CHAPTER 6

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

CHAPTER 6

“If you think education’s expensive, try ignorance!”

-Derek Bok

6-2

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.

6-3

Education: Stylized Facts• Education is strongly correlated with:

o Labor force participation rateso Unemployment rateso Earnings

6-4

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.

6-5

Potential Earnings Streams Faced by a High School Graduate

18 6522Age

wCOL

wHS

-H

Dollars

Goes to College

Quits After High School

0

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.

6-6

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.

6-7

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.

6-8

The Wage-Schooling LocusThe 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.

0 13 14 1812

30,000

20,000

23,00025,000

Years of Schooling

Dollars

6-9

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.

6-10

The Schooling Decision

Years of Schooling

Rate of Discount

s*s

r

r

MRR

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.

6-11

Schooling and Earnings When Workers

Have Different Rates of Discount

Years of Schooling

Years of Schooling

Rate of Interest

1212 1111

rBO

rAL

MRR

Dollars

wDROP PAL

PBO

wHS

6-12

Schooling and Earnings When Workers Have Different Abilities

Years of Schooling

Years of Schooling

Rate of Interest

1211

r

MRRACE

MRRBOB

Dollars

1211

wHS

wACE

PACE

wDROP

ZBob

Ace

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).

6-13

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 rateo s is the years of schoolingo a is the coefficient that estimates the rate of return to an additional year

of schooling

6-14

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.

6-15

School Quality and the Rate of Return to Schooling

2

3

4

5

6

7

8

15 20 25 30 35 40

Pupil/teacher ratio

Rate

of r

etur

n to

sch

oolin

g

2

3

4

5

6

7

8

0.5 0.75 1 1.25 1.5 1.75 2

Relative teacher wageRa

te o

f 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.

6-16

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.

6-17

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.

6-18

Education as a Signal

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.

300,000

250,001 y

20,000 y

0

Dollars

Years of Schooling

Costs

Slope = 25,000

300,000

200,000

0

Dollars

Years of Schooling

Costs

Slope = 20,000

(a) Low-Productivity Workers

y y

(b) High-Productivity Workers

200,000

6-19

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.

6-20

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.

6-21

Age-Earnings Profiles

18 25 32 39 46 53 60200

500

800

1100

1400

1700

2000

2300

2600

Men

Age

Wee

kly

Earn

ings

Some college

College Graduates

High school graduates

High school dropouts

6-22

Age-Earnings Profiles

18 25 32 39 46 53 60100

300

500

700

900

1100

1300

1500

Women

Age

Wee

kly

Earn

ings

Some college

High school graduates

College Graduates

High school dropouts

6-23

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.

6-24

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.

6-25

The Acquisition of Human Capital Over the Life Cycle

MC

MR20

MR30

Dollars

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.

6-26

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.oThe “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.

6-27

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.

6-28

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.

6-29

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.