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14.771 Development Economics: Microeconomic issues and Policy Models
Fall 2008
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Esther Duflo
14.771
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• Private and Social Returns (done!)
• Vouchers for Private School
• Using Regression discontinuity to estimate the impact of class size
• The Cost of Teachers
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• Why should government finance education?
• What should government provide education?
• Vouchers: A way to de-couple financing and provision of education
• The impact of vouchers: a partial equilibrium analysis Angrist et al (2006,2008)
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• Setting: one city in Colombia
• 125,000 Vouchers are randomly allocated to eligible students who applied through a lottery
• Vouchers cover half the cost of private schools
• They are renewed conditional on good performance in school
• Since Vouchers are assigned by lottery, we can follow losers and winners to asses their impact on probability to go to to private school, and their performance.
• First Stage and Reduced form impact of winning:
Table 3
• Short term test score results of winning:
Table 6
• Long term test impact: More likely to graduate high school and take school leaving exam
Table 2
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• Attrition:
•
•
The differential rate at which students take the exam create an attrition problem
They deal with attrition in different ways, notably by constructing bounds
• Without controlling: no difference in test scores.
With
Control: big differences on test scores
• The non compliance problem:
• Some kids do not take the voucher (never takers)
• Some kids get another voucher (always takers) use winning the lottery as an instrument for getting the private school voucher
Table 8
•
•
Are the identification assumption satisfied?
Suppose that we were trying to use this instrument to measure the impact of attending private school, would they be satisfied?
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• Why might the effect of the voucher on a winner not tell us what would the effect be of introducing vouchers in an entire school system?
• If we could do a giant randomized experiment on this, what would it be?
• Hsieh and Urquiola examine the case of Chile
•
•
•
•
In 1981, Chile introduced a nationwide voucher systems
Massive entry of private school :
Graph
Especially
DD in
(panel) richer analysis and of more the urban impact of area school markets that got more private schools: regress change in test scores on change on fraction of students in private school.
•
Results
More Private school not associated with any increase
• in test score
Potential Confounding factors?
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• Explanation: market for schools.
•
•
•
Parents like good schools
They think good school=good test scores
•
•
They look for school with good peers (even if there are no peer effects)
Increased sorting
Table5
Evidence that parents have strong willingness to pay for schools with good peers (even with low value added): Zhang
(2008) find no effect of elite school on test score in China
(lottery), even though parents are willing to pay a lot of money to attend these schools.
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• A classic RD design
• Israel: Class size should not be over 40
• This creates discontinuity in class size at multiple of 40:
Figure
• A Fuzzy RD, since the class size is not exactly following the rule.
• Therefore we use predicted class size (based on the rule) as an instrument for actual class size, controlling for smooth function of the class size.
• Results:
Figure
First Stage and Reduced forms
2SLS
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• Back to Chile...
• Schools are subject to a class size cap (45), and an integer constraints on the number of classroom: they respect this
figure 5
• But they can chose how many kids they enroll, as well as the fee they set.
• Profit-maximizing schools will endogenous choose enrollment and fees to avoid being on the right side of a discontinuity: this will generate bunching
figure 7
• Except if they are targeting parents who really value class size and are willing to pay more for it: they will then raise the fees.
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• The composition of students on the left and right side of a discontinuity will change endogenous as a function of the discontinuity
figure 8
• This is a violation of the RD identification assumption: the potential outcome of the students will also differ.
• There is a RD in test scores
figure 6
but it may be due to the underlying discontinuity in potential outcomes.
•
Table 3
:
nicely estimated effect of class size
•
Table 5 :
controlling for observable differences erase the result!
• Note that this does not invalidate the Angrist Lavy study, since in their set-up, class size was not a choice variables for the school.
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• Suppose returns to education increases (i.e.
because of economic growth)
• This also will bid up the price of teachers
• And thus the cost of education
• This may not lead to an increase in education in steady state
(Banerjee, 2004)
• Effect of education policy in equilibrium depends on:
•
•
What we assume about credit constraints
What we assume about preferences
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Hsieh and Urquiola (2006)
90
80
70
60
Fiscal
Municipal
50
40
Total private
30
Total private
20
10
Voucher private
(previously subsidized private)
0
Tuition-charging private
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
National enrollment shares by sector, 1970-1996. Data assembled from several issues of the
Ministry of Education's Compendio Estadistico .
Figure by MIT OpenCourseWare.
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Table 3
OLS regressions for achievement, 1982–1988 and 1982–1996
Dependent variable—change in average
Language score a
Math score a
(1) (2) (3) (4) (5)
Panel A—1982–1988
Change in priv. enrollment b
Controls: previous trends d
Controls: concurrent trends
N
R
2 e
5.5
(7.5)
6.7
(7.7)
[ 0.08] [ 0.10]
No Yes
No
84
0.006
No
84
0.073
3.4
(8.7)
7.2
(7.6)
[ 0.05] [ 0.10]
Yes No
Yes
84
0.105
No
84
0.010
9.4
(7.5)
[ 0.13]
Yes
No
84
0.087
(6)
Repetition rate
(7) (8) b
(9)
Years of schooling
(10)
9.2
(8.9)
0.10*** 0.09** 0.07*
(0.03) (0.03) (0.04)
0.84
(0.70)
[ 0.12] [0.24]
Yes No
[0.21]
Yes
[0.17]
Yes
[ 0.11]
No
Yes
84
0.156
No
145
0.057
No
145
0.078
Yes
145
0.095
No
85
0.013
(11) c
0.72
(0.67)
[ 0.10]
Yes
No
85
0.203
(12)
0.84
(0.68)
[ 0.11]
Yes
Yes
85
0.239
Panel B—1982–1996
Change in priv. enrollment b
Controls: previous trends d
Controls: concurrent trends e
N
R
2
13.8* 12.3
(7.9) (7.7)
[ 0.24] [ 0.21]
No Yes
No
84
0.056
No
84
0.106
8.9
15.8**
(9.9) (6.5)
[ 0.15] [ 0.27]
Yes
Yes
84
0.145
No
No
84
0.072
No
84
15.0**
(6.7)
[ 0.25]
Yes
0.117
12.8
(8.0)
[ 0.22]
Yes
Yes
84
0.171
(0.4)
[ 0.42]
No
No
2.2***
145
0.179
2.1***
(0.4)
[ 0.40]
Yes
No
145
0.229
2.1***
(0.4)
[ 0.40]
Yes
Yes
145
0.250
Notes: *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. Huber–White standard errors are in parenthesis. Brackets contain the prop. of a standard deviation change in the dependent variable brought about by a one standard deviation increase in private enrollment.
a
Calculated using test system information, data sources (1), (2), and (4), as described in Table A.1
.
b Variable comes from administrative information, data sources (8) and (9), and (10). Repetition is available only up to 1988.
c
Based on micro census data for 1982 (data source 16), and household survey data for 1990 and 1996 (sources 11 and 13).
d Controls for previous trends are: the 1970–1982 change in average years of schooling (from census micro data, sources 15 and 16), the 1980–1982 change in private enrollment (sources 7 and 8), and the 1978–1982 change in the proportion of schools private (sources 19 and 8).
e
Controls for concurrent trends are the 1982–1992 change in population (from data sources 17 and 18), and the 1982–1996 change in mean years of schooling and imputed labor income among adults (from census and household survey information, sources 13 and 16).
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Table 5
Sorting among communes, 1990’s cross-section and 1982–1988 changes
Dependent variable—within commune observations of average characteristic in public schools/average characteristic in all schools
SES index a
Income b
Language a
Mathematics a
Repetition c
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Panel A—1990’s cross sections d
Private enrollment c
Commune controls
Thirteen regional dummies
N
R
2 e
0.20***
(0.02)
[ 0.58]
No
No
296
0.313
0.16***
(0.03)
[ 0.46]
Yes
Yes
296
0.493
0.37***
(0.07)
[ 0.43]
No
No
184
0.171
0.33***
(0.09)
[ 0.38]
Yes
Yes
184
0.285
0.08***
(0.02)
[
No
0.39]
No
296
0.188
0.08***
(0.02)
[ 0.39]
Yes
Yes
296
0.396
0.09***
(0.02)
[ 0.42]
No
No
296
0.215
0.09***
(0.03)
[ 0.42]
Yes
Yes
296
0.346
0.42***
(0.07)
[0.44]
No
No
299
0.193
0.28***
(0.07)
[0.29]
Yes
Yes
299
0.447
Panel B—1982–1988 changes
Change in private enrollment c
Controls: concurrent trends
N
R 2 f
0.21**
(0.10)
[ 0.24]
No
84
0.060
0.22**
(0.10)
[ 0.26]
Yes
84
0.065
0.14*
(0.08)
[ 0.17]
No
84
0.027
0.19**
(0.08)
[ 0.23]
Yes
84
0.097
0.51**
(0.24)
[0.24]
No
163
0.054
0.38*
(0.24)
[0.18]
Yes
163
0.100
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Angrist et al (2001)
Dependent variable
Educational Outcomes and Voucher Status
Loser's means
(1)
Bogota 95
No Ctls Basic
Ctls
(2) (3)
Basic
+19
Barrio
Ctls
(4)
Combined sample
Basic
Ctls
Basic +19
Barrio Ctls
(5) (6)
Using any scholarship in survey year
Ever used a scholarship
Started 6 th
in private
Started 7 th
in private
Currently in private school
Highest grade completed
Currently in school
Finished 6
Finished 7 th th
Repetitions of 6 th
grade
Ever repeated after lottery
Total repetitions since lottery
Years in school since lottery
Sample size
grade
grade
(excludes Bog 97)
Finished 8 th
grade
(excludes Bog 97)
-.066**
(.024)
-.060**
(.023)
-.073**
(.028)
.058
(.052)
.509** .504**
(.023) (.023)
.672** .663**
(.021) (.022)
.063** .057**
(.017) (.017)
.174**
(.025)
.160**
(.028)
.168**
(.025)
.153**
(.027)
.164** .130**
(.053)
.019
(.022)
(.051)
.007
(.020)
.026**
(.012)
.040**
(.020)
.112**
(.027)
.023*
(.012)
.031
(.019)
.100**
(.027)
-.059**
(.024)
-.055**
(.023)
-.067**
(.027)
.034
(.050)
1147
.194
(.454)
.224
(.417)
.254
(.508)
3.7
(.951)
562
.057
(.232)
.243
(.430)
.877
(.328)
.673
(.470)
.539
(.499)
7.5
(.960)
.831
(.375)
.943
(.232)
.847
(.360)
.632
(.483)
.505**
(.023)
.662**
(.022)
.058**
(.017)
.171**
(.024)
.156**
(.027)
.120**
(.051)
.007
(.020)
.021*
(.011)
.029
(.019)
.094**
(.027)
-.059**
(.024)
-.051**
(.023)
-.064**
(.027)
.031
(.050)
.526**
(.019)
.636**
(.019)
.066**
(.016)
.170**
(.021)
.152**
(.023)
.085**
(.041)
-.002
(.016)
.014
(.011)
.027
(.018)
.077**
(.024)
-.049**
(.019)
-.055**
(.019)
-.058**
(.022)
.015
(.044)
1577
-.049**
(.019)
-.053**
(.019)
-.057**
(.022)
.012
(.043)
.521**
(.019)
.635**
(.019)
.067**
(.016)
.173**
(.021)
.154**
(.023)
.078*
(.041)
-.002
(.016)
.012
(.010)
.025
(.018)
.074**
(.024)
Figure by MIT OpenCourseWare.
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Angrist et al (2001) Test Results
OLS estimates
(1)
OLS with covariates
(2)
A. Test scores for all applicants
Total points
Math scores
Reading scores
.217*
(.120)
.178
(.118)
.204*
(.122)
Writing scores
.126
(.121)
Pooled test scores
.205*
(.108)
.153
(.110)
.203*
(.113)
.128
(.114)
Math and reading scores
B. Test scores for female applicants
Total points
.199
(.152)
Math scores
Reading scores
.292**
(.142)
.117
(.156)
Math and reading scores
B. Test scores for male applicants
Total points
.204
(.183)
Math scores
Reading scores
.010
(.142)
.276
(.190)
Math and reading scores
.263**
(.120)
.346**
(.126)
.152
(.135)
.170
(.179)
.004
(.031)
.220
(.176)
RE estimates
(3)
.170*
(.095)
.192*
(.101)
.204
(.130)
.143
(.160)
RE with covariates
(4)
.148*
(.088)
.162*
(.096)
.235**
(.117)
.087
(.160)
Figure by MIT OpenCourseWare.
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Angrist et al (2001)
OLS and 2SLS Estimates of the Effect of Ever Using a Private School Scholarship
Coefficient on ever used a private school scholarship
Dependent variable
Loser's mean
(1)
Bogota 95
OLS
(2)
2SLS
(3)
Combined sample
OLS 2SLS
(4) (5)
Highest grade completed
In school
Total repetitions since lottery
Finished 8 th
Test scores total points
Married or living w/companion
N
7.5
(.965)
.831
(.375)
.254
(.508)
.632
(.483)
-.099
(1.0)
.016
(.126)
562
.167**
(.053)
.021
(.021)
-.077**
(.029)
.114**
(.028)
.379**
(.111)
-.009
(.006)
1147
.196**
(.078)
.010
(.031)
-.100**
(.042)
.151**
(.041)
.291*
(.153)
-.013
(.009)
.141**
(.042)
.033*
(.017)
-.069**
(.023)
.108**
(.025)
--
-.010*
(.006)
1577
.134**
(.065)
-.003
(.026)
-.091**
(.035)
.127**
(.038)
--
-.014
(.009)
Figure by MIT OpenCourseWare.
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Table 2. Voucher Status and the Probability of ICFES Match
Exact ID Match ID and City Match ID and 7-letter Name Match ID, City, and 7-letter Match
(1)
A. All Applicants (N=3542)
.331 Dependent Var. Mean
Voucher Winner .072
.354
.059 .069
(.016) (.015) (.016)
Male
.339
.056
(.014)
-.053
.072
(.016)
.059
(.014)
-.043
.068
.318
.056
(.016) (.014)
-.045
(.014)
Age
(.005)
(.014)
-.156
(.005)
B. Female Applicants (N=1789)
Dependent Var. Mean
Voucher Winner
Dependent Var. Mean
Voucher Winner
.067
.079
.387
.320
(.022)
.056
(.006)
.063
(.020)
.069
(.023) (.021) (.023)
Age
.071
(.022)
.372
.057
(.021)
-.164
(.006)
.055
(.020)
.071
(.023)
C. Male Applicants (N=1752)
.304
.074
(.022)
.361
.302
(.014)
-.153
(.005)
.060
(.021)
-.160
(.006)
.059
(.020)
.073
.348
.288
.065
(.022)
(.014)
-.149
(.005)
.062
(.023) (.021)
-.156
(.006)
.050
(.020)
(.007) (.007)
-.146
(.007)
-.141
(.006)
Notes. Robust standard errors are shown in parentheses. The sample includes all Bogotá 95 applicants with valid ID numbers and valid age data
(i.e. ages 9 to 25 at application). The sample is the same as in Table 1, Column 5.
21 18 / 28

Angrist and Lavy (1999)
Courtesy of MIT Press. Used with permission.
19 / 28

Angrist and Lavy (1999)
Courtesy of MIT Press. Used with permission.
20 / 28

Angrist and Lavy (1999)
Courtesy of MIT Press. Used with permission.
21 / 28

Angrist and Lavy (1999)
Courtesy of MIT Press. Used with permission.
22 / 28

Urquiola and Verhoogen (2008)
Courtesy of the American Economic Association. Used with permission.
23 / 28

Urquiola and Verhoogen (2008)
Courtesy of the American Economic Association. Used with permission.
24 / 28

Urquiola and Verhoogen (2008)
Courtesy of the American Economic Association. Used with permission.
25 / 28

Urquiola and Verhoogen (2008)
Courtesy of the American Economic Association. Used with permission.
26 / 28

Urquiola and
Verhoogen
(2008)
Courtesy of the American Economic Association. Used with permission.
27 / 28

Urquiola and Verhoogen (2008)
Courtesy of the American Economic Association. Used with permission.
28 / 28