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Preliminary draft Please do not cite without permission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.

3

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

13

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.

16

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).

17

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.

21

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

23

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.

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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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