Human capital theory

1. Human Capital
Borrowed in part from:
Daron Acemoglu and David Autor
Lectures in Labor Economics

2. Some Facts/Definitions
• The standard human capital earnings function, or Mincerian model
takes on the following form:
• Log yi =a+bSi +cX +dX2
• where yi is some earnings measure; Si is individual years of schooling;
Xi is experience
• The Mincer equation assumes schooling only affects the experience
profile in levels, and that the log earnings increases with schooling at
a linear rate. This does not have to be the case, but empirically, these
two functional form specifications seems to hold up reasonably well,
explaining 20-35% of variation in earnings.

4. Types of Human Capital
• Human capital can be improved or enhanced in two main different ways:
• Formal Education (our focus)
• On-job-training
• General
• Firm-specific
• The education models can be used to explain investments in training that produces
general human capital (i.e. the worker should be willing to pay some wage if the firm
provides general human capital). For firm-specific human capital life gets more
complicated (the firm has no incentive to pay higher wage post training since the
market won’t pay a higher wage)
• Also note that some human capital is innate (ability?; personality traits?) or chosen
by parents/society.

5. Human Capital investments
• Consider the schooling decision of a single individual facing
exogenously given prices for human capital. For now, assume that
there are perfect capital markets (individuals can borrow at a
constant interest rate r).
• More specifically, consider an individual with a utility function u(c)
that satisfies the standard neoclassical assumptions. In particular, it is
strictly increasing and strictly concave.
• Note in this model all the individual cares about is consumption. Education is
only valuable in as much as it increases productivity and therefore
consumption

6. Human Capital investments
Suppose that the individual has a planning horizon of T (where T = ∞ is
allowed), discounts the future at the rate ρ > 0 and faces a constant
flow rate of death/exit from the labor market equal to ν ≥ 0 The
exit/death rate, ν, is positive, so that individuals have finite expected
lives.
Standard arguments imply that the objective function of this individual
at time t = 0 is

7. Human Capital investments
• The model presented here is a version of Mincer’s (1974) seminal
contribution.
• Let us first assume that T = ∞, which will simplify the expressions.
• Suppose that individual has to spend an interval S with s (t) = 1–i.e., in full-
time schooling, and s (t) = 0 thereafter. At the end of the schooling interval,
the individual will have a schooling level of h(S) = η(S). where η (·) is an
increasing, continuously differentiable and concave function
• (All schooling is full time; the choice is between school and work - there is
no leisure in this model)
• Suppose that this individual is born with some human capital h (0) ≥ 0. For
t ∈ [S, ∞), human capital accumulates over time (as the individual works)
according to the differential equation

8. Human Capital investments
• The individual is assumed to face an exogenous sequence of wage per
unit of human capital
• Suppose also that wages grow exponentially,
w ̇( t ) = g ww( t ) , with boundary condition w (0) > 0.
-Note this model assumes wage growth (maybe returns to
experience/age)
• Finally suppose that gw + gh < r + ν, so that the net present discounted
value of the individual is finite
• the optimal schooling decision must be a solution to the following
maximization problem

9. Human Capital Investments
Since η(S) is concave, the unique solution to this problem is
characterized by the first-order condition: η’(S∗) / η(S∗) = r + ν − gw.
If there is no wage growth and we allow people to live forever then the
equation becomes η’(S*)/ η(S) =r
• Which states that individuals invest in schooling until the marginal return is
equal to the interest rate. This expression is where the term “returns to
schooling” comes from.
• The left hand side of this expression is the marginal benefits from additional
investments in schooling and the right hand side is the marginal cost (the
opportunity cost of the dollar investment, in this case)

10. Human Capital Investments
• This shows that higher interest rates and higher values of ν (cor-
responding to shorter planning horizons) reduce human capital
investments, while higher values of gw increase the value of human
capital and thus encourage further investments.
• Empirical suggests returns to schooling in the range of 0.06 to 0.10.
Equation (1.12) suggests that these are not unreasonable. For
example, we can think of the annual interest rate r as approximately
0.10, ν as corresponding to 0.02 that gives an expected life of 50
years, and gw corresponding to the rate of wage growth holding the
human capital level of the individual constant, which should be
approximately about 2%. Thus we should expect an estimate around
0.10, which is consistent with the upper range of the empirical
estimates.

12. Human Capital Investments: Heterogeneity
• Note however that we have not introduced any source of
heterogeneity that can generate different levels of schooling across
individuals.
• Say ν is lower for women –they spend less time in the labor force; then the
returns to investing should be less and education should be less.
• We can also introduce heterogeneity in the interest rate. A high r i is often
used to proxy for liquidity constraints. Individuals that need to borrow to
attend school but cannot easily do so can be modelled as individuals facing
high values of ri. These individual will get less human capital.
• Clearly the discount rate ρ matters. If people put less weight on the future
they should invest less.
• Lalith Munasinghe & Nachum Sicherman, 2006. "Why Do Dancers Smoke? Smoking,
Time Preference, and Wage Dynamics," Eastern Economic Journal

14. Human Capital Investments: Heterogeneity
• Grilliches, 1977 Econometrica
• We can introduce heterogeneity in costs by modifying the lifetime utility
function to include distaste for school (kind of cheating).
• Allow for heterogeneity in the returns to schooling owing to the interaction
between ability and schooling
• Assume high ability types get more human capital out of a year of schooling than
others- these people should rationally invest in more schooling
• Mathematically this involves adding some terms to the human capital production function
η(S)
• It turns out there is a second sort of ability bias. Some people have higher ability
endowments (think athletes, Bill Gates) these people have a higher opportunity cost
and should get less schooling.

15. Extensions: The Ben-Porath Model
• The baseline Ben-Porath model enriches the models we have seen so
far by al- lowing human capital investments and non-trivial labor
supply decisions throughout the lifetime of the individual.
• the human capital accumulation equation, takes the form
h (t) = φ (s (t) h (t)) − δhh (t) ,
• where δh > 0 captures “depreciation of human capital,” for example
because new machines and techniques are being introduced, eroding
the existing human capital of the worker. The individual starts with an
initial value of human capital h (0) > 0.

16. Raw data (not causal estimates!)

17. A puzzle:
• The returns to schooling (especially advanced schooling) have risen
(by some estimates almost doubled since the 1970s) yet this has not
been accompanied by an increase in the college graduation rates (this
is especially true for young men)
• In fact I document that college has gotten easier/cheaper (the time cost of
college have fallen) pushing the returns even higher.
• Why not????
• -imperfect credit markets
• -ignorance of the increasing returns
• -hyperbolic discounting
• -“low” ability” [Lots of students enter but do not complete.]

18. A review of the returns to schooling literature
• Empirical Problem in estimating the returns to schooling:
• Ability Bias/Selection Bias:
• Another source of bias springs solely from heterogeneity in the returns to
schooling across individuals, bi. Individuals who have more to gain from
schooling will choose to spend more time in school. The greater variability of
the marginal return across individuals σ2 , the greater the amount of selection
in schooling b outcomes and the greater the bias.
• Measurement error in reporting

19. A review of the returns to schooling literature
• IVs
• New School Construction (Duflo) and Destruction (WWII)
• Compulsory Schooling
• (Theory says should be a lower bound –why??) (Think of the LATE)
• Distance to School (Card)
• We are estimating the average effect of schooling on earnings only off of the variation in
schooling from living close to or far away from a 4-year college. Who are the people
affected by this instrument? Likely those from low-income parents who can’t afford, or
don’t want to, send their children to a school out of town. Thus, for this group, the
marginal cost to attend school may be higher than the average marginal cost if liquidity
constraints play a role. The marginal benefits from education may also differ compared
to the average in the sample, or for individuals under other circumstances.

20. IV vs. OLS estimates of the return to schooling
• Card and other finds that the IV estimates for the return to schooling are larger than the OLS results.
Why?
• Not the normal selection or ability bias – They go the wrong way. Note Grilliches model suggest
that those individual with higher in the level of ability/initial earnings will tend to choose less
education.
• Heterogeneous returns to education/LATE. If schooling is an investment then the group of
individuals with low levels of schooling will be those for whom the marginal benefit is low or the
discount rate is high. If the instrument induces people with high discount rates (say the poor) to
get more schooling then the returns will be higher for this subpopulation.
• IV reduce measurement error. Variable that suffer from classical measurement error have
attenuation bias (i.e. they are biased towards zero). If education is measured with classical
measurement error the OLS estimates of the returns to schooling are downward biased. A good
instrument can “fix” measurement error and reduce the corresponding attenuation bias.
• Another possibility, suggested by Ashenfelter and Harmon (1998), is "publication bias". They
hypothesize that in searching across alternative specifications for a statistically significant IV
estimate, a researcher is more likely to select a specification that yields a large point estimate of
the return to education. As evidence of this behavior they point to a positive correlation across
studies between the IV-OLS gap in the estimated return to education and the sampling error of
the IV a large point estimate of the return to education.
• Invalid Instruments