Topic 3
C15 Economic Policy Analysis
Education: School inputs and pupil performance
Kjell G. Salvanes
November 10 and November 17, 2003
School quality is again on top of the policy agenda
Topics:
• Relationship between school inputs (class size,
eduation of teachers) and student performance
(scores, wages)
– Do we need more resources or better teachers?
– For which student outcomes does resources matter for?
– Does it matter for all students?
• Educational attainment at high school and
university level is another issue
– Are compulsory school laws necessary?
2
Topics cont’
• Does privatisaton of schools/universities matter?
• How will increased university fees matter?
• Selective schools or comprehnesive schools?
• How should we evaluate whether school inputs,
compulsory school laws and educational policy in
general matter for student outcomes?
3
Todays lecture
• The impact of school resources and student
performance
• Methodological issues
• The impact of compulsory school laws on
educational attainment wages
4
School resources and student performance
Is there a connection?
TIMSS performance and spending (in US purchasing power, primary
schools)
(countries ranked by TIMSS aggregates)
8000
6000
5000
4000
3000
2000
1000
Israel
Portugal
Italy
Greece
Spain
Denmark
Thailand
France
Norway
Hungary
United
States
United
Kingdom
Germany
Switzerland
Sweden
Czech
Republic
Ireland
Australia
Austria
Belgium1
Netherlands
Japan
0
Korea
spending/student
7000
5
School resources and student performance
• What are we trying to measure
– We have two schools – one using a high level of
resources per students (small classes) and one little
resoruces.
– Pick two identical students and put one in each of the
schools and test performance after a year.
• We cannot do this and we end up comparing
results for students in schools with for instance
large and small classes.
• How can we estimate the causal effect of school
resources on student performance?
6
School resources and student performance
• Problems
– Too little variation in e.g. class size:
• Between 18 and 30 students per class
– Other factors may be important in explaining
differences in student performance and which is
correlated with class size
– Teachers use small classes for less able students
– Parents choose neighbourhood based on school quality
(class size)
– School with small class size may also have other
benefits (attracting better teachers etc)
7
Methods used to evaluate the impact
of school resources
• Experiments
– Randomly assign students to different types of schools
• Cannot do usually
• Collect data and evaluate by estimating
something like:
– Achievement = preparation+ families + peers
+schools
– 1) Natural experiments – Instrumental variables
– 2) Matching
8
Causal effect vs correlation
• Consider the realtionship between student
performance Yi and School resources Si
Yi=a+(b+vi)Si+ui
Si=1 denotes a small class size, b+vi is the
unobserved returns to be in a class with
much resources, and ui represents all other
individual resources determining
performance.
9
Different measures
• The expected (average) performance outcome for
those in a small class (Si=1):
E(YiS=1-YiS=0|S=1)=b+E(vi|S=1)
This measure is called treatment of the treated.
|The second term reflects the way pupils are selected
into small classes: if those who benefit most from small
classes there is a positive correlation between their
characterisics, vi, and small classes, S=1:
E(vi|S=1)>0
10
Different measures
• Compare those in small classed to those in
large classes.
E(Yi|S=1)- E(Yi|S=0)
=b+E(vi|S=1)
+ E(ui|S=1)- E(ui|S=0)
The last term is the selection bias
11
Different measures
• The point is the students in large classes
may be different from the students in the
small classes in a systematic way such that
performance differences are attributed to
these differences in stead of class size.
• Rich /highly educated parents have their
children in schools with more resources and
small classes.
12
Methods to solve these problems
• Experiments
– Construct the assigment such that there is no systematic
relationship between class size and students
background variables:
E(ui|S=1)= E(ui|S=0)
– Hence there is no selection bias
• However:
– Expensive,
– Unethical
13
Other methods
• Natural experiements or IV
– Use information that allocates students to
schools with large and small resources to avoid
selection problems
– Problems:
– Depending on which instrument is being used
to decide allocation into different schools, the
results may only apply for a certain group of
students
14
Other methods
• Matching
– Basically the method is to compare individuals in small
and large class sizes that are identical on observable
characteristics Xi
– I.e. assume that for a set of observed characteristics X
(family background etc), we have that
E(ui|Xi,Si)=jXi
This means that both the allocation rule deciding whether
you og to a small or large school or not and the impact
of that experience depend on observable characteristics.
15
Measuring heterogeneity in returns to
education in Norway using educational
reforms
Arild Aakvik*
Kjell G. Salvanes
Kjell Vaage*
*University of Bergen
Norwegian School of Economics and SSB
November 10 and November 17, 2003
Approaches and results in papers on
the reading list
• Krueger : ”Experimental estimates of
education production functions”
– Class size and test scores
– Method: Experiment ; STAR project in
Tennessee; random assignment of pupils and
teachers after kindergarten to small (1317)/regular (22-25) schools , stayed for 4 years
• Results:
– Effect after one year on standarized tests
– The advantage is kept throughout the 4 years.
17
Approaches and results in papers on
the reading list cont’
• Dearden, Ferri & Meghir
• Method: condition on a lot of background
variables
• Measure educational attainment and wages
on class size, British data
• Impact on women’s wages
• No impact on men’s wages and eduational
attainment
18
Approaches and results in papers on
the reading list cont’
• Dustmann, Rajah, van Soest
– Data: England and Wales
– Method: Controll for background variables
– Measure effect of class size on educational
attainment and wages
– Find strong impact of class size on the decision
to stay on in school after 16 and on wages
19
Measuring the Effect of a School Reform
on Educational Attainment and Earnings
Arild Aakvik*
Kjell G. Salvanes
Kjell Vaage*
*University of Bergen
Norwegian School of Economics, IZA-Bonn and SSB
20
Background
• Controversy regarding returns to education
especially due to selection concerns and
heterogeneity in returns
• The decision to take more education is a complex
process.
– ability, financial constraint and preferences are usually
unobserved for the researcher; endogeneity problem
– heterogeneity in the return heterogeneity arises if
individuals select into education based on their
comparative advantages of education
21
• A natural but mainly unexploited resource of
information to overcome these problems are the
educational reforms in the European countries in
the postwar period.
• The focus in the present paper is to exploit some
interesting features of one of the school reforms in
Norway - the school reform extending the
mandatory years of schooling from 7 to 9 years.
• The reform took 10 years to implement and we
observe same birth cohorts going through both
compulsory school systems.
• Use additional reforms to identify a Roy model
22
• We utilize a flexible framework and a very
rich data set to study different return
parameters of education, both in a linear and
non-linear fashion
• we allow the effect of education to vary both
in terms of observed and unobserved factors.
• This model is termed a random coefficient
model where we estimate returns to different
levels of education (Roy model)
23
Overview
•
•
•
•
•
•
The reform
The reform as an instrument
+ additional identification strategy
The data
Effects on educational attainment
Two model of estimating returns
– Continuous in education
– Using a flexible Roy model for education levels
24
Aims of the reform
• Increase the minimum level of education
• Smooth the transition to higher education
• Enhance equality of opportunities along the
socio-economic and geographical
dimensions
25
The school reform
• From 7 to 9 years of compulsory schooling
Old system:
New system:
• Implemented from 1959-1974 (1961-1970)
• Impl. at municipality level, decided locally
• Social experiment:10 cohorts (1948-1957)
passing through 2 different school systems
• Targeted to certain groups
26
Reforms in other countries
• Similar reforms in Sweden (Meghir &
Palme, 1999, 2001), UK (Blundell et al.
1997), France, Germany, etc.
• The reform went further in Norway in terms
of unification and in promoting equality of
opportunity (Leschinsky and Mayer, 1990)
27
Effects of the school reform?
• Are there different educational outcome for
individuals in the pre vs. post reform system?
• Did the reform help the targeted groups in attaining
higher education?
• Can we use this (potential) variation to estimate the
returns to education, i.e. can we use the reform as
an instrument?
• Using upper secondary reforms/college reform as
additional instruments (distance to higher
education)
28
The reform as an instrument
• Is the reform correlated with the variable
for which it serves as an instrument, i.e. did
it lead to increased educational attainment?
For all? For some?
• Is the reform uncorrelated with earnings
(except indirectly through the schooling
variable), or does it pick up other
characteristics of the municipalities?
29
Reform implementation and
municipality characteristics
• Implementation decided at municipality level,
costs reimbursed by the Government
• Government’s strategy: reform implementation
according to a representative set of municipalities
• No signs of selection on municipality observables
in our data
30
Data
• SN’s administrative registers: earnings, cohort and
county indicators, work experience, education
(highest obtained)
• National census of population and housing: residing
municip. during school, family income from 1970
• Males in full-time job
• Education and earnings measured in 1995
• Reform dummy
• Availability of high school, college, university in
the municipality
31
Construction of reform indicator
• Use census-data on parents’ residence in 1960 and
1970 to assign schooling municipality
• Combine with register-data at municipality level
• Problems:
(i) 20% of the munic. used > 1 year
(ii) Commuting between residence and school
(iii) Special arrangement for the earliest cohorts
(iv) School reform coincides with municipality
reform
32
Construction of reform indicator
(continued)
• SN-data on individual reform assignment, but only
for the group that left school after compulsory
schooling (16%)
• Our strategy: Combine Municipality Register and
SN data, dropping cohorts - but not municipalities!
- with missing or uncertain information
• Use fraction of pupils on reform in the
municipality as the reform indicator
33
School choice
• Continuous (7-20 years)
• Categorical (7 different levels)
1) Pre/post reform compulsory school (7/9 years)
2) Upper secondary school 1 year; mainly vocational
3) Upper secondary school 2-3 years; mainly vocational
4) Upper secondary school 2-3 years; gymnasium
5) University I, post upper secondary school, 1-2 years
6) University II, post upper secondary school, 3-4 years
7) University III, master level, university degree, 5+ years
34
O Probit Models of school choice
• Switching regression
• Covariates:
- Age cohort dummies
- Municipality variables
- Parental education
- Family income (percentiles)
• Derive generalised residuals (li) for the earnings
equation
35
Observed pre and post reform education
•
•
•
•
Birth cohorts 1948-57.
•
•
•
•
•
•
•
•
1 Pre/post comp.
0.213
0.135
-0.078
-36.6
2 Vocational I
0.167
0.180
0.013
7.8
3 Vocational II 0.249
0.303
0.054
21.2
4 Upper secondary
0.043
0.060
0.017
39.5
5 University I
0.134
0.135
0.001
0.8
6 University II
0.092
0.093
0.001
1.1
7 University III
0.099
0.090
-0.009
-9.1
________________________________________________________________
Levels
Pre-reform Post-reform Change Change in %
________________________________________________________________
36
Predicted pre and post reform education
Conditional on cohort, region and family income & education
•
•
•
•
•
•
•
•
•
•
•
•
•
Birth cohorts 1948-57.
Levels
Pre-reform Post-reform Change Change in %
_______________________________________________________________
1 Pre/post comp.
0.195
0.141
-0.054 -27.8
2 Vocational I
0.159
0.183
0.024
15.1
3 Vocational II
0.248
0.307
0.058
23.7
4 Upper secondary
0.044
0.060
0.016
38.3
5 University I
0.139
0.133
-0.006 - 4.5
6 University II
0.098
0.089
-0.008 - 8.9
7 University III
0.114
0.084
-0.030 -26.7
_______________________________________________________________
37
Earnings equations,
sources of possible biases
• Unobserved individual heterogeneity
- ability
- financial constraints
• Heterogeneity in returns
- self selection to education level based on
comparative advantage
• Non-linearity in returns to education
UNIVERSITY OF BERGEN
38
Earnings equations,
specifications
• Instrumental Variable ( LATE):
log yi = Xib + aSi + ai + Ui
log yi = Xib + aSi + rli + Ui
• Random Coefficient Model ( ATE):
log yi = Xib + (d+ti)Si + ai + Ui
log yi = Xib + dSi + qli Si + rli + Ui
39
The Roy model
• Run the Randdom coefficient model for each
education level
E(log yi)=Xib + aSi + rli
We can then estimate the return to education
by comparing the different estimated model
parameters for a given x is simply calculated
from
ΔATE(x) =xi(βl-βl-1)+(rl- rl-1) li
ΔTT(x) =xi(βl-βl-1)+(rl- rl-1) li
40
Earnings equations,
estimated coefficients
Earnings equations, full time men, cohorts 1948-57
OLS
Education
IV
RCM
0,0754451 *
0,1010064 *
0,0546282 *
0,0003998
0,0018642
0,0023033
0,0472469 *
0,0123857 *
0,0033657
0,0035105
Lambda
Education*Lambda
-0,0131717 *
0,0003857
Tenure
Tenure2
Experience
Experience2
R-Squared
Number of Obs,
0,0104852 *
0,0105042 *
0,0005041
0,0005039
-0,0004829 *
-0,000483 * -0,0004832 *
0,0000234
0,0000234
0,0000234
0,0446061 *
0,0453716 *
0,0456544 *
0,0016455
0,0016466
0,0016658
-0,0007032 *
-0,000714 * -0,0007207 *
0,0000409
0,0000409
0.22
134884
0.22
134884
0,0105124 *
0,000504
0,0000413
0.23
134884
41
Result from the Roy model
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Table 6.2. Returns to education in percent.
=======================================================
No selection
Selection
------------------------------------ATE TT
ATE
TT
------------------------------------------------------1
2 -00.2 01.2
04.8 01.5
3
08.3 08.8
08.8 09.2
4
20.7 21.1
22.1 21.7
5
27.0 26.8
23.8 27.4
6
21.8 21.9
15.7 22.7
7
44.6 42.3
31.7 43.3
-------------------------------------------------------
42
Main findings
• The reform enhanced educational attainment for
low achievers
• Pupils from low income families were picked up
by the reform (?)
• OLS gives biased estimates of the returns to edu.
43
Main findings
• Non-linearity in returns to education
• Selection on unobservables appears to be
important
• Appears to be hard to obtain gains from inducing
a very high proportion to university education
44