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Long Term Effects of Preschool on School
Performance, Earnings and Social Mobility*
Dr. Lakshmi K. Raut
Visiting Fellow, University of Chicago
Center for the Economics of Human Development
1126 E. 59th St., Chicago, IL 60637,USA
mailto:lakshmiraut@gmail.com
November 15, 2018
Abstract
Children from disadvantaged families perform very poorly in school and labor mar-
ket because they acquire low level of social, motivational and cognitive skills during
their early childhood development. Using the NLSY data set, this paper formulates
and then estimates the production processes for cognitive and non-cognitive (such
as social and motivational) skills during early childhood development and the long-
term effects of these skills on learning and lifetime earnings of an individual. Using
these estimated relationships, the paper provides a calibrated intergenerational altruis-
tic model of parental investment in children’s preschool. This dynamic model is then
used to estimate the effects of publicly provided preschool to the children of poor SES
*In memory of my mentor, collaborator and very good friend, Professor T.N. Srinivasan who passed away
on November 10, 2018. Earlier drafts of this paper were presented at the 2003 Western Economic Association
Meeting, and at the University of Southern California,Indian Statistical Institute - Kolkata, University of
Nevada - Las Vegas, and California State University at Fullerton. I am grateful to the participants for making
many useful comments. When I was a Visiting Fellow at the University of Chicago during 1998-1999, I had
discussions with Professor James Heckman at an early stage of this preschool research project. In September
2015, my son, Han Altae-Tran, an Engineering undergrad student at Stanford at the time, suggested to me
that emotions are important in socioeconomic behaviors, which triggered me to look into the neurobiology
literature for my preschool research and during that summer, Professor T.N. Srinivasan at a dinner that we
organized in his honor talked about neuroeconomics to us and to encourage Han with his interests in this area,
sent us Camerer et al., 2005 and other references. I am grateful to them. I am also grateful to two anonymous
referees of this journal for many valuable comments. This paper is a slightly updated version of my original
paper, Raut, 2003.
1
(Socio Economic Status) as a social contract on lifetime earnings distribution, inter-
generational college and social mobility and to estimate the tax burden of such a social
contract.
JEL Classifications: J24, J62, O15, I21
Keywords: Preschool Investment, Early Childhood Development, Augmented
Earnings Function,Social Mobility, College Mobility.
1 Introduction
Since the 1980s, the income gap between the rich and the poor and the wage gap between
the college educated and the non-college educated workers have been widening in the US.
In many other countries the trends in wage gaps are similar. A large proportion of the
US workers have not completed college, and a majority of them come from disadvantaged
families. Many studies consistently show that the rate of return from college graduation
is much higher than the market interest rate. Could it be that the students from poor SES
(Socio Economic Status) are liquidity constrained for their college fund? This is the gen-
eral perception. The students from poor SES are, however, eligible for many Federal loan
programs for college education. The interest rates of these loan programs are substantially
lower than the rate of return from college graduation. Yet there is not enough demand for
these loans. Contrary to the general perception, the liquidity constraint is not a major rea-
son why children from disadvantaged families do not attend college. For instance, Carneiro
and Heckman, 2002 use the NLSY data to show that about 4% of the US households only
are liquidity constrained in the provision of post-secondary education to their children.1In
the US equalizing educational differences has remained a main policy instrument to reduce
poverty and income disparities. The basic question is then: Can we conquer poverty and
income disparity through school?
Many are highly skeptical about a positive answer to the above basic question. There are
many reasons for this skepticism. In the US, education up to high school level is virtually
free. Yet many children of poor SES do not complete high school and many of them perform
poorly in schools. This naturally beckons to the possibility that the poor quality of the public
schools that the children of poor SES attend is the reason for such failings. Improving school
quality will improve school performance of these children only marginally. Many empirical
1This might be true for post-secondary education in community colleges. Even for community colleges,
the rate of returns from college education is higher than the interest rate for the Federal college loan program.
A significantly higher percentages of students, however, are liquidity constrained for higher quality colleges,
for which the rates of returns are even higher.
2
studies find that better school quality in terms of lower class size, higher public expenditures
per pupil, improved curriculum, and higher desegregation have only marginal effects on
school performance of the children of poor SES. See Hanushek, 1986 for a survey of studies
along this line. In theoretical overlapping generations growth models, choices from multiple
school qualities can lead to equilibria in which some families choose low quality schooling
for their children, generation after generation, i.e., inhibiting intergenerational social and
schooling mobility (see Raut, 1990 for a model with old-age security motive2and Nishimura
and Raut, 2007 for a model with altruistic motive for parental choice of school qualities for
their children).
A growing consensus reached among educators, media writers (see for instance, Traub,
2000), researchers in sociology, psychology and education (for instance, see Barnett, 1995;
Entwisle, 1995;McCormick, 1989;Reynolds, Temple, et al., 2001;Reynolds, Ou, et al.,
2018;Schweinhart et al., 1993) and researchers in economics, (see for instance, Currie,
2001;Currie and Almond, 2011;Currie, 2011;Duncan et al., 2010;Heckman, 2000;Heck-
man, Moon, et al., 2010;Heckman and Raut, 2013;Heckman and Raut, 2016;Keane and
Wolpin, 1997) is that the children of poor SES are not prepared for college because they
were not prepared for school to begin with. The most effective intervention for the children
of poor SES should be introduced at the preschool stage so that these children are prepared
for schools and colleges. I briefly summarize this literature and the recently emerging mi-
crobiology literature that provides genetic and epigenetic mechanisms for various pathways
of cognitive and noncognitive developments of children.
Most earlier research in the last century focused on cognitive skills as the main deter-
minant of socioeconomic behaviors, school performances and labor market outcomes. One
line of influential but controversial research argues that poor parents have poor cognitive
abilities and that is why they are poor; children of poor SES inherit poor cognitive abilities
from their parents; thus very little can be done to improve the cognitive skills of the dis-
advantaged children, and hence their school performance and labor market outcomes, see
Herrnstein and Murray, 1994 and other references in Plomin and Deary, 2015. This view
has been refuted using more appropriate data, statistical techniques and microbiological
evidence.
Recent research in psychology, neurobiology, experimental game theory, and economics
emphasize that it is the interplay of personality, emotion and cognition that determines most
socioeconomic behaviors. A branch of the psychology literature argues and validates that
2Interpreting no schooling in this model as low quality schooling.
3
the emotional intelligence drives most socioeconomic decisions and behaviors, not the cog-
nitive intelligence alone. Many definitions and measurements for emotional intelligence
exit in the literature, however, the concept more relevant to our context is quoted from
Mayer et al., 2004, ”[Emotional Intelligence is the] capacity to reason about emotions, and
of emotions to enhance thinking. It includes the abilities to accurately perceive emotions,
to access and generate emotions so as to assist thought, to understand emotions and emo-
tional knowledge, and to reflectively regulate emotions so as to promote emotional and
intellectual growth”. Bar-On, 2000;Goleman, 2009 use somewhat broader definitions by
including other personality traits in their definitions. It has been found that measures based
on all these different definitions are highly correlated with each other and each explains
strongly many socioeconomic behaviors independent of cognitive skills, (see Chakrabarti
and Chatterjea, 2017 for some of these results in psychology and for a synthesis of various
definitions, and Raut, 2003;Heckman and Raut, 2013;Heckman and Raut, 2016 for signif-
icant positive effects of non-cognitive skills on labor market earnings, independent of the
effects of cognitive skills).
Humans are social animals. They live in groups and work in groups for most economic
and social activities. Group activities in economics are known as team work. Group out-
comes are generally more efficient than what individuals could do by themselves. Group
activities to attain some common goal, however, require each member of the group to per-
form constant mind reading of the other members and evaluate how others may react to
one’s action. The mechanism by which one reads other’s mind in a conflicting or coopera-
tive situation is known in the psychology literature as the theory of mind, a term introduced
by Premack and Woodruff, 1978, see Doherty, 2008 for a description various mechanisms
for the theory of mind. One who has a better emotional intelligence and a better theory of
mind can be more effective in a group, and can become the leader of the group. A group can
have a higher level of group emotional intelligence and cognitive intelligence than another
group, and can be more efficient and more productive as a result for many activities, (see
Woolley et al., 2010, more on group intelligence and related references). In experimental
game theory such non-cognitive skills—emotional intelligence and theory of mind—play
important role, (see, for instance, Camerer et al., 2005;Kahneman, 2013;Winter, 2014).
The recent economics literature shows that non-cognitive skills such as socialization and
motivation are also important for positive labor market outcomes (See, for instance Deming,
2017;Heckman and Raut, 2016;Raut, 2003). Deming provides a team theory explanation
for why better socialization and motivational skills can lead to higher labor productivity.
4
Where these emotional intelligence or non-cognitive skills are produced? For the effect
of early childhood experiences, especially mother-child interactions, on the development of
the theory of mind of the child, see Doherty, 2008;Ruffman et al., 2002. Another branch
of the psychology literture, e.g. the work of Bowlby, 1982, argues that affect (emotion)
dysregulation which begins to form immediately after birth, especially during the first two
years of age, from low quality interaction of the primary care-taker (generally the mother)
with the baby can have long lasting effects on emotional development of the child in later
ages. NETWORK, 2004 carried out a longitudinal study and found evidence for such affect
dysregulation mechanisms. The emotional dysregulation also conditions cognitive devel-
opments of children. More recent neurobiology research on this phenomena confirms this,
see for instance, A. N. Schore, 2005 and see J. R. Schore and A. N. Schore, 2008 for a sur-
vey of this line of research. When parents are incapable of producing these skills, a good
preschool program can be a good substitute for it.
The rapidly growing microbiology literature that emerged around the turn of the twenty-
first century is focused on genetic and, more emphatically, epigenetic mechanisms of the
personality, emotion and cognitive developments of individuals. The twenty-century em-
phasis that the full DNA mapping of human genome will be able to uncover fully the mech-
anism of human development pathways fell short of explaining why identical twins diverge
so much in their gene expressions or phenotypes as they progress through their lives. All
cells in a body starting with the single fertilized egg have the same genetic mapping (i.e.,the
same DNA sequence) throughout life. It is the epigenetic (literally means on top of genetic)
codes, which are influenced by the internal and external environments of the body cells, in-
deed determine which genes are expressed, silenced, or mutated during cell divisions, and
hence determine the development of the mind and body and their health status. For instance,
stress of various kinds can have effects on epigenetic reprogramming of the plasticity of var-
ious parts of the brain that perform cognitive processing, language processing, emotion or
affect regulations, the size and efficiency of the working memory and the long-term mem-
ory (see McEwen and Gianaros, 2011 for the effects of stress in general, Champagne et al.,
2008 and Hellstrom et al., 2012 for the effects of parenting practices). Other environmental
factors such as the quality of language exposure, the presence of books, computers, musi-
cal instruments at home, the speech pattern, cognitive skills of mother and other care givers
have also significant effects on the development of the neural network of the brain (i.e.,
the network of dendrites, axons and synapses) specialized for language processing, creative
writing or musical talents, (see, for instance Mezzacappa, 2017;Murgatroyd and Spengler,
5
2011).
Using fMRI images of brain areas, a number of neurological studies found that poverty
has significant negative effects on the development of a child’s certain brain areas that are
responsible for personality, emotion and executive functions. For instance, a large scale
neurological study by Noble, Houston, Brito, et al., 2015 found that family income signifi-
cantly affects children’s brain size, particularly in the surface area of the cerebral cortex that
does most of the cognitive processing. See also their earlier study, Noble, Houston, Kan,
et al., 2012 and the commentary in Balter, 2015. In another large longitudinal neurological
study, Hair et al., 2015 followed children starting at an early age up into their school years.
They measured their scores on cognitive and academic achievements, and development of
brain tissues, including gray matter of the total brain, frontal lobe, temporal lobe, and hip-
pocampus. They found significant negative effects of poverty on developments of these
brain areas and on their academic achievements.
Much of the above literature suggests that early age events have many lasting effects.
We cannot study all these effects. In the scope of this paper, the question I address is,
does preschool investment have long-term positive effects on school performance, lifetime
earnings and intergenerational social and schooling mobility?
Most of the studies along this line use data on Head Start preschool program which is
funded by the Federal government. The program is available only to children whose par-
ents earn incomes below poverty line. Not all eligible children are covered by the program,
however. The quality of the program is very poor compared to the pilot programs and most
of the private preschool programs. Some studies (see for instance, Aughinbaugh, 2001)
find that the Head Start Preschool Program has no long-term effect on children’s cogni-
tive achievements and school performance, especially for the black children. Currie and
Thomas, 1995 carried out a careful econometric investigation and concluded that the bene-
fits disappear for the black children because most of the Head Start black children attend low
quality public schools. After controlling for the school quality, however, they found signif-
icant positive effects of Head Start Preschool Program. See Barnett, 1995;Campbell et al.,
2002;Consortium for Longitudinal Studies, 1983;Schweinhart et al., 1993;Yoshikawa,
1995 for surveys and studies on the long-term effects of early childhood programs in the
US.
The above studies are not based on nationally representative samples of children, and
most studies examine only the effects on school performance such as grade retention and
high school and college graduation rates, and do not model parental choice of children’s
6
preschool investment. In this paper, I formulate a model of parental investment in preschool
that is guided by economic incentives. I empirically show that preschool investment ben-
efits children to acquire socialization and motivational skills, especially for the children of
poor SES who live in poor HOME environments, that the motivational skills significantly
improve school performance, and that the socialization and motivational skills improve the
lifetime earnings of children. These significant positive effects are found after controlling
for their education level, innate ability, and family background. I formulate an intergen-
erational altruistic model of parental preschool investment. I use a mixed reduced form
econometric estimation method and a calibration method to numerically specify the pa-
rameters of the model, and then use this model to examine the long-term intergenerational
economic effects of publicly providing preschool to children of poor SES.
The rest of the paper is organized as follows: Section 2 provides the basic decision mak-
ing framework, section 3 provides empirical estimates, and section 4 provides the economic
benefits of the social program of providing preschool to children of poor SES.
2 The Basic Framework
In this section I formulate a model of preschool investment decision of an altruistic parent.
The preschool investment decision of a parent depends on several other decisions made at
later stages by the parent and the child. In this section, I describe each of these decision
stages. In a later subsection, I discuss estimation issues. I report empirical estimates in the
following section. For expositional ease I assume that each family has one parent and one
child, and address them using the male gender.
I assume that an individual’s life comprises of several discrete periods during which
important life-cycle events relevant to learning and earning occur. I aggregate the whole
life-cycle into four periods as follows: [0-5), [5-17), [17-26), [26-]. In each of these periods
some educational and labor market decisions are made and outcomes are observed. During
age [0-5) the parent invests in his child’s preschool activities which develop the child’s
school readiness, and cognitive, social and motivational skills. Let hbe the level of parental
preschool investment. I assume that his annualized over the working years of the parent3.
At the end of this period, the child acquires a level of innate ability or cognitive skill τ, social
skill σand motivational skill µ. The level of each type of skills that the child acquires
3I am assuming that parents are not liquidity constrained for investing in their children’s preschool. This
is a strong assumption given that parents are at their early years of working age when they have children and
might not have built up enough assets to be able to borrow from the market at the market interest rate.
7
depends on other factors as well. For instance, it depends on child-rearing practices at
home, the nature of neighborhood in which the child grows-up, and the level of schooling,
cognitive, socialization and motivational skills of the parent. In the next section I describe
the role of parental preschool investment in the production of these skills and statistically
estimate the effects of preschool in the production of these skills.
During the period [5-17), the child goes to school. The school performance at this stage
depends on the levels of τ,σand µthat the child acquired during the previous stage, the
quality of the school that he attends, and the type of neighborhood kids whom the child
mingles with.4It also depends on the parental home inputs such as how many hours the
parent spend time with the child to do his homework, how many hours the child watches
TV, and how stable and stimulating the relationships among the family members are. Many
of these are choice variables for the parent. Since not much information about these is
available in the data set, I assume that the levels of τ,σand µfrom the previous period
remain constant at the end of the second stage.
During [17-26) the child makes his schooling decisions. Two important ingredients to
this decision are the costs and benefits of attaining a given level of schooling. There are
many dimensions to the cost of schooling, but I make many simplifying assumptions about
it. I assume that he does not work during this schooling period.5During [26-] he works,
forms a family with a child and decides how much to invest in his preschool, elementary
school and high school. At the beginning of the schooling period [17-26), the child decides
how many years of college to have and what type of college to attend. An important de-
terminant of this decision is the financial rewards or earnings in the labor market over the
whole life time that the individual will command from various levels of schooling. Another
non-financial benefit of higher schooling of an individual is that it provides better family
background for his child from which his child benefits. The structure of schooling costs
is generally very complicated. The type of college that he likes to attend depends on how
much college fund he can raise from the market and how much college money he can get
from his parent. I assume that each individual borrows the whole college fund from the mar-
ket. The interest rate rfor borrowing the college fund may depend on his parent’s wealth
position and if there is a government educational loan available at a low interest rate. Let
c(s,r)be the cost of syears of college annualized over the working years of the individual.
4See also the studies by Mohanty and Raut, 2009;Cunha et al., 2010;Del Boca et al., 2014.
5A recent US census reveals that more than 70 percent of college students have worked while attending
schools. I am assuming that their earnings are negligible relative to the cost of college or spent on consumption,
not education, during the period.
8
There are many important life cycle events that also influence the schooling decision of an
adult child. For instance, bad influence and financial responsibilities towards other family
members because of bad health shocks, or loss of employment of the parent may cause a
child choose less education. I represent these factors by an aggregate random variable ϵs.
I take the rewards or benefits from schooling to be the yearly permanent income, which
depends on his number of years of schooling s, his innate ability τ, his level of socialization
skills, σ, his level of motivational skills, µ, and also on his life-cycle experience of random
shocks such as market luck, family connection and network. I represent all these shocks
by an aggregate random variable ϵp. Let the yearly permanent income of the child over the
working years6be denoted by ws;τ,σ,µ,ϵp. His financial rewards net of schooling cost
is then given by ˆ
ws;τ,σ,µ,ϵp=ws;τ,σ,µ,ϵp−c(s,r).
I assume that ϵsis realized prior to making schooling decision during [17-26) and ϵp
is realized during [26-] prior to making preschool investment decision. Given his level of
τ,σand µ, his life-cycle shocks ϵsand the level of parental preschool investment level h,
let s∗(τ,σ,µ,h,ϵs)be his optimal schooling plan.7Even though given the values of τ,σ,
µ,ϵs, the pay-offs to the child during his decision period [17-26) does not depend directly
on h, I however, assume that s∗(τ,σ,µ,h,ϵs)depends on hto allow for the possibility of
strategic threats that the child may use in our Stackelberg situation with parent as the leader
and his child as the follower.
Formally, denote the state variables of our system by the vector z=s,τ,σ,µ,ϵs,ϵp.
Denote by ϵ= (ϵs,ϵp)the vector of unobserved state variables representing the unob-
served heterogeneity and by ˜
z=(s,τ,σ,µ)the vector of observed state variables. I will
sometimes use the notation z=(˜
z,ϵ)to represent the above information. For any variable,
x,I adopt the convention of using xif it refers to parent and x′if it refers to his child.
I assume that given the level of parental preschool investment h, and the realization
of his parent’s state variables z=(˜
z,ϵ), the child’s state variables τ′,σ′,µ′and ϵ′are
produced stochastically and represented by the following conditional probability density
6Since the traditional Mincer earnings function does not incorporate skills such as σand µwhich can
be produced by spending resources, I refer to our yearly permanent income incorporating σand µas an
augmented Mincer earnings function.
7Raut and Tran, 2005 derive and estimate a model of schooling investment s∗as a Nash equilibrium
outcome of a child-parent bargaining game in a model with two overlapping generations.
9
functions: qτ(τ′|τ)
qσ(σ′|τ′,s,τ,σ,µ,h)
qµ(µ′|τ′,s,τ,σ,µ,h)
qϵs(ϵ′
s|τ′,σ′,µ′,s)
qϵpϵp
(1)
In the above, each of those conditional probabilities may depend on many other vari-
ables, but the variables that are shown as the conditioning variables represent our specifi-
cations of the processes generating the state variables. This particular specification that I
use above is based on what is currently known about the production processes of these state
variables. I will discuss each of these production processes in the next section.
Given the density functions in Eq. (1), the preschool investment decision h, and a school-
ing decision rule s′∗ (τ′,σ′,µ′,ϵ′
s,h), the transition probability measure Qh(z,z′)over the
states of our system are determined. The preschool investment decision problem of a parent
is then the following Bellman equation of a dynamic programming problem:
V(z)=max
0≤h≤w(˜
z,ϵp)u˜
w˜
z,ϵp−h+γVz′Qhz,dz′,(2)
where V(.) is the value function, u(.) is the felicity index of yearly permanent con-
sumption ˜
w˜
z,ϵp−hof the parent and γmeasures the degree of parental altruism to-
wards his child. I assume that 0≤γ≤1. Given a particular schooling reaction function
s′∗ τ′,σ′,µ′,ϵ′
s,h, there exists a value function V(z), and optimal decision rule h∗(z)
under quite general conditions on the primitives, u(.),Qh(z,z′),γand ˜
w(z)(see Bhat-
tacharya and Majumdar, 1989). How is the optimal schooling reaction function s′∗ τ′,σ′,µ′,ϵ′
s,h
determined? I use the notion of subgame perfect equilibrium to characterize it.
A subgame perfect equilibrium is a pair of decision rules h=h∗˜
z,ϵpand s′∗ τ′,σ′,µ′,ϵ′
s,h
such that
i) h=h∗˜
z,ϵpsolves Eq. (2) given the reaction function s′∗ τ′,σ′,µ′,ϵ′
s,h, and
ii) s′∗ τ′,σ′,µ′,ϵ′
s,h=argmaxs′Vs′,τ′,σ′,µ′,ϵ′
s,ϵ′
pqϵpϵ′
pdϵ′
p.
It is clear from the second condition that the subgame perfect optimal schooling deci-
sion does not directly react to h. Furthermore, the optimal preschool investment decision
depends on z only through ˜
wand has the form, h∗˜
z,ϵp. In this paper I do not explore
properties of the subgame perfect equilibrium nor do I find conditions under which the
equilibrium exists.
10
2.1 Structural Estimation, Reduced Form Estimation or Calibration?
It is not possible to carry out structural estimation of Eq. (2) non-parametrically since there
will exist many primitives that can rationalize any given subgame perfect solution h∗˜
z,ϵp
and s∗τ′,σ′,µ′,ϵ′
s,h. Structural estimation8of our dynamic model involves two steps:
(i) econometric estimation of the optimal policy function h∗˜
z,ϵp, and (ii) identification
of the structural parameters given the estimates of h∗˜
z,ϵpand s∗τ′,σ′,µ′,ϵ′
s,h.
To estimate the optimal policy functions, one first needs to introduce a stochastic term
in h∗˜
z,ϵp, and s∗τ′,σ′,µ′,ϵ′
s,hso that one can apply the method of moments or
non-linear regression techniques to estimate these using the household level data. There
are many ways to incorporate this. In the above set-up, I assume that the decision maker
observes all the state variables, the econometrician does not observe ϵsand ϵp. These ϵ′s
can then constitute the error terms in the policy functions.
The identification problem reduces to the question: Given optimal solutions h∗˜
z,ϵp
and s∗τ′,σ′,µ′,ϵ′
s,h, does there exist a unique combination of primitives u(.),Qh(z,z′),
γand ˜
w(z)which rationalizes the given optimal solutions? In general there exist many
combinations of primitives that can rationalize the optimal solution, and hence the answer
to the identification problem is in general negative. One approach to the identification prob-
lem is to impose parametric restrictions on u(.),Qh(z,z′), and ˜
w(z). These conditions are
generally very stringent and are worked out only for standard dynamic programming prob-
lem in which there is only one decision maker. Not much is known for our more general
subgame perfect set-up involving more than one decision makers.
In the case of dynamic programming, if the decision variables are discrete, an alterna-
tive approach reduces the above dynamic programming problem to a random utility model
by imposing suitable restrictions on the primitives, (see Rust, 1994a, Theorem 2 and Rust,
1994b, Theorem 3.2). This approach has not been extended to the subgame perfect equi-
librium set-up that incorporates more than one decision makers. I will not pursue it either
in this paper.
The NLSY dataset does not have data on the amount spent on preschool. It has data
only on a binary variable of whether the respondent had preschool or not. Given this data
limitation, I treat parental preschool investment decision variable as a binary variable. Un-
derlying this is the assumption that there are no variations in preschool qualities and the
8Estimation of h∗˜
z,ϵpand s∗τ′,σ′,µ′,ϵ′
s,hdirectly using actual data on preschool investment and
completed schooling level is also known as reduced form estimation.
11
cost. Another serious limitation of the NLSY dataset is that it does not have data on all the
state variables relating to the parents of the respondents. For instance, it does not have data
on τ,σand µ. Furthermore, while the data set has information on τ,σand µfor the respon-
dents, it does not have information on the preschool investment of their own children, and
thus I cannot follow the synthetic cohort approach of using respondents’ data to estimate the
counterfactual optimal preschool decision rule h∗˜
z,ϵpof their parents. Therefore, given
the data limitations, I cannot pursue structural estimation of the model even if I overcome
the identification problem with appropriate restrictions on parametric specifications.
In this paper, I follow a mixed calibration and reduced form estimation procedure as
follows: I drop ϵpfrom the model, i.e., I assume that the permanent yearly income is inde-
pendent of ϵp, and thus it does not enter the optimal preschool choice problem. I estimate
Qh(z,z′),w(˜
z),s∗τ′,σ′,µ′,ϵ′
s,hdirectly using the NLSY data and specify numerically
the felicity index u(.)and parental altruism parameter γ. I then solve the fully specified
dynamic programming problem numerically. I then use these estimates and the optimal
solution to examine the economic effects of providing preschool resources to children of
poor SES.
3 Empirical Findings
3.1 The NLSY79 Dataset
A lot has been written about the NLSY79 data set, so I will not describe the data set in details.
The NLSY79 dataset contains life-cycle information on a nationally representative sample
of 12,686 young men and women who were 14-22 years old when they were first surveyed
in 1979. From 1979 to 1994, these individuals were surveyed annually. Currently they are
interviewed on a biennial basis. Since their first interview 1979, many of the respondents
have made transitions from school to work, and formed their own family instead of living
with their parents. This dataset provides a large sample of American men and women that
were born in the 1950s and 1960s and living in the United States in 1979.
This dataset contains richer information on school and labor market experiences of a
nationally representative sample of individuals. This dataset, however, contains limited
information on early childhood inputs of the sampled individuals. Although there is a recent
dataset that collects panel data on the children of the NLSY respondents, we have to wait
several years to obtain data on labor market outcomes of these children. From all these
considerations, the NLSY dataset stands out as the best choice for our analysis.
12
3.2 Production of Social and Motivational Skills
In this section I consider the production process of the socialization and motivational skills.
In the next two subsections I empirically show that motivational and socialization skills are
important determinants of earnings and learning.
The literature in sociology, psychology, and microbiology of human development sug-
gest that early childhood investment is the most crucial input for development of cognitive,
social and motivational skills.9The studies in these literature link school success to home
environment, child rearing practices, neighborhood type in which the kid is raised. For in-
stance, the Coleman, 1968 report and subsequent studies (Currie and Almond, 2011;Heck-
man, 2000;Mohanty and Raut, 2009, among others) find that the family capital—which
captures family tradition and values towards economic success and education—and the so-
cial capital—which captures the benefits of social bonds, social norms, social networks, the
social bonds between adults and children and among children in a neighborhood—are of im-
mense value during a child’s growing up. These factors affect parental choices of preschool
investment and child rearing methods which in turn determine a child’s cognitive abilities
and social abilities such as motivation and sociability that affect their learning and earning.
Microbiology literature produces ample evidence that the human brain develops extremely
rapidly during ages [2-4], and the type of stimulation regarding health and learning that
the child experiences during this period is a critical determinant of a child’s cognitive, so-
cial and motor developments. Child psychology literature also points out that a structured
preschool stimulation boosts a child’s self-confidence, school preparedness, parents’ and
teachers’ assessment of the child’s ability. These in turn create a conducive learning envi-
ronment for the child over many more years of schooling, beginning with the elementary
school. See Barnett, 1995;Entwisle, 1995;McEwen and Morrison, 2013;McEwen and
Gianaros, 2011;Mezzacappa, 2017;Murgatroyd and Spengler, 2011 for more on this. I
construct the variables of this study as follows:
Early childhood inputs and home environment: I take father’s and mother’s education
levels to measure family background. The NLSY dataset has poor measures of respondent’s
early childhood inputs. It has only a binary variable containing information on whether the
respondent had preschool (does not include Head Start) experience or not. I treated indi-
9The blueprint of the brain developments and the health trajectory of an individual over the life cycle is
strongly shaped by in uterus environments that is produced by the mother during pregnancy. Gluckman et al.,
2008 and others gave a biological mechanism and significant empirical evidence for it. This paper focuses on
postnatal stages of child development and the parental and environmental interventions that are most effective.
13
viduals with Head Start experience as no preschool. Notice that this will lead to underes-
timation of the effect of preschool investment. I use the revised AFQT score to measure
innate ability.
Socialization skill ( σ): Each respondent were asked how social he/she felt towards
others at age 6. This was expressed in a scale of 1 to 4. The highest number represented
most social. I create a binary sociability variable by assigning value 1 if a respondent re-
ported an answer 3 or 4 to this question and assigning 0 otherwise. About 39 percent of the
sample respondents are sociable. This measure of socialization may have recall error, as the
respondents may not correctly recall how they were when they were 6 years old. Deming,
2017 has used a principal component analysis with some other variables observed in later
periods to construct a measure of socialization skills in his paper. I used the early childhood
information only as other information taken from later ages might reflect the time effect and
I did not do a robust analysis with his measure, as his construction was not known to me at
the time of this research.
Motivational skill ( µ): I use three measures of motivation. (i) Job aspiration (µ1) which
I construct as a binary variable taking value 1 if during the first interview in 1979 the re-
spondent aspired for professional jobs, otherwise taking value 0. About 71 percent of the
respondents in the sample are motivated. (ii) The educational goal (µ2) is the grade that
the respondent in 1979 expected to achieve. The sample average is 15 years and standard
deviation is 1.104 (iii) The Rotter’s scale of self-control and self-confidence (µ3) which I
reconstructed from the scores of original four questions in the data set. My measure takes
values 0 to 4, a higher value representing more confident and self-control. The sample
average is 2.57 and standard deviation is 0.066.
The variable Gender = 1 if female, otherwise Gender = 0.
I estimated a Probit model for σand µ1and OLS models for µ2and µ3. The parameter
estimates are reported in table 1.
From Table 1 it is clear that after controlling for parents’ grades, preschool experience
has a significantly positive effect on socialization skill and on all measures of motivational
skills except the Rotter’s scale of self-control. The estimates in the table also show that
innate ability has strong positive effect on all measures of motivational skills but has no
significant effect on socialization skills. Socialization skills are created in the family using
the preschool and neighborhood inputs. The data set does not have information on parent’s
income, age, whether both parents are alive and reside in the same households. These vari-
ables are presumably important factors in the skill formations. The education levels of the
14
Table 1: Determinants of Sociability and Motivations
Variables Sociability Job Aspiration Education Goal Self-Control (Rotter)
(σ) (µ1) (µ2) (µ3)
Intercept -0.6467 -0.6102 11.8089 1.9911
(8.11) (7.24) (98.13) (31.90)
Revised AFQT Score 0.0013 0.0131 0.0311 0.0094
(1.91) (17.80) (31.30) (18.16)
Mother’s grade 0.0115 -0.0064 0.0471 0.01
(1.63) (0.86) (4.45) (1.82)
Father’s Grade 0.0199 0.0207 0.0421 0.0083
(3.43) (3.35) (4.82) (1.84)
Preschool 0.0884 0.1553 0.61 0.0399
(2.12) (3.33) (9.58) (1.21)
Gender -0.0462 0.2884 0.1484 -0.0322
(1.41) (8.17) (2.99) -1.25
N 6072 6072 5961 6041.00
Log-likelihood/R2-4010.09 -3389.02 0.2541 0.0861
Source: The author.
Notes: The first two columns show parameter estimates from the Probit model and the last two
columns show parameter estimates from the ordinary least squares model. The absolute t-value of
a parameter estimate is shown in parentheses below the parameter estimate.
15
parents have captured some of these effects. To the extent these variables are correlated with
the preschool variable, the effect of preschool will be biased. There is no good information
that could be used to estimate the parameters using the Instrumental Variable Method. Thus
the underlying assumption in these estimates is that those variables are not correlated with
the preschool decision.
It will be interesting to see if preschool has stronger positive effect on socialization and
motivational skills of children of poorer SES. If so, then the preschool could be used to com-
pensate for the better HOME environment that the well-to-do counterpart of these children
have. That is, through intervention like preschool, we can achieve a higher equality of op-
portunities by equalizing the differences in the starting social, motivational, and cognitive
skills of the children.
3.3 An Augmented Earnings Function: the Role of Socialization and
Motivational Skills
In this section I examine the effect of social and motivational skills together with the effect of
innate ability and grades on earnings. The previous studies, however, included only innate
ability, schooling level and school quality as the main determinants of earnings. While
preschool investment is an important determinant of these skills, I also included preschool
binary variable as one of the regressors in the earnings function to see if it has an independent
effect. In my specification, I also included a dummy variable for College (taking value 1 if
a respondent graduated from college). This dummy variable after controlling for the grade
variable captures any earnings premiums that a worker earners by graduating from college.
Since I included AFQT score which is a reasonably good measure of one’s innate ability,
the parameter estimates do not have the ability bias problem.
Table 2 shows the parameter estimates of this augmented earnings function. The first
column is for all three races together and the next three columns give the estimates for the
Hispanics, Blacks and the Whites ethnic groups separately. It is clear from the estimates that
after controlling for innate ability, family background and the schooling level, the measures
of socialization and motivational skills have significant positive effect on earnings for all
ethnic groups. Preschool has independent positive effect only for blacks. It is also interest-
ing to note that college graduates earns a 8.35% higher returns in the overall population, and
for Blacks and Hispanics this premium is even higher (slightly above 10%). The sociability
skills are significant only for White but not for Black and Hispanic workers.
16
Table 2: Estimated Parameters of the Augmented Mincer Earnings Function
Variables All Races Hispanic Black White and Others
Intercept 0.4097 0.4716 -1.4676 0.6952
(3.02) (1.51) (4.44) (4.13)
Revised AFQT Score 0.0062 0.0055 0.0068 0.0041
(32.16) (10.53) (12.13) (16.20)
Grade 0.042 0.0291 0.0752 0.0426
(14.68) (5.11) (9.93) (11.51)
High School 0.0662 0.0851 -0.003 0.0881
(7.11) (4.27) (0.14) (7.21)
College 0.0835 0.1003 0.1002 0.0839
(5.91) (2.39) (2.69) (5.18)
Age 0.5313 0.5196 0.5857 0.5244
(52.68) (22.11) (24.17) (42.21)
Age Square -0.0079 -0.0078 -0.0087 -0.0078
(42.05) (17.58) (19.39) (33.69)
Mother’s grade 0.0025 0.0129 0.023 -0.0022
(1.41) (4.13) (5.17) (0.82)
Father’s Grade 0.0077 0.007 -0.0095 0.013
(5.30) (2.45) (2.94) (6.47)
Preschool 0.0055 -0.0373 0.0752 0.0048
(0.52) (1.50) (3.30) (0.35)
Sociability (σ) 0.0226 -0.0314 0.0267 0.0265
(2.72) (1.60) (1.31) (2.62)
Motivation—Job 0.0419 0.0864 0.0427 0.0346
Aspiration (µ1) (4.48) (4.03) (1.90) (2.98)
Motivation—Education 0.0051 0.0278 0.0153 0.0058
Goal (µ2) (2.07) (5.09) (2.59) (1.80)
Motivation—Rotter 0.0305 0.0325 0.0367 0.0362
Scale (µ3) (7.55) (3.46) (3.63) (7.35)
Gender -0.4997 -0.509 -0.371 -0.5549
(61.37) (26.47) (18.64) (55.43)
N 60489 10374 12053 38061
R20.3186 0.3295 0.3152 0.3205
Source: The author.
Notes: Absolute t-values are in parentheses below the parameter estimates.
17
3.4 Estimation of Optimal Schooling Level
I consider two specifications of the optimal schooling function s∗τ′,σ′,µ′,ϵ′
s,hin this
paper. In the first specification, I assume that the schooling level is a continuous variable
and specify the optimal reaction function s∗τ′,σ′,µ′,ϵ′
s,has a linear function. I assume
that the random variable ϵ′
sconstitutes the error term and satisfies all the assumptions of the
OLS model.10 The parameter estimates from this model are shown in Table 3 I included
the socialization and motivational skills together with innate ability and family background
measured by parents’ education levels. It is clear from the estimates that the main determi-
nant of grade is the innate ability measured by AFQT score. After controlling for family
background, I also find that motivation measures have significant positive effect on school-
ing level. Out of the three measures of motivation, the measure µ2based on the expected
grade that the respondent desired to attain while very young turns out to be the most impor-
tant one. Note also that the motivation measure µ1based on job aspiration has significant
positive effect only for the White but not for the Black or the Hispanic. The sociability
skill has, however, no effect on the schooling level. After controlling for all other vari-
ables, preschool has still an independent positive effect on the completed grade of Blacks.
This may be because the preschool creates other skills that are important for school success
but are not captured in the included determinants in our specification of optimal schooling
function.
Notice that even after controlling for innate ability, the family backgrounds measured by
mother’s grade and father’s grade have significant positive effects on the completed grade
of the Black and White but not for the Hispanic.
In the second specification, I consider two levels of schooling: college or higher (s=1),
and no college (s=0). This simplified specification is for the purpose of calibrating the
dynamic programming problem in Equation (2). Again I assume that s∗τ′,σ′,µ′,ϵ′
s,h
is linear, and that ϵ′
sconstitutes the error term and it is normally distributed. This gives
us Probit model of college graduation. The parameter estimates are reported in Table 4.
Here again the innate ability, motivation, preschool and the college status of parents (which
takes 1 if at least one parent had some college, and 0 otherwise) turn out to have significant
positive effects on the probability of college graduation.
10 More generally I could assume that Eϵ′
s|τ′,σ′,µ′,h=0, and use the GLS method to correct for
heteroscedasticity.
18
Table 3: Determinants of Grade
Variables All Races Hispanic Black White and Others
Intercept 3.7172 4.6491 4.4417 3.0849
(22.03) (10.72) (12.51) (13.86)
Revised AFQT Score 0.0288 0.0376 0.0337 0.0279
(30.80) (12.67) (14.98) (22.29)
Mother’s grade 0.0622 0.0289 0.1184 0.0774
(6.91) (1.53) (6.41) (5.58)
Father’s Grade 0.0262 -0.0052 -0.0013 0.0659
(3.54) (0.30) (0.09) (6.41)
Preschool 0.2759 -0.0804 0.288 0.2961
(5.08) (0.54) (2.91) (4.22)
Sociability (σ) 0.0653 -0.1205 0.1528 0.0813
(1.51) (1.00) (1.74) (1.53)
Motivation: 0.1788 0.1473 0.1501 0.2061
Job Aspirations (µ1) (3.64) (1.12) (1.57) (3.33)
Motivation: 0.4615 0.4354 0.3489 0.4674
Education Goal (µ2) (41.18) (14.52) (14.94) (31.40)
Motivation: Rotter Scale 0.0724 0.0732 0.1236 0.0493
of Self-Control (µ3) (3.45) (1.28) (2.84) (1.91)
Gender 0.1532 0.0761 0.478 0.0798
(3.63) (0.65) (5.72) (1.53)
N 5925 1044 1259 3620
R20.5577 0.4825 0.5326 0.5845
Source: The author.
Notes: Absolute t-values are in parentheses below the parameter estimates.
19
3.5 Optimal Parental Preschool Investment
To numerically solve the dynamic programming problem in Eq. (1), one has a few choices.
One could assume that the state variables s,τ, and ϵare continuous and the rest of the
variables are binary, and then use the parametric path method of Judd, 2002 or a suitable
value-iterations or policy iterations methods developed in the numerical dynamic program-
ming literature, see Rust, 1996 for a survey of these methods. Because we have many state
variables, our problem is subject to the well-known ”curse of dimensionality” problem of
numerical dynamic programming methods. I impose the following restrictions to keep the
numerical computation manageable.
I assume that the state variables s,τ,σ,µare binary, the random variable ϵsis contin-
uous which is observed by the decision maker but not by the econometrician, the random
variable ϵpis absent, and the preschool investment decision his a binary variable, taking
value 1when the parents decide to invest in preschool and 0otherwise. For most children,
we have two parents but in the model I have assumed one parent. I have used both parents’
information in computation as follows: I construct parent’s binary schooling variable sby
assigning that s=1if the average grades of two parents is more than 12, otherwise s=0.
I assume that τis biologically inherited and it is not influenced by preschool investment. I
create the binary variable τassigning it the value 1 (interpreted as an individual is highly
talented) if the AFQT score of the individual is 70 or higher, and assigning it the value 0
otherwise. I do not have information on AFQT of parents. The literature on intelligence rec-
ommends that the correlation between parent’s IQ and the child’s IQ is anywhere between
0.3 and 0.7. I assume it to be 0.3 in our numerical exercise. I use the binary job aspiration
variable µ1as the measure of motivational skills. The specifications and the estimates of
the Probit models of s∗,σand µare shown in Table 4. I use these estimates to calculate the
transition matrix Qh.
Schweinhart et al., 1993 took average yearly preschool cost to be US$6178 per year.
Consistent with their study, I take the preschool cost per child to be US$18000 for three
years and annualized it over the working years of an individual. I further assume that the
felicity index is linear and measured in US dollars. I numerically specify the parental altru-
ism parameter to be γ=0.65.
After calibrating the model as above, I use the linear programming approach to solve
Eq. (2) numerically. The optimal preschool investment decision and the value function are
shown respectively in columns 3 and 4 of Table 5. Notice from Table 5 that parents with
income below a cut-off point do not invest in their children’s preschool. I will refer to these
20
parents as parents of poor SES.
Table 4: Estimated forms of earnings function and Probit models of college completion,
socialization and motivation
Variables w(s,τ,σ,µ)Probability of Probability of Probability of
College being sociable being motivated
Intercept 8330.08 -1.43 0.48 -0.30
(15.62) (48.85) (28.32) (18.17)
Schooling ( = 1 6653.93
If College, 0 otherwise (7.50)
Innate ability (τ) 6109.64 1.38
(7.04) (33.84)
Sociability (σ) 1293.89
(1.94)
Motivation: 2731.59 0.13
Job aspiration (µ1) (4.10) (3.54)
Preschool ( h = 1) 2126.56 0.34 0.15 0.07
H=0 no preschool (2.55) (7.51) (3.63) (1.89)
Parent’s schooling ( = 1 0.95 0.20 0.29
If college, 0 otherwise) (13.34) (2.99) (4.78)
Average value of the
Dependent variable 0.21 0.38 0.21
Source: The author.
Notes: Absolute t-values are in parentheses below the parameter estimates.
4 Economic Benefits from Public Provision of Preschool
I have shown that investment in preschool enhances certain skills that are important for
learning and earning. The optimal solution reveals that the parents of poor SES do not invest
in their children’s preschool. If preschool is publicly provided for the children of poor SES,
it will have many economic benefits: It will increase social mobility, it will reduce income
inequality, it will improve college graduation rate, it will improve the community or crim-
inal behavior, and it will also bring higher tax revenues because more workers would earn
higher wages. It is important to note that the magnitude of the effects of publicly provided
preschool depends on whether the social protection is available to all future generations or
it is just a one time deal.
While examining the estimated economic benefits below, it is important to keep in mind
21
Table 5: Solutions of the Subgame Perfect Equilibrium
state invariant distribution
z= (s,τ,σ,µ)w(s,τ,σ,µ)opt. h* V*(z) (without) p* (without) p* (with) V*(z) (with)
(0, 0, 0, 0) 8718.24 0 32951.71 0.0614 0.0409 33471.62
(0, 0, 1, 0) 10122.63 0 34356.11 0.1370 0.1147 34876.02
(0, 0, 0, 1) 10144.64 0 34378.12 0.1310 0.1094 34898.03
(0, 0, 1, 1) 11549.04 0 35782.52 0.3200 0.3289 36302.43
(0, 1, 0, 0) 14975.45 1 41575.34 0.0082 0.0049 41575.34
(1, 0, 0, 0) 15463.37 1 41740.68 0.0028 0.0036 41740.68
(0, 1, 1, 0) 16379.85 1 42979.74 0.0189 0.0139 42979.74
(0, 1, 0, 1) 16401.86 1 43001.75 0.0123 0.0086 43001.75
(1, 0, 1, 0) 16867.77 1 43145.07 0.0073 0.0108 43145.07
(1, 0, 0, 1) 16889.78 1 43167.08 0.0338 0.0438 43167.08
(0, 1, 1, 1) 17806.25 1 44406.14 0.0303 0.0256 44406.14
(1, 0, 1, 1) 18294.17 1 44571.48 0.1066 0.1480 44571.48
(1, 1, 0, 0) 21720.58 1 50395.88 0.0046 0.0043 50395.88
(1, 1, 1, 0) 23124.98 1 51800.28 0.0118 0.0128 51800.28
(1, 1, 0, 1) 23146.99 1 51822.29 0.0279 0.0298 51822.29
(1, 1, 1, 1) 24551.39 1 53226.69 0.0859 0.1001 53226.69
Source: The Author.
22
that the reported effects are underestimated for many reasons: First, I have treated the Head
Start children in the same footing as the children without preschool. Second, the preschool
programs that the respondents went into were the ones that existed during the sixties. The
quality of preschool programs ever since has improved significantly and thus the effects of
current preschool programs will be much higher than the estimates that we have.
Note that since ϵdoes not affect earnings, the optimal h∗depends only on the observable
component of the parent’s state variables. In the absence of a social contract, suppose the
parents follow the optimum preschool investment plan h∗as shown in table 5. The invari-
ant distribution of the corresponding transition matrix Qh∗is also shown in table 5 under
the heading p∗(without). The interpretation of this invariant distribution is as follows: If
p∗(without)is the distribution of population over the observable states of generation t, and
the parents of generation tfollow the optimal preschool investment plan h∗, then the distri-
bution of population of the next generation will also be p∗(without).V∗(z)( without)is
the optimal value function without the public policy. The corresponding variables after the
introduction of the public policy are denoted with a postfix ”(with)” in the table.
4.1 Social Mobility
Given any transition matrix Qh∗over the observable states, there exists a number of mo-
bility measures in the literature. Sommers and Conlisk, 1979 argue that out of the existing
measures, 1−λmax is the most appropriate measure of social mobility, where λmax is the
second highest positive eigenvalue of the transition probability matrix Qh∗(the highest pos-
itive eigenvalue of a transition matrix is always 1). I use this measure of social mobility
to examine how the introduction of a social contract would improve social mobility. The
estimate of this measure of social mobility without a social contract is 0.6163. After the
introduction of a social contract, it improves to 0.6770. The estimate of 0.6163 for the
measure is very close to the estimates found in other studies of social mobility in the US.
4.2 College Mobility
Denote by Qs=qij,i,j=1, 2 the intergenerational college mobility matrix in which
state 1 represents no college and state 2 represents college and higher. The element qij
represents the probability that a child of a parent of college education status jwill move
to college education status i. I report below the estimates of college mobility matrices
Qs, the corresponding invariant distributions ps, and the estimates of the mobility measure
23
1−λs
max, before and after the introduction of the social contract. These estimates indicate
that the introduction of the social contract will increase college graduation rate from 0.24 to
0.28 for a child of non-college parent. And the percentage of college graduate population
will increase in the long-run from the current low rate of 21% to a much higher rate of 41%
with the introduction of the social contract, and to a rate of 38% without the social contract.
That is, there will be a 3% increase in college graduation rate in the long-run.
College mobility statistics before introduction of social contract:
1−λs
max =0.642
ps=0.623 0.377
Qs=0.758 0.400
0.242 0.600
College mobility statistics after introduction of social contract:
1−λs
max =0.680
ps=0.588 0.412
Qs=0.720 0.400
0.280 0.600
4.3 Income Inequality
Preschool experience will increase the income of the children of poor SES and thus it will
reduce the income gap between the rich and the poor. In the long-run, the income dis-
tribution that one observes is the invariant distribution. Taking the Gini-coefficient as a
measure of income inequality, the estimated coefficients of income inequality are respec-
tively 0.1809 without the social contract, and 0.1484 with the social contract. The estimated
Gini-coefficient of 0.1809 turns out to be very close to the estimates found in other studies
on the US. Thus, the social contract of publicly providing preschool to children of poor SES
leads to a significant reduction in income inequality.
4.4 Tax Burden of the Social Contract
Suppose the government provides preschool to the children of poor SES perpetually. We
know that the size of the population of poor SES will become smaller and smaller over
time. Thus the resource needs of the program will become smaller, and the tax revenues
24
will become higher over time. One can look at the stream of these costs and benefits to
the society and then compute the average per period costs and benefits to calculate the tax-
burdens of the social contract. Applying the Ergodic theorem, however, this boils down to
computing the costs and benefits for the invariant distribution that would result after the
introduction of the social contract.
Assuming a flat average income tax rate of 15% for all income groups, I computed that
each dollar spent to provide free preschool to children of poor SES, the tax payers get back
$1.16. This estimate is, however, based on using the cost data of a very high cost program
whose benefits are much higher than the estimated benefits of this model, and also this
benefit calculation does not take into account other public savings such as savings from
welfare assistance and savings to the criminal justice system and victims of crimes. If these
effects are incorporated, the returns would be much higher. Using data from the High/Scope
Perry Preschool Program Schweinhart et al., 1993. estimated a total benefit from all these
sources to be 7.16 dollars for each dollar spent on the preschool program.
5 Conclusion
In this paper, I briefly survey the literature in economics, psychology and genetics-epigenetics
of the developments of non-cognitive and cognitive skills, which predominately suggest
that these skills are produced at the preschool stage of human development with important
parental and environmental inputs. The paper uses two types of cognitive skills—the IQ
score and the schooling level, and four types of non-cognitive skills —a socialization skill,
two motivational skills, measured in terms of job aspiration, and educational aspiration,
and the self-control skill, measured in Rotter’s Locus of Control Scale. I estimate produc-
tion functions of these skills with some of these inputs that could be readily created from
the NLSY79 and NLSY79 Children and Young Adult data sets. I estimated an augmented
Mincer earnings function with these non-cognitive skills together with the other traditional
Mincer function variables as regressors. I find statistically significant positive effects of
non-cognitive skills—independent of the effects of cognitive skills—on schooling level and
earnings. Using these estimated relationships, I provide a calibrated intergenerational altru-
istic model of parental investment in children’s preschool. The calibrated dynamic model
is then used to estimate the effects of publicly provided preschool to the children of poor
SES on the distribution of lifetime earnings, intergenerational college and social mobility.
The paper also calculates the tax burden of the preschool program.
25
The long-run effects of the public preschool policy found in the paper are as follows:
Measured on a scale of 0to 1, the policy improves the intergenerational earnings mobility
from 0.616 to 0.677, and the college mobility from 0.642 to 0.680; reduces the within-
generation lifetime earnings inequality measured by the Gini coefficient from 0.1809 to
0.1484; increases the college completion rate of the children of non-college educated par-
ents from 24 per cent to 28 percent, a 4percentage point increase, and the college educated
population increases from 37 per cent to 41 per cent, also a 4percentage point increase. The
policy results in a net gain (net of taxes) of the long-run per capita earnings. The society
gets back 1.16 dollars for each dollar invested in the public program.
The estimated effects in the paper may be underestimated for many reasons. First, the
preschool programs of the 1960s that the respondents attended were of lower quality than
the quality of the current preschool programs. Second, the pool of skill labor can create a
positive externality in the aggregate production function of the economy, as is assumed in
the endogenous growth models (for two such mechanisms, see Raut, 1995;Lucas, 1988).
Third, the paper does not incorporate other savings to the society such as savings to the
welfare programs, to the criminal justice system and to the victims of crimes that would
accrue because of the public preschool policy. When those effects are incorporated, the
gains from the public preschool policy could be much higher.
26
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