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1 8 6 5 2 2 Age 40,00 0 16,0 00 -5,000 Dollars/ year Goes to College Quits After High School 0 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, (24,000)(65–22) = $1,032,000 (benefit of education) $20,000 The Schooling Decision $64,000 + = $84,000 (total cost of education) $64,000,

18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

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Page 1: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

18 6522Age

40,000

16,000

-5,000

Dollars/year

Goes to College

Quits After High School

0

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.

(24,000)(65–22) = $1,032,000 (benefit of education)

$20,000

The Schooling Decision

$64,000 + = $84,000 (total cost of education)

$64,000,

Page 2: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

0 1 2 3

4 5 64 18

5,000 5,000 5,000 5,000

(1 0.2) (1 0.2) (1 0.2) (1 0.2)

40,000 40,000 40,000... $100,163

(1 0.2) (1 0.2) (1 0.2)

collegewomenPV

0 1 64 18

16,000 16,000 16,000... $95,982

(1 0.2) (1 0.2) (1 0.2)HS

womenPV

• 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%

The Schooling Decision

Page 3: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• 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?

0 1 64 18

16,000 16,000 16,000... $73,142

(1 0.28) (1 0.28) (1 0.28)HS

menPV

0 1 2 3

4 5 64 18

5,000 5,000 5,000 5,000

(1 0.28) (1 0.28) (1 0.28) (1 0.28)

40,000 40,000 40,000... $53,776

(1 0.28) (1 0.28) (1 0.28)

collegemenPV

The Schooling Decision

Page 4: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

0

10,000

20,000

30,000

40,000

50,000

60,000

0 4 8 12 16 20

Years of schooling

Wage

• 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

The Schooling Decision

(41,600-33,600)/33,600 = 23.8%

(46,400-41,600)/41,600 =11.5%

Page 5: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

0

2

4

6

8

10

12

14

0 4 8 12 16 20

Years of schooling

mrr

• 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

Page 6: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

The Schooling DecisionEstimating MRR

• A typical study estimates a regression of the form:

Log(wi) = xi + si

• 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 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 is an estimate for the rate of return to an added year of schooling

MRR

( )ln %

1

w w

s

Page 7: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

0

2

4

6

8

10

12

14

0 4 8 12 16 20

Years of schooling

mrr

The Schooling Decision

• 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.

r

s*

Page 8: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

Years of Schooling

Years of Schooling

Rate of Interest

1616 1212

rBob

rAl

MRR

Dollars

wHS

wBS

The Schooling DecisionIndividuals with different discount rates

Page 9: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• 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,

Years of Schooling

Years of Schooling

Rate of Interest

1612

r

MRRAce

MRRBob

1612

wBob

wAce

wAce

Bob

Ace

Dollars

The Schooling DecisionIndividuals with different abilities

BS

and earns wBOB.

and earns wACE.

Page 10: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• 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.

Years of Schooling

1612

Bob

Ace

Slope is biased

Unbiased slope because ‘ability’ is accounted for in the regression

The Schooling DecisionIndividuals with different abilities

wBob

wAce

Dollars

Page 11: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• 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

The Schooling Decision

2

3

4

5

6

7

8

15 20 25 30 35 40

Pupil/teacher ratio

Rat

e of

ret

urn

to s

choo

ling

2

3

4

5

6

7

8

0.5 0.75 1 1.25 1.5 1.75 2

Relative teacher wage

Rat

e of

ret

urn

to s

choo

ling

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.

Page 12: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

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

Page 13: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• 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.

100,004

80,000

Dollars

Years of Schooling

Costs = 25,001 s

0

Dollars

Years of Schooling

Costs = 20,000 s

(a) Low-Productivity Workers

4 4

(b) High-Productivity Workers

0

100,000

0

100,000

0

Education is a Signal

Page 14: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

Women

200

400

600

800

1000

1200

18 25 32 39 46 53 60

Age

Wee

kly

Earn

ings

Some college

High school graduates

College Graduates

High school dropouts

Men

200

500

800

1100

1400

1700

2000

18 25 32 39 46 53 60

Age

Wee

kly

Earn

ings

Some college

College Graduates

High school graduates

High school dropouts

Men

Women

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

Education is an Investment in Human Capital

Page 15: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

MR30

Human Capital Accumulation and Age

MC

MR20

Dollars

0 Q30 Q20

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.

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

Page 16: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

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

Page 17: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

• Recall that human capital investments are more profitable the earlier they are taken

• The Mincer earnings function:

Log(wi) = si + x + t – 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

Page 18: 18 65 22 Age 40,000 16,000 -5,000 Dollars/year Goes to College Quits After High School 0 A person who quits school after getting his high school diploma

t (age)t*

s + x

Age-Earnings Profile

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.

Log(wi) = s + x + t – t 2