The Schooling Decision
Dollars/year
Goes to College
40,000
(24,000)(65–22) = $1,032,000 (benefit of education)
Quits After High School
16,000
0
18
22
65
Age
$20,000 + $64,000 = $84,000 (total cost of education)
-5,000
A person who quits school after getting his high school diploma can earn $16,000 per year
from age 18 until the age of retirement.
If the person goes to college, she pays $20,000 in tuition and foregoes earning $64,000,
but earns $40,000 per year between the ages of 18 and 22.
The Schooling Decision
•
The previous model ignores the discount rate
•
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”
•
Swann (2003) estimates the annual discount rate of women at r = 20%
HS
PVwomen

16, 000
16, 000
16, 000


...

 $95,982
0
1
64 18
(1  0.2) (1  0.2)
(1  0.2)
5, 000
5, 000
5, 000
5, 000



(1  0.2)0 (1  0.2)1 (1  0.2)2 (1  0.2)3
40, 000
40, 000
40, 000



...

 $100,163
(1  0.2)4 (1  0.2)5
(1  0.2)6418
college
PVwomen

The Schooling Decision
•
Keane and Wolpin (1997) estimate the discount rate of young men at r = 28%
HS
PVmen

16, 000
16, 000
16, 000


...

 $73,142
(1  0.28)0 (1  0.28)1
(1  0.28)6418
5, 000
5, 000
5, 000
5, 000



(1  0.28)0 (1  0.28)1 (1  0.28) 2 (1  0.28)3
40, 000
40, 000
40, 000



...

 $53,776
(1  0.28) 4 (1  0.28)5
(1  0.28)6418
college
PVmen

Do these two results explain why black women graduate
from college at higher rates than black men?
The Schooling Decision
60,000
50,000
40,000
Wage
30,000
20,000
10,000
0
0
4
8
12
16
20
Years of schooling
•
•
•
•
The slope indicates earnings increase in years of education, and the wageschooling locus in concave
The worker makes $33,600 graduating from JHS
(41,600-33,600)/33,600 = 23.8%
The worker makes $41,600 graduating from HS
(46,400-41,600)/41,600 =11.5%
The worker makes $46,400 graduating from Univ
The Schooling Decision
14
12
10
mrr
8
6
4
2
0
0
4
8
12
16
20
Years of schooling
•
The Marginal Rate of Return (to an additional year of schooling) is the
percent change in w given a one-year increase in s
− Finishing the 8th grade increases earnings by 8%
− Finishing 12th grade increases earnings by 4.3%
− Finishing college (rather than dropping out after your junior year)
increases earnings by 2%
The Schooling Decision
Estimating MRR
•
A typical study estimates a regression of the form:
Log(wi) = dxi + asi
•
wi is the wage rate of the i th worker
•
si is the years of schooling of the i th worker
•
In log-linear models, coefficient a represents the
– percent increase in w (we took the log of its values) for a
– 1 year increase in s (we did not take the log of its values):
a
 ln( w) %w

s
1
– Hence a is an estimate for the rate of return to an added year of schooling
a  MRR
The Schooling Decision
14
12
10
mrr
8
6
4r
2
0
0
4
8
*
s
12
16
20
Years of schooling
• A worker maximizes the present value of lifetime earnings by going to school until
the marginal rate of return to schooling equals the discount rate.
• A worker with discount rate r = 4.3% goes to school for s* = 12 years.
The Schooling Decision
Individuals with different discount rates
Rate of
Interest
Dollars
wBS
rAl
wHS
rBob
MRR
12
16
Years of
Schooling
12
16
Years of
Schooling
The Schooling Decision
Individuals with different abilities
Rate of
Interest
Dollars
Bob
wBob
Ace
BS
wAce
wAce
r
MRRBob
MRRAce
12
16
Years of
Schooling
12
16
Years of
Schooling
• Ace and Bob have the same discount rate (r) but each worker faces a different wageschooling locus.
• Ace doesn’t go to college since his MRR = r after graduating HS, and earns wACE.
• Bob graduates from college, and earns wBOB.
The Schooling Decision
Individuals with different abilities
Slope is biased
Dollars
Bob
wBob
Ace
Unbiased slope because
‘ability’ is accounted for in
the regression
wAce
12
16
• The wage differential between Bob and Ace arises both because
Years of
Schooling
‾ We don’t observe either wage school locus
‾ Bob goes to school for four more years 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.
The Schooling Decision
• In studies of twins, presumably holding ability constant, valid estimates of
rate of return to schooling can be estimated
Rate of return to schooling
Rate of return to schooling
• Generally, the rate of return to schooling is higher for workers who were
born in states with well-funded education systems
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.
Education is a Signal
• Education reveals a level of attainment which signals a worker’s
qualifications to potential employers
• Information that is used to allocate a 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
Education is a Signal
Dollars
Dollars
Costs = 25,001 s
Costs = 20,000 s
100,004
100,000
100,000
80,000
0
0
0
4
Years of Schooling
(a) Low-Productivity Workers
0
4
Years of Schooling
(b) High-Productivity Workers
• Workers get paid $200,000 if they get less than 4 years of college, and $300,000 if they get at least 4
years (w = 100,000 if college grad but w = 0 if not).
• Low-productivity workers find it expensive to invest in college and choose w = 0 and s = 0
• High-productivity workers find it inexpensive to invest in college and choose w = 100,000 and s = 4
• As a result, the worker’s education signals if he is a low-productivity or a high-productivity worker.
Education is an Investment in Human Capital
Men
Men
Weekly Earnings
2000
1700
College Graduates
1400
Some college
1100
800
High school graduates
500
High school dropouts
200
18
25
32
39
46
Women
Age
53
60
Women
Weekly Earnings
1200
1000
College Graduates
800
Some college
600
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”)
High school graduates
400
High school dropouts
200
18
25
32
39
Age
46
53
60
Earnings increase faster for
more educated workers
Human Capital Accumulation and Age
At age 20, acquiring an
additional Eunit is easier
(less costly)
Dollars
MC
MR20
MR30
0
Q30 Q20
than it is at age 30
Diminishing returns to
the accumulation of H
explains the curvature
of MC
Efficiency Units
The marginal revenue of an efficiency unit of human capital declines as the worker
ages because the younger you are the longer you have to ‘rent’ the additional Eunit
Hence, marginal revenue of a unit acquired at age 20 (MR20) 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.
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
• Firms only provide general training if they do not pay the costs
• If the firm and the worker share the returns to specific training the
possibility of separation in the post-training period is eliminated
Age-Earnings Profile
• Recall that human capital investments are more profitable the earlier they
are taken
• The Mincer earnings function:
Log(wi) =[a si + d x]+ b t – g t2
The “overtaking age” is t*, indicating 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 do not undertake
similar investments
Age-Earnings Profile
Log(wi) = a s + d x + b t – g t 2
as+dx
t*
t (age)
The age-earnings profile is concave and upward-sloping until age t*.
Older workers (prior to reaching age t*) earn more because they invest less in H and
are collecting returns from earlier investments.
The rate of growth of earnings slows down as they get closer to age t* because
workers accumulate less H as they age.