Empirical Education
Research
Lent Term
Lecture 3
Dr. Radha Iyengar
Last Time

Model of Human Capital Acquisition




Choose optimal schooling where MB=MC
For some individuals, MC lower because of
ability (ability bias)
For some individuals, MB higher because of
group/family factors (heterogeneity)
IV estimates my be “unbiased” for a given
subgroup but the returns in that subgroup may
be very different than other groups
Topics Covered Today
Broadly 3 Major Strands of Empirical Research

Returns to Education (Ability Bias)



Credit Constraints and Education Investment



Angrist and Krueger
Ashenfelter and Rouse
Carneiro and Heckman
Dynarski
Education Production Function




Hanushek
Krueger
Hoxby
Rouse and Figlio
Estimating Returns to Education

Generally 3 approaches:



Cross-sectional variation (Mincer Regression)
Within group differences
Instrumental Variables
Mincer Regression

log( y ) = a + bS + cX + dX2 + e

Estimated worldwide with estimates
ranging from 0.05 to 0.15

Linear model fits the data well even in
countries with very different economies,
education system, etc.
Source: Angrist and Lindhal (2001) JEL
Issues with Mincer Regression

How to interpret the coefficient on
schooling?





Ability bias: Upward “bias”
Heterogeneity in effects: ???
Measurement Error: Downward “bias”
Signalling vs. Human Capital (next week)
In practice, OLS seems to be slightly,
though not significantly smaller than the
IV approaches
Simple Solution to Ability Bias

The simplest way of dealing with this
problem is to find a measure of ability (IQ,
AFQT, or similar) BUT



no good reason to expect the relative ability
bias to be constant across people
This is especially a problem if b differs across
ages and other groups
Also the relationship between ability and
schooling varies greatly across time and
individuals.
Instrumental Variables

Basic goal: Find something that varies schooling
but is uncorrelated with unobserved factors (e.g.
ability)

Estimate the component of schooling predicted
by “instrument”

Use predicted schooling (rather than actual
schooling) to estimate relationship between
schooling and earnings
Various Instruments

Card: Proximity to 2-Year or 4-Year
colleges + Parent’s education

Kane & Rouse: Tuition at local 2-year and
4-year colleges

Angrist & Krueger: Quarter-of-birth and
compulsory schooling laws
Compulsory Schooling IV

Angrist and Krueger (AK) use quarter of birth as
an instrument for education to determine the
impact of education on earnings.

quarter of birth impacts education attainment b/c
compulsory schooling laws,

this source of schooling variation is uncorrelated
with other factors influencing earnings,
Does quarter of birth affect education?

Regress de-trended education outcomes
on quarter of birth dummy variables:
( Eicj  Ecj )    1Q1   2Q2   3Q3   ijc
(individual i, cohort c, birth quarter j,
education outcome E, birth quarter Q)
 This shows that Q does impact education
outcomes such as total years of
education and high school graduation.
Is Schooling related to Quarter of Birth?
Is this due to compulsory schooling laws?- 1

Indirect evidence:


Examine impact of birth quarter on postsecondary outcomes that are not
expected to be affected by compulsory
schooling laws.

No birth quarter impact on postsecondary outcomes is consistent with a
theory that compulsory schooling laws are
behind the birth quarter-education
relationship for secondary education.
Is this due to compulsory schooling laws?- 2

Direct evidence: Construct a difference-indifference measure of schooling law
impact between high age requirement
states and low age requirement states:
Impact of Law  [(% E age16, high  % E age16,low )  (% E age15, high  % E age15,low )]
%Eage 16, high is the fraction of 16 year olds enrolled in high school
in states where attendance in mandatory up to age 17 or 18)
How to estimate: OLS

Wald estimate compares the overall
difference in education and earnings
between Q1 and Q2-4 individuals
Wald 

log WageQI  log WageQII QIV
EducQI  EducQII QIV
Consistency requires that the grouping
variable (Q) is correlated with education
(Educ), but uncorrelated with wage
determinants other than education.

For instance, this assumes that ability is
distributed uniformly throughout the year.
Difference-inDifferences
estimate of
about 4%
Decreasing
effect over
time. Maybe
because of
increasing
returns to
college
IV Estimates
Two-Stage Least Squares (2SLS) uses
quarter of birth to predict education, then
regresses wage on this predicted value of
education to estimate the return to
education (ρ)
 First stage:
E i  X i  C Yic  c  j Yic Qij jc   i


Second stage:
log Wi  X i  C Yic c  Ei   i
Correlation between QOB and Schooling
IV Estimates of Return to Schooling
Summary of AK

Quarter of birth is a valid instrument: affects educational
attainment through compulsory schooling laws, not through
unobserved ability




First quarter individuals (who enter school at an older age and
can leave earlier too) receive about 0.1 fewer years of schooling
and are 1.9% less likely to graduate from HS than those born in
the fourth quarter.
Quarter of birth is found to be unrelated to post-secondary
educational outcomes.
Between 10 to 33% of potential drop outs are kept in school
due to compulsory attendance laws.
Returns to an additional year of schooling are remarkably
similar to those estimated with OLS, approximately 7.5%
depending on the specification.
What about variation in marginal
benefits?

Think that marginal benefits different for
different people

Want to see how shifts in marginal benefit
curve affect investment in schooling

Need assumption on how marginal
benefits vary
Within Family Estimates

Some of the unobserved differences that
bias a cross-sectional comparison of
education and earnings are based on
family characteristics

Within families, these differences should be
fixed.

Observe multiple individuals with exactly the
same family effect, then we could difference out
the group effect
Estimating Family Averages

Can look at differences within family effect

This of this as a different CEF for each family
E[Yij -Yj | S, X, f] = a + b(Sij – Sj) + c(Xij – Xj) +
c(X2ij – X2j)

The way we estimate this:
log( yij)  aˆ  bˆSij  cˆXij  dˆXij 2  fˆj  eˆij
What makes this believable

No within family differences

Might be a problem with siblings generally




Parents invest differently
Cohort related differences—influence siblings
differently
Different “inherited” endowment
More believable with identical twins
A twins sample

Ashenfelter and Rouse (AR) Collect data at
the Twins festival in Twinsburg Ohio

Survey twins:




Are you identical? If both say yes—then included
Ever worked in past two years
Earnings, education, and other characteristics
Useful because also get two measures of
shared characteristics, so can control for
measurement error
Comparing twins to others

Sample at Twinsburg NOT a random sample
of twins



Benefit: more likely to be similar because
attendees are into their “twinness”
Cost: not necessarily generalizable, even to
other twin
Attendees select segment of the population


Generally Richer, Whiter, More Educated, etc.
Worry about heterogeneity of effects across
some of these categories
Where’s the variation

Recall our estimating equation
2
ˆ
ˆ
log( yij)  aˆ  bSij  cˆXij  dXij  fˆj  eˆij

If Sij is the same in both twins, no
contribution to estimate of b

Only estimated off of twins who are
different from each other in schooling
investments
Correlation Matrix for Twins
Education of twin 1, Education of twin 1,
reported by twin1
reported by twin2
ALL of the identification for b comes from the 25% of twins who don’t
have the same schooling
Summary of AR

Consistent with past literature—returns
around 8-10 %

OLS estimate slight upward bias but with
measurement error there’s a slight
downward bias

Ability bias less of a problem than
measurement error
General Conclusions on RTS

Returns appear to be between 8-12 percent in
the US

Not much different between OLS, IV, and within
family estimators



Maybe ability bias not as much of problem as we
thought
Maybe there’s an offsetting bias (marginal benefits,
measurement error etc.)
Maybe the estimation strategies are not
eliminating the source of the bias—i.e. some
other factor is affecting all these estimates.
Credit Constraints and Education

We’re always assuming selection into education
(esp higher education) on ability but may also be
on resources

Can’t borrow against future earnings so if don’t
have high asset endowment, hard to afford extra
schooling
References

Carneiro and Heckman (2002) “The Evidence on credit constraints in
Post-Secondary Schooling” Economic Journal 112: 705-734
Dynarski (2003) “Does Aid Matter: Measuring the Effect of Student Aid on
College Completion” American Economic Review 93(1)
% Attending College related to Parent’s
Income
How do Credit Constraints affect RTS
Estimates?

IV estimates of the wage returns to
schooling (the Mincer coefficient) exceed
least squares estimates (OLS) is consistent
with short term credit constraints.


The instruments used in the literature are invalid
because they are uncorrelated with schooling or
they are correlated with omitted abilities.
Even granting the validity of the instruments, IV
may exceed least squares estimates even if there
are no short term credit constraints
The Quality Margin

The OLS-IV argument neglects the choice
of quality of schooling.


Constrained people may choose low quality
schools and have lower estimated Mincer
coefficients (‘rates of return’) and not higher
ones.
Accounting for quality, the instruments used in
the literature are invalid because they are
determinants of potential earnings.
The general issue

Individuals cannot offer their future earnings as
collateral to finance current education

Individuals from poorer families with limited
access to credit will have more trouble raising
funds to cover college

This affects:



Attendance in college
Completion of college
Quality/content of education
Two theories for the facts

Higher income parents produce higher
“ability” children or invest more in their
children

Access to credit means low-income
individuals don’t attend college, reducing
their human capital and reinforcing the
relationship between schooling and
earnings
Return to our model



Let’s ignore experience (for ease) and so consider
the model
log( y )  Y  a  bS  e
Let’s also define the wages in for two groups:
College Grad and HS Grads
ln( y0 )  Y 0 attendance:
0  U 0
ln( y1 ) decision
Y 1  1  Urule
1
specific
on college


S = 1 if Y1 – Y0 – C > 0, and S = 0 otherwise.
We can think of C as representing the costs of schooling
(e.g. tuition)
Defining IV and OLS Estimates

Suppose the true model we want to
estimate is:
Y  a  bS  A  e

Then for an instrument Z , our OLS and IV
estimates are:
Cov( A, S )
bˆOLS  b  
Var ( S )
Cov( A, Z )
ˆ
bIV  b  
Var ( Z , S )
Why might IV be bigger than OLS

Taking homogeneous returns, if we believe
γ>0, then IV > OLS if
Cov( A, Z ) Cov( A, S )

Cov( S , Z )
Var ( S )

Or rescaling and taking the case were
COV(Z,S)>0
 ZA   SA  SZ
Source: Carneiro and Heckman (2002)
Estimating the effect of Costs

Suppose the instruments are valid and b varies
across the population

Let C=0 then individuals with higher b will get
more schooling

The returns to schooling are

Same true if C not to big and not too strongly
E
[
b
|
S

1
]

E
[
Y

Y
|
S

1
]
1
0
correlated with Y1 – Y0
High costs not so correlated with RTS
people with
characteristics
that make
them more
likely to go to
school have
higher returns
on average
than those with
characteristics
that make
them less likely
to go to school.
Negative Selection

Individuals with high b also have high C
then



Marginal entrants to college have higher
average returns than the population average
In the extreme: dumb kids have rich parents,
smart kids have poor parents
IV estimates will isolate returns of smart kids
and will exacerbate ability bias relative to OLS
High costs correlated with RTS
Does increase Aid increase College
Attendance
Source: Dynarski, 2003
Empirical Evidence for Credit
Constraints

Not much to support it—some evidence of
responses to subsidies but:



Mostly go to people likely to go to college anyway
Hard to separate out relaxing credit constraints from
subsidizing for marginal, unconstrained individuals
Other margins of adjustment


Reduce cost and reduce quality
education of low-income individuals not comparable to
high-income
Education Production

If education is valuable good (i.e. it has high
returns)—need to worry about how it is produced

If can’t get adjustments on the quantity margin—
maybe we can get it at the quality margin

Usually think about education as representing
some intangible thing that’s valuable


Responsible people
Democratic values
Production Function

Define
Eist = f( NSist, Rist, Xist, ε)

NS: Non school inputs, not under control of school s in
year t



R: School inputs NOT under control of school s in year t



Innate ability of students
Parent’s wealth
Resources
Student type (peers)
X: School inputs under control of school s in year t



Class size
Teacher quality
curriculum
Estimation
Usually don’t worry about function form—
just think of it linearly
Eist = α+ β*NSist + γ*Rist +δ*Xist + εist

Can look at the effect of change in any of
the factors on “education”
 Usually looking to estimate either δ
(Returns to resource investment) or γ


Often end up estimate δ+ γ
Outcome measures

Choice matters



depends on what you think the intervention/investment
will effect
Depends on what makes education productive
Common choice



Wages
HS graduation/college attendance
Test scores



Frequent
Cheap
Noisy but correlated with stuff we care about
What to estimate

Value added model


Change in outcomes
Eist – Eist-1

Control for what’s new to students in
current year
Eist = α+ λ*Eist-1 β*NSist + γ*Rist +δ*Xist +
εist

These are the same if λ=1
What have people found?

Hanushek (1997) JEL meta-analysis



Aggregate across papers
No clear relationship between inputs and
schooling
Krueger (2003)



Weight papers equally: systematic positive
relationship
Weight papers in proportion to number of
estimates, not related
Tennessee Star Experiment
Issues with the literature

Class size coefficient mixes up two things



Resources put into teachers (e.g. salary)
Teacher pupil ratio
Define log expenditures as EXP, log
teacher pupil ratio at TP and log teacher
salary as L, which are related as follows:
EXP= L + T
Model of production

The true model we want to estimate is:
E( y ) = α + τ*TP + λ*L

If instead we estimate, we have a problem:
E ( y )  ˆ  ˆ * TP  ˆ * EXP    (   ) * TP   * L

If proportionate changes in the teacher-pupil
ratio and teacher pay have equal effects on
achievement, ψ will be zero.
Why might class-size be important

Lazear (1999) presents a simple model of classsize in




probability of a child disrupting a class is independent
across children,
the probability of disruption is intuitively increasing in
class size.
Assuming that disruptions require teachers to suspend
teaching it will tend to reduce the amount of learning for
everyone in the class.
There may be other benefits to smaller classes as
well such as closer supervision or better tailoring
to individual students.
Evidence on Class Size-1

Tennessee Star Experiment:

Students randomly assigned to one of 3 classtypes:






Small (13-17 students)
Regular(22-25 students)
Regular + Teacher’s aid
Newly entering students randomly assigned to
one of the class-types
Continue assignment through 3rd grade
Analyzed by Krueger (QJE, 1999)
Distribution of treatment effects
Class size Evidence-2

Maimonides Rule (Angrist and Lavy)




Use rule in Israel to determine class-size
25 students: 1 teacher
25-49 students: 1 teacher + aide
50+ students: 2 teachers
Maimonides Rule
Using predicted class-size
Reduced Form Estimates
IV Estimates
General Class-size Evidence

On balance probably increase test scores

Even at young ages, after first year gains
from increase test scores smaller

In later years, gains smaller

Heterogeneous and about 1/3 of students
may not gain in smaller classes
School Incentives

Broadly two types of studies



Incentives from competition (vouchers,
increased number of schools in an area, etc.)
Incentives from monitoring/accountability
standards (e.g. NCLB)
Other work on increases in teacher pay,
but hard to separate selection from
incentives in increased performance
School competition

Best evidence probably from Hoxby
(2000): uses streams to identify school
district boundary. IV estimates suggest
school competition helps

Criticism from Rothstein: sensitivity to
specification and definition of stream.
Results might not be that robust
School Accountability

Mixed Evidence:

Rouse (QJE, 1998):



Wisconsin vouchers program gave students in low
performing schools vouchers to private school
Gains in math, no gains in reading
Rouse (JPubEc, 2006):





Look at FL program, similar to NCLB, imposes standards
and if fall below standards, close schools and issue
vouchers.
Changes in raw test scores show large improvements
associated with the threat of vouchers.
much of this estimated effect may be due to other factors.
The relative gains in reading are largely explained by
changing student characteristics
the gains in math are limited to the high-stakes grade.