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.M415
oevv^y
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
CHANGES
IN
THE WAGE STRUCTURE, FAMILY INCOME,
AND CHILDREN'S EDUCATION
Daron Acemoglu, MIT
Jom-Steffen Pischke,
LSE
Working Paper 00-29
SEPTEMBER 2000
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Network Paper Collection at
http:/ /papers. ssrn. com/paper. taf?abstract_id=246028
Social Science Research
MASSACHUSETTS ilMSTITUTE
OF TECHWOLOGY
OCT
3
2000
LIBRARIES
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
CHANGES
IN
THE WAGE STRUCTURE, FAMILY INCOME,
AND CHILDREN'S EDUCATION
MIT
Jom-Steffen Pischke, LSE
Daron Acernoglu,
Working Paper 00-29
SEPTEMBER 2000
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http:/ /papers. ssrn.com/paper.taf?abstract_id=246028
Abstract
We exploit the changes
in the distribution of family
resources on college education.
the
income
opposite
is
distribution
Our
income
to estimate the effect
strategy exploits the fact that families at the
were much poorer
in the
1990s than they were
true for families in the top quartile of the distribution.
effects of family
income on enrollments. For example, we find
family income
associated with a
is
1
.4
Our
of parental
bottom of
in the 1970s,
while the
estimates suggest large
that a 10 percent increase in
percent increase in the probability of attending a four-
year college.
*Paper prepared for the European Economics Association Meeting 2000, Bolzano,
Italy. We thank seminar participants in the European Economic Association 2000
Conference, the MIT labor lunch, and the University of Chicago Harris School Seminar for
helpful comments.
Some of the work
for this paper
was undertaken while
Pisclike
was
Northwestern University/University of Chicago Joint Center for Poverty
Research. He thanks the Center for their hospitality and financial support.
visiting the
Introduction
1
Wage
and
inequality in the U.S. has increased dramatically since the 1970s (e.g.
Pierce, 1993;
observed
in the return to
returns to
skills
Katz and Minrphy, 1992). For most of the period,
The standard theory
skills.
should encourage investments in
1997) have concluded that
we do
human
of
human
capital.
Juhn,
Murphy
meant an increase
this also
capital implies that higher
Many
observers
(e.g.
Topel,
actually observe faster skill accumulation, and this increase
in the supply of skills should eventually mitigate the increase in inequality.
Rising wage and income inequality affects not only the returns to education, but also the
resources that families have available to finance education.
Family income might matter
education decisions because of credit constraints, or because education
is
good. The change in the structure of wages during the 1980s, which reduced the wages of
skilled workers,
may have made
it
for
not a pure investment
less
harder for children firom these families to attend college,
despite the higher returns.^ In fact, while there
was a large increase
children from the poorest backgrounds
in the college
enrollment
was a much smaller increase
rates for children from richer families during the 1980s, there
for
(McPherson and Schapiro, 1991, Ellwood and Kane,
1999, and Table 1 below).
In this paper,
we
exploit the changes in the distribution of family income that have taken
place over the past 30 years to estimate the effect of parental resources on college education.
Our
strategy exploits the fact that families at the
much poorer
in the
of the income distribution were
1990s than they were in the 1970s, while the opposite
in the top quartile of the distribution.
in family
bottom
income caused by changes
This approach
in the U.S.
is
attractive since
is
it
true for families
exploits variations
income distribution, which are unlikely to be
correlated with other (observed and unobserved) characteristics affecting education choices.
Our estimates suggest
income on enrollments.
large effects of family
that a 10 percent increase in family income
is
For example, we find
associated with a 1.4 percentage point increase
in the probability of attending a four-year college.
Although there are numerous studies investigating the impact of family resources on education outcomes, whether income truly matters
this area just relate schooling
regressions, family
income may be proxying
reduce the
and controls
effect of
1999, Ellwood
for
OLS
In fact,
many
and Kane, 1998, or Cameron and Taber, 2000).
measurement
errors
and
variables correlated with
may be
transitory
seriously biased
movements
permanent income,
'See also Acemoglu and Pischke (1999)
investments in training
in
Most studies
equations. However, in
in
OLS
education
studies find that including par-
the family income on children's education
attenuating the effect of income on education.
"The empirical
in
type of school attended previously or test scores substantially
of the income elasticity of education
stantial
a hotly debated issue. ^
for family characteristics affecting "the
production function" (Lang and Ruud, 1986).
ents' education
is still
outcomes to family income
for
in
(e.g.
Cameron and Heckman,
Nevertheless, such estimates
downwards.
This attenuation bias
like parents'
will
be worse
if
other
education or the type of secondary
the argument that a higher return to
the presence of labor market imperfections.
literature has been surveyed by
First, there are sub-
incomes measured at a point in time,
Haveman and Wolfe
(1995).
human
capital
may reduce
As a
substantially understated. Second,
scores and previous schooling experience are
,
test
may be
estimate of the income effect
school chosen, are included as controls.
result, the
likely to
be endogenous and also affected by family income, so their inclusion may lead to biased
esti-
In fact, our strategy which does not suffer from these problems leads to substantially
mates.
larger estimates of the effect of parents' resources
Our
strategy
effect of
is
more
negative income tax experiments provide the only experimental study of the
The
income.
on children's education.
closely related to studies exploiting exogenous variation in parents'
income on schoohng, but they confound the
effect of
tax rates affecting the decisions of youths to work (see
e.g.
income with changes
Venti, 1984).
have made other attempts to address the possibility that income
unobserved factors which predict schooling outcomes of the
may
child.
A
in
marginal
few recent studies
also be correlated
Duncan
et al.
with
(1998) use
sibhng differences arguing that family income varies while other family characteristics remain
the same.
Shea (2000) uses industry and union wage
to job displacement as instruments for family income
finds
no
effects of parental resources
on education, but
differentials
and income changes due
and argues that these proxy
"luck."
his estimates are quite imprecise.
He
Both
of Shea's instruments are also not entirely convincing, since they are likely correlated with
parental attitudes towards education.'^
Mayer (1997) uses a
variety of approaches to argue
that unobserved family characteristics affecting education are relatively unimportant. She uses
variation in income induced by state welfare rules, compares the impact of different sources
of income,
and compares the
Using her estimates, she also
effect of
tries
income before and
after a child's education takes place.
to assess whether changes
in
income inequality predict the
enrollment patterns for children from different income groups over time. This comes closest to
our strategy of using changes in income inequality as an instrument for family income.
2
A
We now
Our
lasts
Simple Model of Schooling With Credit Constraints
outline a simple
objective
is
model
of investment in schooling based on Becker
and Tomes (1986).^
to obtain a simple estimating framework for our empirical work.
two periods.
In period
1,
an individual (parent) works, consumes
whether to send their offspring to
college, e
The
is
cost of schooling for family
where q denotes the income
below we can allow
i
exp{6i).
(ability) quartile of the family, so that in
income
is
s,
decides
the empirical work
unobserved characteristics across households
(ability) distribution.
education costs captures that there
saves
= or 1, and then dies at the end of the period.
We assume that the distribution of 6i is Gq {0),
for different distributions of
in different parts of the
c,
The economy
heterogeneity
The
among
fact that there
children or
is
among
a distribution of
the attitudes of
Duflo (2000) exploits the expansion of old-age pensions in South Africa to analyze the effect of family
resources on child health. She finds positive effect of resources on health, though given the differences in the
level of
development across South Africa and the U.S.,
it is
not clear whether these results can be generalized
to the U.S. context.
This model is also related to the large macroeconomic literature on credit constraints. See, among others,
Galor and Zeira (1993), Benabou (1996), Durlauf (1996), and Fernandez and Rogerson (1996) on the effect of
credit constraints
on human capital investments, and Acemoglu (1997) on the interaction between credit and
labor market imperfections in determining
human
capital investments.
.
families towards education. Skilled individuals (those with education) receive a
wage ^5 and
an unskilled worker receives WuAll families have utility given as:
Inc
where
+ Plnc
the consumption of the offspring.
c is
future (offspring's) consumption
is
Consider a family with income
(1)
a parameter that measures
/? is
relative to current consumption.
In the absence of credit market problems, this family
y.
would simply maximize net present discounted value of income.
which implies that
how important
We
assume no discounting,
this family should invest in education as long as
e<e = \n[ws- Wu]
The important
point
matter.
very high, but
If 9 is
is
that, because education
than
still less
9,
is
(2)
a pure investment good, income does not
then the family will borrow pledging the future
earnings of their offspring in order to achieve consumption smoothing.
Instead, here,
we assume
that
all
families face credit
pledging the future income of their offspring.
maximize
by choosing
(1)
c, c, s,
and
More
market problems, and cannot borrow
problem of parent
formally, the
i
is
to
e subject to:
+ exp{6i)e + s <yi
c = s + Wy, + {ws — Wu)e
c
(3)
s>0
The
first
condition
sumption of the
investment
first
period,
If
(s
>
lem
in
the budget constraint for the family.
is
child,
and the
final
one
is
The second determines
the "credit constraint". This constraint implies that
education comes at the cost of consumption smoothing (low consumption in the
and high consumption
the level of income
is
in (3) (Becker
in the second period).
high enough, so that parents would like to leave positive bequests
0) to their offspring, credit
market problems
and Tomes, 1986).
will
not matter in the maximization prob-
Such a family already has high enough income, and
consumption smoothing would mean transferring resources to their
so using the
The
most
efficient
combination of
condition guaranteeing that
we
human
income
is
capital investment
high enough that even at the
with optimal investment in
Hence among
skills),
families with
offspring.
2ws
They
will
do
and monetary bequests.
are in the positive bequest region
y>y = Ws + exp \9j —
In this case,
the con-
is
- Wu-
maximum
cost of education (consistent
parents would leave positive bequests.
income y >y, the fraction investing
Gr{9)=Gr{\n[w,-Wu]),
in
education
is
(4)
where Gr
the distribution of education costs
is
main point
to note
among
The
"rich" (unconstrained) famihes.
that the fraction investing depends only on skilled-unskilled wage pre-
is
mium, and not on income.
Next, consider a "poor" family with income y
Then
in schooling.
their hfetime utility will
consume the income
period, they
unskilled earnings, Wy,.
U{e
=
=
1)
ln(y
-
their offspring obtains
in
Wu, and suppose that
=
be U{e
=
0)
+ pinWs.
{wg
— Wu)/wu
investing in education
(3\nWu, since in the
first
Now,
their first period
consumption
is
-
y
exp
(6'i),
who have
abihty 6
e*
=
is
the college premium.
ln
<
Iny
y
w.
is
a cutoff level of
ability, 6*,
such
9* invest in schooling, with
+ /?lnr
Therefore, the fraction of poor families
is
Gp(r)«Gp(lny + /31nr),
where Gp
fraction
3
is
the distribution of education costs
now
but
consumption w^.
that only poor parents with children
=
+
does not invest
the second period, their offspring consumes the
Comparison of these two expressions implies that there
where r
Iny
it
in contrast, they send their child to school, they obtain utility
If,
exp(6'i))
and
y,
<
among poor
(5)
Unlike in eq.
families.
(4),
the
depends not only on the college premium, but also on family income.
Empirical Strategy
The above model
easily translated into a simple linear estimating equation.
is
identify in the data
who
If
we could
we should run
the unconstrained and the constrained families were,
equations of the following form:
where
i
For unconstrained families
:
For constrained families
:
Sijt
sm —
8r-\- Sj
8p
+ 5j
+ 6t + ocrT'jt + ^ijt
+ 5f + O-pTjt + jSp ^liyiqjt + ^ijt,
denotes individual family, j denotes region, and
which denotes whether the individual
error term.
Since
denotes time.
in question attends college, djt
premium and family income
we do not observe which
where the
t
is
Sijt is
a 0-1 variable
an individual specific
These expressions follow from our theoretical model above, and allow both the
effect of the college
effect of family
also allow the relationship
This
may be
of a
more general model
quartiles.
Such a
between income quartile and enrollments to be non-
useful because the poorest households
thanks to need based financial
financial aid,
we think
and poor households.
income on enrollments varies across income
monotonic.
is
to differ across rich
families are constrained,
model would
colleges.
—
may be
relatively unconstrained
aid, while middle-class households,
constrained, especially
if
who do
not qualify for
they wish to send their children to private
This gives us the following model
^iqjt
(5, -f-
6j
+
6t
+ aqTjt + Pq In yrqjt + e^qjt,
(6)
,
where
q denotes
(6) nests our
allows
income
and
We will
= a and 13^ =
j3
as before j denotes region,
=
more general heterogeneous
quartiles.
aq
quartile,
model above when Pg
for rich famihes,
effects of
in order to
make
(6) includes
main
changes in federal financial aid and the
same region
>
for
poor famihes, but
premium
across income
income quartiles by setting
boom
the college
like
The
effects.
related to the
we have written the
In addition,
like.
which implies that families look
latter
Vietnam
relevant
premium that apphes
at the college
in
Both of these assumptions appear reasonable: most people
the region at the time of schooling.
in the
/?
college
income quartile and time
effects of
era,
as Vjt,
denotes time. Expression
t
better use of the limited variation in our data.
capture the effects of aggregate conditions
work
/3g
income and the
will
premium
=
also present results restricting the effects across
Note that equation
college
and
and
as they completed schooling (see
Acemoglu and Pischke, 2000), and
the existing time-series evidence suggests that current returns, not expected future returns
matter most
income
In any case,
(Freeman, 1976).
for schooling decisions
elasticity of college enrollments
is
insensitive to
how we
we show below that the
control for the effect of returns
to college.
Equation
(6)
can be aggregated across individuals to be written in a more compact form:
Sqjt
where
(or
Sqjt
among
6q
+
6J
+6t+ aqTjt + (3 q In Yq;jt + Sqjt,
the fraction of students attending college
those in the right age bracket) in region
and
college,
time
is
=
In Ygt
is
j,
among
those
who completed
income quartile
the log average income of family
is
(7)
g,
in region j,
and time
t
high school
who
income quartile
attend
g,
and
t.
It is
also useful to note that the estimation of equation (7) can
be thought of as instrumental
variables (IV) estimation of
Sqjt
using the
full set
=
6J
+6t
+ aqrjt + /?, In Yq^t + Cqjt
of quartile-region-time interactions as the instruments for In Yqjt.
interpretation clarifies
why our
with parental
labor supply or other reasons.
may be
ability,
correlated with the error
is
empirical strategy
term
in equation (8).
because we are controlhng
attractive.
Family income
As captured
in the
is
likely to
vary
model, these factors
Our
for
the parents' rank in the income distribution,
in InYqjt conditional
structure which have taken place in
differential variation in the parental
wage
on
this rank.
income distribution across
The changes
in
is
the wage
differentials
quartiles.
wage structure over time, our estimation strategy
have changed
also
differently in different states or regions.
relying completely on within region variations we can control
and parental background group
Identification
the United States during the 1970s and 1980s provide
In addition to using variation in the
exploits the fact that
is
strategy avoids the bias that will arise from
close to a sufficient statistic for their unobservable characteristics.
then achieved from the variations
By
is
This IV
correlated with the family's costs (attitudes) of educating their child, so that In Yqjt
this correlation,
which
(8)
at the aggregate level in the college
for
the interactions of time
attendance equation. This
allows us to also estimate models that control for other factors which might have affected the
children of richer or poorer parents differently, like differential changes in tuition costs at
private
and public
universities, or the
changes in the availability of Pell grants and Guaranteed
Student Loans.
Data
4
We study the effect of family income on college attendance,
of high school leavers sponsored
using the three longitudinal surveys
by the U.S. National Center
for
Education Statistics (NCES):
the National Longitudinal Study of the High School Class of 1972 (NLS-72), the High School
and Beyond Survey (HSB), which started with high school seniors and sophomores
and the National Educational Longitudinal Study (NELS), which started with a
graders in 1988.
These surveys roughly span the two decades of the 1970s and the 1980s
which returns to college
Each
on the educational background of the parents
and on family income when the respondent was a senior
various stages during the
(see
Duncan
life
et al., 1998)
might
of a child
and opportunity
variables for income,
affect its
we want
quartile in the
may impede
these two distributions,
We
in
we
Follow-up information after leaving high school was
From
overcome
ever attended a four-year college.
We
this
problem by
fitting
derive the enrollment rate for each
first
in the quartile.
two years
collected
this follow-up wave,
whether an individual ever attended any college
income to cover the
the sample of college entrants and
income distribution and the average family income
spondents were in their senior year.
seems to be
schooling datasets record only bracketed
and there are 10 to 18 brackets.
From
the cognitive
in high school
to focus on the role of
The
costs of attending college.
Family income at
ultimate chance of attending college
income during the senior year
parametric Singh-Maddala distributions to the incomes
in the entire sample.
in high school.
because fewer resources at a young age
child. Nevertheless,
the correct concept for our project because
direct
in
decreased and then increased.
first
of these surveys collected information
development of a
in 1980,
class of 8th
in the interim,
we
after the re-
construct measures of
and whether the individual
derived information on returns from the 1970, 1980,
and 1990 Censuses by calculating the average wages of those with exactly 16 and exactly 12
years of education (those with a college degree and a high school degree, respectively)
workers with
is
1
to 5 years of experience.
Our
definition of the return
approximately equal to the return to one year of
Table
1
gives
summary
statistics for
is
among
\n{wi^/wi2)l^, which
college.
our sample by family income quartiles and year.
The
top panel gives the fraction of children from families of different quartiles ever attending any
college within
two years of high school.
The second panel shows the same information
attending four-year college, and the bottom panel
statistics
by region and
A number
in
year,
and the variation
is
for family
in the college
of patterns are clearly visible from Tables
1
income.
premium
and
2.
Table 2 gives similar
across regions
There has been
the fraction of children attending four-year college between 1972 and 1982.
and 1992, there has been a substantial
children in the upper two quartiles.
increase, but this increase
The bottom
is
for
and time.
little
increase
Between 1982
concentrated
among the
panel in the table shows that family incomes
have only risen
and
quartiles,
top quartile over this period, stagnated for the middle two
for families in the
These patterns are therefore
fallen slightly for families in the lowest quartile.
consistent with substantial income effects on enrollments in the aggregate.
that there
any
a
is
much weaker
This
college.
contrast across quartiles
in line
is
and attending four-year
is
difference
noteworthy
at the fraction ever attending
between attending any college
mostly made up by community colleges, which are very cheap,
and pose a lower opportunity cost
from poor backgrounds since the duration
for families
is
Therefore, in the presence of significant credit market barriers affecting education
shorter.
choices,
The
with our thinking.
college
when looking
It is also
we would expect
community
colleges
families to increase the rate at
much more than
may be
also implies that there
which they send
their children to
to four-year colleges over this period.
This observation
quite significant heterogeneity in the quality of colleges that
children from poorer and richer families are attending within these broad categories of two-year
and four-year
colleges.
Table 2 reveals that there
Northeast and the least
is
substantial variation in the variables of interest across the
Both income and
four Census regions.
but there
is
in the
West.
college enrollment rates have
Returns have moved mostly
some heterogeneity across regions
the 1970s.
in
grown the most
in
the
during the 1980s
in line
This illustrates that the region
variation will be quite helpful in identifying our models.
Results
5
We
is
with the regressions which do not control
start in Table 3
for quartile effects.
equivalent to estimating (8) without instrumenting for family income.
The
This
coefficient
on
family income in these models therefore captures both the effect of income and any other effect
of family
background which
In this
is
and the following
correlated with income.
tables, the first four
college in a region-income quartile-year cell as
dependent variable, while the
are for the fraction attending four-year college.
four columns are
more important
for
columns have the fraction attending any
The
our argument.
It
of the effect of log income
on enrollments, 0.18, implies that a 10 percent increase in family income
1.8 percentage point increase in enrollments.
This
is
four columns
turns out that the coefficients on
The estimate
family income are very stable across specifications.
Isist
discussion above suggests that the last
is
associated by a
a fairly large effect of family income on
college enrollments.
The
first
and
fifth
columns do not control
national changes in family income and
for
time
in the college
effects, so
premium
they effectively exploit the
to identify the effects on enroll-
ments. These columns also show moderate effects of returns of attending college. For example,
the estimate of 0.82 for log returns in column (5) imphes that a 4 log point increase in the
college return, which
is
roughly the increase from 1980 to 1990, should lead to a 3.3 percentage
point increase in college enrollments. In the remaining columns,
second and sixth columns, we drop returns to
to college are included.
In
all
college, while in
we add year
columns
(3)
cases, the estimates of the effect of family
effects.
and
(7),
In the
returns
income on college
attendance
is
is
unaffected.
Interestingly, in
columns
making
consider only the national return in
also
wisdom that returns
and
Although
estimated to be insignificant and negative.
ventional
(3)
the effect of college returns
(7),
may be
this result
college decisions,
because families
sheds some doubt on the con-
it
to education have a major effect on enrollment decisions (see
Acemoglu and Pischke, 2000).
Here we add dummies
Table 4 gives our main results.
for the
income
This
quartile.
should control for any invariant family background effects related to the rank of a family in the
income distribution and
in
columns
Table
3.
and
(1)
time
which do not control
(5),
Nevertheless, there are
Our
college enrollments.
effects
and
many
other aggregate trends, which might have affected
columns
we
and the
That the
3.
some
eliminating
is
family income. Nevertheless,
The
the estimate of the income elasticity.
(6) therefore include
coefficient for family
effect of
family income
is
income
income
for
both enrollment
columns
(3)
and
(7)
has
insignificant.
columns
(4)
Finally,
and
(8)
adding second
not
on
on the
level interactions
changes the general magnitude of
much
the estimates httle, though, since these controls eliminate
is
little effect
Interestingly, in these specifications the estimates
in
is
now
smaller
enrollment (although this difference
in the region in
become
and time
of income quartile, region,
and
of the unobserved characteristics correlated with
effect is larger for four- year college
returns to schooling once again
(2)
find a significant effect of family
Adding returns to coUege
results
are very similar to those in
effects,
exploit only the within region variation.
implies that our strategy
significant).
time
for
preferred specifications, in
lower than those in column (1) and in Table
variables,
income on enrollments. The
isolate the true effect of family
of the variation in the data,
the effects are no longer statistically significant
We therefore conclude that there is
Our
It
a robust effect of family income on enrollments decisions.
baseline estimate of 0.14 indicates an economically very significant effect of family income.
implies that family income, rather than other factors related to family background, explain
27 percentage points of the 36 percentage point difference in the enrollment rates of children
from the bottom and top quartiles
have found positive
in 1992.
income.
effects of
This
is
large
compared to other
studies,
which
For example, Ellwood and Kane (1999) find that family
income explains only 9 percentage points of the 26 percentage points enrollment difference
between the top and bottom quartiles
The framework we
and returns by income
families.
It is
possible to estimate separate effects for family income
The
quartile.
results are less clear-cut,
we do not
1982 after introducing various controls.
outlined above suggested that the effects of family income might differ
between rich and poor
effects are allowed to
in
vary by income quartile.
find that family
income
is
even relatively rich families
some
for reasons other
may
To the degree that there
most important
in the case of four-year college, the opposite
matter
These
results of this exercise are given in Table 5.
mostly because the estimates become relatively imprecise once the
for
are any patterns,
the lowest income families
seems to be true).
(in fact
This might indicate that
not be completely unconstrained. In addition, income
than credit market constraints,
for
example, because college
may
is,
to
degree, a consumption good rather than a pure investment good. Since the estimates are
imprecise,
it is
difficult to
draw firm conclusions from the
results in
Table
5.
Summary
6
The income
nomics
elasticity of
of
a key parameter for the labor and macroeco-
is
knowing how responsive
college enrollments will
income may have become even more important with the increase
schooling, which
be
in the returns to
expected to encourage greater enrollments.
is
we proposed
In this paper,
We
The importance
literatures.
to family
education decisions
a novel identification strategy for estimating this elasticity.
exploited variations in family income over time due to changes in the overall income
distribution.
in family
We
income
find reasonably robust
is
and large income
A
elasticities.
predicted to increase college enrollments by
1
10 percent increase
to 1.4 percentage points.
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Table
1
Means of Fraction Ever Attending Any College Within Two Years of High School and Family Income
by Year and Family Income Quartile, 1972-1 992
12
Family Income Quartile
Year
3
4
Attending Any College
1972
0.37
0.45
0.53
0.69
1980
0.45
0.52
0.60
0.72
1982
0.44
0.54
0.61
0.73
1992
0.56
0.66
0.75
0.87
Attending Four Year College
1972
0.22
0.28
0.34
0.51
1980
0.25
0.30
0.38
0.53
1982
0.26
0.33
0.39
0.53
1992
0.30
0.38
0.47
0.66
Family Income
Note: Cell level
Students
left
means
for
(in
$1,000)
1972
16.8
30.7
43.6
69.8
1980
16.6
28.5
40.9
81.4
1982
16.6
30.4
44.2
77.4
1992
13.7
30.0
48.4
92.2
4 Census regions. Data from the NLS-72,
high school in 1972, 1980, 1982, and 1992.
HSB
Senior and
Sophomore
cohorts, and the
NELS.
Table 2
Means of Fraction Ever Attending Any College Within Two Years of High School and Family Income
by Year and Census Region, 1972-1992
Census Region
V
Year
North
„
North
„
East
Attending
„
,
.
...
^
South
West
Central
Any College
1972
0.53
0.48
0.46
0.57
1980
0.58
0.55
0.52
0.63
1982
0.58
0.57
0.52
0.66
1992
0.76
0.70
0.68
0.69
Attending Four Year College
1972
0.40
0.36
0.33
0.28
1980
0.43
0.41
0.34
0.28
1982
0.43
0.41
0.34
0.34
1992
0.57
0.48
0.42
0.34
Family Income
(in
$1,000)
1972
41.4
41.1
36.7
41.7
1980
47.5
41.7
36.0
42.2
1982
42.3
42.3
37.2
46.8
1992
51.4
46.2
41.0
46.0
Returns
1972
0.125
0.098
0.113
0.079
1980/82
0.076
0.070
0.079
0.069
1992
0.114
0.115
0.116
0.114
Note: Cell level means for 4 Census regions. Data from the NLS-72, HSB Senior and Sophomore cohorts, and the
left high school in 1972, 1980, 1982, and 1992. Returns are calculated from the 1970, 1980, and 1990 Censuses.
NELS.
Students
Table 3
Fixed Effects Regressions for the Probability of Attending College Within
No
Region by Income Quartile
Cells,
Log Mean Family Income
Return to College
0)
of High School
1972-1992
Ever Attending Any College
Independent Variable
Two Years
Controls for Income Quartile
(2)
(V
Ever Attending Four Year College
(4)
(5)
(6)
(7)
(S)
0.186
0.183
0.183
0.182
0.184
0.183
0.183
0.182
(0.016)
(0.007)
(0.007)
(0.006)
(0.011)
(0.008)
(0.008)
(0.008)
1.341
—
-0.790
—
0.822
—
-0.945
—
(0.485)
(0.667)
(0.751)
(0.351)
Region Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
No
No
Yes
No
No
No
Yes
Region
*
Year Effects
cell level means for 4 Census regions, 4 years, and 4 quartiles for the income of the student's family. Number of
Dependent variable is the fraction of students enrolled in any college or in a four year college within two years of high
school graduation calculated from the NLS-72, HSB Senior and Sophomore cohorts, and the NELS. Students left high school in
1972, 1980, 1982, and 1992. Return to college is the relative wage of those with exactly 4 years of college to those with a high
school degree (for workers with 1-5 years of experience) calculated from the Census for 1970, 1980, and 1990.
Note: Data are
cells is 64.
Table 4
Fixed Effects Regressions for the Probability of Attending College Within
Two
Years of High School
Controlling for Income Quartile
Region by Income Quartile
Cells,
1972-1992
Ever Attending Any College
Independent Variable
Log Mean Family Income
Return to College
(1)
(2)
(3)
(4)
Ever Attending Four Year College
(5)
(6)
(7)
(8)
0.218
0.107
0.102
0.146
0.212
0.148
0.142
0.093
(0.101)
(0.044)
(0.044)
(0.107)
(0.065)
(0.041)
(0.040)
(0.108)
...
1.336
-0.887
0.817
-0.994
(0.491)
(0.616)
(0.314)
(0.556)
Region Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Income Quartile Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Income Quartile
*
Region Effects
No
No
No
Yes
No
No
Yes
Yes
Income Quartile
*
Year Effects
No
No
No
Yes
No
No
Yes
Yes
No
No
No
Yes
No
No
No
Yes
Region
*
Year Effects
cell level means for 4 Census regions, 4 years, and 4 quartiles for the income of the student's family. Number of
Dependent variable is the fraction of students enrolled in any college or in a four year college within two years of high
school graduation calculated from the NLS-72, HSB Senior and Sophomore cohorts, and the NELS. Students left high school in
1972, 1980, 1982, and 1992. Return to college is the relative wage of those with exactly 4 years of college to those with a high
school degree (for workers with 1 - 5 years of experience) calculated from the Census for 1970, 1980, and 1990.
Note: Data are
cells is 64.
Table 5
Fixed Effects Regressions for the Probability of Attending College Within
Two Years
of High School
by Income Quartile
Region by Income Quartile Cells, 1972-1992
Effects
Ever Attending Any College
Independent Variable
(1)
Log Mean Family Income
Quartile
1
Return
Quartile
(0.187)
(0.085)
(0.052)
(0.053)
(0.190)
0.229
0.189
0.167
0.201
0.151
0.128
0.087
-0.205
(0.258)
(0.113)
(0.117)
(0.334)
(0.153)
(0.105)
(0.101)
(0.339)
0.617
0.161
0.148
0.328
0.428
0.174
0.150
-0.039
(0.273)
(0.116)
(0.129)
(0.283)
(0.162)
(0.107)
(0.112)
(0.287)
0.405
0.012
-0.005
0.231
0.392
0.212
0.183
0.147
(0.152)
(0.071)
(0.072)
(0.132)
(0.092)
(0.066)
(0.063)
(0.134)
0.691
—
-1.049
—
-0.053
—
-1.577
—
—
0.481
1.367
College
to
—
—
-0.963
—
—
-0.438
—
0.171
—
—
1.304
—
-1.115
—
(0.627)
—
-0.226
—
(0.627)
(0.564)
(0.723)
-1.121
(0.630)
(0.622)
(0.722)
(0.952)
0.599
(0.556)
(0.726)
(1.050)
Quartile 4
-1.032
(0.659)
(0.623)
(0.759)
(0.938)
Return to College
Return
(8)
-0.016
0.139
1.144
Quartile 3
(7)
0.064
(0.064)
Return to College
Quartile 2
(6)
0.108
0.154
(1.052)
1
(5)
0.010
(0.056)
College
to
(4)
0.018
Log Mean Family Income
Quartile 4
(3)
(0.143)
Log Mean Family Income
Quartile 3
<
-0.039
Log Mean Family Income
Quartile 2
(2)
Ever Attending Four Year College
Region Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Income Quartile Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year Effects
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Income Quartile
*
Region Effects
No
No
No
Yes
No
Yes
Yes
Yes
Income Quartile
*
Year Effects
No
No
No
Yes
No
Yes
Yes
Yes
No
No
No
Yes
No
No
No
Yes
Region
*
Year Effects
cell level means for 4 Census regions, 4 years, and 4 quartiles for the income of the student's family. Number of
Dependent variable is the fraction of students enrolled in any college or in a four year college within two years of high
school graduation calculated from the NLS-72, HSB Senior and Sophomore cohorts, and the NELS. Students left high school in
Note; Data are
cells is 64.
is the relative wage of those with exactly 4 years of college to those with a high
of experience) calculated from the Census for 1970, 1980, and 1990.
1972, 1980, 1982, and 1992. Return to college
school degree (for workers with
1
-
5 years
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