ArticlePDF Available

Abstract and Figures

The total return to higher education is the rate of return based on earnings plus non-monetary private and social benefits beyond earnings that captures higher education's contribution to development. A theory of endogenous development is a new scholarly contribution where firm and household production with education externalities and the endogeneity of new ideas leads to an optimal rate of development. This rate is higher than in an economy without these externalities. Since measures of private non-market and social benefit externalities are positive, externalities contribute to higher per capita development. The total return is estimated to be considerably higher than the opportunity cost of funds and the return on physical capital, the first major evidence of serious underinvestment in higher education in the US for optimal development. Policy-relevant treatment effects and policy options with implications for optimal development and for improving the worsening condition of the dissatisfied middle class are considered.
Content may be subject to copyright.
Please
cite
this
article
in
press
as:
McMahon,
W.W.
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
The
Quarterly
Review
of
Economics
and
Finance
(2018),
https://doi.org/10.1016/j.qref.2018.05.005
ARTICLE IN PRESS
G Model
QUAECO-1142;
No.
of
Pages
22
The
Quarterly
Review
of
Economics
and
Finance
xxx
(2018)
xxx–xxx
Contents
lists
available
at
ScienceDirect
The
Quarterly
Review
of
Economics
and
Finance
journa
l
h
om
epage:
www.elsevier.com/locate/qref
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
Walter
W.
McMahon
Department
of
Economics,
University
of
Illinois
at
Urbana-Champaign,
United
States
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
16
October
2017
Received
in
revised
form
8
February
2018
Accepted
21
May
2018
Available
online
xxx
JEL
classification:
I23
I25
I26
I28
H52
O15
Keywords:
Endogenous
development
Human
capital
Growth
Education
for
development
Social
rates
of
return
Education
externalities
Non-monetary
higher
education
benefits
a
b
s
t
r
a
c
t
The
total
return
to
higher
education
is
the
rate
of
return
based
on
earnings
plus
non-monetary
private
and
social
benefits
beyond
earnings
that
captures
higher
education’s
contribution
to
development.
A
theory
of
endogenous
development
is
a
new
scholarly
contribution
where
firm
and
household
production
with
education
externalities
and
the
endogeneity
of
new
ideas
leads
to
an
optimal
rate
of
development.
This
rate
is
higher
than
in
an
economy
without
these
externalities.
Since
measures
of
private
non-market
and
social
benefit
externalities
are
positive,
externalities
contribute
to
higher
per
capita
development.
The
total
return
is
estimated
to
be
considerably
higher
than
the
opportunity
cost
of
funds
and
the
return
on
physical
capital,
the
first
major
evidence
of
serious
underinvestment
in
higher
education
in
the
US
for
optimal
development.
Policy-relevant
treatment
effects
and
policy
options
with
implications
for
optimal
development
and
for
improving
the
worsening
condition
of
the
dissatisfied
middle
class
are
considered.
©
2018
Board
of
Trustees
of
the
University
of
Illinois.
Published
by
Elsevier
Inc.
All
rights
reserved.
1.
Introduction
It
has
long
been
known
by
economists
that
there
has
been
underinvestment
in
higher
education
for
growth.
But
with
grow-
ing
numbers
of
graduates
and
with
rising
private
tuition
costs
and
student
debt
is
this
still
true?
And
beyond
this,
whether
there
is
underinvestment
for
broader
development
has
never
been
inves-
tigated.
Central
to
the
theme
of
this
paper,
there
are
important
non-monetary
private
and
social
benefits
above
and
beyond
earn-
ings
that
affect
individual
life
chances
as
well
as
regional
and
national
development
that
contribute
to
this
but
are
poorly
under-
stood.
In
fact,
the
total
returns,
monetary
and
non-monetary,
have
never
been
comprehensively
measured
or
measured
without
a
lot
of
overlap.
There
are
important
implications
for
public
funding
policies,
for
academic
policies,
for
rates
of
growth
and
develop-
ment
over
time,
and
for
institutions
supporting
democracy,
human
rights,
and
political
stability
that
have
not
been
systematically
explored.
E-mail
address:
wmcmahon@illinois.edu
The
total
return
to
higher
education
includes
earnings
but
also
the
value
of
these
non-market
outcomes
beyond
earnings,
all
in
relation
to
their
full
social
costs.
This
key
measure
of
the
contribu-
tion
of
higher
education
to
development
can
be
compared
to
the
effectiveness
of
other
types
of
investments.
Non-monetary
private
benefits
include
higher
education’s
contribution
to
better
health,
child
development,
longevity,
household
and
asset
management,
and
more.
The
non-monetary
social
benefits
are
externalities
that
include
contributions
to
the
evolution
of
civic
institutions
provid-
ing
for
democracy,
human
(or
civil)
rights,
and
political
stability,
to
lower
crime
rates,
environmental
sustainability,
higher
tax
rev-
enues,
and
more
new
ideas.
These
are
measured
by
regression
methods
although
a
few
are
not
yet
measured
with
much
preci-
sion.
The
unfamiliarity
with
what
these
non-monetary
outcomes
are
leads
to
them
often
being
overlooked
or
de-emphasized,
with
implications
for
higher
education’s
contribution
to
individual
life
chances,
the
quality
of
life,
and
overall
development.
After
offering
a
theory
of
endogenous
development
as
a
frame-
work,
this
paper
presents
new
estimates
of
the
standard
social
rates
of
return
to
higher
education
(i.e.,
the
narrow
monetary
rates)
that
focus
on
the
2
and
4
year
college
levels
but
computes
these
rates
for
https://doi.org/10.1016/j.qref.2018.05.005
1062-9769/©
2018
Board
of
Trustees
of
the
University
of
Illinois.
Published
by
Elsevier
Inc.
All
rights
reserved.
Please
cite
this
article
in
press
as:
McMahon,
W.W.
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
The
Quarterly
Review
of
Economics
and
Finance
(2018),
https://doi.org/10.1016/j.qref.2018.05.005
ARTICLE IN PRESS
G Model
QUAECO-1142;
No.
of
Pages
22
2
W.W.
McMahon
/
The
Quarterly
Review
of
Economics
and
Finance
xxx
(2018)
xxx–xxx
all
levels
for
comparison.
These
are
deliberately
measured
to
reflect
the
full
longer
run
institutional
and
social
costs
of
each
increment.
They
are
followed
by
estimates
of
the
private
and
social
nonmon-
etary
benefits
beyond
earnings
and
their
value,
which
leads
to
the
total
return.
Comprehensive
estimates
have
not
existed
previously,
although
there
are
several
good
surveys
that
contain
overlapping
and
non-comparable
outcomes
and
omit
others.
This
paper
is
not
a
survey,
however.
For
the
non-monetary
out-
comes
in
Section
IV
the
existing
literature
is
a
data
base
from
which
the
best
that
is
known
about
each
outcome
is
extracted,
the
only
feasible
way
to
estimate
a
total
return.
Only
articles
that
contain
the
necessary
coefficients
and
meet
the
scientific
standards
for
the
inference
of
causation
are
used.
Methods
are
developed
to
stan-
dardize
the
coefficients
that
each
study
reports.
Many
studies
are
excluded
because
they
deal
with
intermediate
outcomes
and
there-
fore
overlap
when
summing
final
outcomes
or
because
they
do
not
control
for
per
capita
income
and
therefore
overlap
the
effects
from
the
earnings
benefits.
The
scholarly
contribution
is
in
the
development
of
a
new
theory
of
endogenous
development
leading
to
a
solution
for
the
optimal
rate
of
per
capita
development.
It
also
lies
in
presenting
theoretical
and
empirical
evidence
that
shows
how
higher
education
external-
ities
raise
that
rate.
This
also
results
in
the
theory
and
evidence
that
enables
a
conclusion
to
be
drawn
for
the
first
time
about
whether
there
is
over
or
under
investment
in
higher
education
for
opti-
mal
per
capita
development.
Other
aspects
that
constitute
potential
scholarly
contributions
include
the
incorporation
of
the
endogene-
ity
of
new
ideas
in
a
way
that
generates
hypotheses
about
this
endogeneity
that
can
be
tested
further
empirically.
Further,
the
theory
presented
can
be
interpreted
with
minor
modifications
as
a
theory
of
higher
education
institutions
that
is
more
comprehensive
than
prior
offerings
in
that
it
focuses
on
what
higher
educational
institutions
really
produce,
namely
human
capital
skills
embodied
in
graduates
that
have
important
outcomes,
as
their
central
role,
(but
for
research
universities,
also
direct
R&D
outcomes
of
course).
Other
potential
scholarly
contributions
lie
in
new
methods
for
stan-
dardization
when
one
wishes
to
make
use
of
results
from
diverse
studies
(as
in
Section
V),
a
new
practical
method
for
valuing
out-
comes
including
social
outcomes
based
on
the
cost
of
obtaining
the
same
result
by
other
methods,
and
new
insights
into
the
devel-
opment
of
knowledge-based
institutions
necessary
to
democracy,
human
rights,
and
political
stability
that
are
shown
to
contribute
to
higher
per
capita
growth
and
faster
rates
of
broader
economic
development.
The
policy
significance
of
this
paper
lies
in
the
potential
for
addressing
two
of
the
nation’s
biggest
problems,
the
currently
dis-
tressed
condition
of
the
middle
class,
and
sharply
rising
inequality.
With
respect
to
the
former,
the
64%
of
the
US
population
that
has
high
school
or
less
is
deeply
dissatisfied
due
to
a
flat
or
even
13%
decline
in
their
real
incomes
since
1980.
They
have
not
participated
in
the
benefits
of
growth
from
freer
trade
and
from
new
technol-
ogy.
Those
who
lost
their
manufacturing
jobs
have
suffered
even
more
than
13%.
What
is
needed
is
not
jobs,
----
we
are
now
at
full
employment,
but
instead
the
capacity
to
access
high
paying
higher
skill
jobs.
Those
with
a
college
degree
have
seen
a
49%
increase
in
real
earnings
since
1980.
If
income
from
their
higher
savings
is
included,
their
total
incomes
have
grown
even
faster.
Tennessee,
Oregon,
New
York,
and
now
Rhode
Island
have
recently
made
Com-
munity
Colleges
free.
Most
have
made
this
available
to
only
recent
high
school
graduates,
which
leaves
out
many
dissatisfied
adults.
But
Tennessee
is
making
all
adults
eligible
who
wish
to
study
for
an
associate
degree
and
the
waiting
rooms
have
filled
up.
The
children
of
the
depressed
middle
class
also
benefit,
but
they
have
virtu-
ally
no
chance
of
entering
the
ruling
economic
and
political
elite
without
a
college
degree
so
they
will
perpetuate
rising
inequality
into
the
next
generation.
But
is
the
return
high
enough
to
warrant
the
necessary
investment?
And
is
the
public
investment
necessary
to
lower
tuition
and
student
loan
debt
consistent
with
economic
efficiency
and
with
optimal
growth
and
development?
This
paper
provides
the
framework
and
answers
to
these
kinds
of
important
policy
questions.
2.
The
literature
Early
origins
of
what
is
presented
here
lie
in
Becker
(1960,
1964,
1965,
1967a,
1981)
on
human
capital
as
it
relates
to
earnings,
but
also
to
household
production
using
the
same
human
capital
during
non-labor
market
hours
to
benefit
the
family,
and
when
used
in
the
community,
to
benefit
others
as
external
social
benefits.
These
final
outcomes
contribute
to
individual
development
and
to
economic
development
largely
in
the
communities
where
the
graduates
live.
Effects
on
development
as
used
here
mean
education’s
effects
on
outcomes
beyond
earnings
as
measured,
for
example,
in
the
World
Bank
(2017)
World
Development
Indicators.
Early
origins
of
the
endogenous
development
model
include
Lucas
(1988)
work
on
endogenous
growth
and
on
new
ideas
(Lucas,
2009).
The
new
endogenous
development
model
offered
here
includes
household
production
using
human
capital
producing
non-monetary
outcomes,
education
externalities,
and
a
deliber-
ately
simplified
endogeneity
of
new
ideas.
Early
origins
of
this
will
be
found
in
McMahon
(2002,
2007,
2009,
2017)
and
McMahon
and
Oketch
(2013)
where
there
are
estimates
of
some
of
the
non-
monetary
development
outcomes
but
no
formal
model.
Hu
(2008)
has
a
model
that
contains
home
production
but
it
has
no
applica-
tions
to
development,
no
education
externalities,
no
endogeneity
of
new
ideas,
and
focusses
on
the
transitional
dynamics
of
three
sector
models.
With
respect
to
empirical
estimates
of
the
non-monetary
out-
comes
from
education,
Haveman
and
Wolfe
(1984,
2007)
pioneered
the
measurement
of
some
of
these
and
one
method
of
valuation.
However,
they
include
none
of
the
social
benefits
covered
here.
Theirs
is
a
survey,
which
this
paper
is
not,
and
therefore
they
include
intermediate
and
final
outcomes
that
overlap
if
one
were
to
try
to
get
a
total
return.
Michael
(1982)
and
Grossman
(2006)
sur-
veys
include
important
controls
for
per
capita
income.
Other
recent
surveys
help
to
identify
relevant
coefficients
including
Lochner
(2011A,
2011,
2010A),
Lochner
and
Moretti
(2004),
Oreopoulos
and
Petronijevic
(2013),
Oreopoulos
and
Salvanes
(2011),
Jacobson,
LaLonde
and
Sullivan
(2013A),
Murnane
Richard
(1981A,
2013),
Lochner
and
Moretti
(2004),
and
Moretti
(2004a,
2004b).
None
attempt
to
estimate
a
total
return
and
all
include
many
overlapping
outcomes.
Finally,
other
early
origins
are
in
the
author’s
prior
work
(McMahon,
2002,
2017,
2009).
It
has
some
of
the
preliminary
work
for
Section
V
of
this
paper
but
all
other
parts
of
this
paper
are
totally
new.
For
Section
V
there
were
many
years
of
work
enabling
iden-
tification
and
averaging
of
the
education
coefficients.
McMahon
(2012)
is
a
4
volume
edited
work
reprinting
a
collection
of
back-
ground
articles
with
introductions
that
serve
as
further
references
for
this
paper.
Literature
on
various
issues
is
cited
in
Appendix
A
on
line
at
https://publish.illinois.edu/wmcmahon/.
The
literature
on
some
of
the
higher
education
outcomes
is
cited
later
as
these
outcomes
are
considered.
3.
The
theory
of
endogenous
development
Endogenous
development
builds
on
endogenous
growth,
so
after
a
few
definitions,
endogenous
growth
will
be
briefly
addressed
first.
The
objective
is
not
to
specify
equations
to
be
estimated,
but
to
explore
the
relevance
of
the
social
rates
of
return,
to
provide
the
basis
for
the
main
conclusions,
and
to
discover
the
contribu-
Please
cite
this
article
in
press
as:
McMahon,
W.W.
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
The
Quarterly
Review
of
Economics
and
Finance
(2018),
https://doi.org/10.1016/j.qref.2018.05.005
ARTICLE IN PRESS
G Model
QUAECO-1142;
No.
of
Pages
22
W.W.
McMahon
/
The
Quarterly
Review
of
Economics
and
Finance
xxx
(2018)
xxx–xxx
3
tion
or
the
lack
thereof
made
by
higher
education
externalities
and
by
the
endogeneity
of
new
ideas
to
optimal
growth
and
optimal
development.
There
are
two
rates
of
return
estimated
later
that
are
relevant
to
what
follows
in
this
section.
The
first
is
the
standard
social
rate
of
return.
It
is
based
on
monetary
earnings
only
related
to
the
full
costs
of
the
investment,
private
and
public,
and
it
is
policy-relevant
to
pure
economic
growth.
The
second
is
the
total
rate
of
return
rel-
evant
when
the
objective
is
endogenous
development.
It
includes
in
addition
to
earnings
the
non-market
development
outcomes
beyond
earnings
listed
earlier.
Both
are
relevant
to
economic
efficiency.
Overall
economic
efficiency
by
definition
includes
internal
efficiency
within
higher
education
institutions
(i.e.
production
efficiency)
but
also
the
external
efficiency
(i.e.
exchange
efficiency)
with
which
higher
edu-
cation
outcomes
serve
the
student’s
and
society’s
well-being.
The
later
includes
social
benefits
which
are
externalities
that
benefit
others
and
future
generations.
These
externalities
are
significant
in
that
they
are
the
main
rationale
for
taxpayer
support
of
higher
education
on
efficiency
grounds.
Equity
will
not
be
included
here
although
it
also
is
a
part
of
social
welfare
and
part
of
the
rationale
for
public
support.
It
is
excluded
because
it
is
not
part
of
the
criteria
for
economic
efficiency
which
is
the
focus.
3.1.
Social
rates
of
return
and
optimal
growth
A
brief
summary
of
the
endogenous
growth
model
follows.
It
is
new,
however,
in
that
it
incorporates
the
endogeneity
of
new
ideas,
and
further
develops
the
role
of
externalities,
and
how
they
and
public
support
relate
to
quality.
This
also
provides
key
building
blocks
for
the
new
model
of
endogenous
development.
For
growth,
and
later
for
broader
development,
production
by
firms
is:
Yt=
It[AKt(thtNt)1ˇ]hat.
(1)
Here
Yt=
output
of
goods
and
final
services
as
measured
by
GDP,
A
=
the
level
of
technology,
treated
as
constant
in
the
absence
of
new
ideas,
and
It=
new
ideas
used
to
create
and
adapt
new
technologies.
They
are
endogenous
because
they
heavily
depend
below
on
human
capital
formation
especially
at
Masters
and
PhD
levels.
Ktis
physical
capital,
htis
the
average
human
capital
or
skill
level
per
person
which
includes
new
technologies
embodied
in
human
capital
by
higher
education,
tis
the
fraction
of
time
spent
on
the
job,
and
Nt
is
the
number
of
persons.
hat is
the
average
level
of
education
in
the
community
used
to
represent
education
externalities.
Itand
hat are
shown
outside
the
parentheses
which
emphasizes
that
when
>
0
and/or
It>1
there
are
increasing
returns
to
scale.
This
production
function
is
similar
to
that
in
the
Lucas
(1988,
2011)
endogenous
growth
model
as
well
elements
from
his
“ideas
and
growth”
(2009).
However,
new
ideas
including
significant
adaptations,
I,
are
here
explicitly
incorporated
and
are
soon
made
endogenous.
If
most
externalities
are
to
occur
there
must
be
public
subsidies
or,
in
the
case
of
private
institutions,
large
endowments
because
private
incentives
for
investing
in
outcomes
that
benefit
others
are
insufficient.
Some
liberal
arts
and
humanities
fields
such
as
the
philosophy
of
science
dealing
with
scientific
truth,
literature
with
perspectives
on
ethics,
the
social
sciences,
and
colleges
of
education
that
generate
larger
externalities
depend
more
heavily
on
public
or
endowment
support
and
this
breadth
adds
to
the
quality
of
the
higher
education
students
get
beyond
more
limited
trade
school
benefits.
These
kinds
of
externalities
foster
altruism
and
benefits
to
others
which
are
the
focus
of
the
Golden
Rule.
Public
support
allows
for
wider
access
as
the
result
of
lower
tuition
and
financial
aids,
as
well
as
disproportionate
support
for
history
and
for
research
at
both
public
and
private
research
universities
benefitting
others
and
future
generations.
All
of
this
contributes
to
the
quality
and
diversity
of
higher
education,
and
does
public
support
sufficient
to
avoid
excessive
use
of
teaching
assistants,
academic
profession-
als,
and
adjuncts
in
large
classes
and
often,
now
even
in
the
junior
and
senior
level
courses.
More
formally,
the
fraction
of
total
time
invested
in
human
capital,
(1-t),
is
larger
than
it
would
other-
wise
be,
as
are
both
and
It, both
of
which
are
>0.
This
assumes
that
government
failure
is
negligible
so
that
public
augmentation
of
externalities
and
private
incentives
to
invest
is
consistent
with
overall
economic
efficiency
as
well
as
with
a
a
higher
per
capita
growth
rate
than
in
a
purely
competitive
economy
as
will
be
shown.
3.1.1.
Optimal
growth
For
optimal
growth
over
time,
the
objective
function
seeks
to
maximize
the
utility
of
the
stream
of
real
per
capita
consumption,
ct:
(2)
Here
t
=
0,..,
,
an
infinite
time
horizon,
and
the
stream
of
per
capita
consumption
is
discounted
at
rate
.
These
preferences
have
a
coef-
ficient
of
risk
aversion,
,
that
is
positive.
Assuming
individual
families
and
the
government
look
ahead
over
the
life
cycle
of
the
student
when
planning
long
term
edu-
cational
investments,
there
is
no
significant
difference
to
the
rate
of
return
between
using
a
typical
45–65
year
life
span
after
graduation
as
a
planning
horizon
vs
an
infinite
time
horizon.
See
“Infinite
Planning
Horizons”
in
Lang
and
Merino
(1993,
pp.144–147).
3.1.2.
The
production
of
human
Capital
Per
capita
consumption
over
time
is
maximized
subject
to
the
production
of
output
by
firms,
(Eq.
(1)),
but
also
subject
to
the
production
of
human
capital
by
households:
h/t
=
Gt/Yt[1-t]ht.
(3)
Here
h
/
t
is
gross
investment
in
human
capital
formation,
1-
t
is
the
fraction
of
time
devoted
to
human
capital
production,
is
the
maximum
rate
of
accumulation
of
human
capital
when
(1-
t)
=
1,
Gt/Ytis
the
fraction
of
GDP
invested
by
government
in
education
through
direct
support
of
colleges
and
universities
and
through
student
financial
aids,
most
of
which
students
pass
to
public
and
private
educational
institutions
as
they
pay
tuition,
and
htis
the
initial
human
capital
of
students,
parents,
and
fac-
ulty.
With
lags
this
highlights
the
intergenerational
transmission
of
human
capital.
There
is
a
large
literature
on
this
that
includes
Carneiro,
Meghir,
and
Parey
(2013A)
and
others
suggesting,
among
other
things,
that
the
market
and
non-market
outcomes
considered
here
largely
determine
not
just
the
life
chances
of
families
but
also
of
generations,
differences
that
show
up
over
time
but
also
across
individuals
and
families.
Higher
Gt/Ytraises
the
private
rates
of
return
on
human
capital
investment
encouraging
the
average
frac-
tion
of
time
invested
in
human
capital
formation
to
be
increased
that
shows
up
through
increased
enrollments.
Human
capital,
therefore,
is
produced
by
households
with
the
aid
of
colleges
in
a
dynamic
process
using
the
human
capital
of
the
parents
and
the
human
capital
of
the
faculty
who,
if
qual-
ity
is
adequate,
stimulate
capacities
for
analysis
and
originality
while
accessing
and
contributing
the
newer
ideas
from
worldwide
sources
in
each
field.
There
is
also
a
contribution
from
the
physical
capital
in
universities
such
as
labs
and
classrooms
that
is
omitted
here
to
simplify.
Below
the
limit,
,
when
all
effort
is
devoted
to
human
capital
accumulation,
there
are
no
diminishing
returns
to
the
production
of
human
capital.
Lucas
(1988)
stresses
that
this
is
a
social
process
that
has
no
counterpart
in
the
accumulation
of
physical
capital.
Each
new
family
member
begins
with
an
amount
of
human
capital
that
is
proportional
but
lower
than
the
level
attained
by
older
members
of
the
family.
Please
cite
this
article
in
press
as:
McMahon,
W.W.
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
The
Quarterly
Review
of
Economics
and
Finance
(2018),
https://doi.org/10.1016/j.qref.2018.05.005
ARTICLE IN PRESS
G Model
QUAECO-1142;
No.
of
Pages
22
4
W.W.
McMahon
/
The
Quarterly
Review
of
Economics
and
Finance
xxx
(2018)
xxx–xxx
The
human
capital
production
process
in
an
optimal
growth
model
would
typically
refer
to
all
education,
K-12-
PhD,
and
not
just
to
the
contribution
of
higher
education
which
is
the
focus
here.
In
accord
with
this,
empirically,
the
rates
of
return
to
all
lev-
els
of
education,
K-12
through
PhD,
appear
in
Table
1
Section
IV
revealing
among
other
things
how
the
returns
to
education
vary
by
levels
of
education.
Re-focusing
Eqs.
(3)
and
(1)
on
only
higher
education
makes
it
possible
to
interpret
the
model
as
a
theory
of
higher
education
stressing
that
human
capital
is
what
is
produced
by
higher
education
institutions
in
Eq.
(3),
not
students.
This
leads
to
an
important
insight
into
what
productivity
in
higher
education
really
is,
productivity
in
producing
human
capital
skills
and
hence
monetary
and
development
outcomes,
and
not
just
instructional
units
(IU’s)
which
is
a
very
short
term
and
incomplete
measure
of
true
productivity.
This
also
looks
at
universities
as
sources
of
individual
and
social
economic
growth
as
well
as
of
the
broader
development
of
families
and
societies.
As
such
it
is
a
more
gen-
eral
theory
of
what
Clotfelter
(1999)
refers
to
as
“the
familiar
but
curious
economics
of
higher
education”.
So
interpreted,
Eqs.
(1)(3)
offer
a
more
coherent
and
more
general
theoretical
framework
that
focuses
on
what
higher
education
really
produces,
namely
human
capital
skills,
and
again,
not
students.
The
latter
leads
to
distortion
of
academic
policies
and
misallocation
of
faculty
skills,
such
as
sep-
arating
research
faculty
from
teaching
faculty
and
the
former
from
students,
a
policy
often
found
that
is
implicitly
based
on
the
false
assumption
that
it
is
students
that
are
being
‘produced’.
This
sep-
aration
limits
the
embodiment
in
students
of
the
newer
and
more
advanced
ideas
and
thereby
probably
reduces
true
‘productivity’.
The
new
ideas
and
adaptations,
It,
are
largely
dependent
on
the
human
capital
that
universities
and
households
produce,
ht,
via
Eqs.
(3)
and
(5):
It=
ht,
(4)
ht=
ht-1+h/t–dht-1(5)
Advanced
graduates
of
research
universities
with
MA’s
and
PhD’s
typically
spend
all
day
every
day
working
on
creating
and
adapting
new
ideas
and
technologies
for
years
after
graduation
and
indeed
most
of
their
lives
within
firms,
government
and
other
universities.
Most
technological
advancements
nowadays
require
advanced
education
before
one
can
even
get
started.
Eq.
(5)
defines
human
capital
stock
accumulation
as
last
period’s
stock
plus
the
gross
additions
from
Eq.
(4)
less
depreciation
and
obsolescence
at
rate
d.
The
gross
additions
include
replacement
investment
in
human
capital
replacing
those
who
retire
and
die.
These
new
grad-
uate
replacements
embody
new
knowledge
and
help
to
disseminate
technologies
just
as
much
as
the
net
new
additions
to
the
stock
of
graduates.
This
important
effect
is
overlooked
by
researchers
that
try
to
relate
educational
attainment
(which
is
net
of
replacement
investment)
to
growth
and
development
rather
than
using
gross
investment
in
new
human
capital
formation.
The
aggregate
stock
containing
human
capital
of
these
newer
vintages
is1:
Ht=t=oNtItht.
Additions
of
new
human
capital,
h
/t,
embody
the
new
technologies
and
are
the
key
mechanism
for
the
diffusion
of
tech-
nology
in
endogenous
growth
and
in
this
endogenous
development
model.
This
responds
to
Parente’s
(2001A)
critique
that
endogenous
growth
models
fail
because
they
contain
no
mechanism
for
the
dissemination
of
technology.
Beyond
the
dissemination
through
1This
ignores
the
Cambridge
controversies
and
problems
with
summation
over
different
vintages
of
human
capital.
For
a
theory
of
higher
education
an
additional
term
for
physical
capital
inputs
is
needed.
graduates,
this
model
also
has
an
endogenous
explanation
for
the
creation
and
adaptation
of
new
ideas.
3.1.3.
Optimal
growth
To
solve
for
the
optimal
growth
of
per
capita
consumption
and
per
capita
income,
the
current
value
Hamiltonian
is:
HK,h,1,
2,c,,t=1
1
c1–1+
1[(I[AKˇ(hN)1ˇh
a
Nc)/N
+2[Gt/Ytı(1
t)ht(6)
Eq.
(4)
determining
of
the
flow
of
new
ideas
next
is
substituted
into
the
production
function
above
for
I.
The
Hamiltonian
is
then
differentiated
with
respect
to
the
endogenous
variables
to
obtain
the
first
order
conditions.
In
this
the
two
decision
variables
are
per
capita
consumption,
ct,
and
the
time
devoted
to
production,
t,
which
in
turn
determines
the
fraction
of
time
devoted
to
the
pro-
duction
of
goods
vs
human
capital
production
(1-
t).
Government
investment,
Gt,
is
exogenous.
The
values
of
the
two
endogenous
variables
are
selected
in
solving
to
achieve
the
optimal
path
for
investment
in
human
and
physical
capital
(the
state
variables).
This
also
determines
the
optimal
rate
of
growth
of
per
capita
consump-
tion
and
hence
of
per
capita
income
since
the
latter
is
defined
as
consumption
plus
investment
plus
government
at
each
time,
t,
and
since
the
two
rates
are
equal
in
balanced
growth
This
optimal
rate
of
growth
of
per
capita
consumption
(and
income)
which
is
given
in
Eq.
(7)
below
uses
the
first
two
first
order
conditions,
H/c
and
H/1,
which
are
conditions
that
must
hold
for
per
capita
con-
sumption
over
time
to
be
maximized
and
the
rate
of
growth
to
be
optimal:
(
c/
t)/ct=
MPPKt
(7)
That
is,
the
optimal
rate
of
growth
of
per
capita
consumption2
is
equal
to
the
marginal
productivity
of
physical
capital
discounted
at
rate
.In
a
competitive
economy,
this
discounted
marginal
pro-
ductivity
is
the
rate
of
return
to
physical
capital,
which
in
turn
is
equal
to
the
rate
of
return
to
human
capital
in
its
two
uses:
MPPKt
=
MPPHt
=
(
c/
t)/ct(8)
So
if
the
social
rate
of
return
to
higher
education
is
higher
than
the
rate
of
return
to
physical
capital,
increased
investment
in
higher
education
will
increase
current
output
but
also
in
balanced
growth
will
lead
to
a
higher
sustained
constant
rate
of
growth
of
per
capita
consumption
as
in
Eq.
(8)
and
hence
in
per
capita
income
This
deter-
mines
a
growth
rate
that
is
sustainable
indefinitely
without
bounds!
That
is,
it
is
not
limited
by
diminishing
returns,
an
unsatisfactory
feature
of
the
Solow
model.
3.1.4.
Education
externalities
For
the
role
of
externalities,
totally
differentiate
Eq.
(7)
with
respect
to
time
which
is
of
the
form
F
=
f(Kt,ht)
=
X,
where
X
is
a
constant.
From
this,
the
common
growth
rate
of
per
capita
con-
sumption,
(c/t)/ct,
physical
capital,
and
per
capita
income,
is
related
to
the
growth
rate
of
human
capital
by:
(c/t)/ct=[
1
ˇ
+
+
]
1
ˇ(h/t)/ht(9)
This
shows
that
on
the
balanced
growth
path,
the
common
rate
of
growth
of
per
capita
consumption
and
per
capita
income
is
larger
when
the
rate
of
growth
of
human
capital
investment,
(h/t)/ht,
is
2Strictly,
preferences
for
per
capita
consumption
using
a
coefficient
for
risk
aver-
sion,
.
There
are
also
standard
human
and
physical
capital
accumulation
equations
behind
the
scenes.
Please
cite
this
article
in
press
as:
McMahon,
W.W.
The
total
return
to
higher
education:
Is
there
underinvestment
for
economic
growth
and
development?
The
Quarterly
Review
of
Economics
and
Finance
(2018),
https://doi.org/10.1016/j.qref.2018.05.005
ARTICLE IN PRESS
G Model
QUAECO-1142;
No.
of
Pages
22
W.W.
McMahon
/
The
Quarterly
Review
of
Economics
and
Finance
xxx
(2018)
xxx–xxx
5
larger.
Furthermore,
at
any
given
rate
of
growth
of
investment
in
human
capital,
the
growth
rates
of
consumption
and
income
are
larger
when
either
the
creation
of
new
ideas,
,
and/or
education
externalities,
,
are
larger.
That
is,
the
optimal
efficient
rate
of
growth
with
>
0
and
>
0
is
larger
than
a
competitive
economy
equilibrium
rate
of
growth
where
there
are
no
education
externalities
(i.e.
=
0).
Given
insufficient
private
incentives
to
generate
benefits
that
flow
largely
to
others
and
future
generations,
and
that
quality
and
access
are
also
related
to
resources
per
student,
the
flow
of
new
ideas
and
of
external
benefits,
the
size
of
enrollments,
and
quality
are
all
lower
when
the
per
student
public
support
of
universities
is
cut.
This
result
is
also
reflected
in
the
real
wage.
It
is
the
marginal
product
of
labor
at
a
given
level
of
human
capital
skills.
When
human
capital
skills
are
augmented
by
the
growth
of
per
capita
human
capital
skills
due
to
education,
(h/t)/ht,
the
real
wage,
,
grows
as
the
workers
average
education
level
grows.
This
is
in
addi-
tion
to
the
external
spillover
benefits
from
the
higher
education
of
others
in
the
community.
3.2.
Endogenous
development
When
policy
makers
and
the
public
care
about
higher
education
outcomes
that
include
the
quality
of
life
beyond
earnings
and
jobs,
then
the
objective
function
must
be
re-written
to
include
the
non-
monetary
outcomes.
The
constraints
also
must
include
human
time
used
not
just
in
production
in
firms
and
of
more
human
capital,
but
must
also
include
time
used
in
household
production
during
non-working
hours.
3.2.1.
The
objective
function
The
objective
function
to
be
maximized
now
includes
broader
development
outcomes.
It
is
the
sum
of
the
per
capita
stream
of
discounted
utilities
for
total
consumption
satisfactions, ¯
ct,
over
the
entire
life
cycle
of
each
individual.
These
include
market
goods,
ct,
as
before
but
now
also
non-monetary
satisfactions,
cnmt :3
(11)
If
decision
makers
discount
non-market
outcomes,
is
smaller.4
This
would
occur
if
non-market
outcomes
are
not
well
understood
and/or
are
poorly
perceived.
This
constitutes
market
failure
due
to
poor
information.
An
optimal
solution
based
on
true
preferences
will
not
be
achieved.
3.2.2.
Household
production
Human
capital
is
used
on
the
job
for
production
in
firms
for
the
fraction
of
time,
1,
in
the
production
of
human
capital,
2,
or
in
household
production,
(1-
1-
2).
This
means
that
the
human
cap-
ital
is
used
during
all
waking
hours
each
week
either
on
the
job,
in
school,
or
in
household
production
and
increases
the
productivity
of
time
in
all
uses.
Household
production
produces
final
satisfac-
tions
for
private
benefit
of
the
family
or
produces
social
benefits
largely
during
time
spent
in
the
community:
Cnmt=
A
It[Ct(1-1t-2t )htNt1]hat .
(12)
These
variables
are
as
defined
above
under
Eq.
(1)
where
the
production
of
market
goods
is
determined
since
Ct=
Ntct=
Yt-
It-
3For
a
more
general
specification,
see
Benhabib,
Rogerson,
and
Wright
(1991)
who
uses
a
CES
form.
4If
(
+
)
=
1
there
are
constant
returns
and
in
the
absence
of
risk
aversion
the
intertemporal
elasticity
of
substitution
is
unity
leading
to