EC326 Topics in Applied Economics 2b Topic 2: Economics of Higher Education Robin Naylor EC236:...

EC236: Economics of HE, 2014-15 1

EC326 Topics in Applied Economics 2b

Topic 2: Economics of Higher Education

Robin Naylor



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



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, 1177- 1188.



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…




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:




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



Consider the following simple model

ts n ns

W(s2)W(s1)

w e



• Under the theory of equalising differences:

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:

rts

et

rtns

s

st

rtn

st eDwewew

0

2

0

1




=>

Note that

=>

sn

s

rtsn

rts ewew 2

0

1

sn

s

rt

nrt

s

s

e

e

w

w 01

2

rtrt er

e 1

,11

0 n

rnrt er

e

sn

s

rnrsrt eer

e 11




Hence it follows that:

Thus,

Or

This is the basic human capital earnings equation.

It follows that,

rs

rnrs

rn

s

s

eee

r

er

w

w

11

11

1

2

rsww ss 12 loglog

r

s

wd s

2log

rsxws2log




The human capital earnings equation is often extended to allow for Mincer’s emphasis on the importance of experience:

where e = age - s – 5 = “Mincer experience”.

Problems1. Omitted variable bias

* Ability* Family backgroundFurthermore, likely to be correlated with schooling => estimate of effects of schooling on earnings biased

upwards.

23210log eesxw




2. 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:

S S*

MB

MC MC

MB

MB2

S**

Topic 2: Economics of Higher EducationLecture 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.






IV Candidates?

* Smoking, Rate of discount, Insurance, Distance to college(Results: IV suggests OLS estimates are under-estimates.)

Alternatively,

* Natural experimentsI.e., something which influences length of schooling exogenously (randomly). ROSLA. Again, suggests OLS estimates are under-estimates. Why?

* Twins studies


Twins studies:

ProblemOmitted variable bias if f, a are not observed.

Twins data

Differencing,

So is an unbiased estimate of the return to schooling.

jjjjjj fasxw 1131211101log

jjjjjj fasxw 2232221202log

jjjj ffaa 2121 ,

jjjjjjjj ssxxww 2121121021 loglog

1




So other important influences on earnings:

* Non-competing groupsSo theory of equalising net advantages invalid

* Discrimination

* Signalling/screening

* Product market power

* Labour market institutions





Lecture 2: Signalling Theory

• Spence, QJE, 1973• Phelps, AER, 1972• Arrow, Theory f Discrimination, 1973



1 2

2

1

1

Suppose that there are two types of individual:

types , .

A proportion of the population is of type , and

(1 ) of the population is of type , where 0 1.

As potential workers,

the type have

1

2 2

2 1

productivity given by ,

the type have productivity given by ,

where > .

Consider now the nature of information

regarding the distribution of potential productivity.

m

m

m m


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 wag

1

2

e of each type of

worker?

Wage of -type worker = ,

wage of -type worker = .


20EC236: Economics of HE, 2014-15

B. Imperfect Information

Suppose now that there is imperfect information of the following nature:


(as already stated, we always maintain thi

s 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 w

ould 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

1 2

wage?

Wage of -type worker = wage of -type worker = (?).



1 2

We should be careful here to notice our assumptions

about productivity. We have assumed away any interactions

between either (i) individual or type productivities ( , )

and (ii) productivities and the

m m

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 1to just . In cases like

this there would be an efficiency gain from being able to

identify and separate workers by their -type.

m



2 1

Ruling out any efficiency gain from being able to

identify and separate workers by their -type, the common

wage is given by:

(149) + 1 .w m m




(as

C. Imperfect Information - with Signalling

Consider now a world of imperfect information, of

the type described in B above - that is,

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.



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 th

2

at employers have the perception (belief) that

any worker with a level of schooling greater than or equal to some

ˆcritical value is a worker of -type, while any worker with less than

ˆ is a worker

s

s

1of -type.

Ôbviously, must be greater than the legal minimum level of schooling

(why?).

s



2

1

With this belief, firms would be willing to pay a wage of

ˆto any worker with at least of schooling and a wage of

ˆto workers with less than .

Notice that this gives workers a potential incentiv

m

s m

s

0

0

e to invest

in schooling beyond the legal minimum level, .

ˆNotice also that workers will choose to acquire either or .

They will not rationally choose any other level. Why not?

s

s s

s0 s



2 1

The wage premium for any worker (of either type) who

âcquires of schooling is equal to . This is the

(gross) return on the investment. Notice that it is the same

for everyone, regardless of -ty

s m m

pe.

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 on

2ly -type workers have an

încentive to invest in of schooling. What could this assumption be?s



1

The assumption that drives this possible result is the assumption

that the acquisition of schooling is more costly for -type workers.

That is, productivity and costs of schooling are negatively

correla

0

2 2

ted (or, alternatively, productivity in the labour market

and productivity in schooling are correlated).

Thus, we denote the unit cost of acquiring schooling over and

above as:

for -ty

positively

s

c

1 1

2 1 2 1

pe workers, and

for -type workers,

where < . (Recall that .)

c

c c m m



2

2 1 2

2 1

2

1

Ît follows that the -type workers will acquire if the following

condition is satisfied:

ˆ(149) , i.e.,

ˆ(150) .

What is the equivalent expression for -type workers?

We

s

m m c s

m ms

c

2

2

1

1

have said that in equilibrium, -type workers invest

în acquiring the signal ( ) that they are -type workers, while

ˆ-type workers do not invest in (thereby signalling that

they are -type wo

s

s

rkers), in equilibrium.

Thus we can write the condition for a SIGNALLING equilibrium as:



2 1

2

m m

c

2 1 2 1

1 2

2 1

We can write the condition for a Signalling (or Separating)

equilibrium as:

ˆ(151) .

Notice the significance of the assumption that .

m m m ms

c c

c c

s0 s

2 1

1

m m

c



1

Îf is below this interval to the left, it is too low to generate

a Signalling equilibrium - everyone invests, even the

-type workers.

Îf is above this interval to the right, it is too high to g

s

s

2

enerate

a Signalling equilibrium - no-one invests, not even the

-type workers.

These POOLING outcomes do not represent equilibria if firms

have the (correct) belief that 0 1 of the population are of

ty

2pe .



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.



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

1

?

(iii) In a world of imperfect information, what can you say

about the impact on the welfare of -type workers associated

with the existence of a Signalling equilibrium? In other

w

ords, do these workers gain or lose from equilibirum

signalling?

Let's consider this question . . .



1

1

1 2 1

1

Do -type workers lose in the presence of equilibrium signalling?

Without a signalling mechanism, -type workers earn:

(152) (1 ) .

With equilibrium signalling, -type workers earn:

(153)

Nw m m

1 1

1 1 2 1

1

.

It follows that:

(154) <0.

Thus, -type workers are necessarily worse off in a

Signalling equilibrium. The intuition for this is obvious -

isn't it? Explain.

S

S N

w m

w w m m



2

2

(iv) Do -type workers necessarily gain from equilibrium signalling?

-type workers lose from a signalling equilibrium if:

(a) The signalling condition (151) is satisfied,

and, simultaneously,

(b)

2 2

2 2 2 1 2

2 1

2

0.

The question, then, is "Can these two conditions be satisfied

simultaneously?" Re-writing the second condition:

ˆ(155) 1 , or

ˆ(156) 1 .

S N

S N

w w

w w m m c s

m ms

c



2

2

(iv) Do -type workers necessarily gain from equilibrium signalling?

So, -type workers lose from a signalling equilibrium if

the signalling condition (151) is satisfied simultaneously

with the condit

2 1 2 1

2 2

2 1 2 1

2 1

ion shown in (156).

For these to be satisfied simultaneously, it must be the case that:

(157) 1 < , and

(158) 1 .

m m m m

c c

m m m m

c c

2 1

2

m m

c

s0 s

2 1

1

m m

c



Wages and productivity

SS

Dm

£

0 S



Costs and Schooling

SS

c s£

0

2

1

c s

c

1

2

c



Case 1

SS

Dm = m - m

£

0

2 1

S

Who Invests in schooling in this case?

2c sc s1



Case 2

SS

Dm

£

0 S


2c sc s1



Case 3

SS

Dm

£

0 S


2c sc s1



Case 3

SS

Dm

£

0

S


2c sc s1

SSa b

To what do Sa and Sb correspond?




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)



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

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EC326 Topics in Applied Economics 2b Topic 2: Economics of Higher Education Robin Naylor EC236:...

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