Empirical Education Research

Lent TermLecture 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 TodayBroadly 3 Major Strands of Empirical Research Returns to Education (Ability Bias)

Angrist and Krueger Ashenfelter and Rouse

Credit Constraints and Education Investment 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:

(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.

ijccjicj QQQEE 332211)(

Is Schooling related to Quarter of Birth?

Is this due to compulsory schooling laws?- 1

Indirect evidence: Examine impact of birth quarter on post-

secondary outcomes that are not expected to be affected by compulsory schooling laws.

No birth quarter impact on post-secondary outcomes is consistent with a theory that compulsory schooling laws are behind the birth quarter-education relationship for secondary education.

Direct evidence: Construct a difference-in-difference measure of schooling law impact between high age requirement states and low age requirement states:

%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)

)]%(%)%[(% ,15,15,16,16 lowagehighagelowagehighage EEEELaw of Impact

Is this due to compulsory schooling laws?- 2

How to estimate: OLS Wald estimate compares the overall

difference in education and earnings between Q1 and Q2-4 individuals

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.

QIVQIIQI

QIVQIIQI

EducEduc

WageWageWald

loglog

Difference-in-Differences 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:

Second stage:

ijcijc j icC icii QYYXE

iicC icii EYXW log

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 familyE[Yij -Yj | S, X, f] = a + b(Sij – Sj) + c(Xij – Xj) +

c(X2ij – X2

j)

The way we estimate this:

ˆˆˆˆˆˆ)log( 2ijjijijijij efXdXcSbay

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

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

ˆˆˆˆˆˆ)log( 2ijjijijijij efXdXcSbay

Correlation Matrix for Twins

Education of twin 1, reported by twin1

Education of twin 1, 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

ReferencesCarneiro and Heckman (2002) “The Evidence on credit constraints in Post-

Secondary Schooling” Economic Journal 112: 705-734Dynarski (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

Let’s also define the wages in for two groups: College Grad and HS Grads

specific decision rule on college attendance: 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)

ebSaYy )log(

1111)ln( UYy 0000 )ln( UYy

Defining IV and OLS Estimates Suppose the true model we want to

estimate is:

Then for an instrument Z , our OLS and IV estimates are:

eAbSaY

)(

),(ˆSVar

SACovbbOLS

),(

),(ˆSZVar

ZACovbbIV

Why might IV be bigger than OLS Taking homogeneous returns, if we believe

γ>0, then IV > OLS if

Or rescaling and taking the case were COV(Z,S)>0

)(

),(

),(

),(

SVar

SACov

ZSCov

ZACov

SZSAZA

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 correlated with Y1 – Y0

]1|[]1|[ 01 SYYESbE

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.

High costs not so correlated with RTS

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 Innate ability of students Parent’s wealth

R: School inputs NOT under control of school s in year t 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 linearlyEist = 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 yearEist = 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:

If proportionate changes in the teacher-pupil ratio and teacher pay have equal effects on achievement, ψ will be zero.

LTPEXPTPyE **)(*ˆ*ˆˆ)(

Why might class-size be important Lazear (1999) presents a simple model of class-

size 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 class-

types: 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.