Empirical Education Research

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Empirical Education Research

• Lent Term
• Lecture 3
• Dr. Radha Iyengar

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Last Time

• Model of Human Capital Acquisition
• Choose optimal schooling where MBMC
• 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

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Topics Covered Today

• Broadly 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

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Estimating Returns to Education

• Generally 3 approaches
• Cross-sectional variation (Mincer Regression)
• Within group differences
• Instrumental Variables

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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.

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Source Angrist and Lindhal (2001) JEL
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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

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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.

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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

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Various Instruments

• Card Proximity to 2-Year or 4-Year colleges
  Parents education
• Kane Rouse Tuition at local 2-year and 4-year
  colleges
• Angrist Krueger Quarter-of-birth and
  compulsory schooling laws

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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,

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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.

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Is Schooling related to Quarter of Birth?
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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.

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Is this due to compulsory schooling laws?- 2

• Direct evidence Construct a difference-in-differe
  nce 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)

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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.

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Difference-in-Differences estimate of about 4
Decreasing effect over time. Maybe because of
increasing returns to college
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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 (?)
• First stage
• Second stage

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Correlation between QOB and Schooling
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IV Estimates of Return to Schooling
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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.

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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

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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

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Estimating Family Averages

• Can look at differences within family effect
• This of this as a different CEF for each family
• EYij -Yj S, X, f a b(Sij Sj) c(Xij
  Xj) c(X2ij X2j)
• The way we estimate this

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What makes this believable

• No within family differences
• Might be a problem with siblings generally
• Parents invest differently
• Cohort related differencesinfluence siblings
  differently
• Different inherited endowment
• More believable with identical twins

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A twins sample

• Ashenfelter and Rouse (AR) Collect data at the
  Twins festival in Twinsburg Ohio
• Survey twins
• Are you identical? If both say yesthen 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

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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

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Wheres 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

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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 dont have the same schooling
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Summary of AR

• Consistent with past literaturereturns around
  8-10
• OLS estimate slight upward bias but with
  measurement error theres a slight downward bias
• Ability bias less of a problem than measurement
  error

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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 theres an offsetting bias (marginal
  benefits, measurement error etc.)
• Maybe the estimation strategies are not
  eliminating the source of the biasi.e. some
  other factor is affecting all these estimates.

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Credit Constraints and Education

• Were always assuming selection into education
  (esp higher education) on ability but may also be
  on resources
• Cant borrow against future earnings so if dont
  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)

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Attending College related to Parents Income
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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

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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.

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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

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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
  dont attend college, reducing their human
  capital and reinforcing the relationship between
  schooling and earnings

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Return to our model

• Lets ignore experience (for ease) and so
  consider the model
• Lets 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 gt 0, and S 0 otherwise.
• We can think of C as representing the costs of
  schooling (e.g. tuition)

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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

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Why might IV be bigger than OLS

• Taking homogeneous returns, if we believe ?gt0,
  then IV gt OLS if
• Or rescaling and taking the case were COV(Z,S)gt0

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Source Carneiro and Heckman (2002)
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Estimating the effect of Costs

• Suppose the instruments are valid and b varies
  across the population
• Let C0 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

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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.
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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

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High costs correlated with RTS
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Does increase Aid increase College Attendance
Source Dynarski, 2003
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Empirical Evidence for Credit Constraints

• Not much to support itsome 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

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Education Production

• If education is valuable good (i.e. it has high
  returns)need to worry about how it is produced
• If cant get adjustments on the quantity
  marginmaybe we can get it at the quality margin
• Usually think about education as representing
  some intangible thing thats valuable
• Responsible people
• Democratic values

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Production Function

• Define
• Eist f( NSist, Rist, Xist, e)
• NS Non school inputs, not under control of
  school s in year t
• Innate ability of students
• Parents 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

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Estimation

• Usually dont worry about function formjust
  think of it linearly
• Eist a ßNSist ?Rist dXist eist
• Can look at the effect of change in any of the
  factors on education
• Usually looking to estimate either d (Returns to
  resource investment) or ?
• Often end up estimate d ?

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Outcome measures

• Choice matters
• depends on what you think the intervention/investm
  ent 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

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What to estimate

• Value added model
• Change in outcomes
• Eist Eist-1
• Control for whats new to students in current
  year
• Eist a ?Eist-1 ßNSist ?Rist dXist
  eist
• These are the same if ?1

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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

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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

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Model of production

• The true model we want to estimate is
• E( y ) a tTP ?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, ? will be zero.

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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.

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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 Teachers aid
• Newly entering students randomly assigned to one
  of the class-types
• Continue assignment through 3rd grade
• Analyzed by Krueger (QJE, 1999)

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Distribution of treatment effects
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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

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Maimonides Rule
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Using predicted class-size
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Reduced Form Estimates
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IV Estimates
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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

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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

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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

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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.

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