Transcript The Returns to Education - CERGE-EI

Human Capital and the
Returns to Education
Human Capital
• HC: inherent of acquired talent that has
economic value in the labor market.
• Population HC affects aggregate output.
• HC acquired in schools (public policy)
– The US spends 6.5% of GDP on education.
• Some facts:
– Wages (unempl.) increase (decreases) with schooling
– Young workers switch jobs a lot.
– There is a long right tail to wage distribution.
Data from the US
Human Capital as Investment
(Becker)
• Schooling is investment with opp. costs.
– Credit constraints effects.
– Mincer: how to estimate the return.
• But HC is different from other investments:
– Hard to transfer property rights, can’t use as
collateral
– Hard to diversify
– Non-pecuniary returns.
– General vs. firm-specific HC.
The Individual Decision to Acquire
education: College vs. High School
• College takes 4 years, increases earnings from
E(0) to E(1), pay tuition T, interest rate i.
• Cost: opp. costs + direct costs =
E(0)+E(0)/(1+i)+…+E(0)/(1+i)3+T[1+1/(1+i)+…]
• Benefit: [E(1)-E(0)]/(1+i)4+…+ [E(1)-E(0)]/(1+i)47
(work from 18 to 65)
• High i means college is less attractive. Assume
E(0)=18, E(1)=E(0)*1.25, T=6, PDVs are equal at
roughly i=r=0.035 so with 25% college wage
gain, get college if cost of funds is below 0.035.
The Individual Decision to Acquire
s years of education
• Assume earnings if have s years of (postcompulsory) 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:
PDV  

s
1
e W ( s )dt  W  s  e  rS
r
 rt
The education decision (cont)
• Taking logs this can be written as:
log  PDV   logW  S   rS  log  r 
• The first order-condition can be written as:
W ' s
r
W s
• 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
Equilibrium
• Suppose all individuals identical, but they
require different levels of S in equilibrium
• Then it must be the case that their
log  PDV   logW  S   rS  log  r 
Is equalized for different levels of S, such that
log(W(S)-log(W(S-1))=r(S-(S-1))=r
• 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
An Example
• Two types of labour – college educated
and high-school educated.
• College educated require 4 years of
education
Model of the economy as a whole
Wc/Wh
Supply
Demand
Nc/Nh
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 r
• Supply of educated labour perfectly elastic –
may be true in long-run but not in short-run
• People acquire skills after school (experience):
ln(Wi)=6.2+0.10Si+0.08Expi-0.001Expi2 , R2 =0.29
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.
• Private and social returns may differ.
Estimates of rate of return to education for other countries
Trostel, Walker, Woolley, Labour Economics 2002)
A puzzle
• If rate of return to education is so high,
why aren’t 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
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
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:
ln W   b0  bs  a  
• But a is omitted from regression so
estimate:
ln W   0   s  u
• Standard formula for omitted variables
bias gives us that:
Cov  a, s 
OLS
ˆ
p lim 
b
Var  s 


• So that OLS estimate biased upwards if a
and s are positively correlated (as is very
likely)
Solutions to Omitted Ability Bias
Problems
• Put in better controls for ‘ability’ e.g. use of
IQ tests etc
• Twin studies
• Instrumental Variables
Twin studies
• Pioneered by Taubman (AER, 1976)
• Simple model for earnings of twin 1 and
twin 2 in pair i
ln W1i   b0  bs1i  a1i  1i
ln W2i   b0  bs2i  a2i   2i
• Cannot estimate by OLS as s may be
correlated with a
• but assume that identical twins have
a1i=a2i
• Take differences:
 ln Wi   b0  bsi  i
• 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
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 Δs than s as identical twins tend to have
similar levels of schooling
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 (HarmonWalker AER 95)
– month of birth (del Bono and Galindo-Rueda)
• Often find higher estimates than OLS
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
An example of the ‘first stage’
The IV estimate (as Wald estimate)
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
LATE vs ATE: Oreopoulos 2006
Rising minimum school-leaving age in the
UK from 14 to 15 made half the population
stay in school for one more year. Use this
experiment to see if LATE effects based
on compulsory schooling in the US (where
only small groups are affected) compare to
ATE. Finds that benefits from compulsory
schooling are large whether these laws
have an impact on a majority or minority.
•
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:
1
log yi  a0  ai  bi Si  k1Si2
2
• with marginal return to schooling:
yi'
 bi  k1Si
yi
• Assume marginal costs are given by:
hi'  ri  k2 Si
• Equate MC and MB to get the optimal level of
schooling for individual i:
Si* 
bi  ri bi  ri

k1  k2
k
• bi is about variation in ability to gain from
schooling, ri is about access to funds.
• ATE=β=E[bi –k1Si*] (do we care about ATE?)
• Now try estimate the earnings function:
1
log yi  a0  bSi  k1Si2  ai   bi  b  Si
2
• The last two terms will become the ‘error’.
• This expression makes clear there are two
potential sources of bias in OLS estimation
– 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.
E  ai Si   0  Si  S 
• Assume that:
where lambda is the usual ‘ability bias’
• And that: E bi  b Si   0  Si  S 
psi is the ‘comparative advantage bias’ arising
from differences in gains from schooling
across people (the E[.] term is multiplied by Si)


• So:
1
E  log yi Si   a0  bSi  k1E  Si2 Si   0  Si  S   0 E  Si2 Si   0 Si S
2
• Then using the fact that the expectation of
the quadratic term has slope S-bar we
have:
p lim bOLS  b  k1S  0  0 S    0  0 S
• where β-bar is the average of the marginal
returns to schooling in the sample (ATE)
and the sources of bias are clear.
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
Card’s conclusions on returns to
education
• Average rate of return probably only slightly
below OLS estimate
• There is some variation in return to education
with observable factors
• IV estimates tend to be bigger than OLS maybe
because the IVs exploited pick up the returns for
a group for whom it is large (credit constrained).
• Heckman disagrees: we all have the same
opportunity (ri) and bi is determined in early age.
There is much ongoing work on
credit constraint effects
• First, college proximity may be invalid IV due to
family choice and quality of high-schools (AFQT).
• Still, children of families in top (bottom) income
quartile have 75% (45%) chance of attending a
college. This could be because of
– College tuition credit constraints
– Long-run family income effects on HC formation
• The two types of credit constraints have different
policy implications. (Cameron & Heckman; Kane)
Other issues in the returns to
education
• Have focused on quantity of schooling but
quality and type of schools also important
– e.g. what is effect of class sizes
• Jayachandran & Lleras-Muney QJE 2009:
longer life expectancy (of girls in SriLanka)
raises educ. investment (relative to boys’)
• Why does education raise earnings? Two
main models: it (a) raises human capital,
and/or (b) acts as a signal (Spence).
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 if less costly to acquire for the highly
productive
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)
• 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
signalling
This is their main result
Marriage & Returns to Education
• There is positive sorting on education in marriage
(even among Hollywood actors who do not meet
their spouses in school and whose wages don’t
depend on education, Bruze, 2008).
• Why? Household public goods, complementarity.
• A high share of returns to education is realized
through marriage. Bruze (2008): Time use study:
“better” marriage generates 65% (20%) of the
return to education for women (men) at age 40.
Health Returns to Education
• Deaton (NBER 2003): richer, better-educated
people live longer: top 5% of income have 25%
longer life expectancy than bottom 5% in the US.
• Two-way channel (health info, risky behavior,…)
• Both money and education help.
• Much of Education=>Health happens in childhood
• Oreopoulos & Salvanes (2009, NBER): schooling
makes one enjoy work, make better decisions
about health, marriage, and parenting. It also
improves patience, trust and social interaction.