1. The Schooling Decision
Dollars/year
40,000
Goes to College
(24,000)(65–22) = $1,032,000 (benefit of education)
16,000
Quits After High School
Age 18 22 65
$20,000
= $84,000 (total cost of education)
$64,000
-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.
$64,000,

2. 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%

3. The Schooling Decision
Keane and Wolpin (1997) estimate the discount rate of young men at r = 28%
Do these two results explain why black women graduate
from college at higher rates than black men?

4. The Schooling Decision
The slope indicates earnings increase in years of education, and the wage-schooling locus in concave
The worker makes $33,600 graduating from JHS
The worker makes $41,600 graduating from HS
The worker makes $46,400 graduating from Univ
(41,600-33,600)/33,600 = 23.8%
(46,400-41,600)/41,600 =11.5%

5. The Schooling Decision
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% 5

6. 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):
Hence a is an estimate for the rate of return to an added year of schooling
a  MRR

7. The Schooling Decisionr s*
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.

8. The Schooling Decision
Individuals with different discount rates
The Schooling Decision
Rate of Interest
Dollars
wBS
rAl
wHS
rBob
MRR 12 16
Years of Schooling 12 16
Years of Schooling

9. The Schooling Decision
Individuals with different abilities
The Schooling Decision
Rate of Interest
Dollars
Bob
wBob BS
wAce
Ace
wAce r
MRRBob
MRRAce 12 16 12 16
Years of Schooling
Years of Schooling
Ace and Bob have the same discount rate (r) but each worker faces a different wage-schooling locus.
Ace doesn’t go to college since his MRR = r after graduating HS,
Bob graduates from college,
and earns wACE.
and earns wBOB.

10. The Schooling Decision
Individuals with different abilities
The Schooling Decision
Slope is biased
Dollars
Bob
wBob
Ace
Unbiased slope because ‘ability’ is accounted for in the regression
wAce 12 16
Years of Schooling
The wage differential between Bob and Ace arises both because
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. 10

11. The Schooling Decision
In studies of twins, presumably holding ability constant, valid estimates of rate of return to schooling can be estimated
Generally, the rate of return to schooling is higher for workers who were born in states with well-funded education systems
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

12. 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

13. Education is a Signal
Dollars
Dollars
Costs = 25,001 s
Costs = 20,000 s
100,004
100,000
100,000
80,000 4
Years of Schooling 4
Years of Schooling
(a) Low-Productivity Workers
(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 (Dw = 100,000 if college grad but Dw = 0 if not).
Low-productivity workers find it expensive to invest in college and choose Dw = 0 and s = 0
High-productivity workers find it inexpensive to invest in college and choose Dw = 100,000 and s = 4
As a result, the worker’s education signals if he is a low-productivity or a high-productivity worker.

14. Education is an Investment in Human Capital
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
Women

15. Human Capital Accumulation and Age
At age 20, acquiring an additional Eunit is easier (less costly)
than it is at age 30
Diminishing returns to the accumulation of H explains the curvature of MC
Dollars MC
MR20
MR30
Efficiency Units
Q30
Q20
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.

16. 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

17. Log(wi) = a si + d x + b t – g t2
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
[ ]

18. Age-Earnings Profile Log(wi) = a s + d x + b t – g t 2 a s + d x 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.