Transcript CHAPTER 6

CHAPTER 6
“If you think education’s
expensive, try ignorance!”
-Derek Bok
McGraw-Hill/Irwin
Copyright © 2013 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 job experience and education.
6-2
Education: Stylized Facts
• Education is strongly correlated with:
o Labor force participation rates
o Unemployment rates
o Earnings
6-3
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
o r is the per-period discount rate.
o y is the future value.
o t is the number of time periods.
6-4
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
6-5
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:
o the market rate of interest.
o time preferences: how a person feels about giving up
today’s consumption in return for future rewards.
6-6
The Wage-Schooling
Locus
• The salaries firms are willing to pay workers
depend on the level of schooling.
• Properties of the wage-schooling locus.
o The wage-schooling locus is upward sloping.
o The slope of the wage-schooling locus indicates the increase in
earnings associated with an additional year of education.
o The wage-schooling locus is concave, reflecting diminishing returns to
schooling.
6-7
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
6-8
Education and the Wage Gap
• Observed data on earnings and schooling does
not allow us to estimate returns to schooling,
because more able persons tend to get more
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.
6-9
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.
6-10
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
6-11
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).
6-12
Estimating the Rate of
Return to Schooling
• A typical empirical study estimates a regression
of the form:
Log(w) = a·s + other variables
o w is the wage rate
o s is the years of schooling
o a is the coefficient that estimates the rate of return to an additional year
of schooling
6-13
Some Evidence
• In studies of twins, presumably holding ability
constant, valid estimates of rate of return to
schooling can be estimated.
o 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
well-funded education systems.
6-14
8
Rate of return to schooling
Rate of return to schooling
School Quality and the Rate
of Return to Schooling
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.
6-15
Do Workers Maximize
Lifetime Earnings?
• The schooling model assumes that workers select their
level of education to maximize the present value of
lifetime earnings.
• To test this hypothesis directly, we must observe the
age-earnings profile at two points in time.
o Unfortunately, once a choice is made, we cannot observe the
earnings associated with the non-choice.
o Thus, using the observed wage differential to determine if the
worker selected the “right” earnings stream yields meaningless
results.
6-16
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.”
o Low-productivity workers choose not to obtain X
years of education, voluntarily signaling their low
productivity.
o High-productivity workers choose to get at least X
years of schooling and separate themselves from
the pack.
6-17
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.
6-18
Implications of Schooling as a Signal
• For schooling to act as a signal, schooling must be
more “costly” for low-ability workers compared to
high-ability workers.
• 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.
• Although education may incorporate a signaling
aspect, it is well-accepted that education is more than
a signal. Education is at least partially an investment
in human capital.
6-19
Post-School Human
Capital Investments
• Three important properties of age-earnings profiles:
o Highly educated workers earn more than less
educated workers.
o Earnings rise over time at a decreasing rate.
o The age-earnings profiles of different education
cohorts diverge over time (they “fan outward”).
o Earnings increase faster for more educated workers.
6-20
Age-Earnings Profiles
Men
2600
Weekly Earnings
2300
2000
College Graduates
1700
1400
Some college
1100
High school graduates
800
High school dropouts
500
200
18
25
32
39
46
53
60
Age
6-21
Age-Earnings Profiles
Women
Weekly Earnings
1500
1300
College Graduates
1100
900
Some college
700
High school graduates
500
High school dropouts
300
100 18
25
32
39
46
53
60
Age
6-22
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:
o General: training that is useful at all firms once it is acquired.
o Specific: training that is useful only at the firm where it is acquired.
6-23
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 posttraining period.
6-24
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.
6-25
Age-Earnings Profiles and OJT
• Human capital investments are more profitable the
earlier they are taken.
• The Mincer earnings function:
o Log(w) = a·s + b·t – c·t2 + other variables.
o The “overtaking age” is t* and indicates
the time when the worker slows down
acquisition of human capital to collect the
return on prior investments so as to
“overtake” earnings of those that did not
undertake similar investments.
6-26
The Age-Earnings Profile Implied by
Human Capital Theory
Dollars
Age-Earnings
Profile
Age
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.
6-27
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 self-selection bias.
6-28
Social Experiments
• National Supported Worker
Demonstration (NSW).
o Results of the NSW suggest a 10% return to
investments in human capital for workers treated
under the program.
6-29