Chapter 6
Human Capital
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Introduction
• People bring into the labor market
a unique set of abilities and acquired skills
known as human capital.
• Workers add to their stock of human capital
throughout their lives,
especially via work experience and education.
6-2
Education: Stylized Facts
• Education is strongly correlated with:
– Labor force participation rates
– Unemployment rates
– Earnings
6-3
台灣教育別失業率（1978-2009）
教育別失業率
7
6
5
%
4
3
2
1
0
1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
年度
國中及 以下
高中 (職)
專科
大學及 以上
6-4
男女年齡別薪資(2009)
男女年齡別薪資
50000
45000
40000
月薪資
35000
30000
25000
20000
15000
10000
5000
0
１５～１９歲
２０～２４歲
２５～２９歲
３０～３４歲
３５～３９歲
４０～４４歲
４５～４９歲
５０～５４歲
５５～５９歲
６０～６４歲
years
years
years
years
years
years
years
years
years
years
６５　歲及以上
years & over
年齡
男性月薪資
女性月薪資
6-5
Age-Earnings Profiles
Weekly Earnings
Men
2600
2300
2000
1700
1400
1100
800
500
200
College Graduates
Some college
High school graduates
High school dropouts
18
25
32
39
46
53
60
Age
6-6
台灣 男性 不同教育程度 年齡別薪資(2009)
男性不同教育程度年齡別薪資
80,000
70,000
60,000
小學
國中
高中
高職
專科
大學以上
月薪資
50,000
40,000
30,000
20,000
10,000
0
１５～１９歲
２０～２４歲
２５～２９歲
３０～３４歲
３５～３９歲
４０～４４歲
４５～４９歲
５０～５４歲
５５～５９歲
６０～６４歲 ６５　歲及以
years
years
years
years
years
years
years
years
years
years
上 years & over
年齡別
6-7
Age-Earnings Profiles
Weekly Earnings
Women
1400
1200
1000
800
600
400
200
College Graduates
Some college
High school graduates
High school dropouts
18
25
32
39
46
53
60
Age
6-8
台灣 女性 不同教育程度 年齡別薪資(2009)
女性不同教育程度年齡別薪資
70,000
60,000
月薪資
50,000
國小
國中
高中
高職
專科
大學
40,000
30,000
20,000
10,000
0
１５～１９歲
２０～２４歲
２５～２９歲
３０～３４歲
３５～３９歲
４０～４４歲
４５～４９歲
５０～５４歲
５５～５９歲
６０～６４歲
６５　歲及以
years
years
years
years
years
years
years
years
years
years
上 years & over
年齡別
6-9
Present Value Calculations
• Present value allows comparison of dollar amounts
spent and received in different time periods.
(An
idea from finance.)
• Present Value = PV = y/(1+r)t
– r is the per-period discount rate.
– y is the future value.
– t is the number of time periods.
6-10
Potential Earnings Streams
Faced by a High School Graduate
Dollars
Goes to College
wCOL
Quits After
High School
wHS
0
18
22
65
Age
A person who quits school
after getting her high school
diploma can earn wHS from
age 18 until retirement.
If she decides to go to college,
she foregoes these earnings
and incurs a cost of H dollars
for 4 years and then earns
wCOL until retirement.
-H
6-11
The Schooling Model
• Real earnings (earnings adjusted for inflation).
• Age-earnings profile:
the wage profile over a worker’s lifespan.
• The higher the discount rate,
the less likely someone will invest in education
(since they are less future oriented).
• The discount rate depends on:
– the market rate of interest.
– time preferences:
how a person feels about giving up today’s
consumption in return for future rewards.
6-12
The Wage-Schooling Locus
• The salaries firms are willing to pay workers
depends on the level of schooling.
• Properties of the wage-schooling locus.
– The wage-schooling locus is upward sloping.
– The wage-schooling locus is concave,
reflecting diminishing returns to schooling.
6-13
The Wage-Schooling Locus
Dollars
The wage-schooling locus
gives the salary that
a particular worker would earn
if he completed a particular
level of schooling.
If the worker graduates from
high school, he earns $20,000
annually.
If he goes to college for 1 year,
he earns $23,000. And so on.
30,000
25,000
23,000
20,000
0
12 13 14
18
Years of
Schooling
6-14
Education and the Wage Gap
• Observed data on earnings and schooling does not
allow us to estimate returns to schooling.
• In theory, a more able person gets more from an
additional year of education.
• Ability bias: The extent to which unobserved ability
differences exist affects estimates on returns to
schooling, since the ability difference may be the true
source of the wage differential.
6-15
The Schooling Decision
Rate of
Discount
r
r
MRR
s
s*
Years of
Schooling
The MRR schedule gives the
marginal rate of return to
schooling, or the percentage
increase in earnings resulting
from an additional year of school.
A worker maximizes the present
value of lifetime earnings by
going to school until the marginal
rate of return to schooling equals
the rate of discount. A worker
with discount rate r goes to
school for s* years.
6-16
Schooling and Earnings
When Workers Have Different Rates of Discount
Rate of
Interest
Dollars
wHS
PBO
rAL
wDROP
PAL
rBO
MRR
11
12
Years of
Schooling
11
12
Years of
Schooling
6-17
Schooling and Earnings
When Workers Have Different Abilities
Rate of
Interest
Dollars
Z
Bob
wHS
Ace
wACE
wDROP
r
PACE
MRRBOB
MRRACE
11
12
Years of
Schooling
11
12
Years of
Schooling
Ace and Bob have the same discount rate (r) but each worker faces a different wage-schooling
locus. Ace drops out of high school and Bob gets a high school diploma. The wage differential
between Bob and Ace (wHS - wDROP) arises both because Bob goes to school for one more year and
because Bob is more able. As a result, this wage differential does not tells us by how much
Ace’s earnings would increase if he were to complete high school (wACE - wDROP).
6-18
Estimating the Rate of Return to Schooling
• A typical empirical study estimates a regression of the
form:
Log(w) = a·s + other variables
– w is the wage rate
– s is the years of schooling
– a is the coefficient that estimates the rate of return
to an additional year of schooling
6-19
Some Evidence
• In studies of twins, presumably holding ability
constant, valid estimates of rate of return to
schooling can be estimated.
– Estimates range from 3% to 15% annual return to
a year of education.
• Generally, the rate of return to schooling is higher
for workers who were born in states with wellfunded education systems.
6-20
Rate of return to schooling
Rate of return to schooling
School Quality
and the Rate of Return to Schooling
8
7
6
5
4
3
2
15
20
25
30
Pupil/teacher ratio
35
40
8
7
6
5
4
3
2
0.5
0.75
1
1.25
1.5
1.75
2
Relative teacher wage
Source: David Card and Alan B. Krueger, “Does School Quality Matter? Returns to
Education and the Characteristics of Public Schools in the United States,” Journal of
Political Economy 100 (February 1992), Tables 1 and 2.
The data in the graphs refer to the rate of return to school and the school quality
variables for the cohort of persons born in 1920-1929.
6-21
Do Workers Maximize Lifetime Earnings?
• The schooling model
workers select their level of education
present value of lifetime earnings.
assumes that
to maximize the
– once a choice is made, we cannot observe the earnings
associated with the non-choice.
• Workers may select themselves into jobs for which they are
better suited.
• Self-Selection Bias
6-22
Schooling as a Signal
• Education reveals a level of attainment
which signals a worker’s qualifications or innate ability
to potential employers.
• Information that is used to allocate workers in the labor
market is called a signal.
• There could be a “separating equilibrium.”
– Low-productivity workers choose not to obtain X
years of education, voluntarily signaling their low
productivity.
– High-productivity workers choose to get at least X
years of schooling and separate themselves from the
pack.
6-23
Education as a Signal
Dollars
Dollars
Costs
300,000
300,000
250,001
y
Costs
Slope = 25,000
200,000
200,000
Slope = 20,000
20,000
y
0
y
Years of
Schooling
(a) Low-Productivity Workers
0
y
Years of
Schooling
(b) High-Productivity Workers
Workers get paid $200,000 if they get less than y years of college, and $300,000 if they
get at least y years. Low-productivity workers find it expensive to invest in college, and
will not get y years. High-productivity workers do obtain y years. As a result, the
worker’s education signals if he is a low-productivity or a high-productivity worker.
6-24
Implications of Schooling as a Signal
• Education is more than a signal, it alters the stock of
human capital.
• Social return to schooling (percentage increase in
national income) is likely to be positive even if a
particular worker’s human capital is not increased.
6-25
Post-School Human Capital Investments
• Three important properties of age-earnings profiles:
– Highly educated workers earn more than less
educated workers.
– Earnings rise over time at a decreasing rate.
– The age-earnings profiles of different education
cohorts diverge over time (they “fan outwards”).
– Earnings increase faster for more educated workers.
6-26
On-The-Job Training
• Most workers augment their human capital stock
through on-the-job training (OJT) after completing
education investments.
• Two types of OJT:
– General: training that is useful at all firms once it
is acquired.
– Specific: training that is useful only at the firm
where it is acquired.
6-27
Implications
• Firms only provide general training if they do not pay
the costs.
• In order for the firm to willingly pay some of the
costs of specific training, the firm must share in the
returns to specific training. Engaging in specific
training eliminates the possibility of the worker
separating from the job in the post-training period.
6-28
The Acquisition of Human Capital
Over the Life Cycle
Dollars
MC
MR20
MR30
0
Q30 Q20
Efficiency Units
The marginal revenue of an
efficiency unit of human
capital declines as the worker
ages (so that MR20, the
marginal revenue of a unit
acquired at age 20, lies above
MR30). At each age, the
worker equates the marginal
revenue with the marginal
cost, so that more units are
acquired when the worker is
younger.
6-29
Age-Earnings Profiles and OJT
• Human capital investments are more profitable the
earlier they are taken.
• The Mincer earnings function:
Log(w) = a·s + b·t – c·t2 + other variables.
6-30
The Age-Earnings Profile
Implied by Human Capital Theory
Dollars
Age-Earnings
Profile
The age-earnings profile is
upward-sloping and concave. Older
workers earn more because they
invest less in human capital and
because they are collecting the
returns from earlier investments.
The rate of growth of earnings
slows down over time because
workers accumulate less human
capital as they get older.
Age
6-31
Policy Application:
Evaluating Government Training Programs
• Aimed at exposing disadvantaged and low-income
workers to training programs.
• $4 billion of federal spending per year.
• Studies of the return to these human capital
investments are unclear, largely because of selfselection bias.
6-32
Social Experiments
• National Supported Worker Demonstration
(NSW).
– Results of the NSW suggest a 10% return to
investments in human capital for workers treated
under the program.
6-33