The Structure of Early and Higher Education, Dynamic
Interactions and Persistent Inequality∗
Bledi Taska†
Department of Economics, New York University (NYU)
November 15, 2011
Abstract: Intergenerational earnings mobility is a key determinant of the degree of
cross-sectional inequality that will be transmitted to future generations. Low intergenerational mobility implies that inequality will be persistent. With income inequality increasing
rapidly over the recent years, it is important to understand the underlying sources and
mechanisms of intergenerational earnings persistence. This paper examines the mechanisms
through which early and higher education (individually and jointly) impact intergenerational
earnings mobility. More specifically, I explore the effects that the structure of the education
system and existing methods of financing education can have on earnings persistence. In
order to quantify these effects, I develop a life-cycle model of incomplete markets where
agents differ in wealth, ability, and education. Intergenerational persistence of earnings is
generated endogenously as richer parents invest more in the early and higher education of
their children. Early education investments affect the cognitive ability of children. Higher
ability children earn higher wages, but also have a lower cost of enrolling in college. Higher
education investments, through parental transfers, affect college enrollment, college quality
and college graduation rates. I use PSID, NLSY, NPSAS, and Census micro data to estimate the parameters of the model. I find that differences in higher education account for a
higher percentage of the intergenerational correlation in earnings than do differences in early
education. Liquidity constraints do not seem to be important for early or higher education.
I also show that there exist complementarities between the two periods of investment in
education. Finally, I find that early education is more important for the upward mobility of
low income families.
∗
I want to thank my advisors, Gianluca Violante, Christopher Flinn, Matthew Wiswall and Ahu Gemici for
their valuable comments and encouragement. I have also benefited a lot from discussions and comments from
Raquel Fernandez, Lance Lochner, Joyce Cheng Wong, Ergys Islamaj, Albert Queralto, Saki Bigio, as well
as participants in seminars at the NYU Macro Student Lunch, Midwest Economic Association Conference,
the Midwest Macro Meetings, the MOOD Doctoral Conference and the CRETE Conference. This research
was conducted with restricted access to Bureau of Labor Statistics (BLS) data. The views expressed here
do not necessarily reflect the views of the BLS. All errors are mine.
†
Address: New York University , 19 W. 4th Street, 8FL, Room 804 , New York, NY 10012, e-mail:
bt540@nyu.edu.
1
1
Introduction
This paper examines how the current education system and the particular methods of
financing early and higher education in the United States can affect intergenerational income
mobility. Although primary and secondary education in the U.S is public, total expenditures
per student exhibit large geographical variation. At the same time, college enrollment and
college quality are correlated with private higher education expenditures1 . A better early
education can have a positive effect on future wages and can improve the chances of a student
to enroll in college. Also, a better higher education provides a higher chance of graduating
and higher future wages.
Using the NLSY79 children’s data set, I document a positive correlation between children’s early ability and mother’s ability. Using Census data on education finance, I find
that there is a large variation between primary and secondary expenditures by locality for
the period 1992-20002 . Mapping the Census data to the NLSY79 children’s data, I find that
even if we control for early ability, primary and secondary expenditures have a positive and
important effect on the cognitive ability of children. Last, using the NLSY97 data set I
show that parental income has an effect on college enrollment, college quality, and college
graduation rates even after controlling for cognitive ability 3 .
Based on this empirical evidence, the first question this paper answers concerns the
effects of the structure of the early and higher education system and the existing methods of
financing education on intergenerational mobility. These effects will depend on the relative
returns to education and the constraints that families face. They will also depend on the
opportunities that early and higher education provide for students to sort based on their
family income.
However, if there are dynamic interactions between periods, focusing on only one period
might be misleading. Hence, the second question of the paper is whether there are complementarities between early and higher education. Finally, it might be the case that returns to
education and the constraints on families vary across the distribution of income. Hence, one
education period may have a larger effect on the intergenerational persistence of a particular
group of the population.
In order to answer these questions, I develop an overlapping-generations model of heterogeneous agents and incomplete markets where agents make decisions about investment in
1
See section 2 for a documentation of these facts.
There are several papers that document this variation in local expenditures. See for example Hoxby
[1998], or Corcoran and Evans [2008].
3
This is based on the empirical analysis of Belley and Lochner [2007]. I extend their analysis to include
more recent waves of the NLSY97 data, and at the same time I use these findings to estimate my model.
2
2
the human capital of their children. The model’s parameters are estimated and calibrated
using PSID, NLSY, NPSAS, and Census micro data, such that the model is consistent with
important features of the education system and wage structure in the United States.
In my model parents are assumed to be altruistic towards their children. Young parents
make early educational decisions about their children based on their income and on the child’s
innate ability. The innate ability of the children is assumed to be correlated with the parents’
ability. Parents’ investment in early education, in combination with the innate ability of the
child, translates into cognitive ability through a production function. This cognitive ability
affects both the probability of graduating from high school and future wages.
Older parents decide if they will enroll their children in college and the quality of the
college. At the same time, parents give their child transfers for the next period. Children
can finance their college expenses through parental transfers or by borrowing from the government. College-age children leave home and, depending on the enrollment decision of the
previous period, attend college or not. Cognitive ability is an important determinant of the
decision on whether to graduate from college. Finally, in each period of their life individuals
face some borrowing constraint.
Earnings persistence in the model is generated through all three channels: (i) correlation
in innate abilities, (ii) investment in early education and (iii) investment in higher education.
Since there is a correlation in innate abilities, then abler and richer parents have abler and
richer children. At the same time, richer parents invest more in the early education of their
children. As a result, children from wealthier families graduate at higher rates from high
school and have higher cognitive ability. Even if we condition on these facts, due to higher
parental transfers children from wealthier families have higher college enrollment rates. They
also enroll more in 4-year colleges and have higher rates of graduation.
Results from simulations of the model indicate that higher education accounts for a higher
percentage of the intergenerational elasticity of earnings (IGE) than early education4 . Using
the estimated model, I perform counterfactuals where the effect of either early or higher
education is the same for everyone. I find that early education accounts for 11.3%-27.8%
of the observed persistence, while higher education accounts for 19.6%-32%. Contrary to
Resstucia and Urrutia [2004], I find a weaker effect of early education. One reason for this
result is that the estimated returns to college are higher than returns to early education.
Additionally, in my model individuals have more opportunities to sort in higher education
based on their family income. Children from wealthy families not only enroll more in college,
4
The intergenerational elasticity of earnings measures the correlation of parent’s and children’s earnings,
and it is the most commonly used index of intergenerational mobility. See section 2 for more details.
3
but they also enroll in better colleges and graduate at higher rates.
Increasing credit limits during college has a small impact on enrollment. An increase
of credit limit by 50% increases college enrollment by only 1.3%. This implies that the
positive correlation between parental income and higher education is due to higher transfers
by richer parents and not because of liquidity constraints. There is however a significant
effect on college quality and on graduation rates. Enrollment in 4-year colleges increases by
14%, while college graduation increases by 3.4%. This results in a decrease of the IGE by
4%.
Liquidity constraints also seem to have a small effect on investment in early education.
Increasing the credit limit in the early period by 50% increases investment in early education
by 2.4%. However, the effect on college decisions is stronger. The early investment period
is also the post-college period. Many students are not borrowing up to the limit because
once they graduate they will have large expenses and low wages compared to their lifetime
income. An increase in the credit limits during the post-college period will induce more
college-age students to borrow up to the limit. For example, the percentage of 4-year college
students who are borrowing up to the limit increases from 23% to 30.2% after the increase of
the credit limits in the post-college period. This result implies that post-college constraints
are an important factor to consider when we design policies which affect liquidity constraints
during college.
Because of the increase in investment in early education and the increase in college
borrowing, college enrollment increases by 5.2%, while enrollment in 4-year colleges and
college graduation increases by 17.1% and 4.3% respectively. Overall, reducing liquidity
constraints in early education decreases IGE by 9.3%.
Also, I find that because of dynamic interactions between the two periods, strong complementarities are generated through three mechanisms: (i) the increase in early education
when college education is less expensive, (ii) the increase in college education when early
education is less expensive, and (iii) the increase in college education when the post-college
period is less expensive.
First, making college more affordable increases early expenditures. Since parents now
know that it is easier to enroll their children in college, investing in early education has
a higher value. Second, when early education becomes less expensive, investment in early
education increases. This implies that children will now have higher cognitive abilities. As
a result, college enrollment increases since high school graduation rates increase and the
psychic cost of college decreases. Finally, a more affordable early education implies a less
expensive post-college period. This induces individuals to enroll more in college. At the
4
same time, it increases college quality and graduation rates since more students are willing
to borrow up to the limit. Using my model, I find that increasing tuition subsidies by 50%
in both periods generates a decrease in IGE by 78%. This decrease is more than double the
one that is generated by making college education free.
Finally, early and higher education have different effects on the upward mobility of people
who come from different parts of the income distribution. Early education has a stronger
effect on children who come from the lower part of the income distribution. The reason
that most children from poor families do not attend college or do not graduate is a lack of
adequate preparation. In contrast, the preparation of children from middle class families is
sufficient for them to succeed in college. This implies that policies that target early education
will have a greater effect on the upward mobility of children who come from lower income
quantiles.
Related Literature The seminal papers of Becker and Tomes [1979, 1982] and Loury
[1981] are the first to introduce the idea that heritability of abilities and the investment of
parents in the human capital of their children can generate intergenerational persistence in
earnings. If abilities are genetically transmitted, and earnings depend on ability, then more
able and wealthier parents will have more able and wealthier children. Also under imperfect
markets, parents with higher income invest more in the human capital of their children. The
idea that liquidity constraints can generate intergenerational persistence of earnings is also
present in the seminal papers of Banerjee and Newman [1993] and Galor and Zeira [1993].
My paper is also closely related to the applied micro literature that studies the most
effective time of investment in human capital. The work of Cameron and Heckman [2001],
Carneiro and Heckman [2002] and Keane and Wolpin [2001] try to distinguish between investment in early and higher education. All of these papers arrive at the conclusion that
higher education decisions of individuals are not affected much by short-term credit constraints that apply to college costs. The basic idea is that individuals decide not to enroll
in college not because of insufficient funds, but rather because of insufficient preparation in
early education. However, in all of these papers the early education stage is exogenous and
as a result policy invariant. If for example it becomes easier for students to enroll in college,
this will have no effect in their college preparation.
Macroeconomic variables such as interest rates or wages are very important factors that
affect education decisions. However, policies that affect education decisions may have equilibrium effects on these macroeconomic variables. Fernandez and Rogerson [1998], Caucutt
and Krishna [2003], Akyol and Athreya [2005], and Garriga, and Keightley [2007] develop
and study macroeconomic models of education decision. Also Gallipoli, Meghir and Violante
5
[2011] study the equilibrium effects of education policies. They find that equilibrium effects
are important and that they reduce the effectiveness of public policy. Methodologically my
paper is very close to this literature. However for the moment I do not consider equilibrium
effects. At the same time this literature too has the shortcoming of having only one period
of investment. Also in most of these papers individuals cannot choose the quality of higher
education or when to drop out5 .
Recently there have been papers that study multi-period models of investment in education. In Restuccia and Urrutia [2004], Caucutt and Lochner (2008) and Cuhna, Heckman
and Schennach [2010] all periods of investment are endogenous and can interact with each
other. Caucutt and Lochner (2008) and Cuhna, Heckman and Schennach [2010] focus on
different periods of early education and find that there exist complementarities among the
different stages of investment.
The paper of Restuccia and Urrutia [2004] is the one that is closer to mine. However
in that paper the authors do not study the issue of complementarities, of different distributional effects or the effect of liquidity constraints on mobility. At the same time my
model is significantly different than theirs. Departing from their work, I allow for capital
accumulation in my model. Without capital accumulation it is very difficult to distinguish
between the relative importance of parental transfers and credit constraints6 . In this paper,
I also incorporate two significant margins of higher education, college quality and college
retention7 . When individuals can also choose college quality and graduation, there are more
opportunities to sort in higher education based on family income8 . Last, I use micro data
to estimate the returns to early and higher education, as well as the constraints that the
families face.
There is an extensive literature that studies the effects of family and school on children’s
development. More specifically, papers from Todd and Wolpin [2007], Liu, Mroz and van
der Klaauw [2010], and Del Boca, Flinn and Wiswall [2011] examine the effect of parental
investment on the cognitive development of children. However, in these papers parental
investment is usually defined as the time spent with the child. On the contrary, I focus more
on the choice of location as an index of quality of early education. In addition, I try to study
5
Garriga, and Keightley [2007] are the only paper that allow for endogenous drop-out decisions
Kean and Wolpin [2001] estimate a model where student do not face binding liquidity constraints and all
the correlation between parental income and education decisions is generated because of parental transfers
7
By college quality I imply two versus four-year college. Approximately 40% of all college students enroll
in a two-year college, and the drop-out rate of two-year colleges is 60%-70%. Black and Smith [2004] and
Hoekstra [2009] find that there are important returns to college quality.
8
Meghir and Palme [2005], and Pekkarinen, Uusitalo and Kerr [2009] find that allowing individuals to
have a choice on school quality increases inequality and reduces mobility
6
6
the effect of this early investment on college and labor income.
Last, my paper is related to the nature versus nurture literature. Papers by Sacerdote
[2002], Black et al. [2005] and Bjorklund et al. [2006] have found that the innate ability
of the parent is partially transmitted to their children. My empirical analysis is consistent
with these findings.
The rest of the paper is organized as follows. Section 2 describes the empirical facts
of interest for intergenerational mobility and education. Section 3 presents the model and
defines the equilibrium. Section 4 describes the calibration and estimation strategy. In
section 5, I discuss the model’s fit to the data and the counterfactual analysis. I conclude in
section 6.
2
Empirical Facts
2.1
Intergenerational Mobility in U.S
The most common index that economists use as a measure of mobility, is the correlation
of parental and children’s income. Most of the empirical literature estimates the relation:
f
f
yits = c + βy fit + γ1 Asit + γ2 (Asit )2 + γ3 Ait + γ4 (Ait )2 + εit
where yits is the log of the income of the son, y fit is the log of the average income of the
f
father, Asit is the age of the son and Ait is the average age of the father. The coefficient of
interest is β, which measures the intergenerational elasticity (IGE), while 1 − β is a measure
of intergenerational mobility. Papers by Solon [1992], Zimmerman [1992], and Mazumder
[2005] have established that the intergenerational elasticity in the U.S is in the range of 0.4
and 0.69 .
Although intergenerational elasticity is a very useful measure, it only tells us the degree of regression towards the population’s mean. Hence, it is a more general measure of
total mobility and cannot give us any information about the mobility of some population
subgroups. If for example we want to compare mobility rates among people who belong to
different earnings groups, we need to use transition matrices. Transition matrices tell us the
quintile of the child’s earnings, conditional on the parent’s earnings quintile. Intergenerational mobility is going to be high when the diagonal elements are going to be very small.
The information of the transition matrix can be summarized in a mobility index, which is
9
See Black and Devereux [2010] for a recent literature review.
7
the sum of the out of the diagonal elements. With perfect mobility, this index should be
equal to one.
Bjorklund et al. [2006] estimate a mobility index for the U.S close to 0.86. As shown in
that paper, the reason for this low mobility in the U.S is the high persistence at the extremes
of the earnings distribution. This means that children from very poor families have very few
chances of becoming rich and children of very rich families will probably be rich also. Thus,
riches to rags or rags to riches, is a phenomenon that does not happen as often in the U.S
as people think.
I will call the intergenerational elasticity general mobility and the mobility index group
mobility. In this paper, I focus on both these measures of mobility and decompose them into
their sources. I also see how different education policies can affect intergenerational mobility.
This is the first paper that tries to see the effect of education policy on group mobility.
2.2
Higher Education and Income Mobility
We all know that the cost of higher education in the U.S is financed partially by students
or their families. Although there exists a variety of federal, state and institutional aid,
most individuals have to bear some of the monetary cost themselves. With the increase of
returns to college since the 80s, demand for higher education has also increased. Along with
the increased returns and the increased demand, college costs have also gone up. Under
perfect credit markets, the increased cost would not pose a problem of efficiency, since the
more able students would be able to borrow from their future income. However, if there are
credit constraints then family income might become an important factor in higher education
decisions.
An initial step to check for the effect of higher education on intergenerational income
mobility is to examine the correlation between family income and higher education. A high
correlation would imply that higher education decisions are important for understanding intergenerational mobility. Table 1 shows higher education outcomes by family income tercile.
As we can see, the correlation between family income and higher education outcomes is
very high. Since returns to education are also high, this correlation can result in a correlation
of earnings. However, it is important to notice that the income education correlation can be
generated from any of the three channels that I examine in this paper. It can be the case,
that because of genetic transmission, children of rich and able families are more able. As a
result, they perform better in high school and in college. It can also be the case that richer
families have invested more in the early education of their children, which results in them
being more prepared for college. Or it can also be the case that richer families invest more
8
in the higher education of their child and for this reason we observe the above correlation.
If we want to disentangle the effect of higher education from the effect of the other two
channels we need to find a way to condition on genetic transmission and on early education
investment.
2.3
Innate Ability and Early Investment
In order to account for the effect of nature on higher education decisions, I have to
estimate the correlation between parents’ and child’s ability. Although this correlation can
be seen as a transmission of genes, this does not have to be the only interpretation. Since
due to data limitation we cannot measure ability at birth, this correlation may also imply
any sort of cultural traits that parents can transmit to their children by early age. One
crucial assumption is that this correlation is policy invariant.
As a measure of child’s innate ability I use the Body Parts index from the NLSY79 Child
data set. This is a test that was completed by children of age 1-3 and can be considered as
measure of early ability 10 . For parents, due to data limitations, I do not have a measure of
early ability. Therefore for parents’ ability I use the Armed Forces Qualification Test (AFQT)
scores of the mother. The elasticity of the child’s ability with respect to the mother’s ability
is approximately 0.25, and is consistent with the existing empirical literature 11 .
As early education investment, I consider a very particular type of investment. Parents
do not influence the education of their children by buying them more books, computers or
clothes. They are able to provide a better education by choosing the locality where they
live. Living in a good locality means a better school or better peers.
Although primary and secondary education in the U.S is public, there are big differences
in the amount of money that schools spend. The three main sources of funding for schools
are Federal, State and Local revenues. In Figure 1 I have plotted total spending of schools
per pupil by spending tercile12 . Next to each spending tercile i have plotted the average
federal, state and local revenues for the specific quartile.
As we can see, the variation in total expenditures is generated mainly by the variation in
local revenues. Moving from the first to the last expenditure tercile, local revenues increase
by more than 150%. The respective increase for the sum of federal and state revenues
10
I use this test because it is one of the few available tests at such a young age. At the same time it is a
very good predictor of the cognitive ability of the child at a later age
11
The correlation of Body Parts and AFQT scores is not a correlation of innate abilities because AFQT
is also affected by early education. Nevertheless I use this correlation as a target and in order to estimate
the true correlation of innate abilities.
12
See the appendix for the details on the estimation of early expenditures.
9
together is only 25%.
Local revenues are mainly consisted of property taxes and parent government contributions 13 . In the model, parents are assumed to choose an amount of investment in the early
education of their child. A higher amount represents a better locality they choose to live in,
with higher property taxes and parents’ government contributions.
Hence, in order to account for the causal effect of the higher education expenditures on
income mobility I need to condition on these two initial channels. For this I need an index
that is a function of the innate ability and early education expenditures and measures some
ability and preparation for college. The AFQT score is the most used measure of cognitive
ability or preparation for college. However in order to see the effect of innate ability and
early expenditures I use the PIAT Math scores, since I do not have AFQT scores of the
children of NLSY79.
Table 2 shows the effect of innate ability and local expenditures on the PIAT scores. In
all of the specifications this effect is relatively large and statistically significant.
2.4
Higher Education Structure and the Importance of Family
Income
Cameron and Heckman [2002] and Belley and Lochner [2007] use the Armed Forces
Qualification Test (AFQT) score in order to condition on these early family effects and to
examine the causal effect of family income on higher education decisions. The AFQT score
is assumed to be a proxy of cognitive abilities. Figure 2 shows college enrollment by family
income tercile and children AFQT tercile for the NLSY97 data.
We can see from this figure that even at the highest ability tercile, family income is
crucial for college enrollment. The figures are very similar if we check for college quality and
graduation rates [See Figures 3 and 4].
Using the methodology of Cameron and Heckman [2002], I can estimate the percentage
of the population for which their higher education decisions or outcomes will change if we
keep everything else constant and we move them to the highest income percentile14 . Using
the NLSY97 data I find that an additional 6.6% of the population would enroll in college if
they parental income belongs to the higher income tercile. For college quality and graduation
from college the respective numbers are 6.9% and 5.7%. So among enrolled student, 12.65%
13
These two together explain more than 85% of the variation in local revenues.
It is important to notice that the effect of parental income on education decision remains even if we
control for many characteristics of the parents and of the family [See section 7.3.3 of the Appendix for details
on the estimation].
14
10
of them would change their education decision in reference to college quality and college
graduation. This implies that family income would affect more than 19% of the population
in their higher education decisions15 .
Both Cameron and Heckman [2002] and Belley and Lochner [2007] interpret these numbers as an indication of the strength of credit constraints in higher education. However, as
shown by Keane and Wolpin [2001] even if family income is important for college decisions
this does not imply that students are credit constraint. The reason may be because richer
parents transfer more money to their children for higher education. We can see this from
Figure 5 that plots total average college transfers.
This may imply that even if credit limits are very low, relaxing these limits may not
affect college decisions. One reason may be that students may not want to accumulate too
much debt during their studies. In this paper I do not adopt any interpretation but instead
use these numbers in my calibration in order to inform the model on the joint importance
of family income and credit constraints for college decisions.
3
Model
The environment I analyze is an overlapping generation model of T periods (Auerbach
and Kotlikoff [1987]) with heterogeneous agents and incomplete markets ( Bewley [1983],
Huggett [1993] and Aiyagari [1994]). The agents differ in the level of their asset-holding,
abilities and the education level they have accomplished. Agents are also assumed to be
one-sided altruistic as in Barro and Becker [1989].
3.1
The Economy
The agents in the model live for T periods. I denote them as j=1,...,T, where j=1 is the
first period when an agent starts to make economic decisions. After period T, agents die with
certainty. The population is assumed to remain constant and so in each period the economy
is populated by T overlapping generations of measure one. The life-cycle of an agent has
four different stages. For parameterization purposes, I choose T=7 and the duration of life
to be 81 years. The timing of the model can be seen in Figures 6 and 716 .
15
This number is almost five times higher than the one that Restuccia and Urrutia [2004] use in order to
calibrate their model. This is one of the reasons as to why I reach into different conclusions about the effect
of higher education on mobility.
16
During ages 0-9 and 10-18 the child makes no economic decisions. I have included these ages in the
timing of the model mainly for illustrative purposes.
11
In period two, individuals have one child who has inherited a proportion of their innate
ability. This ability is known to the parent and determines their investment in the early
education of their child. Parents also make consumption and savings decisions. Next period,
this investment in combination with the innate ability of the child translates into cognitive
ability through a production function. Cognitive ability also determines the probability of
graduating from high school. Children that do not finish high school are not able to attend
college.
During the third period, parents decide whether they will enroll their child in college
and the quality of the college. This decision depends on the ability of the child, on parental
income, and on the borrowing constraints that the child will face next period. At the same
time parents give their child some transfers for the next period. Individuals can finance their
college expenses through their parents’ transfers or by borrowing from the government.
After the third period of their lives, parents live by themselves and make consumption
and saving decisions. It is assumed however that parents are altruistic and care for the
utility of their children. This altruism is an important factor that affects their education
investment decisions. Once the sixth period starts, individuals retire and receive a pension
from the government.
In the first period college-age children leave home, and conditional on the decision of their
parents, they will be enrolled in college or not. During this period, they make their own
consumption and savings decisions. If they are enrolled in college they also decide whether
they will graduate or not. The graduation decision depends on two factors, the disutility
from college and the opportunity cost. It is assumed that children derive some disutility
from college which is decreasing in cognitive ability. This disutility is known to the child
only after he enrolls in college. The opportunity cost of college involves the direct pecuniary
cost of college and the lost income by being enrolled in college. If students do not have
enough assets they may prefer to drop-out so that they can increase their consumption.
Individuals can trade a risk-free one-period bond, which pays a constant rate of return
(1+r). During college students can borrow only from the government at an interest rate
(1+r*). At different stages of their life individuals face different borrowing constraints.
The government offers aid to college students, which depends on their ability, their
parental income and the type of college they are enrolled in. It also provides loans at a
subsidized interest rate (1+r*). The amount of the loan depends on the type of college that
individuals attend. The government also pays a flat pension to individuals during the last
two periods of their life. The government finances these expenditures together with other
government expenditures G through taxes on consumption, capital and labor earnings. The
12
government’s budget is assumed to be balanced each period.
3.2
The individual problem through the life cycle
In this section, I present the individual problem at each period in a recursive form. I
start by presenting the problem of agents in period two17 .
3.2.1
Age 28-36, j=2 of the Parent
Individuals in period two have one child who has inherited some part of their innate ability. Agents have preferences over consumption and make consumption and savings decisions.
They also decide about the investment in the early education of their child. The problem in
recursive form can be written as:
Vj (ac , qj , ach , ed) =
s.t.
max
cj ≥0, ε≥0
U (cj ) + βEhsg [Vj+1 (ac , ach
c , qj+1 , hsg, ed) ]
(1 + τc )cj + qj+1 + ε =
= wj + (1 + r∗ )qj − T (wj , qj )
if 0 > qj & ed > 0
= wj + (1 + r)qj − T (wj , qj )
wj = wed eed
j (ac )
ach
= φ(ach , ε, g)
c
qj+1 ≥ −αjpvt
The states of an agent in this period are his cognitive ability ac , his asset holdings qj ,
his education level ed, and the innate ability of his child ach . The education level can take
four values, ed {0, 1, 2, 4}, respectively for high school graduates, college dropouts, twoyear college graduates and four-year college graduates. Cognitive ability and the education
ed
for each
level determines the efficiency unit of labor eed
j (ac ), while the constant wage w
education is determined by the production function. Function T , represent the tax function
of capital and labor. Also if agents were in school in the previous period and have negative
assets, they could have only borrowed from the government. Hence they have to repay this
debt at an interest rate 1+r*.
17
I present the problem of the agent in the first period after the description of the third period. Since the
generations are connected, starting the description from the second period is more intuitive.
13
The investment in early education ε, together with government expenditures g in early
education and the child’s cognitive ability, determine the child’s cognitive ability ach
c in the
ch
next period through the production function φ(a , ε, g). High school graduation, takes two
values, hsg {0, 1}, respectively for high school dropouts and graduates. The probability of
graduating from high school p(ach
c ) is increasing in cognitive ability. The parameterization of
the early production function and of the high school graduation probability is very important.
Since these two functions capture some of the returns to early investment, they are crucial
for the decomposition of intergenerational mobility into its sources. Last, each period, agents
face an exogenous borrowing constrain αjpvt .
3.2.2
Age 37-45, j=3 of the Parent
Agents in period three decide if they will enroll their children to college or not and the
quality of the college. Children that did not graduate from high school cannot enroll in
college. At the same, time they decide on the amount of transfers that they will give the
child next period. Their problem can be written as:
Vjs (ac , ach
c , qj , hsg, ed) =
s.t.
max
cj ≥0, tr≥0
U (cj ) + βVj (ac , qj+1 , ed) + βωEv [Wjθ (ach
c , tr, Ip , s, a, v)]
(1 + τc )cj + qj+1 + tr = wj + (1 + r)qj − T (wj , qj )
wj = wed eed
j (ac )
qj+1 ≥ −αjpvt
The agent’s problem is somehow different, because now we have an extra term in his
value function which is the continuation value of his child Wj . The agent is connected to his
child through the altruism parameter ω. Parameter v represents the shock in the disutility
from college that the student faces. This shock is unknown to the parent in this period and
that is why there is an expectation term before the continuation value of the child. As a
result, it is unknown to the parent if the child will graduate or not, (if he is enrolled in
college).
The transfers of the parent will be the asset level of the child in the next period, while
parental income Ip is important in order to determine the tuition subsidy. The parameter
s{0, 2, 4} defines the higher education institution at which the child was sent and respectively means, no college, two-year college and four-year college. This is a choice that the
14
parent makes in this period and at the same time with consumption, savings and transfer
decisions. The parent’s choice of whether to send the child to college or not reads as:
Vj (ac , ach
c , qj+1 , hsg, ed)
3.2.3
= max
s{0,2,4}
s
Vj
(ac , ach
c , qj+1 , hsg, ed)
Age 19-27, j=1 of the Child
In period one, besides other aspects, agents differ on whether they enrolled in college or
not. High school graduates only make consumption and savings decision. The agents that
are enrolled in college also have to decide if they will graduate or not. The college graduation
decision is
Vj (ac , tr, Ip , s, a, v) = max {Vjθ0 (ac , tr, Ip , s, a, v), Vjθ1 (ac , tr, Ip , s, a, v)}
θ{0,1}
Where Vjθ1 is the value of graduating from college. The college graduation decision is
taken simultaneously with the consumption and savings decision. This problem is similar
for all agents and can be written as:
Vjθ (ac , tr, Ip , s, a, v) = max U (cj ) − ψ(nθs , ac , v) + βEach [Vj+1 (ac, qj+1 , ach , ed)|a]
cj ≥0
s.t. (1 + τc )cj + qj+1 = wj (1 − nθs ) + (1 + r)tr − T (wj , tr) − nθs (f (s) − g s (Ip, ac ))
wj = wed eed
j (ac )
qj+1 ≥ −nθs αgov
if
− nθs > 0
qj+1 ≥ −αjpvt
if
− nθs = 0
For individuals not sent to college θ is equal to 0. The time that high school graduates,
college drop-outs, two-year college graduates and four-year college graduates spend at college
is given by nθs {1, 2, 3.5, 5} 18 . The function ψ(nθs , ac , v) represents the psychic cost of
college and is increasing in time spent at college n, and decreasing in cognitive ability ac and
the shock v. Also it is assumed that ψ(0, ac , v) = 0.
I am making two crucial assumptions on this part. The first is that students and their
parents do not know their true college ability before they enroll in college. For example
18
The college enrollment is defined by s while college graduation by θ. So for example if s=2 and θ=1 the
person is a 2-year college graduate and nθs = 3.5
15
someone may not know if he is college material, if he is sociable, or he misses home. This
assumption is consistent with the findings of Altonji [1993], Stinebrickner and Stinebrickner
[2008] and Stange [2009], who document that students update their beliefs about ability
once they enroll in college. The second assumption, consistent with the findings of Cuhna,
Heckman and Navarro [2005], is that students derive some disutility from going to college.
College costs are given by the function f (s) while tuition subsidies gcs (Ip, ac ) depend on
ability, parental income and the type of college enrolled in. The choice of whether to graduate
from college depends on the total cost of college. The total cost is not only the direct cost
of college nθs (f (s) − gcs (Ip, ac )), but also the psychic cost ψ(nθs , ac , v) and the opportunity
θs
cost wed eed
j (ac )n . In general, individuals with lower ability and who are more liquidity
constrained tend to drop out of college more. However the total cost of college also affects
the enrollment decision of the previous period. Children of higher ability or children from
richer families enroll at higher rates.
The period after college, individuals also have a child of their own. Agents do not know
the true innate ability of their child, but they do have some expectations over it. In order
to form these expectations the innate ability of the individual needs to be in his state space.
3.2.4
Age 46-81, j=4,5,6,7 of the Parent
After the third period has finished the problem of the individual becomes simpler, since
the child leaves home. During period four, five and six agents only make consumption and
savings decisions while in the last period they consume all of their income. The problem of
the agent during the fourth period is:
Vj (ac , qj , ed) = max U (cj ) + βVj+1 (ac , qj+1 , ed)
cj ≥0
s.t. (1 + τc )cj + qj+1 = wj + (1 + r)qj − T (wj , qj )
wj = wed eed
j (ac )
qj+1 ≥ −αjpvt
The problem of the fifth period is the same with the only difference that the continuation
value Vj+1 does not depend on cognitive ability since in the sixth period the agents retire
and do not receive a wage. The problem of the sixth period reads as:
16
Vj (qj , ed) = max U (cj ) + βVj+1 (qj+1 , ed)
cj ≥0
(1 + τc )cj + qj+1 = ped + (1 + r)qj − T (ped , qj )
s.t.
qj+1 ≥ −alphapvt
j
In the last period there is no continuation value and the individual does not save or
borrow.
3.3
Definition of stationary recursive equilibrium
In order to make the notation more simple I define χj , for j=1,...,7 the individual state
space for each period. A stationary partial equilibrium for this economy is; A collection
value functions {Vj (χj ) }; Individual decision rules for consumption and asset holdings
{cj (χj ), qj (χj )}; Drop-out decision rule θ1 (χ1 ), early expenditure decision rule ε2 (χ2 ), college
enrollment decision rule s3 (χ3 ) and transfers decision rule tr3 (χ3 ); Government expenditures
g; Prices {r, (wed )}; M easures {mu j (χj )} such that
1. Given prices {r, (wed )} and government expenditures g, the individual decision rules
{cj (χj ), qj (χj ), θ1 (χ1 ), ε2 (χ2 ), s3 (χ3 ), tr3 (χ3 )}, solve the respective individual problems and
{Vj (χj ) } are the associated value functions.
2. The government budget is balanced
g+
4
p
ed
7 j=6
ed=1
= τc C + τk rK + τl
dμed
j (χj )
+ I{q1 < 0, s > 0}
χj
q1 (χ1 )dμ1 (χ1 ) + Gc + G =
χ1
4 5 ed=1 j=1
∗
ed ed
w e (χj )dμj (χj ) + (1 + r ) I{q2 < 0, s > 0}
χj
q2 (χ2 )dμ2 (χ2 )
χ2
Where aggregate government expenditures Gc , in higher education subsidies equals
n1 gc2 (Ip ,
Gc =
χ1
+
n2 gc2 (Ip,
ac )I{θ = 0}I{s = 2}dμ1 (χ1 ) +
n1 gc4 (Ip , ac )I{θ = 0}I{s = 4}dμ1 (χ1 ) +
χ1
n4 gc4 (Ip , ac )I{θ = 1}I{s = 4}dμ1 (χ1 )
ac )I{θ = 1}I{s = 2}dμ1 (χ1 ) +
χ1
χ1
3. The distributions {μj (χj )} are determined as an operator that maps current period
17
distribution into next period distribution, using the optimal policy rules of the individuals
and the law of motion for each period.
4
Parameterization of the Benchmark Economy and
Identification
In this section, I describe in detail the calibration of the model. I use three sets of parameters to calibrate the benchmark economy. The first set of parameters is taken from
previous studies, and is parameters that are frequently used in the literature. The second
set of parameters is directly estimated from the data by taking into consideration the restrictions of the model. The rest of the parameters are calibrated internally so that equilibrium
outcomes of the model can match important moments of the education structure and of the
wage structure in the United States.
4.1
Preferences
Agents have preferences over consumption. The utility function is a CRRA of the type
c1−σ
−1
j
U (cj ) =
1−σ
cj
if j = 2, 3
cj =
1.3
For the periods that the child lives with the parent, household consumption is scaled
using the OECD modified equivalence scale. This scale, first proposed by Hagenaars et al.
[1994], assigns 1 to the first household member and 0.3 for each additional child. I choose
the parameter of relative risk aversion σ to equal 1.5. A value of σ between 1 and two is
commonly used in the consumption decision literature (see Attanasio [1999] and [2010]).
Students that are enrolled in college have preferences over consumption, but at the same
time they receive some disutility from college. The disutility from college is assumed to be
of the form:
nθs
+v
m0 (1 + ac )m1
v ∼ N (μv , σv2 )
ψ(nθs , ac , v) =
18
The disutility from college is increasing in the time that you are enrolled nθs and decreasing in cognitive ability ac . However once in college you receive a shock v that affects
this disutility. Only once you are enrolled you can really know if you like college, or if you
are really good at it. I use only three values for this shock, which are different for 2 and
4-year colleges. The parameters m0 , m1 and σv2 is calibrated so that they match the average
drop-out rate of two and four year colleges. However these parameters also affect the enrollment decision. We see in the data that children of higher cognitive ability enroll more in
college and also enroll more in 4-year colleges. These enrollment rates by ability tercile are
also matched, and are used to estimate the disutility parameters. Last, I set the discount
rate β to be equal to 0.76, which is equivalent to an annual β of 0.97.
4.2
Innate ability and early education
One of the assumptions of the model is that innate abilities across generations are correlated. This assumption, although common in the theoretical literature, has only recently
been justified in empirical grounds. Papers by Bjorklund et al [2006], Black et al [2005], Plug
and Vijverberg [2003] Sacerdote [2002, 2007] all find that the innate ability of the biological
parent can explain some part of the innate ability or schooling of the child.
In this paper, I assume that innate ability follows an AR(1) process
ln ach = ρa ln a + u
u ∼ N (0, σu2 )
Following Tauchen [1986], I approximate this continuous AR(1) process by a discrete
Markov process. The correlation coefficient ρa is calibrated so as to match the correlation of
children’s innate ability and mothers’ cognitive ability. The variance of the error term σu2 is
calibrated internally so as to match the variance of the AFQT scores. As an index of innate
ability I use the Body Part text from the NLSY79 Child data. For parents’ ability I use the
AFQT test scores of the mothers.
The interpretation of investment in early education that I adopt in the paper is not one
of direct investment. So I do not assume that parents can affect the quality of their children
by buying more books, better computers or other college supplies. The main assumption
is that parent can affect the quality of early education by taking their children to a better
school. Although primary and secondary education in the U.S is mainly public, there are
large differences among the local funding of the schools. The local funding of primary
19
and secondary education in the U.S is closely related to property taxes of each locality.
Hence parents can choose a better quality school by moving to a better and more expensive
neighborhood. The extra cost that the family is going to incur by moving to more expensive
neighborhood is going to be assumed to be the private investment in early education.
Parent’s investment in early education, together with the children’s innate ability and
government expenditures in early education determine the child’s cognitive ability. The
production function for cognitive ability is of the form:
ac = aγ0 [sε ε + (1 − sε )g]γ1
This function form implies that the returns to private investment increase with ability. I
assume decreasing returns to investment ((i.e. γ < 1). In order to calibrate the production
function I use data for the U.S Census Bureau Statistical Abstract on federal, state and local
expenditures on primary and secondary education. Following Restuccia and Urrutia I assume
that government expenditures in the model correspond to federal and state expenditures,
while private expenditures represent local expenditures. Using the Census data, I calculate
average annual expenditures per pupil over the period 1992-2000 for each county. I assume
that each parent chooses a county to live in. Having the county level expenditures and using
the BLS county identifier I can connect them to the NLSY79 Child data. The share sε is
calibrated to match the ratio of public to private expenditures. The ratio of public to private
expenditures since 1997 has been fairly constant and approximately 56%. The parameters γ0
and γ0 is calibrated to match the regression coefficients of Body Parts and Local Revenues
from the third column of Table 4.
Early education quality has also an indirect effect on children. Children of higher cognitive ability graduate from high school at higher rates. As a result their college enrollment
rate is also higher, since it is assumed that high school drop-outs cannot enroll in college. I
assume a graduation probability of the form:
ch ps2
p(ach
)
c ) = min(1, ps0 + ps1 ∗ (ac )
The three parameters of this function are calibrated so that they can match the average
graduation rate from high school but also the graduation rates by cognitive ability tercile.
4.3
Higher education
The time in college nθs , is set to represent the real average time in college for each
education group, which is estimated using the NLSY97 data. The average time in college
20
for college drop outs is set to be 0.11, 0.22 corresponding to 1 and 2 years. The average
graduation time from a two-year and a four-year college is 3.5 years and 5 years respectively,
which correspond to 0.39, and 0.55 in the model.
To calibrate the borrowing limits for higher education I match the percentage of students
that are borrowing the maximum amount of federal loans. Among students that are enrolled
in 2-year colleges and have federal loans, approximately 5.5% are borrowing the maximum
amount, compared to 24% of 4-year college student19 .
The higher education cost is one of the most important parameters of the model, since it
determines to a large extent the correlation between parental income and higher education.
However estimating the net attendance cost of higher education is not straight forward.
The amount of tuition and fees that higher education institution charge are not the real
amount that a student pays. Most of the colleges provide a general subsidy on these posted
tuition and fees, which depends mainly on the type of the college. Also most of the students
receive different grants, which are mainly income based. There are some merit based grants
as well, but are mostly limited to four-year colleges. The cost of attendance also includes
expenses for room and board, transportation and college supplies. Someone may argue that
these expenses can be considered as regular consumption. Thus students would have to
incur these costs even if they did not attend college. However, as shown by Kaplan [2010],
most individuals that do not attend college live with their parents as a way of reducing
their expenses. This implies that a big part of these non-tuition expenses can be avoided
if individuals decide not to attend college and thus should be included in the direct cost of
higher education.
I use estimates from an analysis of the National Center for Education Statistics of the
National Postsecondary Student Aid Study of 2003-04 (see Student Financing). This analysis
provides estimates of the net cost of attendance by college type and parental income group.
The net price of attendance is estimated by subtracting the amount of financial aid from
the price of attendance. The price of attendance includes tuition and fees, room and board,
college supplies and other college related expenses. The total aid includes federal grants,
state grants, institutional grants and work study.
For two-year colleges I use these estimates and inflate them by the time spent in college.
For four-year colleges I use a weighted average of costs for four-year public, four-year private
not for profit and four-year private for profit colleges. Out of the students that enroll in
four-year colleges 58% enroll in public colleges while 33% enroll in not for profit private
19
See Berkner, Carroll and Wei [2008] for these calculations
21
colleges. The college costs by college type and family income can be seen in Table 1520 .
While these figures do not include the amount that a student can borrow, they do include
all possible aid and grants.
These estimates however do not contain any information about merit aid. I use data on
college aid and ability from NLSY97, in order to estimate how college aid varies with ability.
I find that for two-year colleges aid has no correlation with cognitive ability. For four-year
colleges a 10% increase in the AFQT score increases total aid by almost 6%.
4.4
Wage structure
The wage structure is one of the most important factors in determining intergenerational
mobility. The wage at each period is assumed to depend on the cognitive ability of the
individual and his educational level. Hence, one way that the parents can increase the income
of his child is through investment in early education, which affects his cognitive ability.
Also parents can decide to give more transfers to the child and increase his educational
level. Hence which investment is more effective, depends among other things, on the relative
returns to ability and higher education. I estimate these returns using the PSID and NLSY
data. I assume a deterministic (there is no idiosyncratic risk) wage structure of the form
ln Wj (ac , ed) = ln wed + ζ ed ln ac + kjed
where wed can be thought as the marginal product of human capital for each education
category. ζ ed is the marginal effect of the log of cognitive ability and kjed is period specific
constant for each education category.
The constant wages wed are calibrated internally, so that the average wages by each
educational category to match the data counterpart.
The period specific constant is assumed to be a polynomial of the fourth degree. I use
the PSID annual earnings data in order to estimate these period effects 21 . I use the waves
between 1980 and 2007 and construct mean earnings for each period. In order to account
for ability bias, and since ability is assumed to not be changing over time, I use fixed effects.
Using these mean period earnings I construct a panel where the same person may have
earnings at different periods. I estimate the period effects by regressing period earnings on
a fourth degree polynomial for each education group.
20
The cost of college that I use in the model is a weighted average of the net price of attendance and of
the net tuition. I assume that 40% of the students live with their parents and pay only the net tuition, while
the rest pay the total attendance cost.
21
See appendix for the details and the results of the estimation
22
The marginal returns to ability are estimated from NLSY79 data. The wage data in
NLSY97 are only available for the first period so they cannot be used for this estimation.
However I do estimate the returns to ability for the first period in NLSY97 and compare it
with the estimates from NLSY79. The comparison shows that the assumption of stationarity
in returns to ability seem not to be a bad approximation. I use the waves from 1979 until
2008 and construct mean earnings for each period. I subtract the period effects from the
previous estimation and I construct residual wages. Then I regress the log period earning
on the log of the AFQT score for each education group (See appendix for details).
4.5
Fiscal Policy
The government finances its expenditures through taxes on consumption, capital and
labor. The consumption tax is calibrated so that the government budget is balanced. I
assume a flat capital tax and a progressive labor tax. Hence the tax function is of the form
τ 2 +1
wj L
T (wj , qj ) = (wj − τL1 2
) + rτK qj
τL + 1
Following Gallipoli, Meghir,and Violante [2011] I set flat taxes on capital with τk = 0.4.
From Kaplan [2010] the parameters for the labor tax are set τL1 = 0.637 and τL1 = −0.136.
I also assume a constant lump sum pension which the same for each education group and
following Heathcote, Storesletten and Violante [2010] is set to be equal to the 24% of the
average pre-tax labor earnings.
5
Results
5.1
The Fit of the Benchmark Model
Tables 3a, 3b and 3c show how the model is able to match important moments of mobility,
early and higher education and of the wage structure22 .
As we can see from table 3a, most mobility indexes are close to their data counterpart.
It is important to notice that I am also matching two additional mobility indexes. The
correlation of children’s cognitive ability and parental income is matched in order to be sure
that the early production function and the constraints that the families face in the model
are close to the ones in the data. The intergenerational correlation in cognitive abilities is
22
The parameters used for the benchmark economy are shown in Table 18.
23
also matched. This is also a very important moment because it measures the correlation of
income that can be generated if there was no higher education.
In order to have a measure of the strength of the constraints in early education I am
matching the ratios of average expenditures of the other terciles over the first expenditure
tercile. If these ratios were very high this would imply that both the returns to early education and the constraints that the families face are also very high23 . The average expenditures
for early education are slightly lower that their data counterpart. In the model early local
expenditures are made only because of the returns to early education. However in real life
some of these expenditures may be solely for the quality of the locality, where people live.
College enrollment, college quality and college graduation are also matched in the aggregate. It is important to notice that the model is able to endogenously generate college
retention, which is different for four and two-year colleges.
Table 3c shows the match of the wage distribution. One moment that the model cannot
match is the standard deviation of the log of the average wage. The wage dispersion in the
model is very low compared to the data. The main reason for this result is that wage shocks,
such as unemployment or health shocks are not part of my model. The wage function that
I am using is deterministic one and adding a stochastic term would improve the fit.
In order to account for the role of parental income in mobility, higher education decisions
should also be matched by conditioning on parental income and also on children’s cognitive
ability. We can see from Figure 8 that the model fits the data relatively well and can capture
the monotonicity in college decisions by income and cognitive ability.
The correlation between parental income and higher education decisions makes sure that
the model can generate the intergenerational mobility that we observe in the data. A steeper
relation would imply a higher mobility. The main factors that generate this positive correlation are the liquidity constraints in early and higher education.
The correlation between children’s cognitive ability and higher education decisions is
important in order to account for the effect of innate ability and early education in mobility.
If this effect was stronger this would imply a steeper slope for the educational decisions. The
two main factors that contribute to this correlation are the probability of graduating from
college and the profile of the psychic cost of college.
23
As a comparison the model of Restuccia and Urrutia [2004] generates a ratio of the third over the first
early expenditure tercile close to 30.
24
5.2
The Match of Non-targeted Moments
As an external validity of the model is important to see how it performs with moments
that are not targeted. Figure 9 shows higher education decisions, conditioning on both
parents income and children’s cognitive ability.
We can see that the model still preserves monotonicity for college enrollment college
quality and college graduation. However the decision to enroll in a 4-year college is more
correlated with parental income than in the data.
The fitting of these moments is extremely hard for various reasons. First the distribution
of parental income and children’s ability has to be close to the true one. Also there are
forces in the model that can generate the opposite results. Although liquidity constraints
make sure that children from richer families enroll more in college, the tuition subsidies that
are decreasing in parental income can result in a negative correlation. There is no explicit
mechanism in the model so as how the students choose between two and four-year colleges.
Their choice is based mainly on the relative returns and the liquidity constraints.
Also even though high ability children graduate more from high school and have a lower
psychic cost of college the IES may be such that they prefer not to enroll since they prefer
to consume more now 24 .
The fitting of these moments show that the model is relatively successful in fitting the
data. A better matching may require preference heterogeneity and the calibration of college
aid.
5.3
5.3.1
The Effect of Early and Higher Education on Mobility
The Effect on Generating Persistence
With the model fitting relatively well to the data, we can be confident and use it to
perform counterfactual analysis. The first question I want to answer to what extent early
and higher education are responsible for the earning’s persistence which is created. In order
to see this effect, we can shut down each channel separately and measure the persistence
that is generated.
To observe what percentage of the persistence is generated by higher education, I make
the cost of college very large. This way no one will enroll, and as a result the earning’s persistence is generated only because of the correlation of the innate ability and the investment
in early education.
24
For a similar mechanism where enrollment may be decreasing in ability see Lochner and Monge-Naranjo
[2010].
25
Similarly, to study the effect of early education on persistence, I impose everyone to invest
only the minimum amount in early education25 This implies that everyone in the economy
will have the lowest possible early education. However, given the estimated parameters of
the model very low ability people will not want to enroll in college. Hence, in order to
observe the effect of college enrollment on generating persistence, I change the disutility of
college, so as to have the same enrollment rates as in the benchmark model. The results of
these counterfactuals are shown in Table 4a.
With no college enrollment, the IGE that is generated is 19.6% lower. There still is a
considerable amount of persistence that is generated because of the ability correlation and
investment in early education26 . As we can see, parents in the third income tercile invest
37% more than parents in the lowest tercile. Nevertheless, incentives for investment in
early education are reduced, and we can see this from the average amount invested being
significantly lower.
When there is a minimum investment in early education, IGE is reduced by 27.8%. In
this study, my results differ substantially from the results of Restuccia and Urrutia who
find a very large decrease. The main reason for the difference is that in my model, even
when there are no differences in early education, there is still sorting of individuals not only
by college enrollment but also by college quality and college graduation. Figure 9 shows
that the pattern of college enrollment with minimum early education is very similar to the
benchmark model.
Additionally, in order to see the effect of college quality and college graduation on persistence, I simulate the model with minimum early education and a very large cost for a
4-year college. So, now students can only enroll in 2-year college which is less expensive.
The results are shown in Table 4b. As we can see, intergenerational persistence now drops
to 0.146 27 . This implies that quality and graduation margins are important in order to
understand the intergenerational persistence that we observe.
5.3.2
The Effect on Reducing Persistence
Early and higher education not only generate persistence, but they can also reduce it. In
fact, education is considered by many as the great equalizer. This implies that if everyone
25
This amount is the minimum amount that individuals are willing to invest in the estimated model.
Since now cognitive ability is the only component of wages, the intergenerational correlation in earnings
will be determined only by the intergenerational correlation in cognitive abilities. The intergenerational
correlation in cognitive abilities in the benchmark model is 0.45
27
This is approximately the number that Restuccia and Urrutia estimate when they impose no early
education.
26
26
could get an education, not only would intergenerational persistence be lower, but potentially
even differences at birth would not have a large effect in generating inequality.
In order to assess the possibility that education can reduce persistence, I perform two
additional counterfactuals. First, I make college education completely free. This would imply
that almost everyone goes to college. At the same time, parents may increase investment in
early education since they have more incentives to prepare their children for college.
I then impose all children to have the maximum amount of early education. Since everyone is getting the highest possible early education, then more children graduate from high
school and enroll in college. For this counterfactual, college costs are the same as in the
benchmark model. The results of these experiments are presented in Table 5.
We observe that making higher education free has a large impact on intergenerational
mobility. The IGE decreases by 32%. The reason behind this large decrease is that now
everyone enrolls in college. However, not only college enrollment increases massively, but
college quality and graduation are similar since everyone enrolls in a 4-year college. We
should notice that even with free higher education, wealthier parents still invest more in
their children. Nevertheless, since returns to higher education are higher than returns to
early education, early investment does not have a big effect on persistence28 .
With maximum early education for everyone, IGE reduces by only 11.3%. The reason for
this small reduction is again the sorting of students by college quality and graduation. With
everyone having high quality early education, college enrollment increases since students
graduate more from high-school and have a lower psychic cost of college. However, students
from poor families are enrolling more in 2- year colleges and are graduating at lower rates.
The results of these counterfactuals imply that equalizing college quality will potentially
have a greater effect on increasing intergenerational mobility than equalizing early education.
5.3.3
The Effect of Liquidity Constraints
There is a large debate in the literature on whether there are liquidity constraints in
college or not. Bewlley and Lochner [2007] for example interpret the positive correlation of
parental income with college enrollment, (conditioning on cognitive ability), as an indication
for the existence of liquidity constraints in higher education. Also in another paper Caucutt
and Lochner [2008] claim that the existence of liquidity constraints in early education may
be responsible for the differences that we observe in educational attainment.
28
The average period wage of a 4-year college graduate is more than double the wage of a high school
graduate. On the contrary, the wage increases by only 32% if parental investment in early education changes
from the lowest to the highest amount.
27
In general the existence of liquidity constraints is a very difficult question to tackle. And
the main reason is that the data cannot speak directly as to who is constrained or not. For
this reason a structural model is more suited to answer this question. The model can be
a lab where we can relax the borrowing constraints and see how individuals change their
decisions.
In order to evaluate whether there are liquidity constraints in early or in higher education
I perform two counterfactuals. I increase the credit limits by 50% in each period by keeping
credit limits in the other period the same. The results of these experiments are shown in
Table 6.
As we can see the increase in credit limits increases college enrollment by only 1.3%. This
is in spite of the fact 23% of 4-year college students are borrowing the maximum amount.
There are two reasons why students choose not to borrow when credit limits are less tight.
First there is a precautionary motive. In the next period, these students will be parents and
will want to invest in their children. Since they do not know how much they will invest they
may not be so willing to borrow29 . Another reason, as I will explain below, is the tightness
of the borrowing limits in the next period.
Nevertheless reducing credit constraints has an effect on college quality and college graduation. Enrollment in 4-year colleges increases by 14%, while college graduation increases
by 3.4%. This has an effect on IGE which reduces by 4%.
When I increase credit limits in the early period, investment in early education increases
by only 2.4%. This implies that for early investment, credit limits are not an important
factor. On the other hand this experiment has a stronger effect on college enrollment which
increases by 5.2%. The early investment period is also the post-college period. Many students
are not borrowing up to the limit because once they graduate they will have large expenses
and low wages compared to their lifetime income. An increase of the credit limits of the post
college period will induce more college-age students to borrow up to the limit.
This fact can be seen by the last two rows of Table 5. These rows show the percentage of
people that are enrolled in college and are borrowing the maximum amount. These are the
people for which the constraints in college are binding. We can see from the third column
that once the constraints of the post college period are increased, the percentage of people
that are enrolled in two and four-year college and are borrowing the maximum amount also
increases. The percentage of 4-year college students that are borrowing up to the limit
increases by almost 30%, while the percentage of 2-year college students increases by 38%.
Because of more students borrowing up to the limit, enrollment in 4-year colleges and
29
The ability of the child is not known in this period
28
college graduation increases by 17.1% and 4.3% respectively. Overall, reducing liquidity
constraints in early education, decreases IGE by 9.3%.
My results show that for college education decisions, liquidity constraints during college
are not the only important factor. For a policy to be effective it should take into account the
constraints that students may face after college. This is a period that most people have low
incomes since they have no work experience. At the same time they have higher expenditures
since they have to start a family or buy a house.
5.4
Complementarities Between Early and Higher Education
The literature on education has mainly focused on whether early or higher education
policies are more effective on increasing enrollment and mobility. The main reason for this
approach is that most papers focus only on one period, with the other period being exogenous.
However, if there are dynamic interactions between the two periods then there might also be
strong complementarities. Since both periods in my model are endogenous, I can examine
what will happen if there is a subsidy in both early and higher education.
In this section, I examine the effect of a combined education policy. As a policy experiment, I increase tuition subsidies in both periods by 50%. The results of this counterfactual
can be seen in Table 6.
We can see that a combined policy generates a decrease in IGE of 78%. This decrease is
more than double the one which is generated by making college free. Also, it is important to
notice that IGE becomes even smaller than the correlation of innate abilities. This implies
that there is some support for the common belief that education can indeed be the great
equalizer.
The complementarities are generated through three different mechanisms: (i) the increase
in early education when college education is less expensive, (ii) the increase in college education when early education is less expensive and (iii) the increase in college education when
the post-college period is less expensive.
When early education becomes cheaper parents invest more, and as a result more children
enroll in college. This is a well-known mechanism that has been examined extensively by the
literature. However, even when higher education becomes cheaper parents still invest more
in the early education of their children. The reason is that now they know their children can
enroll in college, and as a result it is worth investing in their early education. Last, making
early education cheaper leads to an increase in college enrollment. However, now it is for a
different reason. Knowing that in the post-college period students have to spend less money,
makes them more willing to invest in college and take out loans.
29
5.5
Distributional Effects
Last, I use the model to analyze the different distributional effects of early and higher
education on the IGE. There is some discussion in the literature about whether higher
education policies affect people who come from different groups of the income distribution
disproportionately. There are findings which suggest that students from poor families may
benefit more from tuition subsidies (See Kane [2006] for a discussion). However, no paper so
far has tried to analyze whether these two policies also differ on their effect on people from
different parts of the income distribution.
In order to answer this question, I compare the effects of early education and higher
education on group mobility. The complement of the mobility index measures the persistence
that is generated. This persistence can also be interpreted as the percentage of children that
their income is in the same decile as their parent’s income. In this section I examine the
persistence that is generated for children that come from poor or rich families when early
education or higher education is free. To estimate the persistence of low income children, I
first sum the diagonal elements of the mobility matrix for the first five deciles, and I then
take the complement of this index. For rich children I perform the same estimation on the
last five deciles. These results can be seen Table 8.
First we should notice that in both cases persistence increases. The reason for this
result is that the income distribution changes significantly. With a free early education
the persistence for children from rich families increases. Since everyone has the same early
education downwards mobility becomes even smaller. On the other hand, a free higher
education increases the persistence for children of poor families. The children of these families
have low ability, and as a result cannot take advantage of the free college. Since the rest of
the children enroll in college the gap between poor and rich becomes even larger.
However with free early education the persistence of the poor decreases by 10.9%. On the
other hand, free higher education decreases the persistence of the rich by 5.6%. This implies
that early education is more important for the upward mobility of low income people, while
higher education is more important for the upward mobility of middle income people. The
intuition behind this result is simple. Students with parents from low income terciles are
more constrained in their early education. Increasing college subsidies has no effect on them
because they are academically unprepared. Students with parents from middle income are
financially constrained on higher education, but they have a higher academic ability.
30
6
Conclusions
Many papers document a strong correlation between education decisions and parental
income in the United States. This correlation, which is also high for college quality and
college graduation, can potentially generate the existing intergenerational persistence in
earnings. Using micro data, I document that this correlation can be generated from three
channels that consist of genetic transmission of abilities, investment in early education, and
investment in higher education.
Based on this empirical evidence, I develop and structurally estimate a dynamic model
of education choices. The model is able to capture and generate important features of early
and higher education system and the wage structure in the United States. It is also able to
generate the observed intergenerational earnings persistence.
By performing counterfactuals on the estimated model, I find that early education accounts for 11.3%-27.8% of the observed persistence, while higher education accounts for
19.6%-32%. I find a weaker effect for early education than Restuccia and Urrutia [2004]
because in my model individuals can also decide on college quality and college graduation.
Also, the estimated returns to early education are lower than the returns to higher education.
In addition, I find that students are not credit constrained during college period. An
increase on the credit limits has a very small positive effect on borrowing. Students are not
borrowing because of precautionary reasons and because next period when their wages will
be low, they may face tight borrowing constraints.
Increasing credit limits in the early education period has small effects on investment in
early education. However, since this is also the post-college period there is a positive effect
on college enrollment, college quality and graduation rates. This result implies that policies
which aim at reducing constraints during college should also take into account constraints
that students may face after college.
I also find that a policy that subsidizes both early and higher education has a very
large effect on reducing the IGE. The reason for this strong effect is the complementarities
generated from the dynamic interaction of early and higher education.
Last, I find that higher education is more important for the upward mobility of children
from low income families. These children would not benefit from a college tuition subsidy
since their parents do not invest much into preparing them for college. On the other hand,
children from middle income families seem to benefit from college tuition subsidy since they
do possess the cognitive abilities, but are financially constrained.
My model has several limitations. One main limitation is the assumption that parents
can only transfer one kind of ability to their children which is valued by the market. However,
31
besides cognitive abilities parents transfer many non-cognitive traits, which might be equally
important for someone to succeed in his career. By including non-cognitive abilities, the effect
of early investment in intergenerational persistence may increase.
An important feature that is missing from my model is income shocks. Persistence would
be reduced with shocks to income. Since these shocks are more probable to be shocks to
ability, this implies a smaller role for early education in generating persistence. I leave these
extensions for future work.
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7
Appendix
I use mainly four data sets in order to estimate the model. All prices are in $2000 prices
and are deflated using the urban consumers price index.
7.1
PSID Data
The Panel Study of Income Dynamics (PSID), begun in 1968, is a longitudinal study of
a representative sample of U.S. individuals. The sample size has grown from 4,800 families
in 1968 to more than 7,000 families in 2001. I use the waves from 1980 until 2007, and
only the cross-sectional national sample. I use the PSID data set in order to estimate
the income process for different education categories. Also, with the PSID data set I am
able to calculate the wage ratios of different education groups which I use to calibrate the
productivity parameters of the production function and the degree of complementarity among
different categories of human capital.
7.1.1
Sample Selection and Estimates
In order to estimate the income process, I use the labor income of the males who are
the household head at the time of the interview. I only use incomes which are greater than
$600 in 2000 prices or smaller than $750, 000. I restrict my sample to ages between 19 and
63. In order to calculate the education level, I use the number of years of education of an
individual, in combination with the highest degree obtained.
Using all the observations I construct a small panel which has an individual’s average
income at different periods of his life. The main reason for the construction of the panel is
so that I can account for individual fixed effects. In this way I am trying to separate the
effect of experience from the effect of cognitive ability on wages.
The periods that I use in order to calculate average incomes, match the periods of the
model. For example, for the first period, I take the labor income of individuals between the
age of 19 and 27 and calculate an average over this period. This average is the income of
my first period. The length of the created panel is 4. For more precise estimates I drop
individuals that have less than two observations each period.
37
After obtaining average incomes, I regress the log of the average incomes on a polynomial
in period of order 4, for each education group. The results of the estimation are given in
Table 9. The standard errors in the parenthesis are clustered at the individual level.
The average income for each education group together with the standard deviation of
the pooled labor income, are also used as moments to match in order to calibrate the model.
These estimates are given in Table 10.
7.2
NLSY79 Data
The NLSY79 is a nationally representative sample of 12,686 young men and women
who were 14-22 years old when they were first surveyed in 1979. These individuals were
interviewed annually through 1994 and are currently interviewed on a biennial basis. In
order to estimate the effect of cognitive ability on labor income I use all the waves from 1979
up until 2008.
7.2.1
Returns to Ability
As measure of income I use both the annual labor income of males and females. I only
keep observations that are not enrolled during the year of the interview. Last, I keep only
observations with positive annual labor income. As a measure of cognitive ability I use the
Armed Force Qualification Test(AFQT) scores which were revised in 1989.
Using the same method as with the PSID data, I construct a panel with the average
period incomes. Now I only have four periods since the oldest individual in my sample is
54 years old. From the period income, I subtract the age effects which I estimated from the
PSID data set. Then I regress the residual log incomes on log AFQT and period dummies. I
do this for every education groups and for the whole sample. The effects of cognitive ability
together with the interaction terms are presented on Table 11. The standard errors are
clustered at the individual level. It seems that returns to ability are initially high for high
school graduates but do not increase during the lifetime. For college drop-outs seems that
there is some sort of penalty initially but returns increase during the life-cycle.
7.3
NLSY97 Data
The National Longitudinal Survey of Youth 1997 (NLSY97) consists of a nationally representative sample of approximately 9,000 youths who were 12 to 16 years old as of December
31, 1996. I use the full data set from 1997 until 2008 in order to estimate important features
of the structure of higher education in the United States, such as enrollment and graduation
38
rates, or the graduation time from different colleges. Also using the same data set I extend
the analysis of Belley and Lochner [2007] and calculate the importance of parental income
for college enrollment, college quality and college graduation. Last I estimate the average
transfers of parents towards their children. These transfers are estimated for each parental
income quartile.
7.3.1
Sample Selection
For my sample selection and estimation of the importance of parental income, I follow
closely Carneiro and Heckman [2002] and Belley and Lochner [2007]. I use the full data
set from 1997 up until the most recent available wave, which is 2008. I only use the crosssectional sample and drop observations who do not live with their parents during 1997.
As a measure of cognitive ability I use the AFQT test scores and I assign each individual
into a AFQT quartile. As a measure of parental income I construct an average of family
income from 1997 until 2001. By averaging out I am able to eliminate some of the temporary
fluctuations in income, or measurement error. As a result, I can have a more correct measure
of permanent family income during the years which are most important for college decisions.
Starting from 2008 and checking each year’s enrollment status I can identify if an individual has enrolled in college or not. Starting from 1997 and checking each year’s enrollment
status I can see if the first institution that a person enrolled was a two-year or a four-year college. Last by using each year’s enrollment status and the highest degree I assign individuals
into college graduates or drop-outs.
7.3.2
Returns to Ability
As a measure of income, I use annual labor income from 1997 until 2008. I only keep
observations that are not enrolled in college during the year of the interview. With these
observations I construct the average income over this period. Then I regress the log of the
average income on the log of AFQT for all education groups. The results are shown in Table
12. The coefficient for the hole sample is very similar to the estimate I obtain from the
NLSY79 data set. Again the returns to ability for the college drop-outs are smaller than
those of high school graduates.
7.3.3
The Importance of Parental Income for Education Decision
In order to estimate the number of people who would change their college decision if their
parents belonged to the highest income tercile, I regress college decision on parental income
39
tercile dummies and a set of control for each AFQT tercile. The descriptive statistics of the
set of controls, together with other constructed variables can be seen in Table 18 in section
7.7.
The difference between the coefficient of the highest income tercile and the coefficient
of another income tercile is the gap in education decision that is created solely because of
parental income. If I multiply this gap with the percentage of population that belongs to this
AFQT and parental income tercile I have an estimate of the percentage of the population that
would change its education decision if their parents belonged to the highest income tercile.
If I sum up over all the AFQT, and parental income tercile, I have the total percentage of
the population that would change its decision. The estimates of the gaps, together with the
standard errors are given in Table 13. Table 14 presents the estimates of the percentage of
the population that would change their college decision.
These estimates are relatively higher than the ones by Carneiro and Heckman [2002].
Also it is important to notice than the total percentage of the population that would change
their college decision is more than 19%. This is approximately five times higher than the
number that Restuccia and Urrutia [2004] use in order to calibrate the strength of the credit
constraints in their economy.
7.3.4
Parental Transfers
The importance of parental income for college decisions has been interpreted by the
literature as an indication of credit constraints. However as shown by Keane and Wolpin
[2001], although parental transfers are important, increasing credit limits might not change
education decision. Despite of the importance of parental transfers, Keane and Wolpin do
not use actual data for these transfers. With the NLSY97 data set I can estimate the average
transfers that children receive during college age.
The variable that I use in order to estimate average college transfers is constructed by
the answer to the following question :Altogether, how much [has/did] your [parents, mother.
father, grandparents, friends, other] [given/give] you in gifts or other money you are not
expected to repay to help pay for your attendance at this school/institution during this
term?. I include zero transfers in my sample, but missing values are dropped out. The years
that I use are from 1998 until 2006, and I only keep individuals that are enrolled in college
during the interview year.
In order to calculate average transfers that parents make to their children even if they
are not enrolled, I use two other questions of NLSY97. The first question refers to the total
amount of allowance that parents give to the child. The second question is the total amount
40
of income (besides allowance) that parents give to the child. By summing up these two
variables, I construct the unconditional transfers. If the total amount of income that parents
give to the child is missing, then I use the total amount of income that the father or the
mother gives to the child. I only keep individuals that are not enrolled in college. I sum
up the yearly transfers so as to create total transfers for the ages 18-28. The average and
median total transfers by parental income are shown in Table 15.
It is obvious from Table 12 the difference in parental transfers between rich and poor
families. However, this difference is mainly for college transfers. Parents that belong to the
highest income tercile give to their children on average more than three time the amount
than parents who belong to the lowest income tercile do. This difference increases even more
if we focus on median transfers. For unconditional transfers the difference for the means is
approximately 32%.
7.3.5
U.S. Census Bureau Data
The U.S. Census Bureau conducts a Census of Government Finance and an Annual Survey
of Government Finances. The Census of Government Finances has been conducted every
5 years since 1957, while the Annual Survey of Government Finances has been conducted
annually since 1977 in years when the Census of Government Finances is not conducted.
The Annual Survey of Government Finances, covers the entire range of government finance
activities-revenue, expenditure, debt, and assets.
The Census of Governments Survey of Local Government Finances -School Systems collects data on the financial activity of public elementary and secondary school systems from
each state. The survey cycle begins in January when states begin submitting data for the previous fiscal year. The data collection process is typically completed by April of the following
year. The information included is intended to provide a complete picture of a government’s
financial activity.
For my analysis I use data from 1992-2000. These are the years in which the cohorts of
the NLSY97 are enrolled in elementary and middle schools. From my sample I drop schools
that have less than 100 pupil. Using these years I construct an averages of revenues and
expenditures at a county level. The summary statistics for the total averages expenditures
are presented in Table 16a. Table 16b shows the summary statistics for the county level
averages.
Using the BLS geocode identifiers, I connect these county level early expenditures with
the NLSY79 Child data. Individuals that live in the same county are assumed to have the
same local and government early expenditures. Hence I will try to see how much of the
41
variation in cognitive abilities can the cross county variation in expenditures explain.
7.4
NPSAS
The NPSAS is a comprehensive study that examines how students and their families pay
for postsecondary education. It includes nationally representative samples of undergraduates,
graduate and first-professional students; students attending public and private less-than-2year institutions, community colleges, 4-year colleges, and major universities
As the cost of higher education for different colleges I use estimates of the net cost of
attendance from the NPSAS:04. As argued by Kaplan [2010] more than 45% of individuals
of between ages of 17 and 23, who do not attend college, do not move away from their home.
Also in his sample more than 40% of the individuals that did move, at some point they
returned back home. From this evidence it seems that a very large part of individuals that
do not go to college, use their parental home as a way to save on expenses. Hence, in order
to calculate the average attendance cost of college I use a weighted average of the net cost
of attendance and of the net tuitions.
The net price of attendance is the price that students and their families pay to attend a
postsecondary institution after taking financial aid into account. This price is calculated by
subtracting total financial aid from the sum of tuition, fees and other college expenses. The
amount of loans that a student may take is not included since this is going to be a choice
variable in my model. Also in the other college expenses the cost of living is also included.
The average prices are calculated by taking into account all students and not only those who
receive some grand.
Net tuition is defined as total tuition and fees minus all grants. For my model I use the
annual values from the NPSAS:04 and inflate them by the average time that students spend
in college. These estimates are given in Table 17.
7.5
Computational Procedures
In order to solve the model, I discretize the state space. First I choose grid points for the
ability space and the early educational expenditures space. The number of grids are denoted
as Na and Ne . I use Na = 9 and Ne = 10. The educational expenditures are on the range of
[0.02, 0.3] and are not equally spaced. For lower expenditures I make the grid points finer.
√
For innate ability, using the Tauchen’s method30 , ln(a) lies in the range ±3σa / 1 − ρa .
30
Tauchen 1986[53]
42
Having constructed the ability space and the early expenditure space, I construct the
acquired ability space using the functional form I have assumed. The number of grids for
the acquired ability space will be Na Ne . The number of grid points for asset holdings Nq
and transfers Ntr that I use is 30.
After I have constructed the state space I solve backwards the value functions starting
from the last period until period 4. I make an initial guess for the value function at period
1. Given V10 , V41 , and using the law of motion and expectations over the ability shock I can
update V31 . Given V31 , and the law of motion we can obtain V21 . Given V21 the stochastic
process for innate ability, and the law of motion I can obtain V11 . I check for convergence
between V10 and V11 . If the value functions are close we set V10 =V11 , otherwise I continue the
iteration process. Using the value functions I obtain the policy functions.
Having the policy functions in hand I can simulate the economy. After drawing an initial
distribution of education, assets, AFQT and child’s innate ability for parents in period 2,
I simulate the economy for 10.000 individuals and 100 periods. Once the economy has
converged to a stationary distribution I, estimate the different moments of the economy.
The method I use to estimate the parameters is that of simulated method of moments. The
estimator is such that :
Arg min[φ − φ(θ)sim ] W −1 [φ − φ(θ)sim ]
θ
Where φ are the true moments and φ(θ)sim are the simulated moments, which depend
on the parameters of the model. As a weighting matrix W, I use the identity matrix. I
minimize this function using the Nelder-Mead Simplex Algorith. Overall I use 53 moments
to estimate 32 parameters. The estimates for the benchmark model are presented in Tables
18a, 18b and 18c .
43
8
Figures and Tables
Figure 1: Annual Primary and Secondary Expenditures per Pupil
$10,000
$9,384
$9,000
$8,000
$6,809
$7,000
$6,000
$5,566
Federal
$5,000
$4,599
State
Local
$4,000
Total
$3,000
$2,000
$2,648
$1,754
$1,000
$0
TotalExp_T1
TotalExp_T2
TotalExp_T3
Source:Public Elementary and Secondary Education Finance Data from the U.S Census Bureau. Annual
average expenditures per pupil in primary and secondary education. These expenditures are at a county level
and for the years 1992-2000.
44
Figure 2: College Enrollment by Parental Income and Children’s AFQT
100%
96%
90%
79%
80%
77%
70%
59%
60%
Inc_T1
49%
50%
Inc_T2
Inc_T3
40%
30%
30%
20%
10%
0%
AFQT_T1
AFQT_T2
AFQT_T3
Source: National Longitudinal Survey of Youth 1997
Figure 3: 4 Year College Enrollment by Parental Income and Children’s AFQT
100%
90%
82%
80%
70%
59%
60%
60%
Inc_T1
50%
Inc_T2
38%
40%
30%
40%
Inc_T3
27%
20%
10%
0%
AFQT_T1
AFQT_T2
AFQT_T3
Source: National Longitudinal Survey of Youth 1997
45
Figure 4: College Graduation by Parental Income and Children’s AFQT
100%
90%
80%
74%
70%
60%
56%
53%
Inc_T1
50%
Inc_T2
41%
Inc_T3
40%
30%
29%
24%
20%
10%
0%
AFQT_T1
AFQT_T2
AFQT_T3
Source: National Longitudinal Survey of Youth 1997
Figure 5: Total College Transfers by Parental Income and Children’s AFQT
$25,000
$21,256
$20,000
$15,000
Inc_T1
$12,082
Inc_T2
$10,000
Inc_T3
$9,086
$7,983
$5,000
$4,351
$3,531
$0
AFQT_T1
AFQT_T2
AFQT_T3
Source: National Longitudinal Survey of Youth 1997
46
Figure 6: Timing of the Model
Periods
College Period
Actions Consumption/
Savings
College
Graduation
Investment in Children
Life After Children
Consumption/ Consumption/ Consumption/
Savings
Savings
Savings
Early
Education
Investment
Retirement
Consumption/
Savings
College
Enrollment
Transfers
Figure 7: Timing of the Model
Periods
Parents
Age
College
19--27
Investment in
Children
28-36
37-45
Periods
Children
Age
Life After Children
46-54
College
0--9
10--18
19--27
55-63
Retirement
64-72
Investment in
Children
28-36
37-45
Periods
Grand
Children
73-81
Life After
Children
46-54
College
Age
0--9
47
10--18
19--27
Figure 8: College Decisions by Parental Income or Children’s AFQT
College Enrollment by Income
College Enrollment by AFQT
100%
100%
Data
Model
50%
0%
50%
0%
income−Tercile1 Income−Tercile2 Income−Tercile3
4 Year College Enrollment by Income
100%
50%
50%
0%
income−Tercile1 Income−Tercile2 Income−Tercile3
College Graduation by Income
AFQT−Tercile3
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
College Graduation by AFQT
100%
100%
50%
50%
0%
AFQT−Tercile2
4 Year College Enrollment by AFQT
100%
0%
AFQT−Tercile1
0%
income−Tercile1 Income−Tercile2 Income−Tercile3
48
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
Figure 9: College Enrollment by Parental Income and Children’s AFQT
College Enrollment Data
100%
College Enrollment Model
100%
Income−Tercile1
Income−Tercile2
Income−Tercile3
50%
0%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
0%
Four−Year College Enrollment Data
100%
50%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
0%
College Graduation Data
100%
50%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
College Graduation Model
100%
0%
AFQT−Tercile2
Four−Year College Enrollment Model
100%
0%
AFQT−Tercile1
AFQT−Tercile3
49
0%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
Figure 10: College Enrollment by Parental Income and Children’s AFQT with
Minimum Early Expenditures
College Enrollment Benchmark
100%
College Enrollment Model
100%
Income−Tercile1
Income−Tercile2
Income−Tercile3
50%
0%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
0%
Four−Year College Enrollment Benchmark
100%
50%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
0%
College Graduation Benchmark
100%
50%
50%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
College Graduation Model
100%
0%
AFQT−Tercile2
Four−Year College Enrollment Model
100%
0%
AFQT−Tercile1
AFQT−Tercile3
50
0%
AFQT−Tercile1
AFQT−Tercile2
AFQT−Tercile3
Table 1 : ”Higher Education Outcomes By Family Income ”
Income Tercile
College Enrollment
4 Year College
Graduation Rates
1st Tercile
44%
42%
35%
2nd Tercile
62%
54%
46%
3rd Tercile
81%
69%
62%
Source: Author’s Calculations from NLSY97
Table 2: The Effect of Innate Ability and Early Education Investment
Log Piat Math (age14-15)
log Body Parts
log Local Rev
log Gov Rev
Female
R2
Observations
All
Only White
Only White and Under 3
0.245***
0.204**
0.230*
(0.048)
(0.079)
(0.089)
0.161
0.297*
0.358*
(0.096)
(0.129)
(0.140)
0.098
0.203
0.305
(0.184)
(0.228)
(0.258)
-0.119
-0.186
-0.235
(0.090)
(0.113)
(0.127)
0.056
0.052
0.070
504
269
223
Standard errors in parentheses ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
51
Table 3a: Benchmark Model: Mobility
Data
Model
Intergenerational Elasticity
0.5
0.485
Mobility Index
0.86
0.824
Intergenerational Education Correlation
0.45
0.436
Correlation AFQT and Parental Income
0.31
0.34
Intergenerational Correlation in AFQTs
0.42
0.45
Mobility
Table 3b: Benchmark Model: Early and Higher Education
Data
Model
Q3/Q1
2.6
2.4
Q2/Q1
1.5
1.5
$3,600
$2,824
College Enrollment
0.63
0.62
4-Year College Enrollment
0.35
0.35
2-Year College Enrollment
0.28
0.27
4-Year College Graduates
0.68
0.675
2-Year College Graduates
0.32
0.34
Early Education Expenditures
Average Private Expenditures
Higher Education
52
Table 3c: Benchmark Model: Income
Data
Model
$45,403
$46,573
0.64
0.36
Mean Wages of High School Graduates
$34,091
$34,308
Mean Wages of College Drop-Outs
$40,894
$ 41,097
Mean Wages of 2-Year College Graduates
$50,955
$52,791
Mean Wages of 4-Year College Graduates
$66,193
$70,455
Income Distribution
Mean Wages
Standard Deviation of log(Mean Wages )
53
Table 4a: The Effect of Early and Higher Education in Generating Persistence
Model
No Early Education
No Higher Education
Minimum Expenditures
College Cost=inf
0.484
0.35
0.39
IncQ3/Q1
1.73
1
1.37
IncQ2/Q1
1.38
1
1.19
$2,824
$800
$1,973
College Enrollment
0.62
0.63
0
College Graduation
0.525
0.534
0
4-Year College
0.35
0.36
0
2-Year College
0.27
0.27
0
Mobility
Intergenerational Elasticity
Early Education Expenditures
Average Private Expenditures
Higher Education
54
Table 4b: The Effect of Early and Higher Education in Generating Persistence
No Early Education
No Early Education
2 and 4-year College
Only 2-year College
0.35
0.146
College Enrollment
0.63
0.536
College Graduation
0.534
0.33
4-Year College
0.36
0
2-Year College
0.27
0.536
Mobility
Intergenerational Elasticity
Higher Education
55
Table 5: The Effect of Early and Higher Education in Reducing Persistence
Model
Free Early Education
Free Higher Education
Maximum Expenditures
College Cost=0
0.484
0.43
0.33
IncQ3/Q1
1.73
1
1.38
IncQ2/Q1
1.38
1
1.15
$2,824
$8,800
$4,000
College Enrollment
0.62
0.81
0.89
College Graduation
0.525
0.513
0.67
4-Year College
0.35
0.41
0.89
2-Year College
0.27
0.4
0
Mobility
Intergenerational Elasticity
Early Education Expenditures
Average Private Expenditures
Higher Education
56
Table 6: Credit Constraints in Higher Education
Model
Mobility
Reducing College Constraints
Reducing Post-College Constraints
(increase limits by 50%)
(increase limits by 50%)
Intergenerational Elasticity
0.485
0.465
0.44
Average Private Expenditures
$2,824
$ 2,869
$ 2,893
College Enrollment
0.62
0.628
0.652
College Graduation
0.532
0.55
0.555
4-Year College
0.35
0.4
0.41
2-Year College
0.27
0.224
0.242
4-Year College Constrained
0.23
0
0.302
2-Year College Constrained
0.06
0
0.083
Table 7: Complementarities Between Early and Higher Education
Free Early Education
Free Higher Education
Maximum Expenditures
College Cost=0
Subsidizing Early and
and Higher Education
(subsidize cost by 50%)
Intergenerational Elasticity
0.43
0.33
0.1052
College Enrollment
0.817
0.89
0.95
College Graduation
0.514
0.675
0.675
4-Year College
0.42
0.89
0.95
2-Year College
0.397
0
0
Mobility
57
Table 8: Distributional Effects
Model
Free Early Education
(Maximum Expenditures)
Free Higher Education
(College Cost=0)
1-Mobility Index
0.1764
0.1786
0.1854
1-Mobility of Poor (1-5 decile)
0.0974
0.0868
0.1108
1-Mobility of Rich (6-10 decile)
0.079
0.0918
0.0746
Mobility
Table 9: Period polynomials’ coefficients
High School
Graduates
period
period2
period3
period4
R2
Observations
Log Period Average Income ($2000)
College
Two-Year
Drop-Outs
College Graduates
Four-Year
College Graduates
0.377***
(0.062)
-0.183*
(0.078)
0.050
(0.032)
-0.006
(0.004)
0.561***
(0.099)
-0.307*
(0.123)
0.084
(0.050)
-0.009
(0.006)
0.572**
(0.172)
-0.257
(0.205)
0.071
(0.083)
-0.009
(0.010)
0.979***
(0.093)
-0.396***
(0.108)
0.086*
(0.043)
-0.008
(0.005)
0.147
3885
0.190
1544
0.240
580
0.417
2237
Standard errors in parentheses ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
58
Table 10: Log Annual Average Income ($2000)
High School
College Drop-Outs
Two-Year College
Four-Year College
Pooled
Mean
10.288
10.470
10.667
10.894
10.517
Sd
0.568
0.564
0.591
0.636
0.642
Observations
3885
1544
580
2237
8944
Table 11: The Returns to Cognitive Ability-NLSY79
Log Period Average Income ($2000)
logAFQT
logAFQT*period2
logAFQT*period3
logAFQT*period4
Female
Not White
R2
Observations
High School
Some College
College Graduates
Pooled
0.184***
(0.01)
0.010
(0.012)
0.014
(0.014)
0.009
(0.020)
-0.540***
(0.017)
-0.058**
(0.020)
0.098***
(0.024)
0.021
(0.024)
0.043
(0.030)
0.07
(0.038)
-0.440***
(0.025)
0.009
(0.03)
0.158***
(0.038)
0.059
(0.040)
0.079
(0.043)
0.142
(0.074)
-0.497***
(0.027)
0.075*
(0.032)
0.283***
(0.010)
0.008
(0.009)
-0.037**
(0.011)
0.045*
(0.017)
-0.489***
(0.016)
0.124***
(0.018)
0.192
17548
0.144
7017
0.189
6053
0.164
33521
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
59
Table 12: The Returns to Cognitive Ability-NLSY97
logAFQT
Female
Not White
R2
Observations
High School
Log Period Average Income ($2000)
Some College College Graduates
Pooled
0.076***
(0.021)
-0.451***
(0.038)
-0.238***
(0.039)
0.054*
(0.026)
-0.322***
(0.036)
-0.043
(0.040)
0.149***
(0.033)
-0.139***
(0.034)
0.040
(0.036)
0.298***
(0.014)
-0.295***
(0.022)
-0.092***
(0.025)
0.082
2546
0.044
2003
0.023
1691
0.145
5915
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Table 13: Gaps in College Decision by Parental Income
AFQT T1
AFQT T2
AFQT T3
College Enrollment
t3-t1
0.160
0.110
0.129
t3-t2
0.085
0.058
0.060
Four versus Two-year College
t3-t1
0.137
0.121
0.121
t3-t2
0.067
0.122
0.055
College Graduation
t3-t1
0.152
0.128
0.024
t3-t2
0.034
0.076
0.071
60
Table 14: Percentage of Population Constrained
AFQT T1
AFQT T2
AFQT T3
Total
College Enrollment
t1
0.0258
0.0096
0.0073
0.0427
t2
0.0091
0.0074
0.0068
0.0233
Total
0.0349
0.0170
0.0140
0.0659
Four versus Two-year College
t1
0.0199
0.0117
0.0088
0.0403
t2
0.0072
0.0151
0.0065
0.0288
Total
0.0271
0.0267
0.0153
0.0691
College Graduation
t1
0.0220
0.0123
0.0017
0.0360
t2
0.0037
0.0093
0.0084
0.0214
Total
0.0256
0.0216
0.0102
0.0574
Total
0.1924
61
Table 15: Total Parental Transfers
T1
T2
T3
Mean
$5,167
(341)
$7,840
(358)
$16,680
(576)
Median
$1,664
$3,516
$8,648
$1,777
(95)
$2,109
(135)
$2,349
(234)
$990
$1,000
$1,198
Parental Income Tercile
Conditional
Unconditional
Mean-NonCollege
Median-NonCollege
Standard errors in parentheses
Table 16a: Average Early Expenditures
Table 16b: Average Early Expenditures
Total Revenues
$7723
(10.90)
$7739
(10.97)
$454
(2.38)
$3617
(6.09)
$3651
(9.08)
County Total Revenues
116048
Observations
Total Expenditures
Federal Revenues
State Revenues
Local Revenues
Observations
County Total Expenditures
County Federal Revenues
County State Revenues
County Local Revenues
62
$7284
(42.89)
$7274
(39.67)
$538
(8.76)
$3730
(25.04)
$3016
(40.10)
3127
Table 17: College Costs
Net Price of Attendance ($2000)
Two-Year
Graduates
Four-Year
Graduates
Two-Year
Drop-Outs
Four-Year
Drop-Outs
$15,801
$18,961
$23,920
$25,962
$27,712
$38,119
$48,792
$59,136
$65,743
$79,082
$7,407
$8,888
$11,213
$12,170
$12,990
$18,265
$23,380
$28,336
$31,502
$37,893
Parental Income
Less than $20,000
$20,000-39,999
$40,000-59,999
$60,000-90,000
More than $90,000
Net Tuition ($2000)
Less than $20,000
$20,000-39,999
$40,000-59,999
$60,000-90,000
More than $90,000
$1,459
$1,750
$2,917
$3,209
$2,236
$13,275
$17,062
$21,792
$25,144
$33,076
63
$684
$820
$1,367
$1,504
$1,572
$6,361
$8,175
$10,442
$12,048
$15,849
Table 18a : ’Parametrization of the Benchmark Economy”
Parameters set Externally
Parameter
Description
Value
β
Discount factor
σ
Risk aversion parameter
r
Interest Rate
nθs
Time spent in college
taul
Labor tax rates
0.637, -0.136
tauk
Capital tax rate
0.4
p
Replacement rate
0.24
ζ
Returns to AFQT
0.4
ked
j
Wage period constant
g
Government early expenditures
f(s)
College Cost
See Appendix
gsc (Ip, ac )
College Aid
See Appendix
0.76
1.5
0.55
0.11, 0.22, 0.39, 0.55
See Appendix
0.1
Table 18b : ’Parametrization of the Benchmark Economy”
Parameters Calibrated Internally
Parameter
Description
Value
ω
Warm glove parameter
0.6
σa
Innate ability sd
0.8
ρa
Innate ability correlation
γ1
Returns to early education
γ0
Returns to innate ability
0.25
s
Share of private expenditures
0.47
a4gov
a2gov
a1gov
4-Year College borrowing limits
0.27
2-Year-College borrowing limits
0.193
Drop-Out borrowing limits
0.03
apvt
High-School Graduates borrowing limits
0.01
64
0.25
0.6
Table 18c : ’Parametrization of the Benchmark Economy”
Parameters Calibrated Internally
Parameter
Description
Value
w0
Wage of High-School Graduates
0.22
w1
Wage of College Drop-Outs
0.23
w2
Wage of 2 -Year College Graduates
0.26
w4
Wage of 4 -Year College Graduates
0.26
ps0
High School Graduation Parameter
0.5
ps1
High School Graduation Parameter
0.05
ps2
High School Graduation Parameter
0.57
mean(ψ2 )
Psychic cost of 2 Year College Graduates
0.7949
mean(ψ12 )
Psychic cost of 2 Year College Drop-Outs
0.2310
mean(ψ4 )
Psychic cost of 4 Year College Graduates
1.0576
mean(ψ14 )
Psychic cost of 2 Year College Drop-Outs
0.3707
std(ψ2 )
Psychic cost of 2 Year College Graduates
0.6481
std(ψ4 )
Psychic cost of 4 Year College Graduates
0.6211
65
Table 19: Sample Descriptive Statistic
Completed High School
89.81%
Attended College
63.04%
First Enrolled in a Two-year College
42.43%
Male
51.40%
Black
16.06%
Latino
13.57%
Asian
23.80%
Living in North Central at age 12
26.73%
Living in the South at age 12
34.12%
Living in the West at age 12
20.41%
Intact Family during Adolescence
54.10%
Mother’s Age at Birth
23.33
Mother HS Graduate
81.89%
Mother at Least Some College
44.88%
Mother College Graduate
20.12%
Average Family Income in Tercile 1
$ 18,547
Average Family Income in Tercile 2
$47,955
Average Family Income in Tercile 3
$110,785
Household Size
4.4
Sample Size
6599
66