, teacher training, etc.) to non-profit
institutions only. This distinction should be known by parents when they are choosing the school
for their children.
46
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