Chapter 6
Human Capital
“If you think education’s expensive, try
ignorance.”
-Derek
Bok
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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.
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Education: Stylized Facts
Education is strongly correlated with:
• Labor force participation rates
• Unemployment rates
• Earnings
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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.
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Potential Earnings Streams Faced by a High School
Graduate
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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.
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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
The salaries firms are willing to pay workers depend on
the level of schooling.
Properties of the wage-schooling locus.
• 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 is concave, reflecting
diminishing returns to schooling.
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The Wage-Schooling Locus
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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.
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The Schooling Decision
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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.
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Schooling and Earnings When Workers Have Different
Rates of Discount
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Schooling and Earnings When Workers Have Different
Abilities
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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).
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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.
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Estimating the Rate of Return to Schooling
A typical empirical study estimates a regression of the form:
Log(wi) = a + b·si + other variables
• w is the wage rate
• s is the years of schooling
• b is the coefficient that estimates the rate
of return to an additional year of schooling
• a is the constant
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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.
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School Quality and the Rate of Return to Schooling
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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),
Table 1. The data in the graph refer to the rate of return to school and the school quality variable for the
cohort of persons born in 1920-1929.
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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 ageearnings
profile at two points in time.
• Unfortunately, once a choice is made, we cannot observe the
earnings associated with the non-choice.
• Thus, using the observed wage differential to determine if the
worker selected the “right” earnings stream yields meaningless
results.
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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.
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Education as a Signal
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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.
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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 wellaccepted
that education is more than a signal. Education is at
least partially an investment in human capital.
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