Chapter 6

Human Capital

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin

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 work experience and education.

6-3

Education: Stylized Facts

• Education is strongly correlated with:– Labor force participation rates– Unemployment rates– Earnings

6-4

台灣教育別失業率（ 1978-2009）

教育別失業率

0

1

2

3

4

5

6

7

1978 19791980 19811982 19831984 1985 19861987 19881989 19901991 19921993 19941995 19961997 19981999 20002001 2002 20032004 20052006 20072008 2009

年度

%

國中及以下 ( )高中 職 專科 大學及以上

6-5

男女年齡別薪資 (2009)

男女年齡別薪資

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

１５～１９歲

years

２０～２４歲

years

２５～２９歲

years

３０～３４歲

years

３５～３９歲

years

４０～４４歲

years

４５～４９歲

years

５０～５４歲

years

５５～５９歲

years

６０～６４歲

years

６５ 歲及以上

years & over

年齡

月薪資

男性月薪資 女性月薪資

6-6

Age-Earnings Profiles

Men

200500800

110014001700200023002600

18 25 32 39 46 53 60

Age

We

ek

ly E

arn

ing

s

Some college

College Graduates

High school graduatesHigh school dropouts

6-7

台灣 男性 不同教育程度 年齡別薪資 (2009)

男性不同教育程度年齡別薪資

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

１５～１９歲years

２０～２４歲years

２５～２９歲years

３０～３４歲years

３５～３９歲years

４０～４４歲years

４５～４９歲years

５０～５４歲years

５５～５９歲years

６０～６４歲years

６５ 歲及以 years & over 上

年齡別

月薪資

小學國中高中高職專科大學以上

6-8

Age-Earnings Profiles

Women

200400

600800

1000

12001400

18 25 32 39 46 53 60

Age

Wee

kly

Ear

ning

s

Some college

High school graduates

College Graduates

High school dropouts

6-9

台灣 女性 不同教育程度 年齡別薪資 (2009)

女性不同教育程度年齡別薪資

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

１５～１９歲years

２０～２４歲years

２５～２９歲years

３０～３４歲years

３５～３９歲years

４０～４４歲years

４５～４９歲years

５０～５４歲years

５５～５９歲years

６０～６４歲years

６５ 歲及以 years & over 上

年齡別

月薪資

國小國中高中高職專科大學

6-10

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

– r is the per-period discount rate.– y is the future value.– t is the number of time periods.

6-11

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.

6-12

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:– the market rate of interest.– time preferences:

how a person feels about giving up today’s consumption in return for future rewards.

6-13

The Wage-Schooling Locus

• The salaries firms are willing to pay workers depends on the level of schooling.

• Properties of the wage-schooling locus.– The wage-schooling locus is upward sloping.– The wage-schooling locus is concave,

reflecting diminishing returns to schooling.

6-14

The Wage-Schooling Locus

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.

0 13 14 1812

30,000

20,000

23,000

25,000

Years of Schooling

Dollars

6-15

Education and the Wage Gap

• Observed data on earnings and schooling does not allow us to estimate returns to schooling.

• In theory, a more able person gets more from an additional year of 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.

6-16

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.

6-17

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

6-18

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

Z

Bob

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).

6-19

Estimating the Rate of Return to Schooling

• A typical empirical study estimates a regression of the form:

Log(w) = a·s + other variables

– w is the wage rate– s is the years of schooling– a is the coefficient that estimates the rate of return

to an additional year of schooling

6-20

Some Evidence

• In studies of twins, presumably holding ability constant, valid estimates of rate of return to schooling can be estimated.– 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.

6-21

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

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.

6-22

Do Workers Maximize Lifetime Earnings?

• The schooling model assumes that workers select their level of education to maximize the present value of lifetime earnings.

– once a choice is made, we cannot observe the earnings associated with the non-choice.

• Workers may select themselves into jobs for which they are better suited.

• Self-Selection Bias

6-23

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.”– 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.

6-24

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

6-25

Implications of Schooling as a Signal

• Education is more than a signal, it alters the stock of human capital.

• 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.

6-26

Post-School Human Capital Investments

• Three important properties of age-earnings profiles:– 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.

6-27

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.

6-28

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.

6-29

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.

6-30

Age-Earnings Profiles and OJT

• Human capital investments are more profitable the earlier they are taken.

• The Mincer earnings function:

Log(w) = a·s + b·t – c·t2 + other variables.

6-31

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.

6-32

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.

6-33

Social Experiments

• National Supported Worker Demonstration (NSW).– Results of the NSW suggest a 10% return to

investments in human capital for workers treated under the program.