The Structure of Early and Higher Education, DynamicInteractions 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 ofcross-sectional inequality that will be transmitted to future generations. Low intergenera-tional mobility implies that inequality will be persistent. With income inequality increasingrapidly over the recent years, it is important to understand the underlying sources andmechanisms of intergenerational earnings persistence. This paper examines the mechanismsthrough which early and higher education (individually and jointly) impact intergenerationalearnings mobility. More specifically, I explore the effects that the structure of the educationsystem and existing methods of financing education can have on earnings persistence. Inorder to quantify these effects, I develop a life-cycle model of incomplete markets whereagents differ in wealth, ability, and education. Intergenerational persistence of earnings isgenerated endogenously as richer parents invest more in the early and higher education oftheir children. Early education investments affect the cognitive ability of children. Higherability children earn higher wages, but also have a lower cost of enrolling in college. Highereducation investments, through parental transfers, affect college enrollment, college qualityand college graduation rates. I use PSID, NLSY, NPSAS, and Census micro data to esti-mate the parameters of the model. I find that differences in higher education account for ahigher percentage of the intergenerational correlation in earnings than do differences in earlyeducation. 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 ineducation. Finally, I find that early education is more important for the upward mobility oflow income families.

∗I want to thank my advisors, Gianluca Violante, Christopher Flinn, Matthew Wiswall and Ahu Gemici fortheir valuable comments and encouragement. I have also benefited a lot from discussions and comments fromRaquel Fernandez, Lance Lochner, Joyce Cheng Wong, Ergys Islamaj, Albert Queralto, Saki Bigio, as wellas 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 researchwas conducted with restricted access to Bureau of Labor Statistics (BLS) data. The views expressed heredo 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.

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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 chil-

dren’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 comple-

mentarities 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 het-

erogeneous agents and incomplete markets where agents make decisions about investment in

1See section 2 for a documentation of these facts.2There are several papers that document this variation in local expenditures. See for example Hoxby

[1998], or Corcoran and Evans [2008].3This 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.

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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 gov-

ernment. 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,

4The 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.

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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 com-

plementarities 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

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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 in-

vestment 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 con-

straints 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 equi-

librium 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

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[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 edu-

cation. 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 distri-

butional 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

5Garriga, and Keightley [2007] are the only paper that allow for endogenous drop-out decisions6Kean 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 transfers7By 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] andHoekstra [2009] find that there are important returns to college quality.

8Meghir and Palme [2005], and Pekkarinen, Uusitalo and Kerr [2009] find that allowing individuals tohave a choice on school quality increases inequality and reduces mobility

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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:

ysit = c+ βyfit + γ1Asit + γ2(A

sit)

2 + γ3Af

it + γ4(Af

it)2 + εit

where ysit is the log of the income of the son, yfit is the log of the average income of the

father, Asit is the age of the son and Af

it 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 de-

gree 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. Intergenera-

tional 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

9See Black and Devereux [2010] for a recent literature review.

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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 in-

tergenerational 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

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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

10I use this test because it is one of the few available tests at such a young age. At the same time it is avery good predictor of the cognitive ability of the child at a later age

11The correlation of Body Parts and AFQT scores is not a correlation of innate abilities because AFQTis also affected by early education. Nevertheless I use this correlation as a target and in order to estimatethe true correlation of innate abilities.

12See the appendix for the details on the estimation of early expenditures.

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together is only 25%.

Local revenues are mainly consisted of property taxes and parent government contribu-

tions 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%

13These two together explain more than 85% of the variation in local revenues.14It 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 detailson the estimation].

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 num-

bers 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.

15This number is almost five times higher than the one that Restuccia and Urrutia [2004] use in order tocalibrate their model. This is one of the reasons as to why I reach into different conclusions about the effectof higher education on mobility.

16During ages 0-9 and 10-18 the child makes no economic decisions. I have included these ages in thetiming 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 abil-

ity. 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) = max

cj≥0, ε≥0

{U(cj) + βEhsg[Vj+1(ac, a

chc , qj+1

, hsg, ed)}

]

s.t. (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 = wedeedj (ac)

achc = φ(ach, ε, g)

qj+1 ≥ −αpvtj

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 ε {0, 1, 2, 4}, respectively for high school graduates, college dropouts, two-

year college graduates and four-year college graduates. Cognitive ability and the education

level determines the efficiency unit of labor eedj (ac), while the constant wage wed for each

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*.

17I present the problem of the agent in the first period after the description of the third period. Since thegenerations 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 achc in the

next period through the production function φ(ach, ε, g). High school graduation, takes two

values, hsg ε {0, 1}, respectively for high school dropouts and graduates. The probability of

graduating from high school p(achc ) 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 αpvtj .

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:

V sj (ac, a

chc , qj , hsg, ed) = max

cj≥0, tr≥0

{U(cj) + βVj(ac, qj+1

, ed) + βωEv[Wθj (achc , tr, Ip, s, a, v)]

}s.t. (1 + τc)cj + qj+1 + tr = wj + (1 + r)qj −T (wj, qj)

wj = wedeedj (ac)

qj+1 ≥ −αpvtj

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

sε{0, 2, 4} defines the higher education institution at which the child was sent and respec-

tively 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, achc , qj+1

, hsg, ed) = maxsε{0,2,4}

{V s

j(ac, a

chc , qj+1

, hsg, ed)}

3.2.3 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) = maxθε{0,1}

{V θ0j (ac, tr, Ip, s, a, v), V θ1

j (ac, tr, Ip, s, a, v)}

Where V θ1j 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:

V θj (ac, tr, Ip, s, a, v) = max

cj≥0

{U(cj)− ψ(nθs, ac, v) + βEach [Vj+1(ac,qj+1, a

ch, ed)|a]}

s.t. (1 + τc)cj + qj+1 = wj(1− nθs) + (1 + r)tr −T (wj, tr)− nθs(f(s)− gs(Ip,ac))

wj = wedeedj (ac)

qj+1≥ −nθsαgov if − nθs > 0

qj+1≥ −αpvtj 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 ε {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

18The college enrollment is defined by s while college graduation by θ. So for example if s=2 and θ=1 theperson 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 gsc(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) − gsc(Ip,ac)), but also the psychic cost ψ(nθs, ac, v) and the opportunity

cost wedeedj (ac)nθs. 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) = maxcj≥0

{U(cj) + βVj+1(ac,qj+1

, ed)}

s.t. (1 + τc)cj + qj+1 = wj + (1 + r)qj −T (wj, qj)

wj = wedeedj (ac)

qj+1≥ −αpvtj

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) = maxcj≥0

{U(cj) + βVj+1(qj+1

, ed)}

s.t. (1 + τc)cj + qj+1 = ped + (1 + r)qj −T (ped, qj)

qj+1≥ −alphapvtj

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)};Measures {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∑

ed=1

ped7∑j=6

∫χj

dµedj (χj) +

(I{q1 < 0, s > 0}

∫χ1

q1(χ1)dµ1(χ1)

)+Gc +G =

= τcC + τkrK + τl

4∑ed=1

5∑j=1

∫χj

wedeed(χj)dµj(χj) + (1 + r∗)

(I{q2 < 0, s > 0}

∫χ2

q2(χ2)dµ2(χ2)

)

Where aggregate government expenditures Gc, in higher education subsidies equals

Gc =

∫χ1

n1g2c (Ip, ac)I{θ = 0}I{s = 2}dµ1(χ1) +

∫χ1

n1g4c (Ip, ac)I{θ = 0}I{s = 4}dµ1(χ1) +

+

∫χ1

n2g2c (Ip, ac)I{θ = 1}I{s = 2}dµ1(χ1) +

∫χ1

n4g4c (Ip, ac)I{θ = 1}I{s = 4}dµ1(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 pa-

rameters 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 restric-

tions 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

U(cj) =c̃1−σj − 1

1− σc̃j =

cj1.3

if j = 2, 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:

ψ(nθs, ac, v) =nθs

m0(1 + ac)m1+ v

v ∼ N(µv, σ2v)

18

The disutility from college is increasing in the time that you are enrolled nθs and de-

creasing 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 σ2v is calibrated so that they match the average

drop-out rate of two and four year colleges. However these parameters also affect the en-

rollment 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 cor-

related. 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, σ2u)

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 σ2u 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 [sεε+ (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 cogni-

tive 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:

p(achc ) = min(1, ps0 + ps1 ∗ (achc )ps2)

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

19See 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

lnWj(ac, ed) = lnwed + ζed ln ac + kedj

where wed can be thought as the marginal product of human capital for each education

category. ζed is the marginal effect of the log of cognitive ability and kedj 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.

20The cost of college that I use in the model is a weighted average of the net price of attendance and ofthe net tuition. I assume that 40% of the students live with their parents and pay only the net tuition, whilethe rest pay the total attendance cost.

21See 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

T (wj, qj) = (wj − τ 1Lwτ2L+1j

τ 2L + 1) + rτKqj

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 τ 1L = 0.637 and τ 1L = −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

22The 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 educa-

tion 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 ag-

gregate. 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 corre-

lation 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.

23As a comparison the model of Restuccia and Urrutia [2004] generates a ratio of the third over the firstearly 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 The Effect of Early and Higher Education on Mobility

5.3.1 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 per-

sistence is generated only because of the correlation of the innate ability and the investment

in early education.

24For 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 per-

sistence, 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

25This amount is the minimum amount that individuals are willing to invest in the estimated model.26Since 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 intergenerationalcorrelation in cognitive abilities in the benchmark model is 0.45

27This is approximately the number that Restuccia and Urrutia estimate when they impose no earlyeducation.

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 every-

one 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.

28The average period wage of a 4-year college graduate is more than double the wage of a high schoolgraduate. On the contrary, the wage increases by only 32% if parental investment in early education changesfrom 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 grad-

uation. 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

29The 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 experi-

ment, 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 educa-

tion 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 ac-

counts 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 rep-

resentative 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 cross-

sectional 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 indi-

vidual 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 col-

lege. 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 col-

lects 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 pre-

vious 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-2-

year 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.

30Tauchen 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 NaNe. 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 V 01 , V 1

4 , and using the law of motion and expectations over the ability shock I can

update V 13 . Given V 1

3 , and the law of motion we can obtain V 12 . Given V 1

2 the stochastic

process for innate ability, and the law of motion I can obtain V 11 . I check for convergence

between V 01 and V 1

1 . If the value functions are close we set V 01 =V 1

1 , 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 :

Argminθ

[φ− φ(θ)sim]′W−1[φ− φ(θ)sim]

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

$1,754

$2,648

$4,599

$5,566

$6,809

$9,384

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

$8,000

$9,000

$10,000

TotalExp_T1 TotalExp_T2 TotalExp_T3

Federal

State

Local

Total

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

30%

59%

77%

49%

79%

96%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

AFQT_T1 AFQT_T2 AFQT_T3

Inc_T1

Inc_T2

Inc_T3

Source: National Longitudinal Survey of Youth 1997

Figure 3: 4 Year College Enrollment by Parental Income and Children’s AFQT

27%

40%

60%

38%

59%

82%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

AFQT_T1 AFQT_T2 AFQT_T3

Inc_T1

Inc_T2

Inc_T3

Source: National Longitudinal Survey of Youth 1997

45

Figure 4: College Graduation by Parental Income and Children’s AFQT

24%

29%

56%

41%

53%

74%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

AFQT_T1 AFQT_T2 AFQT_T3

Inc_T1

Inc_T2

Inc_T3

Source: National Longitudinal Survey of Youth 1997

Figure 5: Total College Transfers by Parental Income and Children’s AFQT

$3,531 $4,351

$7,983

$9,086

$12,082

$21,256

$0

$5,000

$10,000

$15,000

$20,000

$25,000

AFQT_T1 AFQT_T2 AFQT_T3

Inc_T1

Inc_T2

Inc_T3

Source: National Longitudinal Survey of Youth 1997

46

Figure 6: Timing of the Model

Periods

College Period

Investment in Children

Life After Children

Retirement

Actions Consumption/ Savings

Consumption/ Savings

Consumption/ Savings

Consumption/ Savings

Consumption/ Savings

College Graduation

Early Education Investment

College Enrollment

Transfers

Figure 7: Timing of the Model

Parents

Periods College

Investment in Children

Life After Children

Retirement

Age 19--27 28-36 37-45

46-54

55-63

64-72 73-81

Children

Periods College Investment in Children

Life After Children

Age 0--9 10--18

19--27 28-36 37-45

46-54

Grand Children

Periods

College

Age

0--9 10--18 19--27

47

Figure 8: College Decisions by Parental Income or Children’s AFQT

income−Tercile1 Income−Tercile2 Income−Tercile3 0%

50%

100%College Enrollment by Income

DataModel

income−Tercile1 Income−Tercile2 Income−Tercile3 0%

50%

100%4 Year College Enrollment by Income

income−Tercile1 Income−Tercile2 Income−Tercile3 0%

50%

100%College Graduation by Income

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Enrollment by AFQT

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%4 Year College Enrollment by AFQT

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Graduation by AFQT

48

Figure 9: College Enrollment by Parental Income and Children’s AFQT

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Enrollment Data

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%Four−Year College Enrollment Data

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Graduation Data

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Enrollment Model

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%Four−Year College Enrollment Model

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Graduation Model

Income−Tercile1

Income−Tercile2

Income−Tercile3

49

Figure 10: College Enrollment by Parental Income and Children’s AFQT with

Minimum Early Expenditures

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Enrollment Benchmark

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Enrollment Model

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%Four−Year College Enrollment Benchmark

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%Four−Year College Enrollment Model

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Graduation Benchmark

AFQT−Tercile1 AFQT−Tercile2 AFQT−Tercile3 0%

50%

100%College Graduation Model

Income−Tercile1

Income−Tercile2

Income−Tercile3

50

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)

All Only White Only White and Under 3

log Body Parts 0.245*** 0.204** 0.230*

(0.048) (0.079) (0.089)

log Local Rev 0.161 0.297* 0.358*

(0.096) (0.129) (0.140)

log Gov Rev 0.098 0.203 0.305

(0.184) (0.228) (0.258)

Female -0.119 -0.186 -0.235

(0.090) (0.113) (0.127)

R2 0.056 0.052 0.070

Observations 504 269 223

Standard errors in parentheses ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1

51

Table 3a: Benchmark Model: Mobility

Data Model

Mobility

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

Table 3b: Benchmark Model: Early and Higher Education

Data Model

Early Education Expenditures

Q3/Q1 2.6 2.4

Q2/Q1 1.5 1.5

Average Private Expenditures $3,600 $2,824

Higher Education

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

52

Table 3c: Benchmark Model: Income

Data Model

Income Distribution

Mean Wages $45,403 $46,573

Standard Deviation of log(Mean Wages ) 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

53

Table 4a: The Effect of Early and Higher Education in Generating Persistence

Model No Early Education No Higher Education

Mobility Minimum Expenditures College Cost=inf

Intergenerational Elasticity 0.484 0.35 0.39

Early Education Expenditures

IncQ3/Q1 1.73 1 1.37

IncQ2/Q1 1.38 1 1.19

Average Private Expenditures $2,824 $800 $1,973

Higher Education

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

54

Table 4b: The Effect of Early and Higher Education in Generating Persistence

No Early Education No Early Education

Mobility 2 and 4-year College Only 2-year College

Intergenerational Elasticity 0.35 0.146

Higher Education

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

55

Table 5: The Effect of Early and Higher Education in Reducing Persistence

Model Free Early Education Free Higher Education

Mobility Maximum Expenditures College Cost=0

Intergenerational Elasticity 0.484 0.43 0.33

Early Education Expenditures

IncQ3/Q1 1.73 1 1.38

IncQ2/Q1 1.38 1 1.15

Average Private Expenditures $2,824 $8,800 $4,000

Higher Education

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

56

Table 6: Credit Constraints in Higher Education

Model Reducing College Constraints Reducing Post-College Constraints

Mobility (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 Subsidizing Early and

and Higher Education

Mobility Maximum Expenditures College Cost=0 (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

57

Table 8: Distributional Effects

Model Free Early Education Free Higher Education

Mobility (Maximum Expenditures) (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

Table 9: Period polynomials’ coefficients

Log Period Average Income ($2000)

High School College Two-Year Four-Year

Graduates Drop-Outs College Graduates College Graduates

period 0.377*** 0.561*** 0.572** 0.979***

(0.062) (0.099) (0.172) (0.093)

period2 -0.183* -0.307* -0.257 -0.396***

(0.078) (0.123) (0.205) (0.108)

period3 0.050 0.084 0.071 0.086*

(0.032) (0.050) (0.083) (0.043)

period4 -0.006 -0.009 -0.009 -0.008

(0.004) (0.006) (0.010) (0.005)

R2 0.147 0.190 0.240 0.417

Observations 3885 1544 580 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)

High School Some College College Graduates Pooled

logAFQT 0.184*** 0.098*** 0.158*** 0.283***

(0.01) (0.024) (0.038) (0.010)

logAFQT*period2 0.010 0.021 0.059 0.008

(0.012) (0.024) (0.040) (0.009)

logAFQT*period3 0.014 0.043 0.079 -0.037**

(0.014) (0.030) (0.043) (0.011)

logAFQT*period4 0.009 0.07 0.142 0.045*

(0.020) (0.038) (0.074) (0.017)

Female -0.540*** -0.440*** -0.497*** -0.489***

(0.017) (0.025) (0.027) (0.016)

Not White -0.058** 0.009 0.075* 0.124***

(0.020) (0.03) (0.032) (0.018)

R2 0.192 0.144 0.189 0.164

Observations 17548 7017 6053 33521

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

59

Table 12: The Returns to Cognitive Ability-NLSY97

Log Period Average Income ($2000)

High School Some College College Graduates Pooled

logAFQT 0.076*** 0.054* 0.149*** 0.298***

(0.021) (0.026) (0.033) (0.014)

Female -0.451*** -0.322*** -0.139*** -0.295***

(0.038) (0.036) (0.034) (0.022)

Not White -0.238*** -0.043 0.040 -0.092***

(0.039) (0.040) (0.036) (0.025)

R2 0.082 0.044 0.023 0.145

Observations 2546 2003 1691 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

Parental Income Tercile T1 T2 T3

Conditional

Mean $5,167 $7,840 $16,680

(341) (358) (576)

Median $1,664 $3,516 $8,648

Unconditional

Mean-NonCollege $1,777 $2,109 $2,349

(95) (135) (234)

Median-NonCollege $990 $1,000 $1,198

Standard errors in parentheses

Table 16a: Average Early Expenditures

Total Revenues $7723

(10.90)

Total Expenditures $7739

(10.97)

Federal Revenues $454

(2.38)

State Revenues $3617

(6.09)

Local Revenues $3651

(9.08)

Observations 116048

Table 16b: Average Early Expenditures

County Total Revenues $7284

(42.89)

County Total Expenditures $7274

(39.67)

County Federal Revenues $538

(8.76)

County State Revenues $3730

(25.04)

County Local Revenues $3016

(40.10)

Observations 3127

62

Table 17: College Costs

Net Price of Attendance ($2000)

Two-Year Four-Year Two-Year Four-Year

Graduates Graduates Drop-Outs Drop-Outs

Parental Income

Less than $20,000 $15,801 $38,119 $7,407 $18,265

$20,000-39,999 $18,961 $48,792 $8,888 $23,380

$40,000-59,999 $23,920 $59,136 $11,213 $28,336

$60,000-90,000 $25,962 $65,743 $12,170 $31,502

More than $90,000 $27,712 $79,082 $12,990 $37,893

Net Tuition ($2000)

Less than $20,000 $1,459 $13,275 $684 $6,361

$20,000-39,999 $1,750 $17,062 $820 $8,175

$40,000-59,999 $2,917 $21,792 $1,367 $10,442

$60,000-90,000 $3,209 $25,144 $1,504 $12,048

More than $90,000 $2,236 $33,076 $1,572 $15,849

63

Table 18a : ’Parametrization of the Benchmark Economy”

Parameters set Externally

Parameter Description Value

β Discount factor 0.76

σ Risk aversion parameter 1.5

r Interest Rate 0.55

nθs Time spent in college 0.11, 0.22, 0.39, 0.55

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

kedj Wage period constant See Appendix

g Government early expenditures 0.1

f(s) College Cost See Appendix

gsc(Ip,ac) College Aid See Appendix

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 0.25

γ1 Returns to early education 0.6

γ0 Returns to innate ability 0.25

sε Share of private expenditures 0.47

a4gov 4-Year College borrowing limits 0.27

a2gov 2-Year-College borrowing limits 0.193

a1gov Drop-Out borrowing limits 0.03

apvt High-School Graduates borrowing limits 0.01

64

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