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**Unformatted text preview: **Fortin – Econ 560 V. Social Mobility and Social Interactions Plan
D. Evidence of Neighbourhood, Network and Peer Effects
1. Peer Effects in Education
2. Neighbourhood Effects
3. Network Effects Lecture 5D Fortin – Econ 560 Lecture 5D 1. Peer Effects in Education
• Expressions of the popular belief in sizeable peer interaction effects in schooling is reflected
by the actions of parents who pay sizeable tuition fees to send their children to private schools
or sizeable housing premium for schools in better neighbourhoods.
• The literature on peer-group in education really began with the Coleman Report (1966) which
indicated that the educational achievement of black students was positively related to the
fraction of students in their school that were white.
• This early and controversial study were very influential as it has been held as primarily
responsible for the school busing desegregation movement in the US, but it was plagued with
all the problems noted earlier, except with the simultaneity problem (that the extent that being
white is a characteristic rather than an interaction effect).
• Since the early studies, there have been numerous papers on peer effects in education. Many, if
not the majority of studies (see for example, Schofield, 1995) find non-existent or weak effects
of peers, that are fragile and non-robust to specification and the inclusion of controls.
• Studies of peer effects in education that find stronger results use a definition of closer peers,
namely roommates. Fortin – Econ 560 Lecture 5D • Another study by Bruce Sacerdote (2001) that is based on random assignment exploits the fact
that Freshmen entering Dartmouth College (a highly selective, medium-sized, liberal arts
institution located in New Hampshire) are randomly assigned to dorms and to roommates
thereby eliminating the problem of peers selecting each other based on observable and
unobservable characteristics.
• Sacerdote (2001) finds that peers have an impact on GPA and on decisions to join social
groups such as fraternities, which can be important for career networks and for lifelong
friendships which ultimately may have a high impact on outcomes.
• Peer effects in GPA occur at the individual room level, whereas peer effects in fraternity
membership occur both at the room level and the entire dorm level. In contrast, the peer effect
in GPA does not display any dorm level or floor level effect; it is observed only at the room
level.
• On the other hand, he finds that residential peer effects are markedly absent in other major
life decisions such as choice of college major.
• This provides some evidence that the reference group or relevant peer group can differ
dramatically across different activities and outcomes. 692 Source: Sacerdote (2006) TABLE III
PEER EFFECTS IN ACADEMIC OUTCOMES Roommates’ GPA
HS academic score
(self)
HS academic score
(roommates’)
roommates’ academic
score bottom 25
percent
roommates’ academic
score top 25 percent
roommates’ intention
to graduate w/honors
(1–4)
own academic score
bottom 25 percent (2)
Fresh year
GPA w/
dorm f.e. (3)
Senior
year GPA 0.120**
(0.039)
0.014**
(0.0008)
Ϫ0.001
(0.001) 0.068**
(0.029)
0.015**
(0.0007)
Ϫ0.0003
(0.0009) 0.008
(0.026)
0.013**
(0.0009)
0.0009
(0.001) (4)
Fresh
year GPA (5)
Fresh
year GPA (6)
Fresh
year GPA 0.014
(0.025) 0.017
(0.025) 0.060**
(0.028) 0.047*
(0.026) 0.043*
(0.026)
0.082**
(0.037) Ϫ0.284**
(0.025) Ϫ0.282**
(0.025) (8)
Econ major Ϫ0.0001
(0.0003)
0.0003
(0.0003)
0.016
(0.028) (7)
Graduate
late 0.003**
(0.0006)
Ϫ0.0001
(0.0006) QUARTERLY JOURNAL OF ECONOMICS (1)
Fresh
year GPA Dummies for housing
questions
F test of roommate
background
coefﬁcient ϭ 0
R2
N 0.174**
(0.025) 0.175**
(0.025)
0.008
(0.029) yes .38
1589 yes .18
1441 yes yes yes F ϭ 2.31
P ϭ 0.10
.24
1589 yes F ϭ 1.63
P ϭ 0.20
.19
1589 .19
1589 .06
1589 .07
1589 F ϭ 2.74
P ϭ 0.04 .05
1589 yes Ϫ0.018
(0.026)
yes Standard errors are in parentheses and are corrected for clustering at the room level. In cases with more than one roommate, roommate variables are averaged. ** ϭ p-value Ͻ
.05. * ϭ p-value Ͻ .10.
Regression (1) is OLS of own GPA on roommate GPA and controls. If own and roommate academic indices are excluded, the coefﬁcient on roommate GPA falls to .111, and the
standard error falls to 0.037.
Regression (2) adds dorm ﬁxed effects. The coefﬁcient on roommate GPA falls, but remains signiﬁcant. Regression (3) is OLS of own senior year GPA on freshman year roommates’
senior year GPA. Senior year GPA includes all grades in ﬁnal year and excludes grades from earlier years.
Regressions (4)–(6) are OLS of own GPA on own and roommate background. These regressions use dummies for own and roommate academic index are in the bottom 25 percent,
middle 50 percent (excluded category), or top 25 percent of their respective distributions. Regression (4) shows that “roommate top 25 percent” is signiﬁcant in predicting own GPA.
The level of signiﬁcance on “roommate top 25 percent” falls to .10 when two dummies for own academic index are added. (This is regression (5).) Regression (6) shows that roommate
intention to graduate with honors also predicts own GPA. This variable is a self-assessed probability of graduating with honors and is coded as a 1, 2, 3, or 4 for the responses of
no chance, very little chance, some chance, or a very good chance. Regression (6) also includes a dummy for “roommate intend to graduate with honors” missing. See text for more
discussion of this variable.
Regressions (7) and (8) are probits of own “graduate late” and own “major choice ϭ econ” on roommate graduate late and roommate major choice ϭ econ. ץy/ ץx is shown. PEER EFFECTS WITH RANDOM ASSIGNMENT own academic score top
25 percent
Roommate graduate
late
Roommate econ major 693 Source: Sacerdote (2006)
PEER EFFECTS WITH RANDOM ASSIGNMENT 699 TABLE V
PEER EFFECTS IN SOCIAL OUTCOMES
(1)
Member
frat/
soror (2)
Member
frat/
soror roommate member of
fraternity/sorority/coed
dorm average of
fraternity/sorority/coed
roommate varsity athlete 0.078**
(0.038) 0.056
(0.037)
0.321**
(0.135) HS academic score (self) 0.0098
(0.0010)
Ϫ0.0017
(0.0011) 0.0011
(0.0011)
Ϫ0.0016
(0.0011) yes yes 0.0010
(0.0011)
Ϫ0.0016
(0.0011)
0.135**
(0.038)
Ϫ0.025
(0.026)
(0.026)
0.287**
(0.146)
yes .02
1589 .02
1589 .03
1589 HS academic score
(roommates’)
Own use of beer in high
school (0–1)
Roommates’ use of beer
in high school (0–1)
Dormmates’ use of beer
in high school (0–1)
Dummies for housing
questions
R2
N (3)
Member
frat/
soror (4)
Varsity
athlete 0.045
(0.033)
Ϫ0.004**
(0.001)
Ϫ0.0002
(0.0007) yes
.05
1589 Standard errors are in parentheses and are corrected for clustering at the room level. In cases with more
than one roommate, roommate variables are averaged. ** ϭ p-value Ͻ .05.
Columns (1)–(4) are Probits. ץy/ ץx is shown.
In regression (2), dorm average of frat membership excludes own observation, and standard errors are
corrected for clustering at dorm level.
In regression (3), use of beer in past year is coded 0 –1 as follows: 0 ϭ not at all, occasionally or
frequently ϭ 1. Dorm use of beer excludes own room and standard errors are corrected for clustering at dorm
level. tials are reported rather than probit coefﬁcients.) If my freshman
year roommate joins a fraternity, I am 8 percent more likely to do
so myself. This occurs in spite of the fact that students do not even
execute this decision during their freshmen year. Students are
not allowed to join until sophomore year, and only 16 percent of
people keep any of the same roommates.
More remarkable is the frequency with which students join
the same house as their randomly assigned roommate. When I
limit the sample to rooms of two where both roommates have
joined a fraternity, I ﬁnd that 27 percent of the roommate pairs Fortin – Econ 560 Lecture 5D • When one is not fortunate enough to find a situation where there is random assignment, one
can exploit some bureaucratic idiosyncrasies. A few recent studies have exploited such
idiosyncracies in school environment to use an identification strategy based on instrumental
variables.
• For example, Angrist and Lang (2004) study the impact of busing on students in Metco
schools, a voluntary program that sent mostly black students out of the Boston district into
schools in the surrounding, mostly white suburban districts.
• In particular, they estimated the effect of Metco students on the achievement of non-Metco
students using school/grade/year average national percentile rank of non-Metco students on the
fraction Metco in a grade, school, and year as well as individual data.
• Their OLS estimates for black residents of Brookline show that most estimates are not
significant, except for some of the estimates for third graders which are negative and
significant.
• They also perform an IV estimation that exploits the fact that Metco students are assigned to
Brookline schools partly on the basis of a space constraint of 25 students, a strategy similar to
what Angrist and Lavy (1999) termed Maimonides' rule, after the biblical scholar, who
proposed a maximum class size of 40 in a Talmudic commentary. VOL. 94 NO. 5 ANGRIST AND LANG: DOES SCHOOL INTEGRATION GENERATE PEER EFFECTS? 1621 TABLE
4--TEST SCORES RACEAND METCO
BY
STATUS
Non-Metco
Grade 3 Subject
Core
Reading
Math
Language 5 Core
Reading
Math
Language 7 Core
Reading
Math
Language Metco All
(1) Black
(2) Hispanic
(3) Asian
(4) White
(5) All
(6) Black
(7) Non-black
(8) 71.6
(24.2)
16.81
70.7
(24.7)
15.91
72.0
(24.7)
V.31
67.8 51.2
(27.6) 54.2
(27.6) 71.9
(22.8) 74.3
(22.7) 47.2
(25.1) 60.1
(25.2) 51.7
(28.4) 54.9
(26.4) 63.7
(23.8) 74.8
(22.8) 46.1
(26.8) 58.8
(24.8) 50.8
(28.4) 54.9
(28.0) 76.4
(22.6) 74.0
(23.3) 49.0
(25.5)
122.21
47.9
(26.8)
[2 1.41
47.9
(26.4)
122.91 45.7
(26.3) 62.0
(23.4) i2.3(22.7)
[5.11
72.4
(22.7)
L4.31
70.6
(23.2)
L6.11
69.2
(24.4)
l6.1I
76.4
(21.8)
14.71
77.0
(22.6)
L4.41
74.0
(23.4)
15.01
73.9
(22.4)
15.31 49.8
(25.7) 49.9 52.2
(25.9)
47.8 Notes: Columns (1) to (5) show statistics for the population of tested non-Metco students. Columns (6) to (8) show statistics
for the population of tested Metco students. Reported test scores are means of the National Percentile Rank from the Iowa
Test of Basic Skills administered from the 1994-1995 school year through the 2000-2001 school year. Standard deviations
are reported in parentheses. Standard deviations for schooL/grade/year cell means appear in brackets. from Boston, a project we hope to pursue in the
future.
C. Metco and the School Environment
Differences in average achievement between Brookline residents and Metco students
are large enough for the presence of Metco
students to reduce average test scores in Brookline. This can be seen in the top panel of
Table 5. Columns (1) to (4) of the table report
unweighted estimates of the grouped equation (1) Yg,, = ag + p, + yr + Sms,, + As,, + ugjr where y,,, is the average score in the grade
glschool jlyear t cell, s,., is class size in the cell,
including Metco, and m,, is fraction Metco
(based on tested students) [where g X j X t =
3 X 8 X 7 = 168 cells]. Columns ( 5 ) to (8)
report estimates treating individual students as
the unit of observation and replacing y,, with
y,gr(,,, average score of students in the cell,
the
excluding student i. These estimates capture the Source: Angrist and Lang (2004) 1622 THE AMERICAN ECONOMIC REVIEW
TABLE
5-METCO EFFECTS
ON THE DECEMBER 2004 SCORE
DISTRIBUTION ALL STUDENTS
FOR Grouped data
Subject (1)
Pooled (2)
3rd (3)
5th Micro data
(4)
7th (5)
Pooled (6)
3rd (7)
5th (8)
7th Panel A. Dependent variable: mean test score
Peer means Cell means
Core
Reading
Math
Language
N
Panel B. Dependent variable: second decile of test score
Cell quantiles
Core
Reading
Math
Language
N -51.4
(14.4)
-45.2
(15.2)
-37.6
(17.1)
-35.7
(14.1)
168 -61.7
(31.8)
-58.3
(35.1)
-48.3
(34.6)
-43.0
(3 1.2)
56 -37.8
(23.3)
-41.3
(22.0)
-31.4
(28.7)
-1.79
(23.4)
56 Quantile regression
-48.6
(23.1)
-41.1
(23.8)
-35.3
(29.3)
-44.5
(21.7)
56 -48.6
(15.5)
-43.3
(16.5)
-44.4
(14.5)
-40.3
(15.6)
8,629 -56.7
(38.0)
-57.5
(33.8)
-40.5
(47.1)
-47.4
(42.8)
2,798 -43.0
(3 1.2)
-45.8
(25.8)
-40.0
(36.7)
-23.0
(3 1.5)
2,966 -51.9
(28.1)
-31.7
(32.0)
-31.2
(33.2)
-49.6
(29.5)
2,865 Notes: The table reports the coefficient on fraction Metco estimated from the Riverside testing data using equation (1) in the
text. Standard errors are reported in parentheses. Standard errors in columns (1) to (4) are robust. Standard errors in columns
(5) to (8) of panel (A) are clustered by grade/school/school-year cell. Standard errors in columns (5) to (8) of panel (B) are
boostrapped. In columns (1) to (4) of panel (A) the dependent variable is the mean test score for the grade/school/school year
cell. In columns (5) to (8) of panel (A), the dependent variable is the peer mean score. The peer mean score is the
grade/school/school year cell mean score omitting the student's own score from the mean. In columns (1) to (4) of panel (B)
the dependent variable is the second decile of the test score. Columns (5) to (8) of panel (B) report microdata quantile
regression estimates for the second decile of the test score. Covariates include class size and fixed effects for school and school
year. Columns (1) and (5) include cohort and grade fixed effects. The N row displays the number of observations (or cells)
in the regression. For columns (5) to (8), the N row displays the number of observations in the core test score regression. effect of fraction Metco on non-Metco students'
peer means, since Metco students are included
in y,,(,, but excluded from the estimation sample.
Except for the fact that the dependent variable is a
peer mean and the equation includes individuallevel controls, the resulting estimates are similar to
estimation using cell means weighted by the number of non-Metco students in a ce11.13
The results tell a similar story for both estimation strategies. As with the school-level data,
the presence of Metco students has a marked
l 3 The standard errors in columns (5) to (8) are adjusted for
cell-clustering. All models using data p l e d across grades include
a set of cohort effects (for 11 graddyear cohort groups). Models
using microdata include dummies for sex and race. negative effect on average performance. Increasing the number of Metco students by ten
percentage points in Brookline (about two per
class) lowers average scores by almost 2% percentage points, or about 40 percent of the standard deviation of the group averages. Of course,
this may be a pure composition effect arising
from the large gap between the scores of Metco
and non-Metco students, a point to which we
return below.
Because Metco students' scores are concentrated in the lower tail of the Brookline residents' score distribution, increasing the fraction
Metco shifts the overall score distribution most
sharply in the lower tail. To illustrate this point,
the bottom panel of Table 5 shows the effect of Source: Angrist and Lang (2004) 1624 DECEMBER 2004 THE AMERICAN ECONOMIC REVIEW Grouped data
Subject Pooled
(1) 3rd
(2) Micro data
5th
(3) 7th
(4) Pooled
(5) 3rd
(6) 5th
(7) 7th
(8) -1.60
(10.9)
-3.93
(9.74)
4.46
(12.1)
-11.5
(1 1.6)
2,672 -6.50
(10.2)
-5.82
(1 1.2)
-11.8
(12.9)
-3.18
(10.2)
2,796 -3.45
(8.16)
0.067
(6.89)
-2.86
(9.42)
-4.96
(8.11)
2,678 Panel A. All non-Metco students
Core
Reading
Math
Language
N 3.19
(7.52)
5.30
(6.91)
4.53
(8.72)
0.53 1
(8.11)
168 1.41
(14.2)
-2.06
(13.9)
4.66
(16.7)
-4.63
(14.1)
56 1.57
(13.7)
-1.14
(13.5)
-0.322
(17.5)
4.91
(13.9)
56 6.62
(12.3)
10.2
(10.1)
8.34
(14.1)
5.42
(12.3)
56 -5.18
(5.88)
-2.78
(5.09)
-4.81
(7.03)
-8.38
(6.57)
8,146 Panel B. Black non-Metco students
Core
Reading
Math
Language
N -78.1
(36.6)
-66.2
(36.0)
-50.0
(37.0)
- 102
(41.O)
146 -218
(92.8)
-288
(94.9)
-92.1
(81.O)
-237
(65.7)
45 21.8
(79.8)
14.9
(62.1)
22.5
(81.6)
0.529
(88.9)
49 -68.0
(45.0)
-2.40
(43.6)
-61.2
(5 1.9)
-83.4
(52.5)
52 -33.1
(24.5)
-29.7
(24.5)
-5.4
(28.3)
-47.3
(25.0)
534 - 170
(54.4)
- 180
(56.6)
-31.1
(66.1)
-175
(52.9)
169 26.9
(49.8)
20.0
(39.5)
32.7
(55.6)
29.4
(57.8)
183 -3.75
(30.4)
19.2
(33.2)
2.62
(36.5)
- 12.4
(32.0)
182 Notes: Columns (1) to (4) report OLS estimates of the coefficient on the fraction Metco variables in equation (2) using cell
means. Columns (5) to (8) report student-level estimates from equation (3). The fraction Metco variable was constructed from
the Riverside testing data. Robust standard errors are reported in parentheses in columns ( I ) to (4). Standard errors in columns
(5) to (8) are clustered by grade/school/school-year. The dependent variable is the relevant test score. Covariates include class
size and fixed effects for school and school year. Models for columns (5) to (8) also include race, gender, ESLiTBE, and
special education indicator variables as covariates. Models for columns (1) and (5) contain grade and cohort fixed effects. The
N row shows the number of observations in the core regression (or the number of cells). command. In practice, the standard errors from
this procedure may be misleading, especially
when there are few clusters, and inference using
grouped data has been shown to be more reliable (see, e.g., Ziding Feng et al., 2001; Stephen
Donald and Kevin Lang, 2001). This leads us to
report results using both cell means and individual data. Both the grouped and micro equations use the fraction Metco tested for in,, since
this is more consistently measured and probably
more accurate than the fraction Metco enrolled
(though estimates using both measures are
similar).
Pooled estimates of equation (2) generate
small positive, but insignificant, effects-of fraction Metco on average non-Metco scores in
each subject. This can be seen in the first four
columns of panel (A) in Table 6. The estimates
using microdata, reported in columns (5) to (8),
are negative but again small and insignificant,
suggesting that the proportion Metco has no effect on non-Metco students. On the other
hand, it should be noted that the standard errors
for the microdata estimates in column (5) are
such that the smallest negative effect that could
be detected (i.e., the effect that would be significant at the 5-percent level in a one-tailed
test) is about 5.9 X 1.64 = -9.7. Since the
effect of fraction Metco tested on peer means is
-24 (see column [5] in Table 5 ) , the smallest
detectable peer effect that operates solely
through the test scores of all classmates is about
0.4. On the other hand, if the lower tail of the
score distribution matters for achievement, then
peer effects as small as 0.2 would be significant.
The results therefore reject effects in the upper range of those found in prior research on
peer effects, but smaller effects cannot be ruled
out. For example, using data from Texas
schools, Hoxby (2000) reports estimates of the
effect of the average peer score ranging from
0.1 to 0.55. Our estimates for Brookline rule out Source: Angrist and Lang (2004) 1628 THE AMERICAN ECONOMIC REVIEW
TABLE
7-OLS, FIRST-STAGE, AND DECEMBER 2004 REDUCED-FORM
ESTIMATES ALLNON-METCO
FOR
THIRD
GRADERS
Dependent raiable
Math Core
(71 (8) Language
(91 (10) (11) 112) -1 64
(1.63)
-0037
(0.082)
-0.530 -0.429
(1.53)
0.015
(0.080)
0.620
(0.243) - 1.85
(1.49) -3.13
(1 75)
0.025
(0.076)
-0.530 Panel A. OLS
Number Metco In
class
Number non-hletco
enrolled
Number non-hletco
~n class
N 0.586
(0.601)
-0.033
(0.0761
0 658
(0.215) 0 162
(0.626) -0 145
(0.713)
-0.038
(0.077)
-0.530 2.672
Panel B. First-stage-Dependent Instrument
Number non-hletco
enrolled
Number non-Metco
~n clasc
N 0.921
(0 185)
0 0014
(0.0 16)
0.0205
(0.0401 0 875
(0.163) variable is number Metco In class 0.873
(0.170) 0.0016 (0 016) 2,812
Panel C Reduced form Instrument
Number non-hletco
enrolled
Number non-Metco
tn class
N -0.069
11.39)
-0.029
(0.078)
0.610
(0.259) -1.50
(1.33) 2.672 -2.67
( I 60)
-0.021
(0.073)
-0.530 0.280
(1.01)
-0.00?0
(0.062)
0 586
(0.241 -1 10
(1.02) 2,773 -2.36
(1 32)
0.0087
(0.058)
-0.530 0 3...

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- Fall '13
- NicoleFortin
- Economics, Econometrics, Regression Analysis, The Land, standard errors, Effect size, Metco