Application 3: Estimating the Effect of Education on Earnings

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Application 3 Estimating the Effect of Education
on Earnings

• Methods of Economic Investigation
• Lecture 9

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Quick Asymptotics reminder

• In class Not really about proving consistency
  or asymptotic bias in estimates
• When appropriate, will mention these bias terms
  which are asymptotically zero but not zero in
  finite samples

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What should you know?

• What happens to something in its probability
  limit
• That our estimates will, in the limit, as N goes
  to infinity, under regularity conditions

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What you do not need to know

• Behind these results are various theorems
• Laws of Large Numbers for plims
• Central Limit Theorems for asymptotic normality
• Various mathematical conditions
• e.g contiunuous mapping theorem
• You do not have to know
• which theorems you are using
• You do not have to be able to prove these results
  with the theorems

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Bottom Line

• Understand the role of N?8
• the mean of the sample mean is µ
• The variance goes to zero
• If something is scaled by (N)-2 can converge in
  distribution
• So far, typically rely on concept of bias but
  in large samples, consistency is more useful
  term.
• If bias is decreasing as sample is increasing,
  then worry less about it
• If even in large samples, our estimate is not
  close to the true value, worry more about it

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Todays Lecture

• Review Error component models
• Fixed Effects
• Random Effects
• Application Estimating the Effects of Education
  on Earnings
• Difficulty in Causal Estimation
• Within-family estimator
• Some limitation of fixed effects

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Error has different components

• Suppose we had to estimate where
• If unobserved factors are uncorrelated with Xs
  can do OLS w/ robust standard errors or FGLS
• If unobserved factors correlated with Xs, can
  include group-specific fixed effect

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Fixed effects versus Dummy Variables

• These are not mutually exclusive categories
• Dummy variables are just a categorical variable
  that is zero sometimes and one sometimes
• control variables, which have a direct meaning,
  may sometimes be dummy variables
• Fixed Effects, which tell us something about the
  structure of our error term, are also dummy
  variables.

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Motivation for todays example

• Want to know why do people earn different amounts
• Specifically, what are the returns, in terms of
  increased wages, for various investments people
  make
• Most common labor improving investment Education

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Motivation-2

• Simple Linear regression first introduced by
  Mincer

Index this by individual i in group j
Experience were going to include a quadratic
specification which is most commonly used
Measure of schooling were going to use years of
education
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Basic Problem with estimating this

• Lots of reasons why different people may invest
  at different levels of education
• Some of those reasons are probably correlated
  with how much money a person would earn as well
  as how much they will invest in education
• Unobserved ability
• Family factors, such income, parental
  involvement, genetic stuff, etc.

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How might these bias our estimates?

• Lets say what we want to estimate is
• Interpret higher f as something like family
  income or family investment
• Recall the OVB formulacare about two things
• Correlation between f and y probably positive
• Correlation between f and S positive

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Why is OLS biased?
Y
S
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How could we fix this?

• Some of the unobserved differences that bias a
  cross-sectional comparison of education and
  earnings are based on family characteristics
• Key Assumption 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) d(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

• 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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Twins sample issues

• 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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External validity

• Twins may not be very comparable to other
  familiesface different costs and benefits to
  schooling
• Twinsburg sample not representative of twins
• Maybe not even externally valid for twins
• Worry that selection into sample will give us an
  estimate that is not consistent with the
  population average

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Fixed effects (same as first difference w/ only
two obs/family
Control for avg. family schoolingability
measure
No family effect, cross-section regression
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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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Measurement Error

• Seems that twins not perfect at reporting each
  others schooling 5-10 measurement error
• May be generating a different bias
• Can use instrumental variables to try to address
  this (more on this after we do Instrumental
  Variables methods)
• Need to worry about Data Quality too, cant just
  worry about OVB

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Limitations of Fixed Effects

• Relies on within variation
• Not transparent what is generating that variation
• The variation thats left may be random but may
  be limited in its external validity
• Must be the case that there is NO within group
  variation AND homogeneous effects between groups
  (i.e. b the same across groups)
• May be less believable if family inputs have
  non-linear effects on income or education

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What did we learn today

• When have unobserved group effects can be two
  issues
• Uncorrelated with Xs OLS not efficient, can fix
  this with GLS
• Correlated with Xs OVB, can include fixed
  effects
• Fixed effects, within-group differences, and
  deviation from means differences can all remove
  bias from unobserved group effect

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Next Class

• Application The effect of Schooling on wages
• Ability Bias
• Fixing this with twins and siblings models