Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural...

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


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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


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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


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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


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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


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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


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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


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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


40/47

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


41/47

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


42/47

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


43/47

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


44/47

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


45/47

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


46/47

Gains from a Differentiated Voucher, Positive Effect on ScoresFigure 8B


47/47

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

Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural...

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Transcript of Gallego, F. & Hernando, A. on the Determinants and Implications of School Choice. Semi-Structural...