Chapter 7

Human Capital

Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Labor Economics, 4th edition

7 - 3

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

7 - 4

Education: Stylized Facts

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

7 - 5

Present Value: Borrowing a Technique from Finance

• Present value allows comparison of dollar amounts spent and received in different time periods

• PV = y/(1+r)t

• r is the discount rate

7 - 6

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 his high school diploma can earn wHS from age 18 until the age of retirement. If he decides to go to college, he foregoes these earnings and incurs a cost of H dollars for 4 years and then earns wCOL until retirement age.

7 - 7

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)

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The Wage-Schooling Locus

• What salary will firms be willing to pay workers for given levels of schooling

• Three properties:- The wage-schooling locus is upward sloping- The slope of the wage-schooling locus indicates the

increase in earnings associated with an additional year of education

- The wage-schooling locus in concave

7 - 9

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.

0 13 14 1812

30,000

20,000

23,000

25,000

Years of Schooling

Dollars

7 - 10

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 effects estimates on returns to schooling (since the ability difference may be the true source of the wage differential)

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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.

7 - 12

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

7 - 13

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 (or 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 (or wACE - wDROP).

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Estimating the Rate of Return to Schooling

• A typical 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 one added

year of schooling

7 - 15

Some Evidence

• 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

7 - 16

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.

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Do Workers Maximize Life-Time Earnings?

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

• The only way to test this hypothesis is if we can observe the age-earnings profile of a worker in two ways: if he chooses college, or if he stops education investments

• Unfortunately, once a choice is made, we cannot observe the earnings stream associated with the non-choice

• Thus, using the observed wage differential to determine if the worker selected the “right” earnings stream yields meaningless results

7 - 18

Self-Selection Bias

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

• Therefore, wage differentials may not be associated with education

• Then what is the point of investing in education?

7 - 19

Schooling as 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

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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

25,001 y

20,000 y

200,000

0

Dollars

Years of Schooling

Costs

Slope = 25,001

300,000

200,000

0

Dollars

Years of Schooling

Costs

Slope = 20,000

(a) Low-Productivity Workers

y y

(b) High-Productivity Workers

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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

7 - 22

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

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Age-Earnings Profiles

Men

200

500

800

1100

1400

1700

2000

18 25 32 39 46 53 60

Age

Wee

kly

Ear

nin

gs

Some college

College Graduates

High school graduates

High school dropouts

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Age-Earnings Profiles

Women

200

400

600

800

1000

1200

18 25 32 39 46 53 60

Age

Wee

kly

Ear

nin

gs

Some college

High school graduates

College Graduates

High school dropouts

7 - 25

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

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Implications

• 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

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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.

7 - 28

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- The “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 do not undertake similar investments

7 - 29

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.

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Policy Application: Evaluating Government Training Programs

• Aimed at exposing disadvantaged and low-income workers to training programs

• $4 billion (Federal) spending per year• Studies of the return to these human capital investments are

unclear (self-selection bias)

7 - 31

Social Experiments

• National Supported Worker Demonstration (NSW)• The study suggests a 10% return to investments in human

capital for workers treated under the program

7 - 32

End of Chapter 7