Download Lecture 2: Labor Supply : Theory and Evidence

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Lecture 7: Human Capital: Education and Earnings
The theory of compensating differentials suggests that wages will
vary among workers because jobs are different. Wages will also vary
among workers because workers are different. We each bring into the
labor market a unique set of abilities and acquired skills, or human
capital.
We begin our study of human capital by focusing on the decision to
acquire formal education. The skills we acquire in school make up an
increasingly important component of our stock of knowledge.
1. Education in the Labor Market: Some Stylized Facts
表一 勞動參與率與教育程度
教育程度
國中及以下
高中（職）
大專及以上
七十年
56.69
54.76
63.13
七十五年
58.89
57.87
66.19
八十年
56.55
60.22
67.27
八十五年
53.00
60.53
67.97
單位：%
九十年
47.71
61.34
66.82
表二 就業者與教育程度
教育程度
國中及以下
高中（職）
大專及以上
七十年
69.31
20.08
10.61
七十五年
64.05
23.85
12.11
八十年
54.26
29.89
15.85
單位：%，千人
八十五年
九十年
44.34
35.64
33.69
35.97
21.96
28.39
表三 失業者與教育程度
教育程度
國中及以下
高中（職）
大專及以上
七十年
0.70
1.95
1.23
七十五年
1.63
3.89
2.93
八十年
0.98
2.05
1.78
八十五年
1.83
3.00
2.41
單位：%
九十年
4.59
4.65
3.20
2. The Schooling Model
What factors motivates some workers to remain in school while other
workers dropout before they finish high school? We assume that
workers acquire the skill level that maximizes the present value of
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lifetime earnings.
(1) Present Value of Age-Earnings Profiles
The present value of the earnings stream if the worker only gets a high
school education is:
PVHS  wHS 
46
wHS
wHS
wHS
wHS


...



2
46
1  r  1  r 
1  r  t 0 1  r t
(7-1)
The parameter r is the worker’s rate of discount. There are 47 terms in
this sum, one for each year that elapses between the ages of 18 and 64.
The present value of the earnings stream if the worker gets a college
diploma is:
PVCOL   H 
w
w
wCOL
H
H
H


 COL 4  COL 5  ... 
2
3
1  r  1  r  1  r  1  r  1  r 
1  r 46
Direct Costs of Attending College
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=
t 0
46
H
1  r 
t

t 4
(7-2)
Post-College Earnings Stream
wCOL
1  r t
The first four terms in this sum give the present value of the direct
costs of a college education, while the remaining 43 terms give the
present value of lifetime earnings in the post-college period.
We assume that a person’s schooling decision maximizes the present
value of lifetime earnings. Therefore, the worker attends college if the
present value of lifetime earnings when he gets a college education
exceeds the present value of lifetime earnings when he gets only a high
school diploma, or:
PVCOL  PVHS
(7-3)
Dollars
wCOL
Goes to College
wHS
Quits after High School
Age
18
22
65
-H
FIGURE 7-1 Earning Streams Faced by a High School Graduate
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(2) The Wage-Schooling Locus
The wage-schooling locus gives the salary that employers are willing
to pay for every level of schooling. The wage-schooling locus is
market-determined. In other words, the salary for each level of
schooling is determined by the intersection of the supply of workers with
that particular schooling and the demand for those workers.
Dollars
30,000
25,000
23,000
20,000
0
12
13 14
18
Years of schooling
FIGURE 7-2 The Wage-Schooling Locus
The wage-schooling locus has three important properties:
(a) The wage-schooling locus is upward sloping. More educated
workers must earn more as long as educational decisions are
motivated only by financial gains. To attract more educated
workers, employers must compensate those workers for the costs
incurred in acquiring an education.
(b) The slope of the wage-schooling locus tells us by how much a
worker’s earnings would increase if she/he were to obtain one more
year of schooling.
(c) The wage-schooling locus is concave. As with most production
process, there are diminishing returns to getting an education.
Defn. The Marginal Rate of Return to Schooling
The percentage change in earnings resulting from one more year of
school is defined to be the marginal rate of return to schooling.
(3) The Stopping Rule, or When Should I Quit School?
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Suppose that the worker has a rate of discount r that is constant; that
is, it is independent of how much schooling the worker gets. The
stopping rule that maximizes the worker’s present value of earnings over
the life cycle is given by:
Quit school when the marginal rate of return to schooling = r
This stopping rule maximizes the worker’s present value of earnings
over the life cycle.
Rate of interest
r’
r
MRR
s’
s*
Years of Schooling
FIGURE 7-3 The Schooling Decision
3. Is Education a Good Investment?
(1) Is Education a Good Investment for Individuals?
The rate of return typically estimated for the U.S. generally fall in the
range of 5-15 percent.
 At first glance, an investment in education is about as good as an
investment in stocks, bonds, or real estate.
A. The Upward Bias
The typical estimates of the rate of return on further schooling
overstate the gain an individual student could obtain by investing in
education because they are unable to separate the contribution that ability
makes to higher earnings from the contribution made by schooling.
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i.e., Some of the added earnings college graduates typically receive
would probably be received by an equally able high school graduates who
did not attend college.
Methods to correct this bias:
(a) Separating effects of ability and schooling by including the
aptitude-test scores such as IQ.
(b) Controlling for all the unmeasured aspects of ability by using data on
twins.
 Part of earnings differentials associated with higher levels of
schooling are due to inherently abler persons obtaining more schooling.
B. The Downward Bias
(a) Some benefits of college attendance are not necessarily reflected in
higher productivity.
(b) Most rate-of-return studies fail to include fringe benefits.
 Fringe benefits, usually as a fraction of total compensation, tend to
rise as money earnings rise.
(c) Some of the job-related rewards of college are captured in the form
of psychic or nonmonetary benefits.
C. Selection Bias
The measured rate of return on a college education may understate the
actual return for those who choose to attend college. Likewise, the
measured rate of return may overstate the return that would have been
received by those terminating schooling with higher school had they
instead chosen to attend college.
Measured benefit Bt: Bt = Ecc,t – Ehh,t
Ecc,t: the earnings in a college-level job of those who choose to go to
college.
h
E h,t: the earning in a high school-level job of those who choose not to
go to college.
Let Ech,t: the earnings in a high school-level job of those who choose to
attend college terminating schooling at high school.
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Ech,t is perhaps less than Ehh,t.
 Bct = Ecc,t - Ech,t > Bt – measured benefit
Ehc,t: the earnings in a college-level job of those who choose not to
attend college were to alter their decisions.
Ehc,t is perhaps less than Ecc,t
 Bht = Ehc,t - Ehh,t < Bt – measured benefit
 When abilities are diverse, the principle of comparative advantage is
an important factor in making choices about schooling and occupations.
(2) Is Education a Good Social Investment?
Some critics have suggested that to a large degree, education acts
merely as a “sorting device”.
 Schooling does nothing to alter productive characteristics. The
education is simply as a filter that has the effect of “signaling” which
people are likely to be most productive.
Note: Even if schooling were only a screening device, it could have social
value. Employers need a reliable method by which to select employees.
Investment in schooling sends a signal to the labor market that one has a
certain level of ability.
 School would have net social value if the decision to attend and the
success one attained in school sent accurate signals about productive
characteristics to employers in the least costly way.
Either education does enhance worker productivity or it is a cheaper
screening tool than any other that firms could use. In either case, the fact
that employers are willing to pay a high price for an educated work force
seems to suggest that education produces social benefits.