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7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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Documento de TrabajoISSN (edicin impresa) 0716-7334
ISSN (edicin electrnica) 0717-7593
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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Versin impresa
Versin electrnica
PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE
INSTITUTO DE ECONOMIA
Oficina de Publicaciones
Casilla 76, Correo 17, Santiagowww.economia.puc.cl
ON THE DETERMINANTS ANDIMPLICATIONS OF SCHOOL CHOICE:
SEMI-STRUCTURAL SIMULATIONS FOR CHILE
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INDEX
ABSTRACT
1. INTRODUCTION
2. THE CHILEAN SYSTEM
3. LITERATURE AND RESULTS
4. SIMULATIONS
5. CONCLUSIONS
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On the Determinants and Implications of School Choice: Semi-Structura
for Chile*
Francisco A. Gallego
Pontificia Universidad Catlica de Chile
Andrs E. Hernando
Harvard University
This Version: July 15, 2008
First Version: February 27, 2008
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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1. Introduction
School choice is one of the most debated policies aimed at increasing stud
different countries. Proponents argue that school choice may create incentiv
to increase productivity, offer a product closer to student demands, and exp
set for poor students. Opponents, in contrast, argue that school choice
segregation, decrease school quality to poor students by moving good p
schools, and produce competition in irrelevant attributes if parents do n
education outcomes. Most literature use reduced form methods to study the
instance, some papers analyze the effect of inter-school competition on t
other measures finding mixed evidence.1 Other papers study the process
parents using a variety of methods. This paper uses semi-structural estima
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of relatively low transportation costs,3 and high entry of voucher schools
data for 2002, so it corresponds to a period in which the choice system
consolidated (for instance, information on test scores is available, at least i
since the mid 1990s and the bulk of school entry already took place). We
structural estimates from Gallego and Hernando (2008), which follow th
horizontal differentiation in the attribute space developed by Berry et al.
among others4. We model school choice as a discrete process in which p
schools considering attributes such as characteristics of peers (mean
deviation of income and mother education at the school level), indi
development of cognitive abilities (test scores), indicators of the develop
cognitive skills (discipline and the teaching of religious values), proxies for
costs (distance from school to the centroid of the county in which the stude
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similar to structural estimates and moreover we find that students r
differences in quality in urban markets with more competition, as expected.
The estimates of deep parameters allow us to implement a number
related to the effect of different policies on consumers welfare. The
simulations we pursue is related to the value of school choice. i.e., how
parents would lose were the degree of choice limited in different dim
implement three counterfactuals. In the first, keeping the current supp
constant, we compare consumer welfare in the current system with the
system in which students are randomly allocated to schools in the county th
they do not have to pay school fees. In the second simulation, we decrease
schools so as to allow only 15% of students in each county to attend vou
We assign these students randomly among voucher and public schools we
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system in Chile seems to be driven mainly by demand factors. The potenti
fees and the use of lotteries in the context of free application to all schoo
to decrease segregation in a significant way.
To our knowledge, the methodology applied in this paper, by com
structural estimates of preferences and policy simulations, is new in the
tries to assess in a quantitative way the effects of school choice on student
paper presents the effects of several features of school choice on welfa
multi-dimensional approach (and not just effects on one dimension) and
effects in money equivalents. However, there are some limitations to our a
we do not explicitly model potential direct effects of school choice on
attributes (such as effects of inter-school competition on school quality),
require an estimation of the supply side equations which (due to data pro
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2. The Chilean system8
Before 1981, public schools in Chile depended from the central governmen
funds independently of the number of students that actually attended the s
could choose to opt out from the public system and have two main alte
private schools that charged high fees and free private schools. These p
received some discretional funds from the government that covered a
operating costs (equivalent to 50% of the costs of similar public schools)
government implemented a reform that included: (i) transferring public sch
central to the local governments (municipalities); (ii) giving total freedom
apply to any free private and public school that would receive a per-st
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schools are operated by non-for-profit organizations that raise addition
relatively competitive market for donations to be spent in schools (Aedo, 19
In contrast, public schools work under "softer" budget constraints: when n
schools that are losing students receive transfers, above and beyond the vo
their expenses (Gallego, 2006; Sapelli, 2003). In addition, while vouchers
public intervention in the K-12 sector during the 1980s, governments dur
channeled additional resources to "vulnerable" schools and increased
spending. In addition, some programs operate more as supply subsidies t
therefore, limit the mobility of students across schools. For instance, Sape
(2000) present evidence that free-lunch public programs tend to decrease m
schools because poor students cannot move with their free lunches to
Therefore, these programs may tend to actually create segregation of po
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schools, selection for academic purposes covers less than 50% of voucher s
the same time, public schools do have selection processes).
Two recent surveys applied to representative samples find interes
terms of the selection process. First, more than 90% of parents say that
attend the school they wanted them to attend (the CEP survey is the survey
reputation in Chile). Second, the mean number of applications that parents
1.1 (which increases to about 1.25 in Santiago) and just about 4% of pa
children were not accepted in a school they applied to (results from Galleg
Certainly, survey data have important problems, but the order of magn
results suggest that the observed stratification of the Chilean vo
(documented in the paper by Hsieh and Urquiola, 2006) may be a conseq
selection or selection from the demand side, rather than from the supply sid
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tend to value test scores more. The authors also find a lot of heterogeneity
after controlling for observables.
Bayer, Ferreira, and McMillan (2003) exploit residential choices by
San Francisco Bay Area to estimate the determinants of the demand for
using a household location model in the spirit of Berry, Levinsohn, and
The household location decision depends on a vector of neighborhood char
they allow preferences to be heterogeneous depending on the hou
characteristics. Their main results imply a relatively small willingness to p
quality of about $26 in monthly rent, for a one standard deviation incre
quality and a lot of heterogeneity in preferences.
In terms of papers that study school choice in Chile, while Gallego
(2008) is the only paper that uses structural econometric methods, othe
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Second, our estimates of preferences come from a setup in which the
system operates under a choice system which has been in place for a long p
This allows us to avoid biases created by contexts where choices may no
proof (as in the papers by Staiger et al., 2006 and Elacqua et al., 2006) an
not able to really estimate preference parameters.
In concrete, we model the school choice of a household as a discre
single school. The utility function specification is based on the random
developed by McFadden (1974) and the specification of Berry, Levinso
(2004), which includes choice-specific unobservable characteristics. We p
description of the implementation of this idea in the context of school ch
(Gallego and Hernando, 2008 present a more detailed description).
Let Xj={x j1 , x j2 , . . ., x jK} represent the set of observable
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K
=k
jjkkj +x=1
we get
rk
ij
r
ijirrijjkirrkjij +dz+d+xz+=u ,
Households are assumed to choose the school that maximizes (5
since j is known to both, the school owner (or administrator) and the h
likely to be correlated with school characteristics, particularly, with its co-
is the reason why we cannot estimate (4) directly and obtain consistent es
two stages procedure is needed.
Gallego and Hernando (2008) apply their procedure to fourth-grad
schools in Santiago in 2002. We use data on students' educational ou
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include a dummy that takes a value of 1 if the school is a single-gender
dummy variable that takes a value of 1 if the school participates in a gover
extended-time program.
We use information on the distance from each school to the centroid
in which they live. This variable measures the linear distance of each scho
populated place in a county.13 Therefore, this variable is an imperfect
distance of the place where a student lives to all the schools. In addition, we
the distance from each school to a subway station and, using this inform
dummy that takes a value of 1 if the school is less than 500 meters fr
station.14
The BLP framework may not lend itself readily for application
choice systems: For example, schools may not be able to significantly
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assigned to schools using lotteries).15 If, on the contrary, household's do n
what school their children must attend but also the provision of some
relevant to the child educational process (e.g. homework support, in-home
then the coefficients of the indirect utility function are complicated
preferences and technological parameters that do not reveal preferences.
specially affects the coefficients regarding school's test scores and copa
worse, the direction of the specific biases is not obvious).16 Notice, neverth
problem only accrues when household inputs are determined simultaneo
school decision. If all of them are predetermined (like pre-school level of
attendance to a pre-school institution, for example) then our estimates are s
our simulations are valid.
The above problem may be solved by micro-funding the utility function
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to do better in school tend to travel more and are willing to pay more for sch
interesting result is that parents of female students tend to put more w
cognitive skills than on cognitive skills and value more a single-sex schoo
of male students.
As a benchmark we estimate a reduced form model in which
decision of a student to attend a school not located in her home county.
regressors the mean and standard deviation of test scores in the home a
county, and a vector of socioeconomic controls (dummies for mothers edu
of household income, and household size). We run probit regressions for
sample of 4th graders in 2002 that took the SIMCE test and for sub-sampl
urban/rural areas, areas with and low inter-school competition, and the Met
of Santiago. Table 2 presents standardized marginal effects of each var
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the copayment in the utility function for each consumer. These numbers allo
both changes in total welfare and the distribution of these changes.
The second metric we use is the effect of each policy change on the
the school system. In order to implement this idea we use the Duncan dissi
(Duncan and Duncan, 1955). This index is defined as follows:
where i represents schools, Vand NVare the number of vulnerable and n
students respectively17. The index can take values in the [0,1] interval, w
complete desegregation and 1 complete segregation. The index can be inte
fraction of vulnerable students that would have to switch schools to ach
distribution in Santiago (Valenzuela et al., 2008). This index has b
I
=i
ii ,NV
NV
V
V=D
12
1
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specific and homogeneous groups of students find that they cannot exi
system they may leave the market. Since they are very attractive for the g
designed to serve and (probably) very unattractive for the majority of the h
effect of those schools existing would be to decrease the utility of some ind
increasing that of the majority. A similar (with reverse effects) argument m
bad quality schools find an incentive to stay longer in the market know
while at least, they will still receive students coming from the lottery system
In our first scenario, students are assigned uniformly to all the availa
the county and the government covers any co-payments. As a result all
county have the same number of students, segregation is (by design)
geographic segregation of the city and all schools in a county have the sa
SES index distributions. The monthly government cost of this policy i
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co-payments to schools) and changes in other attributes of the schools the
to in equilibrium.
Tables 3 and 4 presents a summary of results from our simulati
shows the distribution of the difference in welfare between the choice (co
and each of the specified scenarios. The message of Figure 2 is clear: cho
although not all the individuals benefit from it (and not all those who
equally).23
The first panel in Figure 2 shows the gain for households in going f
lottery with lump sum taxes to a choice system with copayments. As repor
the average student gains the equivalent to US$4.10 (0.9% of the househo
about 14% of the value of the voucher) a month.24 As a whole all students
surplus in US$3.38M (1.27% of total income). Nevertheless, as it is clear fr
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59.7% of the individuals would actually prefer the lottery to the choice
average among them loses the equivalent to US$ 5.0 (4.1% of the househo
month by moving to the choice system. The result that the gains from choi
are much moderated is due to the fact that bigger schools tend to be more p
smaller schools and therefore a lottery that allocates more students to bigg
lower welfare losses than a lottery that do not considers the size of the schoo
Panels 3 and 4 show the case when students do not have to pay by
the form of co-payments or lump sum taxes. Not surprisingly comparisons
more favorable to the choice system because students do not have to foo
which are in average above lump sum taxes (the average student has to
month in addition). In Panel 3, 36.8% of the students would prefer the lo
choice system. The average student gains the equivalent to US$4.34 a mont
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in the same extent. We know try to answer the obvious question, who doe
the school choice system?
To try to address this question, we calculated the results shown in
and Table 4 where we decompose the welfare gains of choice respect t
alternative systems by the sample income quintile, mother education, and
each student.26We start analyzing scenarios 1 and 3. In scenario 1 only stud
first income lose from moving to the choice alternative. In turn, as suggeste
scenario 3, this is due to the fact that students have to pay fees that are hig
than lump sum taxes. In all the other groups, students benefit from movin
alternative with and without copayments, with students with higher income
most from school choice. For instance, while students in the top income
choice in US$19 a month (2% of their household income), students in the
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good school opportunities. Therefore, this scenario, in particular highlights
which expanding choice disproportionally benefits the poor.
To analyze the effects of different restrictions to choice on se
compute the Duncan segregation index at the city level under two differ
lotteries (as previously discussed, by construction a lottery without fees
same segregation level as the county distribution itself) and county-restricte
In general, as expected from the results presented above school c
increase segregation in a significant way. For instance, while with lotteri
index reaches a level of 0.18 (similar to the geographic segregation of
Santiago), allowing unrestricted choice increases the segregation level to ab
shows the fact that school choice from the demand side increase
significantly. Interestingly, however, restricting geographic mobility o
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as in the previous scenarios, uniformly and in proportion to their current re
addition, we assume all schools are free in order to isolate the supply effect
Results are presented in the first two columns of Table 5, Table 6,
This exercise suggests that the increase number of voucher schools
consumers in an average of $7 a month, in the uniform lottery. Interestingl
time, not all the students benefit from this increase in supply of schools,
students decrease their welfare in an equivalent to $1.4 a month. The
increases by about of US$5.8M. All these values decrease in the case of th
lottery, mimicking our previous results.
In terms of the effects on different groups. In this case, compensati
positive for all the subgroups of the population, but larger for higher
educated, and non-vulnerable groups. This is expected, as voucher school
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decrease in school revenue on school quality (or that the government fi
payments) and a situation in which school quality decreases as a conseque
in the funds that the school receives using estimates of school productiv
with SES from Gallego (2006).
We make two additional assumptions related to the potential allocati
schools that face surplus demand. First, we assume the school capacity to b
,
where is the ceiling function (that rounds up a number to the next wh
the number is not already an integer), andEis school's enrollment. This is
that, by regulation, schools must have at most 45 students in their class
4545
E=C
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Most interestingly, distributional effects of this policy suggest that middle
are those that tend to benefit the most from this policy. Both students in t
poorest groups tend to benefit, but by less than middle class students. To u
result it is worth noting, first, that vulnerable students do not tend to pay c
the current system, so they do not benefit directly from the abolition of fe
the absence of fees, rich students tend to travel more than before to get to b
Finally, fees in Chile are relatively low (the mean copayment among studen
top ups is close to $11) so the decrease in quality should not be signific
context it seems that the middle class benefits the more from the aboliti
they pay higher top ups than poor students and their marginal utility of inc
than for rich students.
In terms of the effects on segregation, our model predicts that the ab
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differentiated voucher.) As in previous simulations we use estimates of p
school expenditure from Gallego (2006) that allows the effect to vary b
education groups. We further assume that all the extra resources wil
increasing test scores uniformly among both vulnerable and non-vulnerab
the schooli.e., there is an externality from beneficiaries to non-beneficiar
Tables 5 and 6 and Figure 8 present results of these simulations
effect is positive, with the average student gaining an equivalent to $2.2
increase of social value of about $1.8M a month. There is however some he
this result. Vulnerable students (who are direct beneficiaries of the sp
benefit the more, with an average increase in welfare of between $8 and $9,
the potential impact on quality. Non-vulnerable students benefit by a small
scores increase or lose welfare by a small amount if test scores do not in
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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To the best of our knowledge, the methodology applied in t
combining structural estimates of preferences and policy simulations,
literature that tries to assess in a quantitative way the effects of school cho
welfare. This paper presents the effects of several features of school choice
using a multi-dimensional approach (and not just effects on one dimension)
the effects to monetary equivalents. However, there are some limitations t
that should be addressed in future research. First, we do not model explic
side. For instance, we do not study directly effects of school choice on
attributes (such as effects of inter-school competition on school quality
consider a static model in which students and schools do not have e
decisions from the market. Finally, we assume that we are estimatin
preferences of consumers, it may well be the case that (due for instance to
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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Elacqua, G., M. Schneider, & J. Buckley School (2006) School choice in Chile: Is it class Journal of Policy Analysis and Management Vol. 25, Issue 3.
Engel, E., A. Galetovic, and C. Raddatz (1999) Reforma Tributaria y Distribucin del I
Serie Economia 40, CEA-University of Chile.Gallego, F. (2006) Voucher-School Competition, Incentives, and Outcomes: EvidenMimeo, Catholic University of Chile.
Gallego, F. (2008) Comment to P. McEwan, M. Urquiola, and E. Vegas.Economia, forthcGallego, F. and A. Hernando (2008) School Choice in Chile: Looking at the Deman
Catholic University of Chile.Gallego, F., F. Lagos, P. Marshall, Y. Stekel (2008). Anlisis del Impacto del Siste
Evaluacin de Desempeo a Nivel de la Comunidad Escolar, Mimeo, Catholic UniveGallego, F. and C. Sapelli (2007). El esquema de financiamiento de la educaci
evaluacin. Revista de Pensamiento Educativo 40 (1): 263-284.Hastings, J., T. Kane, and D. Staiger (2005) Parental Preferences and School Competitio
a Public School Choice Program. Mimeo, Yale University.Hastings, J., R. Van Weelden, and J. Weinstein (2007) Preferences, Information, and
Behavior in Public School Choice. NBER Working Paper 12995.Hastings, J. and J. Weinstein (2007) No Child Left Behind: Estimating the Impact on Ch
Outcomes, NBER Working Paper No. 13009, 2007.Hoxby, C. (2000). Does Competition Among Public Schools Benefit Students and Taxpa
Economic Review 90 (5): 1209-1238.Hsieh C and M Urquiola (2006) When school compete how do they compete? An ass
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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Estimation Technique Student Level Variables
Coeff. Std. Err. Z-stat C
Inc. per Cap. 0.0190 0.0107 1.78 Inc. per Cap. Inc. per Cap. (x1,000)
Moth. Educ. -0.2261 0.1509 -1.50 Moth. Educ.
Simce 2.6823 0.7673 3.50 Simce
Copayment -0.2212 0.0276 -8.02 Rel. Values
Discipline 0.7380 0.1669 4.42 Subway
Rel. Val ues -1.5453 0.4596 -3.36 Std. Dev. Incc
J EC 0.0138 0.1082 0.13 Std. Dev. Edm
Single Gender -1.2079 0.2495 -4.84 Distance
Subway 0.7594 0.2042 3.72
Std. Dev. Incc -0.0042 0.0044 -0.96 Moth. Educ. Moth. Educ.
Std. Dev. Edm -0.2307 0.1197 -1.93 Simce
Di st anc e -1.084 0.004 -269.339 Std. Dev. Incc
Std. Dev. Edm
Distance
Mother Age Inc. per Cap.
Moth. Educ.
Copayment
Std. Dev. Incc
Std. Dev. Edm
Distance
Table 1: Semi-Structural Estimates, Gallego and Hernando (2008
OLS
Panel A: Main effects, IV regression Panel B: Interaction Effe
School Le
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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(1) (2) (3) (4) (5) (6)
-0.236*** -0.249*** 0.016 -0.289*** 0.077*** -0.303***
0.034*** 0.023*** -0.003 0.039*** -0.048*** 0.032***
0.195*** 0.202*** -0.045* 0.249*** -0.048*** 0.253***
-0.023*** -0.015*** 0.011 -0.016*** 0.047*** -0.015***
Mother Edu Primary 0.013*** 0.012*** 0.028*** 0.01*** 0 0.009***
-0.002 -0.004 0.009* -0.002 -0.004 -0.003
Table 2: Probit Regressions, Standarized marg
Probability of Attending Scho
Average test score indestination county
S.D of test score in
destination county
Average test score in
home county
S.D of test score in
home county
Higher
Independent Variable
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Scenario
1 4.10 -0.1% 40.2% -3.98 -2 0.94 -1.8% 59.7% -5.04 -
3 4.34 0.9% 36.8% -2.12 -
4 1.69 -0.6% 63.5% -3.12 -
5 43.87 26.7% 11.8% -4.98 -
Scenario
1 3.38 1.3% -1.3 -2.3%
2 0.78 0.3% -2.5 -2.6%
3 3.58 1.3% -0.6 -1.0%
4 1.39 0.5% -1.6 -1.4%
5 36.20 13.6% -0.5 -1.3% 3
Table 3B: Value of Choice, total benefits, under different scenarios (in US$
Total benefit Total benefit over
Total income
Benefits if CV
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ScenarioCategories
Mother's education level
1 2.15 0.2% -0.81 -2.1% 0.48
2 1.84 -0.9% -1.28 -2.6% 2.31
3 2.75 -0.5% -0.45 -2.0% 3.71
4 8.42 0.7% 5.04 -0.4% 11.80
5 10.89 0.9% 7.47 -0.1% 13.59
6 22.24 2.1% 18.49 1.4% 22.30
7 40.51 3.4% 36.41 2.8% 40.23
Quintile of Income
1 -2.28 -3.2% -4.99 -6.8% 0.35
2 0.25 -0.3% -2.73 -1.9% 0.83
3 0.60 0.1% -2.46 -1.2% 1.59
4 3.45 0.8% 0.18 -0.2% 3.79
5 19.49 2.1% 15.66 1.5% 16.05
Student's vulnerability
1 2 3
Table 4: Value of choice, average compensating variation, by mother's education
CV CV/Income CV CV/Income CV
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Simulation
Uniform lottery Proportional lottery No effects on SIMCE Low value
Scenario 1 2 1
Compensating Variation 7.01 5.66 10.84 8CV/Income 2.3% 1.5% 6.0% 4.
negative 14.3% 28.3% 0.3% 0.
CV if CV0 2.8% 2.4% 6.0% 4.
Simulationcv1 cv2 No effects on SIMCE Low value
Scenario 1 2 1
Total benefit 5.78 4.67 8.95 6
Total benefit over Total income 0.02 0.02 0.03 0
Benefits if CV0 2.5% 2.3% 3.4% 2.
Table 5B: Value of Choice, total benefits, under different sc
Decrease in Voucher Schools Enrollment No
Table 5A: Value of Choice, average student compensating vari
Decrease in Voucher Schools Enrollment No
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Scenario
Categories
Mother's education level
1 9.57 7.4% 7.24 5.7% 7.73 6.0%
2 11.34 6.3% 8.49 4.8% 9.08 5.1%
3 11.45 5.7% 8.51 4.3% 9.12 4.5%
4 11.35 4.0% 8.27 3.0% 8.91 3.2%
5 11.31 3.8% 8.26 2.8% 8.89 3.0%
6 11.16 2.4% 8.11 1.8% 8.74 1.9%
7 12.29 2.4% 9.37 1.8% 9.97 1.9%
Quintile income
1 9.73 13.1% 7.43 10.0% 7.91 10.7%
2 10.66 5.9% 8.06 4.5% 8.60 4.8%
3 11.28 4.9% 8.48 3.7% 9.06 3.9%4 11.55 3.5% 8.57 2.6% 9.19 2.8%
5 11.26 1.9% 8.08 1.4% 8.74 1.5%
Student's vulnerability
0 11.31 5.2% 8.40 3.9% 9.00 4.2%
1 9.30 8.6% 7.07 6.6% 7.54 7.0%
CV CV/Income CV CV/Income
1 2 3
Table 6B: Value of choice, average compensating variation, by categories
Table 6A: Value of choice, average compensating variation, by categories
CV CV/Income CV CV/Income CV CV/Income
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0
10
20
30
P
ercent
0 5 10 15Avg. Income
0
5
10
15
20
P
ercent
100 50 0Avg. Mother Ed
25 2
5
Figure 1: Average Marginal Effects by School
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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0
5
10
15
20
P
ercent
0 5 10 15 20
JEC
0
5
10
15
20
25
P
ercent
400 300 200 Single Gend
25
30
Figure 1: Average Marginal Effects by School
1Value of choice (with fees) v . uniform lottery (lumpsum taxes)
ds 1
Value of choice (with fees) v. pro
dsFigure 2
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25 20 15 10 5 0 5 10 150
0.2
0.4
0.6
0.8
Value in 2002 $
Proportion
ofHousehold
25 20 15 100
0.2
0.4
0.6
0.8
Value in
Proportion
ofHousehold
20 10 0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1Value of choice (no fees) v. uniform lottery (no taxes)
Value in 2002 $
Proportion
ofHouseholds
20 10 0 100
0.2
0.4
0.6
0.8
1Value of choice (no fees) v.
Value in
Proportion
ofHouseholds
40 20 0 20 40 60 80 100 1200
0.2
0.4
0.6
0.8
1Value of choice (with fees) v. constrained choice (with fees)
Value in 2002 $
Proportion
ofHouseho
lds
1s
Value of choice (with fees) v . uniform lottery (lumpsum taxes)by Income Quintile
1s
Value of choice (with fees) v. proby IncomFigure 3
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30 20 10 0 10 20 30 400
0.5
1
Value in 2002 $
Proportion
ofHouseholds
30 20 10 00
0.5
1
Value in
Proportion
ofHouseholds
20 0 20 40 60 80 1000
0.5
1
Value in 2002 $
Proportion
ofHouseholds
Value of choice (no fees) v. uniform lottery (no taxes)by Income Quintile
20 0 20 40
0.5
1
Value in
Proportion
ofHouseholds
Value of choice (no fees) v. by Incom
40 20 0 20 40 60 80 100 1200
0.5
1
Value in 2002 $
Proportion
ofHousehold
s
Value of choice (with fees) v. constrained choice (with fees)by Income Quintile
1st. Sa
2nd. S
3rd. Sa
4th. Sa
5th. Sa
1s
Value of choice (with fees) v . uniform lottery (lumpsum taxes)by Level of Mother Education
1s
Value of choice (with fees) v. proby Level of MoFigure 4
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40 20 0 20 40 60 80 1000
0.5
1
Value in 2002 $
Proportion
ofHouseholds
40 20 0 200
0.5
1
Value in
Proportion
ofHouseholds
20 0 20 40 60 80 100 120 140 1600
0.5
1
Value in 2002 $
Proportion
ofHouseholds
Value of choice (no fees) v. uniform lottery (no taxes)by Level of Mother Education
20 0 20 40 600
0.5
1
Value in
Proportion
ofHouseholds
Value of choice (no fees) v. by Level of Mo
40 20 0 20 40 60 80 100 120 140 1600
0.5
1
Value in 2002 $
Proportion
ofHouseholds
Value of choice (with fees) v. constrained choice (with fees)by Level of Mother Education
Primary
High Sc
High Sc
Superio
Profess
College
Post Gra
1s
Value of choice (with fees) v . uniform lottery (lumpsum taxes)by SES vulnerability
1s
Value of choice (with fees) v. proby SES vuFigure 5
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25 20 15 10 5 0 5 10 150
0.5
1
Value in 2002 $
Proportion
ofHousehold
25 20 15 10 50
0.5
1
Value in
Proportion
ofHousehold
20 10 0 10 20 30 40 50 600
0.5
1
Value in 2002 $
Proportion
ofHouseholds
Value of choice (no fees) v. uniform lottery (no taxes)
by SES vulnerability
20 10 0 10 20
0.5
1
Value in
Proportion
ofHouseholds
Value of choice (no fees) v.
by SES vu
40 20 0 20 40 60 80 100 120 140 1600
0.5
1
Value in 2002 $
Proportion
ofHouseholds
Value of choice (with fees) v. constrained choice (with fees)by SES vulnerability
Vuln
Non
Value of Choice (no fees) v. Uniform Lottery (no taxes)15% of Students attend Voucher Schools
Figure 6A
7/28/2019 Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural Simulations for Chile.
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10 0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Pr
oportion
ofHouseholds
20 0 20 40
0.2
0.4
0.6
0.8
1
Value in 2
Pr
oportion
ofHouseholds
20 10 0 10 20 30 40 50 60 700
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Proportion
ofHo
useholds
Vulnerable
Non vulnerable
20 0 20 40 600
0.2
0.4
0.6
0.8
1
Value in 2
Proportion
ofHo
useholds
Value of Choice (no fees) v. Proportional Lottery (no taxes)15% of Students attend Voucher Schools
Figure 6B
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10 0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Pr
oportion
ofHouseholds
20 0 20 40
0.2
0.4
0.6
0.8
1
Value in 2
Pr
oportion
ofHouseholds
20 10 0 10 20 30 40 50 60 700
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Proportion
ofHo
useholds
Vulnerable
Non vulnerable
20 0 20 40 600
0.2
0.4
0.6
0.8
1
Value in 2
Proportion
ofHo
useholds
Value of Eliminating Fees Assuming no Change in QualityFigure 7A
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15 10 5 00
0.2
0.4
0.6
0.8
1
Value in
Proportion
ofHouseholds
1st. Sample Quintile2nd. Sample Quintile
3rd. Sample Quintile4th. Sample Quintile
5th. Sample Quintile
10 5 0 5 10 15 200
0.2
0.4
0.6
0.8
1
Value in 2002 $
Proportion
ofHo
useholds
Vulnerable (SES)
Non Vulnerable (SES)
20 15 10 5 0 50
0.2
0.4
0.6
0.8
1
Value in
Proportion
ofHo
useholds
PrimaryH.S. Science
H.S. VocationalTechnicalProfessional Inst.
CollegePost Graduate
10 5 0 5 10 15 200
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Proportion
ofHouseholds
Value of Eliminating Fees Assuming Drop in QualityFigure 7B
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15 10 5 00
0.2
0.4
0.6
0.8
1
Value in
Proportion
ofHouseholds
1st. Sample Quintile
2nd. Sample Quintile
3rd. Sample Quintile4th. Sample Quintile5th. Sample Quintile
10 5 0 5 10 15 200
0.2
0.4
0.6
0.8
1
Value in 2002 $
Proportion
ofHo
useholds
Vulnerable (SES)
Non Vulnerable (SES)
20 15 10 5 0 50
0.2
0.4
0.6
0.8
1
Value in
Proportion
ofHo
useholds
PrimaryH.S. Science
H.S. VocationalTechnicalProfessional Inst.
CollegePost Graduate
10 5 0 5 10 15 200
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Proportion
ofHouseholds
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Gains from a Differentiated Voucher, Positive Effect on ScoresFigure 8B
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4 2 0 2 4 6 8 10 12 14 160
0.2
0.4
0.6
0.8
1
Value in 2002 $
Proportion
ofHo
useholds
Vulnerable
Non Vulnerable
6 4 2 0 2 40
0.2
0.4
0.6
0.8
1
Value in
Proportion
ofHouseholds
5 0 50
0.2
0.4
0.6
0.8
1By Mother Ed
Value in
Proportion
ofHo
useholds
4 2 0 2 4 6 8 10 12 140
0.2
0.4
0.6
0.8
1
Value in 2002 US$
Proportion
ofHouseholds