EC326
Topics in Applied Economics 2b
Topic 2: Economics of Higher Education
Robin Naylor
EC236: Economics of HE, 2014-15
1
Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory
Lecture 2:
Signalling theory
Lecture 3:
The causal effect of education on
earnings
Lecture 4:
Evidence of returns to HE in the UK
Lecture 5:
Cohort effects: theory
Lecture 6:
Cohort effects: evidence
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Bibliography
Blundell, R., Dearden, A., Goodman, A. and Howard, R. (2000), The returns to higher
education in Britain: evidence from a British cohort, Economic Journal, 110, F82-F99.
Card, D. (1999), The Causal effect of education on earnings, Ch. 30, Handbook of Labor
Economics vol. 3A, Ashenfelter, O. and Card, D. (Eds), North-Holland.
Chevalier, A., Conlon, G., Galindo-Rueda, F. and McNally, S. (2001), The returns to higher
education teaching, Centre for the Economics of Education.
Feng, A. and Graetz, G. (2013), A question of degree: the effects of degree class on labor market
outcomes, Centre for Economic Performance Discussion Paper 1221.
O'Leary, N. and Sloane, P. (2011), The wage premium for university education in Great Britain during a
decade of change, Manchester School, 79, 740-764.
Walker, I. and Zhu, Y. (2008), The college wage premium and the expansion of higher
education in the UK, Scandinavian Journal of Eocnomics, 110, 695-709.
Walker, I. and Zhu, Y. (2011), Differences by degree: Evidence for the net financial rates of return to
undergraduate study for England and Wales, Economics of Education Review, 30, 11771188.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1: Human capital theory and signalling theory
Some evidence on education and earnings*
US
Card, D. (1999) Figure 1 (separate handout)
Card, D. (1999) Figure 2 (separate handout)
Card, D. (1999) Table 1 (separate handout)
UK, Europe and beyond
Harmon, C., Oosterbeek, H. and Walker, I. Table 2.1 (separate handout)
BCS70: some DIY estimates…
*We are focusing on earnings, but education affects very many outcomes…
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1: Human capital theory and signalling theory
Human Capital Theory (Becker (1964), Mincer (1974)
(i) Competitive labour market => w/p = MPL
(ii) MPL = f(Human Capital)
(iii) Human Capital = f(Education, Training)
(iv) Education (Training) involves opportunity costs (and possible
direct costs too)
(v) Theory of equalising differences:
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1: Human capital theory and signalling theory
Theory of equalising differences:
In a competitive labour market equilibrium, wage differentials compensate
workers for (opportunity and direct) costs of human capital acquisition =>
(a)
Supply and demand for workers of each education level
are equated
(b)
No worker wishes to alter his/her schooling level
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1: Human capital theory and signalling theory
Consider the following simple model
W(s2)
W(s1)
we
s
n
EC236: Economics of HE, 2014-15
ns
t
7
Topic 2: Economics of Higher Education
Lecture 1:
•
Human capital theory and signalling theory
Under the theory of equalising differences:

n
0
s1  rt
t
w e


ns
s
s 2  rt
t
w e

 w
s
0
e
t
 D e rt
where r is the rate of return to educational investments and other terms are as
defined in the lecture.
Let we - D = 0. Assume also that, conditional on the level of education, wages
per worker are constant over the lifetime. Finally, assume that n = ns.
Then the equation simplifies to:
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory

n
s1  rt

w e
0
ws 2e rt
s
s2
w

s1
w
=>

n s


n
e rt
0
n s
e rt
s
Note that
e
n
=>
0

 rt
1
e rt   e rt
r


1 rn
  e 1 ,
r

n s
s
e
 rt


1 rs rn
  e e 1
r
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
Hence it follows that:



1 rn
e 1
r
ws 2
rs


e
w s1  1 e rs e rn  1
r


Thus, log w s 2   log w s1   rs  
Or
log ws 2   x  rs  
This is the basic human capital earnings equation.
It follows that,
d logw s 2 
r
s
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
The human capital earnings equation is often extended to allow for
Mincer’s emphasis on the importance of experience:
log w   0 x  1s   2e   3e2  
where e = age - s – 5 = “Mincer experience”.
Problems
1. Omitted variable bias
*
Ability
*
Family background
Furthermore, likely to be correlated with schooling
=>
estimate of effects of schooling on earnings biased
upwards.
EC236: Economics of HE, 2014-15
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Lecture 1:
2.
Topic 2: Economics of Higher Education
Human capital theory and signalling theory
Selectivity bias:
Length of schooling is not randomly assigned across individuals
but is the outcome of rational decision-making: it is endogenously
determined. So ‘S’ in the human capital earnings equation above is
not exogenous and the estimate of ß1 is likely to be biased.
Causes of endogenous selection:
MB
MC
MC
MB2
MB
S*
S**
EC236: Economics of HE, 2014-15
S
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
Why might MB shift up to the right?
Family background
Alternatively, why might MC shift down to the right?
Family background (access to capital)
Ability
From your lecture notes in either EC226 or EC203, you will have seen that OLS
yields biased or inconsistent estimates if a relevant RHS variable is either
omitted or is endogenous. You will also have seen that the use of Instrumental
Variables is one possible way around this. You should check your EC226/203
notes on this material. In our context, an IV would be a variable which is
correlated with schooling but which does not exert an independent effect on
earnings.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
IV Candidates?
*
Smoking, Rate of discount, Insurance, Distance to college
(Results: IV suggests OLS estimates are under-estimates.)
Alternatively,
*
Natural experiments
I.e., something which influences length of schooling exogenously
(randomly). ROSLA. Again, suggests OLS estimates are underestimates. Why?
*
Twins studies
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
Twins studies:
log w1 j   0 x1 j  1 s1 j   2 a1 j   3 f1 j   1 j
log w2 j   0 x2 j  1 s2 j   2 a2 j   3 f 2 j   2 j
Problem
Omitted variable bias if f, a are not observed.
Twins data
a1 j  a2 j , f1 j  f 2 j
Differencing,
log w1 j  log w2 j   0 x1 j  x2 j   1 s1 j  s2 j    1 j   2 j
So  1 is an unbiased estimate of the return to schooling.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 1:
Human capital theory and signalling theory
So other important influences on earnings:
*
Non-competing groups
So theory of equalising net advantages invalid
*
Discrimination
*
Signalling/screening
*
Product market power
*
Labour market institutions
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 2: Signalling Theory
•
•
•
Spence, QJE, 1973
Phelps, AER, 1972
Arrow, Theory f Discrimination, 1973
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Suppose that there are two types of individual:
types 1 ,  2 .
A proportion  of the population is of type  2 , and
(1   ) of the population is of type 1 , where 0    1.
As potential workers,
the 1 type have productivity given by m1 ,
the  2 type have productivity given by m2 ,
where m2 >m1.
Consider now the nature of information
regarding the distribution of potential productivity.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
A. Perfect Information
Suppose that there is perfect information: that is,
(i) Each individual knows the  -type to which they belong
(we shall always maintain this assumption),
(ii) Employers observe (directly/costlessly) each individual's type.
Assume (also throughout) that markets are perfectly competitive:
hence we can impose a zero-profit condition.
Under these assumptions, what would be the wage of each type of
worker?
Wage of 1 -type worker =
,
wage of  2 -type worker =
.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
B. Imperfect Information
Suppose now that there is imperfect information of the following nature:
(i) Each individual knows the  -type to which they belong
(as already stated, we always maintain this assumption),
(ii) Employers do not observe each individual's type. They
know only the distribution of ability (productivity):
that is, they know the value of .
Under these assumptions, what would be the wage of each type of
worker?
It must be the case that everyone receives the same wage
(just as there must be a common price for Good and Bad cars in
the Market for Lemons). What is this common wage?
Wage of 1 -type worker = wage of  2 -type worker =
EC236: Economics of HE, 2014-15
(?).
20
Topic 2: Economics of Higher Education
We should be careful here to notice our assumptions
about productivity. We have assumed away any interactions
between either (i) individual or type productivities (m1 ,m2 )
and (ii) productivities and the nature of information.
If it were the case, for example, that the inability to separate
workers by their  -type caused a reduction in productivity, then
the common wage would be less than the (weighted) average
of the two productivities.
For example, suppose that production was based on a continuous
'conveyor-belt' process operated at the speed of the slowest worker.
Then the common wage would be equal to just m1. In cases like
this there would be an efficiency gain from being able to
identify and separate workers by their  -type.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Ruling out any efficiency gain from being able to
identify and separate workers by their  -type, the common
wage is given by:
(149)
w   m2 + 1    m1.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
C.
Imperfect Information - with Signalling
Consider now a world of imperfect information, of
the type described in B above - that is,
(i) Each individual knows the  -type to which they belong
(as already stated, we always maintain this assumption),
(ii) Employers do not observe each individual's type. They
know only the distribution of ability (productivity):
that is, they know the value of  .
But now suppose that there exists a mechanism by
which (at non-zero cost) workers' abilities might be
signalled to employers.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Suppose that this signalling mechanism takes the form of schooling,
with employers perceiving that workers with more schooling are
workers of higher ability (i.e., productivity).
Specifically, assume that employers have the perception (belief) that
any worker with a level of schooling greater than or equal to some
critical value sˆ is a worker of  2 -type, while any worker with less than
sˆ is a worker of 1 -type.
Obviously, sˆ must be greater than the legal minimum level of schooling
(why?).
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
With this belief, firms would be willing to pay a wage of m2
to any worker with at least sˆ of schooling and a wage of m1
to workers with less than sˆ.
Notice that this gives workers a potential incentive to invest
in schooling beyond the legal minimum level, s0 .
Notice also that workers will choose to acquire either s0 or sˆ.
They will not rationally choose any other level. Why not?
s0
ŝ
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
The wage premium for any worker (of either type) who
acquires sˆ of schooling is equal to m2  m1. This is the
(gross) return on the investment. Notice that it is the same
for everyone, regardless of  -type.
In equilibrium, however, it must be the case that only  of
the population acquire the signal. (Why?)
Therefore, there must be some mechanism - some assumption which creates the possibility that only  2 -type workers have an
incentive to invest in sˆ of schooling. What could this assumption be?
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
The assumption that drives this possible result is the assumption
that the acquisition of schooling is more costly for 1 -type workers.
That is, productivity and costs of schooling are negatively
correlated (or, alternatively, productivity in the labour market
and productivity in schooling are positively correlated).
Thus, we denote the unit cost of acquiring schooling over and
above s0 as:
c2 for  2 -type workers, and
c1 for 1 -type workers,
where c2 <c1. (Recall that m2  m1.)
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
It follows that the  2 -type workers will acquire sˆ if the following
condition is satisfied:
(149) m2  m1  c2 sˆ,
(150)
sˆ 
i.e.,
m2  m1
.
c2
What is the equivalent expression for 1 -type workers?
We have said that in equilibrium,  2 -type workers invest
in acquiring the signal (sˆ) that they are  2 -type workers, while
1 -type workers do not invest in sˆ (thereby signalling that
they are 1 -type workers), in equilibrium.
Thus we can write the condition for a SIGNALLING equilibrium as:
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
We can write the condition for a Signalling (or Separating)
equilibrium as:
m2  m1
m2  m1
 sˆ 
.
c1
c2
(151)
Notice the significance of the assumption that c2  c1.
s0
ŝ
m2  m1
c1
m2  m1
c2
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
If sˆ is below this interval to the left, it is too low to generate
a Signalling equilibrium - everyone invests, even the
1 -type workers.
If sˆ is above this interval to the right, it is too high to generate
a Signalling equilibrium - no-one invests, not even the
 2 -type workers.
These POOLING outcomes do not represent equilibria if firms
have the (correct) belief that 0    1 of the population are of
type  2 .
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Efficiency
(i)
Suppose that the signalling equilibrium condition (151) is satisfied.
The equilibrium could be anywhere within the interval defined
by this condition.
Which is the most efficient outcome within the interval? Why?
Notice that there is no reason why the signalling
equilibrium need coincide with this most efficient level.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Efficiency (continued)
(ii) Compared to the world of imperfect information and no
Signalling - and with no production externalities - notice
that any signalling equiibrium is inefficient. Why?
(iii) In a world of imperfect information, what can you say
about the impact on the welfare of 1 -type workers associated
with the existence of a Signalling equilibrium? In other
words, do these workers gain or lose from equilibirum
signalling?
Let's consider this question . . .
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Do 1 -type workers lose in the presence of equilibrium signalling?
Without a signalling mechanism, 1 -type workers earn:
(152)
w1N   m2  (1   )m1.
With equilibrium signalling, 1 -type workers earn:
(153)
w1S  m1.
It follows that:
(154)
w1S  w1N    m2  m1  <0.
Thus, 1 -type workers are necessarily worse off in a
Signalling equilibrium. The intuition for this is obvious isn't it? Explain.
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
(iv) Do  2 -type workers necessarily gain from equilibrium signalling?
 2 -type workers lose from a signalling equilibrium if:
(a)
The signalling condition (151) is satisfied,
and, simultaneously,
(b)
w2S  w2N  0.
The question, then, is "Can these two conditions be satisfied
simultaneously?" Re-writing the second condition:
(155)
w2S  w2N  1    m2  m1   c2 sˆ, or
(156)
 m2  m1 
sˆ  1    
.
 c2 
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
(iv) Do  2 -type workers necessarily gain from equilibrium signalling?
So,  2 -type workers lose from a signalling equilibrium if
the signalling condition (151) is satisfied simultaneously
with the condition shown in (156).
For these to be satisfied simultaneously, it must be the case that:
(157)
 m2  m1  m2  m1
, and
1    
<
c2
 c2 
(158)
 m2  m1  m2  m1
.
1    

c1
 c2 
s0
ŝ
m2  m1
c1
m2  m1
c2
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
£
Dm
S0
Ŝ
S
Wages and productivity
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
£
c1s
c2s
c1
c2
S0
S
Costs and Schooling
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Case 1
£
c1s
c2s
Dm = m 2 - m 1
Who Invests
in schooling
in this case?
S0
S
Ŝ
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Case 2
£
c1s
c2s
Dm
Who Invests
in schooling
in this case?
S0
Ŝ
EC236: Economics of HE, 2014-15
S
39
Topic 2: Economics of Higher Education
Case 3
c1s
£
c2s
Dm
Who Invests
in schooling
in this case?
S0
Ŝ
EC236: Economics of HE, 2014-15
S
40
Topic 2: Economics of Higher Education
Case 3
c1s
£
c2s
Dm
Who Invests
in schooling
in this case?
Ŝ
S0
S
a
S
b
S
To what do Sa and Sb correspond?
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Signalling: is it sustainable in the long run?
Employer Learning
(Altonji and Pierret, QJE, 2001)
(Farber and Gibbons, QJE, 1996)
Statistical Discrimination in the Short-run
Evidence?
(Layard and Psacharopoulos, JPE, 1974)
(Riley, JPE, 1979)
(Feng and Graetz (2013): see subsequent lecture)
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 3: The causal effect of education on earnings
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 4: Evidence of returns to HE in
the UK
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 5: Cohort effects: theory
EC236: Economics of HE, 2014-15
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Topic 2: Economics of Higher Education
Lecture 6: Cohort effects: evidence
EC236: Economics of HE, 2014-15
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