The Returns to Education

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The Returns to Education
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The Individual Decision to Acquire education

• Assume earnings if have s years of
  (post-compulsory) schooling is W(s)
• Assume only cost of education is forgone earnings
  no direct cost
• Assume everyone lives for ever
• PDV of s years of education is

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The education decision (cont)

• Taking logs this can be written as
• The first order-condition can be written as
• i.e. acquire education up to the point where the
  increase in log earnings is equal to the rate at
  which future earnings are discounted

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Equilibrium

• Suppose all individuals identical
• Suppose require different levels of education in
  equilibrium
• Then must be the case that
• Is equalized for different levels of s
• Think of including years of education on RHS of
  earnings function coefficient on s is measure
  of r rate of return to education
• This earnings function is a labour supply curve

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An Example

• Two types of labour college educated and
  high-school educated.
• College educated require 4 years of education

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Model of the economy as a whole
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Things to note

• Return to education supply-determined
  determined by r
• Can think of it as a compensating differential
  for the time taken to acquire education
• Demand shifts have no effect on rate of return to
  education
• Supply of educated labour perfectly elastic may
  be true in long-run but not in short-run

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Estimates of rate of return to education

• For US a typical OLS estimate from an earnings
  function is about 8
• Other countries are a bit different
• Suggests education a very good investment few
  other investments offer an 8 real return.

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Estimates of rate of return to education for
other countriesTrostel, Walker, Woolley, Labour
Economics 2002)
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A puzzle

• If rate of return to education is so high, why
  arent more people acquiring education
• Possible answers
• Liquidity constraints
• Bias in OLS estimate so rate of return not really
  that high
• Heterogeneity in the returns to education

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Liquidity Constraints

• In perfect capital market r should be rate of
  interest
• But if imperfect capital market may be much
  higher.
• Why might it be higher hard to borrow money
  against human capital as no collateral

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Bias in OLS estimate

• Why might OLS estimate be biased?
• Most common answer is ability bias
• Ability has effect on wages independent of
  education but is positively correlated with
  schooling and typically not controlled for in
  regression.
• Suppose true model is

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• But a is omitted from regression so estimate
• Standard formula for omitted variables bias gives
  us that
• So that OLS estimate biased upwards if a and s
  are positively correlated (as is very likely)

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Solutions to Omitted Ability Bias Problems

• Put in better controls for ability e.g. use of
  IQ tests etc
• Twin studies
• Instrumental Variables

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Twin studies

• Pioneered by Taubman (AER, 1976)
• Simple model for earnings of twin 1 and twin 2 in
  pair i
• Cannot estimate by OLS as s may be correlated
  with a
• but assume that identical twins have a1ia2i

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• Take differences
• Now regressor uncorrelated with error so estimate
  will be consistent
• Estimate from twins studies typically suggest
  lower rate of return to education than OLS
  suggestive of ability bias

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Problems with Twin Studies

• Do identical twins really have identical ability
  identical genes but perhaps not everything in
  the genes
• Measurement error problems measurement error
  leads to attenuation bias, measurement error like
  to be bigger in ?s than s as identical twins tend
  to have similar levels of schooling

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The Instrumental Variable Approach

• Basic Idea of IV in this context find
  instrument(s) correlated with s but uncorrelated
  with a
• A number of studies have used different
  instruments
• quarter of birth (Angrist-Krueger QJE 91)
• proximity to a college (Card)
• Changes in minimum school leaving age
  (Harmon-Walker AER 95)
• month of birth (del Bono and Galindo-Rueda)
• Often find higher estimates than OLS

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Look at one in more detail (del Bono an
dgalidno-Rueda)

• The idea until 1977 UK compulsory schooling
  laws allowed those in a school cohort born
  between 1st Sept and 31st January to eave school
  at Easter and not take exams.
• This had the effect of reducing the probability
  of getting an academic qualification for those
  born before February

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An example of the first stage
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The IV estimate (as Wald estimate)
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Comment

• Note use employment as outcome variable as do
  not have large enough sample size to estimate
  precise wage effects
• So cannot use results directly to compute rate of
  return to education
• But idea should be clear

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Problems with IV

• IV requires 2 assumptions
• instrument relevance correlated with variable
  of interest
• Instrument exogeneity uncorrelated with
  error/excluded variables
• Both can be problematic
• Exogeneity assumption cannot be tested and may be
  debatable e.g. quarter of birth
• Relevance can be tested by often weak instruments
  that lead IV estimate to perform poorly
• See my MEI notes for more details

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Heterogeneity in Returns to education (Card, JOLE
1999)

• Uses idea that there is likely to be
  heterogeneity in both return to school and the
  cost of schooling (the discount rate)
• Assume that the earnings function for individual
  I is given by
• with marginal return to schooling

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• Assume marginal costs are given by
• The optimal level of schooling for individual i
  is then given by
• Now suppose we are trying to estimate the
  earnings function in using data on a sample.
  Write as
• The last two terms are going to be the error.

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• This expression makes clear there are two
  potential sources of bias in OLS estimation of
• the correlation of ai with Si - ability bias
• the correlation of (bi-b) with Si e.g. if those
  with high returns get more schooling.
• Assume that
• And that

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• Then
• Then using the fact that the expectation of the
  quadratic term has slope S-bar we have
• where ß-bar is the average marginal return to
  schooling in the sample.

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What does IV estimate when returns are
heterogeneous

• This is a surprisingly complicated question
• Angrist-Imbens LATE tells us that it picks up the
  average returns for education for those whose
  behaviour is altered by the instrument
• Unlike IV estimate for homegenous case this means
  estimate will vary with the instrument
• This issue comes up in other areas where IV is
  increasibly popular

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Cards conclusions on returns to education

• Average rate of return probably only slighlt
  below OLS estimate
• There is some variation in return to education
  with observable factors
• IV estimates tend to be bigger than OLS estimates
  probably because the interventions exploited pick
  up the returns for a group for whom it is large

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Other issues in the returns to education

• Have focused on quantity of schooling but quality
  and type of schooling also important e.g. what
  is effect of class sizes
• Why does education raise earnings two main
  models
• Raises human capital
• Acts as a signal (Spence)

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Signaling Model the Basic Idea

• Hard for employers to observe productivity
• Good workers want to convey this information to
  employers
• But talk is cheap so saying you are good is not
  credible
• Acquiring education may be a credible signal is
  less costly to acquire for the highly productive

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Testing the Signaling Model- Altonji and Pierret

• Basic idea is that information problem most acute
  for young workers but employers learn true
  ability over time
• Implication is that ability measure initially
  unobservable to employers should become more
  important in explaining wages over time while
  variables (e.g. education) that are initially
  used as signal should become less important
• Generally hard to implement because rare to have
  variable observed by econometrician but not by
  employer (typicallly they know more than we do)

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• Altonji-Pierret use fact that NLSY has AFQT
  measure for teenagers as measure of ability
• Main results are on next slide they are quite
  striking
• Suggest that part though not all of apparent
  return to education is from signaling

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This is their main result