The Tower of Babel in the Classroom?
Immigrants and Natives in Italian Schools
Rosario M. Ballatore
1
Margherita Fort
2
Andrea Ichino
3
1
Bank of Italy
University of Bologna, CESifo and IZA
3
EUI & University of Bologna, CEPR, CESifo and IZA
2
Preliminary
May 2014
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Overview
What are we looking for?
We are specifically interested in
the causal effect of the number of immigrants in a class
on the school performance of natives
keeping class size constant
e.g. adding one immigrant to a class and reducing by one the number of natives
Since class size and class composition are chosen jointly by principals, this
should be the parameter of interest for policy makers
It has been neglected in the literature
We call this parameter the Pure Composition Effect (PCE)
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Overview
This Paper
We extend Lazear’s model (2001) of the educational production function
to the presence of two types of students (natives & immigrants)
allowing for positive externalities in the classroom
We use data on Italian primary schools and standardised test scores
Identification of the PCE is achieved exploiting discontinuities generated by
institutional rules of class formation (Angrist & Lavy, 1999; Angrist & Lang, 2004)
We find that the PCE is -1% in language and mathematics test scores, for
students in grade 2 (age 7) or grade 5 (age 10)
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Theory
A model to think about the problem
Lazear’s educational production function (2001):
Consider a class with C students
P ∈ [0, 1] is the probability that a student does not ask the teacher for
specific attention at the expenses of other students.
V̄ is the max performance if P = 1 (no disruption)
The actual performance is V = V̄ P C < V̄
The principal maximizes
MaxV(C ) :
PC −
W
C
At the optimum C ∗ = f (P , W )
+ +
Optimal class size is a function of students’ characteristics
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Theory
Extensions
C = Natives (N ) + Immigrants (I )
Each group of students has its own disruption probability : Pn 6= Pi 6= P
φ ∈ R\{0}; e.g. positive externalities are possible
The extended educational production function is:
φ N
φih I
Vh = V̄h Pn nh Pi
where h ∈ [n, i ]
A. Ichino (EUI)
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Theory
Group and composition effects
Using small letters for variables in logs:
vh = v̄h + pn φnh N + pi φih I
The structural effects of changing class size when natives (immigrants) change
keeping immigrants (natives) constant are respectively:
βh
=
∂vh
∂N
= pn φnh
γh
=
∂vh
∂I
= pi φih
From these group specific effects we can derive the :
Pure Composition Effect (PCE) = δh =
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∂vh
∂I
= γh − β h
C =c
May 17th 2014
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Theory
Why the PCE is important and how it can be identified
Principals jointly choose class size and class composition to reduce the
negative externalities coming from disruption
This choice is generally based on priors concerning disruption, not on facts
Reliable estimates of the PCE would improve this joint choice: the PCE is
the relevant policy parameter
Existing literature does not realise the importance of separating class size
changes from class composition changes
We exploit institutional features of class formation in Italy to identify the effect of
composition when class size changes for exogenous reasons
→
Angrist and Lavy (1999), Angrist and Lang (2004)
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Theory
Identification in the literature
Across schools: aggregation at higher than school level (Card et al. 2007,
Brunello et al. 2011, Jensen and Rasmussen 2011)
Within school: variation across classes (Ammermuller et al. 2009, Contini
2011, Ohinata & al 2011, Bossavie 2011)
Within school: variation across cohorts (Hoxby 2000, Gould et al. 2009,
Tonello 2012, Geay 2013)
No evidence on the Pure Composition Effect
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Institutional framework
Italian institutional framework
Students can pre-enroll in February for the following academic year
Schools decide the number of classes (and hence class size) on the basis of
pre-enrollment
Rules for class formation (primary schools):
No less than 10 students per class
No more than 25 students per class
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Institutional framework
Actual &Theoretical Class Size in Italy
( as in Angrist and Lavy, 1999)
Grade 2 & Grade 5
15
Class Size
20
25
Language Sample
10
Predicted
Actual (avg.)
0
50
100
Enrollment in Building
150
Class size is a discontinuous function of school enrollment
by grade
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Institutional framework
Space for immigrants
(as in the METCO approach of Angrist and Lang, 2004)
Principals set the average class size considering the number of pre-enrolled
natives
Due to higher geographic mobility and lack of information, immigrants
typically do not pre-enroll
Within school networks (under the same principal), immigrants are directed
towards schools where the predicted number of natives per class is lower:
Instructions by the Ministry of Education
Rules of class formation create exogenous variability in the average number of
natives per class and therefore in “space for immigrants”
We use this exogenous variability in the number of natives
to identify β, γ (and hence the PCE δ)
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Institutional framework
Space for immigrants based on predicted # of natives
10
15
20
Expected Avg. Number of Natives in Class
25
10
15
20
Expected Number of Natives in Class
25
d) Natives enrollment ∈ [76 − 100]
Relative Space for Immigrant in Class, net of controls
-.1
0
.1
.2
.3
.4
Relative Space for Immigrant in Class, net of controls
-.5
-.4
-.3
-.2
-.1
c) Natives enrollment ∈ [51 − 75]
16
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b)Natives enrollment ∈ [26 − 50]
Relative Space for Immigrant in Class, net of controls
-.4
-.2
0
.2
Relative Space for Immigrant in Class, net of controls
-.4
-.2
0
.2
Natives enrollment∈ [10 − 25]
18
20
22
Expected Number of Natives in Class
24
19
The Tower of Babel
20
21
22
Expected Number of Natives in Class
23
24
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Institutional framework
Space for immigrants based on predicted # of natives
Relative Space for Immigrant in Class, net of controls
-.4
-.2
0
.2
.4
a)Natives enrollment∈ [10 − 60]
10
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20
30
40
Enrolled Number of Natives
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50
60
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Data & estimation
Data
We use the INVALSI dataset for the universe of Italian primary schools in the
academic year 2009-10.
For each student in grades 2 and 5 the data set contains information on:
network, school, grade and class identifiers
class size and class composition at the beginning of the year
immigrant status based on citizenship
test scores in language and math
individual and family background information
We focus on school networks with immigrants and more than one school (80% of
the students in grade 2 and 5 in 2010 are enrolled in these school networks)
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Data & estimation
Descriptive statistics
Mean
S.D.
p10
p25
p50
p75
p90
Language sample:
Class size
19
4.1
13
16
19
22
24
Number of natives
17
4.2
11
14
17
20
22
Number of immigrants
2
2.1
0
.54
1.5
3
5
Enrollment
34
22
13
18
28
44
64
Test score language, Natives
0.67
0.11
0.54
0.60
0.67
0.73
0.80
Test score language, Immigrants
0.54
0.19
0.31
0.42
0.53
0.65
0.81
Test score math, Natives
0.64
0.19
0.39
0.5
0.64
0.78
0.89
Test score math, Immigants
0.55
0.19
0.32
0.41
0.54
0.68
0.82
655,132 students (584,025 natives and 71,107 immigrants)
4,333 networks and 11,955 schools
38,537 classes
Descriptives are similar for the math sample
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Data & estimation
Estimation
The reduced form educational production function of a representative native is:
0
vikgj = αg + βNkgj + γIkgj + Xikgj
λ + eikgj
(1)
where the observation is a student i in class k of grade g ∈ [2, 5] in school j:
β is the effect of one additional native on test scores for natives
γ is the effect of one additional immigrant on test scores for natives
0
Xikgj
is a vector of individual and class level controls
The dependent variable is the log test score of a native student
An equivalent equation for an immigrant student can be considered
A. Ichino (EUI)
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Results
Conventional evidence
(within school strategy; pooled across grades)
Number of natives: β̂
Number of immigrants: γ̂
Pure Composition Effect: δ̂
Observations
A. Ichino (EUI)
Language
Mathematics
0.003***
0.003***
(0.001)
(0.001)
-0.001
-0.001
(0.001)
(0.001)
-0.004***
-0.004***
(0.001)
(0.001)
584,025
556,292
School-grade FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
Mean score
0.67
0.71
(S.D.)
0.11
0.10
(S.D. Log score)
0.32
0.25
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Results
Conventional evidence
(within school strategy; language; separate by grade)
N. natives: β̂
N. immigrants: γ̂
(Pure) Composition: δ̂
Observations
A. Ichino (EUI)
2nd grade
5th grade
0.004***
0.003***
(0.001)
(0.000)
-0.000
-0.001
(0.003)
(0.001)
-0.004***
-0.004***
(0.001)
(0.000)
292,166
291,856
School FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
Mean score
0.67
0.71
(S.D.)
0.22
0.16
(S.D. Log score)
0.62
0.44
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Results
Conventional evidence
(within school strategy; math; separate by grade)
N. natives: β̂
N. immigrants: γ̂
(Pure) Composition: δ̂
Observations
A. Ichino (EUI)
2nd grade
5th grade
0.004***
0.003***
(0.000)
(0.000)
-0.000
-0.001
(0.002)
(0.001)
-0.004***
-0.004***
(0.001)
(0.001)
277,420
278,870
School FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
Mean score
0.67
0.71
(S.D.)
0.20
0.16
(S.D. Log score)
0.59
0.43
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Results
IV strategy
the METCO approach, Angrist and Lang (2004)
Let Z be the predicted class size based on natives school enrolment (Ejg ) for each
school and grade:
Zjg =
Int
Ejg
Ejg −1
+1
25
(2)
As in Angrist and Lang (2004) we derive our set of instruments by constructing
indicator variables from Zjg
min
Γ ∈ [1(Zjq
≤ Zjg < Zjqmin + 1), ...., 1(Zjqmax ≤ Zjg < Zjqmax + 1)]
(3)
e.g. 1(1 ≤ Zjg < 2),....,1(25 ≤ Zjg < 26)
We control also for school networks fixed effects
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Results
New “Metco type” evidence
N. Natives β̂
(pooled across grades)
Language
Mathematics
-0.0018***
-0.0020***
(0.001)
(0.001)
N. Immigrants γ̂
-0.0144***
-0.0156***
(0.004)
(0.004)
(Pure) Composition δ̂
-0.0126***
-0.0137***
(0.004)
(0.004)
Observations
584,023
556,290
Network of schools FE
YES
YES
Grade FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
F-test excluded instruments
Natives
464.1
440.6
Immigrants
309.7
324.7
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Results
New “Metco type” evidence
(language; separate by grade)
N. Natives β̂
2nd Grade
5th Grade
-0.0021**
-0.0020***
(0.001)
(0.001)
N. Immigrants γ̂
-0.0114*
-0.0178***
(0.007)
(0.005)
(Pure) Composition δ̂
-0.0093
-0.0158***
(0.006)
(0.004)
Observations
292,166
291,856
Network of schools FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
Natives
232.4
230.4
Immigrants
45.5
159.3
F-test excluded instruments
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Results
New “Metco type” evidence
(math; separate by grade)
N. Natives β̂
2nd Grade
5th Grade
-0.0025**
-0.0025***
(0.001)
(0.001)
N. Immigrants γ̂
-0.0132**
-0.0196***
(0.007)
(0.005)
(Pure) Composition δ̂
-0.0107*
-0.0171***
(0.006)
(0.004)
Observations
277,420
278,870
Network of schools FE
YES
YES
Individual specific controls
YES
YES
Class level controls
YES
YES
Natives
233.7
227.3
Immigrants
53.3
159.1
F-test excluded instruments
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Results
Concluding remarks
We propose:
a an extension of Lazear’s educational production function to emphasize
that the effect of immigrants on natives is confounded by adjustments in
class size
a strategy to identify the pure class composition effect, controlling for
class size changes, that exploits rules of class formation
Preliminary results:
Modest composition effect (≈ −1%) in both language & mathematics
- for students enrolled in the 2nd (age 7) and 5th grade (age 10)
- the size of the effect is about 15% of the effect of poor parental background
IV estimates larger than OLS because in the latter the PCE is confounded
by class adjustments
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Results
Thank You
It is preliminary
Questions and comments
are welcome
You can contact us at
rosariomaria.ballatore@bancaditalia.it
margherita.fort@unibo.it
andrea.ichino@unibo.it
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Results
Actual and Theoretical Class Size in Italy
2nd Grade
5th Grade
Grade 5
Language Sample
15
15
Class Size
20
Class Size
20
25
25
Grade 2
Language Sample
0
50
100
Enrollment in Building
Predicted
Actual (avg.)
10
10
Predicted
Actual (avg.)
150
0
50
100
Enrollment in Building
150
Very similar pattern in grade 2 and 5
Back
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Results
Rules concerning space for immigrants
Ministero dell’Istruzione, dell’Università e della Ricerca
Dipartimento per l’Istruzione
Direzione Generale per gli Ordinamenti del Sistema Nazionale di Istruzione e per l’Autonomia Scolastica - Ufficio Sesto
Circolare n. 4
MIURA00DGOS prot. n. 381/R.U.U
Roma, 15 gennaio 2009
...
10.2 Accordi di rete e intese territoriali
È opportuno che le istituzioni scolastiche, al fine di evitare la concentrazione in talune scuole di iscrizioni di alunni con cittadinanza
non italiana e conseguenti squilibri e disagi della popolazione scolastica, realizzino accordi di rete per una razionale distribuzione
terri- toriale delle domande, procedendo, quindi, ad un’equa assegnazione degli alunni alle diverse classi
(cfr DPR 31 agosto 1999 n. 394, art. 45, commi 3 e 5).
I Direttori Generali degli Uffici scolastici regionali avranno cura di promuovere le iniziative ritenute più opportune al fine di
attivare gli accordi di rete.
Le scuole, possibilmente con azioni in rete, vorranno, pertanto, sollecitare o assecondare attivamente le iniziative degli
Enti locali e/o di altri soggetti a livelli istituzionali per l’adozione di misure di prevenzione, orientamento e controllo
circa l’assolvimento dell’obbligo di istruzione.
Nelle città e nei grandi centri urbani in cui sono presenti ampie reti di scuole, le iscrizioni di alunni con cittadinanza non
italiana anno gestite in maniera partecipata e programmata, in modo che la domanda e l’offerta di servizi scolastici risultano
equamente distribuite.
...
Back
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Results
First stage
Relative Space for Immigrant in Class, net of controls
0
.1
-.2
-.1
.2
Expected Relative Space For Immigrants in Class
based on expected # of natives in class & rules for class splitting
10
15
20
Expected Number of Natives in Class
25
Back
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