Role of Income and Family Influence on Child Outcomes


  • James J. Heckman

    1. University of Chicago, Chicago, Illinois, USA
      University College Dublin, Dublin, Ireland
      American Bar Foundation, Chicago, Illinois, USA
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Address for correspondence: James J. Heckman, Department of Economics, University of Chicago, 1126 E. 59th St., Chicago, IL 60637. Voice: 773-702-0634; fax: 773-702-8490.


This chapter examines the role of income and family background in models of capability formation that explains a variety of findings established in the child development and child intervention literatures.

It is well documented that people have diverse abilities, that these abilities account for a substantial portion of the variation across people in socioeconomic success, and that persistent and substantial ability gaps across children from different socioeconomic groups emerge before they start school. The family plays a powerful role in shaping these abilities through genetics, parental investments, and choice of child environments. From a variety of intervention studies, it is known that ability gaps in children from different socioeconomic groups can be reduced if remediation is attempted at early ages. The remediation efforts that appear to be most effective are those that supplement family environments for disadvantaged children. Cunha, Heckman, Lochner, and Masterov (CHLM) present a comprehensive survey and discussion of this literature.1

This chapter examines the evidence on the importance of income and early environments on child outcomes by using a simple economic model of skill formation to organize the evidence summarized here and the findings of related literatures in psychology, education, and neuroscience. The existing economic models of child development treat childhood as a single period.2–4 The implicit assumption in this approach is that inputs into the production of skills at different stages of childhood are perfect substitutes. To account for a large body of evidence, it is necessary to build models of skill formation with multiple stages of childhood, where inputs at different stages are complements and where there is self-productivity of investment.

There are three distinct constraints operating on the family and its children. The first constraint is the inability of a child to choose his or her parents—the fundamental constraint imposed by the accident of birth. The second constraint is the inability of parents to borrow against their children's future income to finance investments in them. The third constraint is the inability of parents to borrow against their own income to finance investments in their children.

This report summarizes findings from the recent literature on child development and presents a model that explains them. A model that is faithful to the evidence must recognize that (1) parental influences are key factors governing child development; (2) early childhood investments must be distinguished from late childhood investments; (3) an equity–efficiency tradeoff exists for late investments, but not for early investments; (4) abilities are created, not solely inherited, and are multiple in variety; (5) the traditional ability–skill dichotomy is misleading. Both skills and abilities are created; and (6) the “nature versus nurture” distinction is obsolete. These insights change how analysts should interpret evidence and design policy about investing in children. Point 1 is emphasized in many reports. Point 2 is ignored in the many models in the social science literature that consider only one period of childhood in building models of investment. Points 3–5 have received scant attention in the literature on child investment. Point 6 is ignored in the large and misleading literature that partitions the variance of child outcomes into additive components due to nature and components due to nurture.

Observations about Human Diversity and Human Development

Any analysis of human development must reckon with three empirically well-established observations about ability. The first observation is that ability matters. Many empirical studies document that cognitive ability is a powerful determinant of wages, schooling, participation in crime, and success in many aspects of social and economic life. The frenzy generated by Richard J. Herrnstein and Charles A. Murray's book, The Bell Curve, because of its claims of genetic determinism, obscured its real message, which is that cognitive ability is an important predictor of socioeconomic success.5,6

A second observation, more recently established, is that abilities are multiple in nature. Socioemotional abilities, sometimes called “noncognitive” abilities (perseverance, motivation, time preference, risk aversion, self-esteem, self-control, preference for leisure), have direct effects on wages (controlling for schooling), schooling, teenage pregnancy, smoking, crime, performance on achievement tests, and many other aspects of social and economic life.7–9

The third observation is that the nature-versus-nurture distinction that has dominated thinking about family influence is obsolete. The modern literature on epigenetic expression teaches us that the sharp distinction between acquired skills and ability featured in the early human capital literature is not tenable.10,11,a Additive “nature” and “nurture” models, although traditional and still used in many studies of heritability and family influence, mischaracterize how ability is manifested. Abilities are produced, and gene expression is governed by environmental conditions. Abilities are susceptible to environmental influences, including in utero experiences, and also have genetic components. These factors interact to produce behaviors and abilities that have both a genetic and an acquired character. The practice of partitioning outcomes into components due to nature and nurture lacks scientific foundation. An extensive literature suggests that gene–environment interactions are central to explaining human and animal development. Rutter provides an accessible introduction to this literature.10,b

For example, work by Caspi, Williams, et al. shows that children's intellectual development is influenced by both genetic and environmental factors.14 Breast-fed children attain higher IQ scores than non–breast-fed children. This association is moderated by a gene (FADS2) that controls fatty acid pathways. Fraga et al. show how monozygotic (identical) twins are affected by experience that substantially differentiates the genetic expression of adult twins.15 Caspi, Sugden, et al. show that one gene (a serotonin transporter, 5-HTT) moderates the influence of stressful life events on depression.16 Caspi, McClay, et al. show that the effect of growing up in a harsh or abusive environment on adult antisocial behavior depends on the presence of a particular variant of the MAOA gene.17 Both genetic and environmental factors must be at work to produce adverse consequences. Cole et al. show the effect of social environments (isolation) on gene expression that moderates adverse health outcomes.18 The research of Champagne and Curley and of Champagne et al. shows that environmental effects are inherited across generations and that early environmental influences are especially important.19,20 Suomi reports related findings on genetic moderation of environmental influences.21,22 Turkheimer et al. report findings of a strong role of environment on heritability of IQ.23,c,d

Taking these observations as established, Cunha and Heckman develop a simple economic model to explain the following six facts from the recent empirical literature.24 First, ability gaps between individuals and across socioeconomic groups open up at early ages, for both cognitive and noncognitive skills. See Figure 1 for a prototypical figure that graphs a cognitive test score by age of child by socioeconomic status of the family.e CHLM present many additional graphs of child cognitive and noncognitive skills by age showing early divergence and then near parallelism during schoolgoing years across children with parents of different socioeconomic status. Levels of child skills are highly correlated with family background factors, such as parental education and maternal ability that, when statistically controlled for, largely eliminate these gaps (see Carneiro and Heckman, CHLM, and the Web site for Cunha and Heckman).24,25 Experimental interventions with long-term follow-up confirm that changing the resources available to disadvantaged children improves their adult outcomes (see the studies surveyed in CHLM or Blau and Currie).26 Schooling quality and school resources have relatively small effects on ability deficits and have little effect on test scores by age across children from different socioeconomic groups, as displayed in Figure 1 and related graphs.27,28

Figure 1.

Source: Full sample of the Children of the National Longitudinal Survey of Youth.

Children of the National Longitudinal Survey of Youth. Average standardized score for Peabody Individual Achievement Test (PIAT) math by permanent income quartile. See our Web site for a full explanation of this figure.

Second, in both animal and human species, there is compelling evidence of critical and sensitive periods in the development of the child. Some skills or traits are more readily acquired at certain stages of childhood than other traits (see the evidence summarized in Knudsen et al.29). For example, on average, if a second language is learned before age 12, the child speaks it without an accent.30 If syntax and grammar are not acquired early, they appear to be difficult to learn later in life.31 A child born with a cataract will be blind if the cataract is not removed within the first year of life.

Different types of abilities appear to be manipulable at different ages. IQ scores become stable by age 10 or so, suggesting a sensitive period for their formation below age 10.32 There is evidence that adolescent interventions can affect noncognitive skills (see CHLM). This evidence is supported by the neuroscience that establishes the malleability of the prefrontal cortex into the early 20s.33 This is the region of the brain that governs emotion and self-regulation.

On average, the later remediation is given to a disadvantaged child, the less effective it is. A study by O'Connor et al. of adopted Romanian infants reared in severely deprived orphanage environments before being adopted supports this claim.34 The later that a Romanian orphan was rescued from the social, emotional, and cognitive isolation of the orphanage, the lower was his or her cognitive performance at age 6. Classroom remediation programs designed to combat early cognitive deficits have a poor track record.

At historically funded levels, public job training programs and adult literacy and educational programs, such as the GED (general equivalency diploma or general educational development), which attempt to remediate years of educational and emotional neglect among disadvantaged individuals, have a low economic return and produce meager effects for most persons. A substantial body of evidence suggests that returns to adolescent education for the most disadvantaged and less able are lower than the returns for the more advantaged.25,35,36

The available evidence suggests that for many skills and abilities, later remediation for early disadvantage to achieve a given level of adult performance may be possible but is much more costly than early remediation.37 The economic returns to job training, high school graduation, and college attendance are lower for less able persons.25

Third, despite the low returns to interventions targeted toward disadvantaged adolescents, the empirical literature shows high economic returns for remedial investments in young disadvantaged children.1,24,38 This finding is a consequence of dynamic complementarity and self-productivity captured by the technology summarized in the next section.

Fourth, if early investment in disadvantaged children is not followed up by later investment, its effect at later ages is lessened. Investments appear to be complementary and require follow-up to be effective. Currie and Thomas document a decline in the performance of Head Startf minority participants after they leave the program, return to disadvantaged environments, and receive the low levels of investment experienced by many disadvantaged children.39,g

Fifth, the effects of credit constraints on a child's outcomes when the child reaches adulthood depend on the age at which they bind for the child's family. Recent research summarized in Carneiro and Heckman and in CHLM demonstrates the quantitative insignificance of family credit constraints in the child's college-going years in explaining a child's enrollment in college.25,41 Controlling for cognitive ability, under meritocratic policies currently in place in American society, family income during the child's college-going years plays only a minor role in determining child college participation, although much public policy is predicated on precisely the opposite point of view. Holding ability fixed, minorities are more likely to attend college than others despite their lower family incomes.42 Augmenting family income or reducing college tuition at the stage of the life cycle when a child goes to college does not go far in compensating for low levels of previous investment.

Carneiro and Heckman present evidence for the United States that only a small fraction (at most 8%) of the families of adolescents are credit constrained in making college participation decisions.25,41 This evidence is supported in research by Cameron and Taber and by Stinebrickner and Stinebrickner.43,44 Permanent (long run) family income plays an important role in explaining educational choices, insofar as it is a proxy for the high level of investment in abilities and skills that wealthier families provide, but it is not synonymous with family income in the adolescent years or with tuition and fees. Research by Belley and Lochner suggests that in recent years, family income may have become more important in accounting for college-going decisions, but cognitive ability is still the main determinant of college attendance.45

There is evidence, however, that credit constraints operating in the early years affect adult ability and schooling outcomes.46–49 Carneiro and Heckman show that controlling for family permanent income reduces the estimated effect of early income on child outcomes but does not eliminate the effect.25 Long-term or “permanent” income has a strong effect on child outcomes. The strongest evidence for an effect of the timing of parental income for disadvantaged children is in their early years. The best documented market failure in the life cycle of skill formation in contemporary American society is the inability of children to buy their parents or the lifetime resources that parents provide and not the inability of families to secure loans for a child's education when the child is an adolescent.

Sixth, socioemotional (noncognitive) skills foster cognitive skills and are an important product of successful families and successful interventions in disadvantaged families. Emotionally nurturing environments produce more capable learners. The Perry Preschool Program,h which was evaluated by random assignment, did not boost participant adult IQ but enhanced performance of participants on a number of dimensions, including scores on achievement tests, employment, and reduced participation in a variety of social pathologies. See Schweinhart et al. and the figures and tables on the Perry program posted on the Web site of Cunha and Heckman.24,50

A Model of Skill Formation

Cunha and Heckman develop a model of skill formation that can explain the six facts just presented as well as additional findings from the literature on child development.24 They use the terms skill and ability interchangeably. Both are produced by environments, investment, and genes.

Agents possess a vector of abilities at each age. These abilities (or skills) are multiple in nature and range from pure cognitive abilities (e.g., IQ) to noncognitive or socioemotional abilities (patience, self-control, temperament, risk aversion, time preference). These abilities are used with different weights in different tasks in the labor market and in social life more generally.i Achievement test scores, sometimes confused with IQ scores, are not pure measures of ability and are affected by cognitive, noncognitive, and environmental factors.51–53

The human skill formation process is governed by a multistage technology. Each stage corresponds to a period in the life cycle of a child. Inputs or investments at each stage produce outputs at the next stage. Although the child development literature recognizes stages of development,54 the economics of child development has only recently begun to.

An important feature of the technology of Cunha and Heckman is that the skills produced at one stage augment the skills attained at later stages. This effect is termed self-productivity.24 It embodies the idea that skills acquired in one period persist into future periods. It also embodies the idea that skills are self-reinforcing and cross-fertilizing. For example, emotional security fosters child exploration and more vigorous learning of cognitive skills. This effect has been found in animal species and in humans.21,55–58 A higher stock of cognitive skills in one period raises the stock of next-period cognitive skills. A second key feature of skill formation is dynamic complementarity. Skills produced at one stage raise the productivity of investment at later stages. In a multistage technology, complementarity implies that levels of skill investments at different ages bolster each other. They are synergistic. Complementarity also implies that early investment should be followed up by later investment for the early investment to be productive. Together, dynamic complementarity and self-productivity produce multiplier effects, which are the mechanisms through which skills beget skills and abilities beget abilities.

Dynamic complementarity, self-productivity of human capital, and multiplier effects imply an equity–efficiency tradeoff for late child investments but not for early investments. These concepts, embedded in alternative market settings, explain the six facts from the recent literature summarized in the previous section. These features of the technology of skill formation have consequences for the design and evaluation of public policies toward families. In particular, they show why the returns to late childhood investment and remediation for young adolescents from disadvantaged backgrounds are so low, whereas the returns to early investment in children from disadvantaged environments are so high.

Cunha and Heckman formalize these concepts in a model with overlapping generations.24 Assume for simplicity that individuals live for 2T years. The first T years, the individual is a child of an adult parent. From age T+ 1 to 2T, the individual lives as an adult and is the parent of a child. The individual dies at the end of the period in which he is 2T years old, just before his child's child is born. At every calendar year there is an equal and large number of individuals of every age t∈{1, 2, …, 2T}.j To simplify the notation, I do not explicitly subscript generations.

A household consists of an adult parent and his child. Parents invest in their children because of altruism. They have common preferences and supply their labor effort to the market inelastically. (Thus, I ignore any wage effects on labor supply.) Let It denote parental investments in child skill when the child is t years old, where t= 1, 2, …, T. The output of the investment process is a skill vector. The parent is assumed to fully control the investments in the skills of the child, whereas in reality, as a child matures, he gains much more control over the investment process.k,l Government inputs (e.g., schooling) are a component of It.

Consider how skills evolve over time. Assume that each child is born with initial conditions θ1. Let h denote parental characteristics (e.g., IQ, education). At each stage t, let θt denote the vector of skill stocks. The technology of production of skill when the child is t years old is


for t= 1, 2, …, T. Assume that ft is strictly increasing and strictly concave in It and twice continuously differentiable in all its arguments.m

Technology (1) is written in recursive form. Substituting in (1) for θt, θt−1, …, repeatedly, one can rewrite the stock of skills at stage t+ 1, θt+1, as a function of all past investmentsn:


Dynamic complementarity arises when 2ft(h, θt, It)/∂θtIt > 0, that is, when stocks of skills acquired by period tt) make investment in period t (It) more productive. Such complementarity explains why returns to educational investments are higher at later stages of the child's life cycle for more able children (those with higher θt). Students with greater early skills (cognitive and noncognitive) are more efficient in later learning of both cognitive and noncognitive skills. The evidence from the early intervention literature suggests that the enriched early preschool environments provided by the Abecedarian,o Perry, and the Chicago Parent–Child Center (CPC)p interventions promote greater efficiency in learning in school and reduce problem behaviors.1,26

Self-productivity arises when ft(h, θt, It)/∂θt > 0, that is, when higher stocks of skills in one period create higher stocks of skills in the next period. For skill vectors, this includes own and cross-effects. The joint effects of self-productivity and dynamic complementarity help to explain the high productivity of investment in disadvantaged young children and the lower return to investment in disadvantaged adolescent children for whom the stock of skills is low and hence the complementarity effect is lower. These are facts two and three presented in this chapter's first section, “Observations about Human Diversity and Human Development.”

This technology is rich enough to describe learning in rodents and macaque monkeys. More emotionally secure young animals explore their environments more actively and learn more quickly. This technology also explains the evidence that the ability of the child to pay attention affects later academic achievement. Cross-complementarity serves to explain fact six. This technology also captures the critical and sensitive periods in humans and animals.29 I now define these concepts precisely.

Period t* is a critical period for θt+1 if




This condition says that investments in θt+1 are productive in period t* but not in any other period st*. Period t* is a sensitive period for θt+1 if


That is, period t* is a sensitive period relative to period s if, at the same level of inputs, investment is more productive in stage t* than in another stage st*.q

Suppose for simplicity that T= 2, so there are two stages to childhood. In reality, there are many stages in childhood, including in utero experiences.r Assume that θ1, I1, and I2 are scalars.s The adult stock of skills, h′ (=θ3), is a function of parental characteristics, initial conditions, and investments during childhood I1 and I2:


The literature in economics assumes only one period of childhood. It does not distinguish between early investment and late investment. This approach produces the conventional specification that is a special case of technology (3), where


and γ= 1/2. Here adult stocks of skills do not depend on how investments are distributed in different periods of childhood. For example, take two children, A and B, who have identical parents and the same initial condition θ1 but have different investment profiles: Child A receives no investment in period one and receives I units of investment in period two, IA1= 0,  IA2=I, where as child B receives I units of investment in period one and zero units of investment in period two, IB1=I,  IB2= 0. According to (4), when γ= 1/2, children A and B will have the same stocks of skills as adults. In this model, the timing of investment is irrelevant. Neither period one nor period two is a critical period.

The polar opposite of perfect substitution is perfect complementarity:


Technology (5)—sometimes called the “Leontief” technology case in honor of Nobel laureate Wassily Leontief—has the feature that adult stocks of skills critically depend on how investments are distributed over time. For example, if investment in period one is zero, I1= 0, it does not pay to invest in period two. If late investment is zero, I2= 0, it does not pay to invest early. For the technology of skill formation defined by (5), the best strategy is to distribute investments evenly, so that I1=I2. Complementarity has a dual face. It is essential to invest early to get satisfactory adult outcomes. But it is also essential to invest late to harvest the fruits of the early investment.t Such dynamic complementarity helps to explain the evidence by Currie and Thomas that for disadvantaged minority students, early investments through Head Start have weak effects in later years if not followed up by later investments.39 This is fact four in the introductory list of facts. This explanation is in sharp contrast to the one offered by Becker, who explains weak Head Start effects by crowding out of parental investment by public investment.61 That is a story of substitution against the child who receives investment in a one-period model of childhood. The story of Cunha and Heckman is one of dynamic complementarity.24,u

A more general technology that captures technologies of (4) and (5) as special cases is a standard constant elasticity of substitution (CES):


for φ≤ 1 and 0 ≤γ≤ 1. The CES share parameter γ is a skill multiplier. It reveals the productivity of early investment not only in directly boosting h′ (through self-productivity) but also in raising the productivity of I2 by increasing θ2 through first-period investments. Thus, I1 directly increases θ2, which in turn affects the productivity of I2 in forming h′. The γ value captures the net effect of I1 on h′ through both self-productivity and direct complementarity.v

The elasticity of substitution 1/(1 −φ) is a measure of how easy it is to substitute between I1 and I2. For a CES technology, φ represents the degree of complementarity (or substitutability) between early and late investment in producing skills. The parameter φ governs how easy it is to compensate for low levels of stage 1 skills in producing later skills.

When φ is small, low levels of early investment I1 are not easily remediated by later investment I2 in producing human capital. The other face of CES complementarity is that when φ is small, high early investment should be followed with high late investment if the early investment is to be harvested. In the extreme case when φ→−∞, (6) converges to (5). This technology explains facts two and three—why returns to education are low in the adolescent years for disadvantaged (low h, low I1, low θ2) adolescents but are high in the early years. Without the proper foundation for learning (high levels of θ2) in technology (1), adolescent interventions have low returns.

In a one-period model of childhood, inputs at any stage of childhood are perfect substitutes. Application of the one-period model supports the widely held but empirically unsupported intuition that diminishing returns make investment in less advantaged adolescents more productive. As noted in fact two of this chapter's “Observations about Human Diversity and Human Development,” the evidence suggests that just the opposite is true. Per Cunha and Heckman, I embed the technology in a market environment with parental choice of inputs.24

Optimal Life Cycle Profile of Investments

Using technology (6), I now show how the ratio of early to late investments varies as a function of φ and γ as a consequence of parental choices in different market settings. The argument is somewhat technical but can be understood at an intuitive level. Let w and r denote the wage and interest rates, respectively, in a stationary environment. At the beginning of adulthood, the parent draws the initial level of skill of the child, θ1, from the distribution J1). Upon reaching adulthood, the parent receives bequest b. The state variables for the parent are the parental skills, h, the parental financial resources, b, and the initial skill level of the child, θ1. Let c1 and c2 denote the consumption of the household in the first and second period of the life cycle of the child, respectively. The parent decides how to allocate the resources among consumption and investments at different periods as well as bequests b′, which may be positive or negative. If human capital (parental and child) is scalar, the budget constraint is


Let β denote the utility discount factor and δ denote the parental altruism toward the child. Let u(·) denote the utility function. The recursive formulation of the problem of the parent is


The problem of the parent is to maximize (8) subject to (7) and technology (6).w

When φ= 1, so early and late investment are perfect CES substitutes, the optimal investment strategy is straightforward. The price of early investment is $1. The price of late investment is $1/(1 +r). Thus, the parent can purchase (1 +r) units of I2 for every unit of I1. The amount of human capital produced from one unit of I1 is γ, whereas $(1 +r) of I2 produces (1 +r) (1 −γ) units of human capital. Thus, two forces act in opposite directions. High productivity of initial investment (the skill multiplier γ) drives the parent toward making early investments. The interest rate drives the parent to invest late. It is optimal to invest early if γ > (1 −γ)(1 +r).

As φ→−∞, the CES production function converges to the “Leontief” case and the optimal investment strategy is to set I1=I2. Here investment in the young is essential. At the same time, later investment is needed to harvest early investment. On efficiency grounds, early disadvantages should be perpetuated, and compensatory investments at later ages are economically inefficient.

For −∞ < φ < 1, the first-order conditions are necessary and sufficient given concavity of the technology in terms of I1 and I2. For an interior solution, one can derive the optimal ratio of early to late investment:


Figure 2 plots the ratio of early to late investment as a function of the skill multiplier γ under different values of the complementarity parameter φ, assuming that r= 0. When φ→−∞, the ratio is not sensitive to variations in γ. When φ= 0, the function (6) is


Here, from (9), the optimal I1/I2 is close to zero for low values of γ but explodes to infinity as γ approaches 1.x

Figure 2.

Source: CHLM.1

Ratio of early to late investment in human capital as a function of the skill multiplier for different values of complementarity.

When CES complementarity is high, the skill multiplier γ plays a limited role in shaping the ratio of early to late investment. High early investment should be followed by high late investment. As the degree of CES complementarity decreases, the role of the skill multiplier increases, and the higher the multiplier, the more investment should be concentrated in the early ages.

Accounting for Income and Resource Constraints

In a model of perfect markets, when agents can lend and borrow freely, optimal investment levels are not affected by parental wages or endowments, or the parameters that characterize the utility function u(·).y However, even in this “perfect” credit market setting, parental investments depend on parental skills, h, because these characteristics affect the returns to investment. From the point of view of the child, this is a market failure due to the accident of birth. Children would like to choose the optimal amount of parental characteristics h to complement their initial endowment, θ1.z

Consider the second credit constraint mentioned in the introduction: parental bequests must be nonnegative; that is, parents cannot leave debts to their children. The problem of the parent is to maximize (8) subject to (7), technology (6), and the liquidity constraint:


If constraint (10) binds, then early investment under lifetime liquidity constraints, inline image, is lower than the early investment under the perfect credit market model, denoted I*1. The same is true for late investment: inline image. Under this type of market imperfection, underinvestment in skills starts at early ages and continues throughout the life cycle of the child. This explains fact one—that skill gaps open up early and are perpetuated.aa

In this second case, both early and late investment depend on parental initial wealth b for the families for whom constraint (10) binds. Children who come from constrained families with lower b will have lower early and late investment. Interventions that occur at early stages would exhibit high returns, especially if they are followed up with resources to supplement late investment. Once the early stage investment is realized, however, late remediation for disadvantaged children would produce lower returns if early and late investment are not perfect substitutes and late investment is more productive the higher the level of early investment. This helps to explain fact five in Section 1.

The effects of government policies on promoting the accumulation of human capital depend on the complementarity between early and late investment as well as on whether the policies were anticipated by parents. For example, the short-run effects of an unanticipated policy that subsidizes late investment will have weaker effects the greater the complementarity between early and late investment. If the technology is Leontief, there is no short-run effect of the policy on adolescent investment. When the policy is announced, poor parents have already made their early investment decisions and, in the Leontief case, it is not possible to compensate for early disadvantage by increasing late investment as a response to the subsidy.

There is, however, a long-run effect of the policy. If the policy is a permanent change announced before the child is born, new parents will adjust both early and late investment in response to the subsidy to late investment. Note that the same is true for an exogenous increase in the return to education. If there is strong complementarity between early and late investment, in the short run one would expect weak reactions to the increase in returns to education as gauged by adolescent investment decisions for the children from very poor family backgrounds, but stronger reactions in the long run. This analysis explains why the college enrollment response to unanticipated increases in the returns to college were initially so strong for adolescents from advantaged families and initially so weak for adolescents from less-advantaged families. Adolescents from less-advantaged families are more likely to lack the foundational skills that make college going productive than are adolescents from more-advantaged families. Cunha and Heckman present evidence on this point on their Web site.24

There is no tradeoff between equity and efficiency in early childhood investment. Government policies to promote early accumulation of human capital should be targeted to the children of poor families. However, the optimal second-period intervention for a child from a disadvantaged environment depends critically on the nature of technology (6). If I1 and I2 are perfect CES complements, then a low level of I1 cannot be compensated for at any level of investment by a high I2. On the other hand, suppose that φ= 1, so the technology m2 can be written with inputs as perfect CES substitutes. Here a second-period intervention can, in principle, eliminate initial skill deficits (low values of I1). At a high enough level of second-period investment, it is technically possible to offset low first-period investment, but it may not be cost effective to do so. If γ is low enough relative to r, it is more efficient to postpone investment.

The concepts of critical and sensitive periods are defined in terms of the technical possibilities of remediation. Many noneconomists frame the question of remediation for adverse environments in terms of what is technically possible—not what is economically efficient. The analysis of Cunha and Heckman considers both technological possibilities and costs.24 From an economic point of view, critical and sensitive periods should be defined in terms of the costs and returns of remediation and not solely in terms of technical possibilities.

Another source of market failure arises when parents are subject to lifetime borrowing constraints and constraints that prevent them from borrowing against their own future labor income, which may affect their ability to finance investment in the child's early This is the third constraint considered in the introduction to this chapter. To analyze this case, assume that parental productivity grows exogenously at rate α. Let s denote parental savings. We write the constraints facing the parent at each stage of the life cycle of the child as:


where s≥ 0 and b′≥ 0. The restriction s≥ 0 says that parents cannot borrow income from their old age to finance consumption and investment when the child is in the first stage of the life cycle. Some parents may be willing to do this, especially when α is high. When s≥ 0 and b′≥ 0 bind, and investments in different periods are not perfect substitutes, the timing of income matters. To see this, note that if u(c) = (cσ− 1)/σ, the ratio of early to late investment is


If early income is low with respect to late income, the ratio I1/I2 will be lower than the optimal ratio. The deviation from the optimal ratio will be larger the lower the elasticity of intertemporal substitution of consumption (captured by the parameter σ). Early income would not matter if σ= 1, which would be the case when consumption in stage one is a perfect substitute for consumption in stage two. Substitutability through parental preferences can undo lack of substitutability in the technology of skill formation.

This analysis of credit-constrained families joined with a low value of φ interprets the evidence presented by Duncan et al., Duncan and Kalil, and Dahl and Lochner that the level of family income in the early stages of childhood affects the level of ability and achievement of the children. This is fact five of Section 1. This analysis also interprets the evidence of Carneiro and Heckman and of Cameron and Taber that, conditioning on child ability, family income in the adolescent years has only a minor effect on adolescent schooling choices.41,43,cc

Adverse Family Trends and the Proper Measure of Child Poverty and Disadvantage

The evidence on the importance of family factors in explaining ability gaps is a source of concern because, of all American children being born today, a greater fraction is being born into disadvantaged families. A divide is opening up in American society. Those born into disadvantaged environments are receiving relatively less stimulation and resources to promote child development than those from more-advantaged families. A gap has emerged between the environments of children of more-educated women and the environments of children of less-educated women. More-educated women are having their children later after they have completed their education and have a steady flow of resources from their own income and that of their spouses.

More-educated women are working disproportionately more than less-educated women. Fewer than 10% of the more-educated women bear children out of wedlock. In families with educated parents, fathers' involvement with children has increased over the past 30 years.63 More-educated women marry later, have more resources, have fewer children, and provide much richer child-rearing environments that produce dramatic differences in child vocabulary by 26 months.64,65

As noted in a comprehensive survey by Bianchi et al., the evidence from time diary studies suggests that college-educated mothers devote more time to child rearing than less-educated mothers, especially in child enrichment activities.66 They spend more time reading to children and less time watching television with their children. College-educated mothers spend more time in direct child care. The evidence on growing differences of child investment by education and social class is less clear cut.

These trends are of great concern because the percentage of less-educated women is rising and they bear and raise a disproportionate number of children. In the words of McLanahan, “diverging destinies” now characterize the lives of American children from different backgrounds.63 Whereas more-educated women are working more, their families are also spending more time in child development activities than are less-educated women. The children in affluent homes are bathed in financial and cognitive resources. Those in less-advantaged circumstances are much less likely to receive cognitive and socioemotional stimulation and other family resources. Adverse backgrounds produce much greater risk for the persons involved and their children. These patterns of single motherhood, employment, and age at first birth of child by educational status are found in many countries around the world, so this analysis is relevant for many Western countries.63 The family environments of single-parent homes compared with those of intact families are much less favorable for investment in children.

There is a substantial body of suggestive evidence that the conventional measures of family disadvantage used by economists to study child outcomes, such as “broken home” or family income, are crude proxies for the real determinants of child outcomes.67–70 Presence of a father can be a negative factor if he shows antisocial tendencies. Genetic factors determine the response to maltreatment.71 This evidence suggests that a major determinant of child poverty is the quality of the nurturing environment rather than just the financial resources available or the presence or absence of parents. This evidence is supported by the evidence on the effects of early parenting enrichment programs summarized in CHLM.

The evidence from psychology and psychiatry coupled with Mayer's research suggests that the measures of childhood adversity commonly used by social scientists are crude.68 Strengthening this observation is a study by Costello et al.72 An American Indian population enriched by the opening of a casino showed a substantial improvement in baseline measures of child disruptive behavior after the increase in income. The beneficial effects were mediated by changes within the family. Parental supervision of children improved and there was greater parental engagement. Income improved parenting, but it was parenting that reduced disruptive behavior.

A proper measure of disadvantage would account for parenting inputs, but data on parenting are limited. The traditional focus on family income as a source of childhood disadvantage is probably misleading. Affluent families may create impoverished child-rearing environments. Economically disadvantaged families may provide ideal parenting environments. Efficient targeting of disadvantaged environments would focus on the quality of parenting in addition to the resource flow available to families.

The adverse trends in family environments in American society raise an environmental version of concerns about the quality of the future population analogous to the concerns expressed by the eugenics movement a century ago. Then the concern was expressed that “genetically inferior” populations were breeding at a higher rate and diluting population quality. Because genetics was assumed to be beyond the control of any intervention, the eugenicists forecast a dim future for the human race.

Recent evidence suggests that early environments play a powerful role in shaping adult outcomes. Relatively more children are growing up in those adverse environments. The good news is that environments can be shaped in ways that were thought impossible under traditional assumptions about genetics. The recent literature suggests that early environments powerfully affect genetic expression and that society need not passively watch its own decline. Policy can matter.

Cognitive and Noncognitive Skill Formation

A large body of research documents the socioemotional basis of reason.73,74 The analysis of Cunha and Heckman goes beyond this literature to formalize a body of evidence that emotional skills promote learning.24 Mechanisms relating cortisol to stress and the effects of cortisol on the brain development of animals have been documented by Suomi and Meaney.21,55 Duncan et al. and Raver et al. show that a child's ability to pay attention facilitates later learning.57,58

The framework developed in Section 2 readily accommodates skill vectors.24 The evidence summarized in the first section of this chapter shows the importance of both cognitive and noncognitive skills in determining adult outcomes. Child development is not just about cognitive skill formation, although much public policy analysis focuses solely on cognitive test scores. Let θt denote the vector of cognitive and noncognitive skills: θt= (θCt, θNt). Let It denote the vector of investment in cognitive and noncognitive skills: It= (ICt, INt). Use h= (hC, hN) to denote parental cognitive and noncognitive skills. At each stage t, one can define a technology for cognitive skills (k=C), and noncognitive skills, (k=N):


Technology (11) allows for cross-productivity effects: Cognitive skills may affect the accumulation of noncognitive skills and vice versa. They also allow for critical and sensitive periods to differ by skill, as is required to account for fact two.

If cognitive and/or noncognitive skills determine costs of effort, time preference, or risk aversion parameters, parental investments affect child and adult behavior. This analysis of preference formation contrasts with the analyses of Akabayashi and Weinberg.75,76 Those authors build models where the parent and the child agree on contracts in which parents' financial transfers are conditional on observable measures of effort (e.g., test scores in school). These contracts are designed so that the children are driven toward the level of effort desired by the parents. In the model of Cunha and Heckman, parents directly shape child preferences.24

Accounting for preference formation enables Cunha and Heckman to interpret the success of many early childhood programs targeted to disadvantaged children that do not permanently raise IQ but that permanently boost social performance.24,dd This is fact six of this chapter's first section. The controversy over Head Start fadeout may have been a consequence of relying only on cognitive measures to gauge performance. The Perry Preschool Program had an IQ fadeout but a lasting effect on a variety of participants through age 40. They work harder, are less likely to commit crime, and participate in many fewer social pathologies than do control group Heckman, Moon, et al. show that the Perry program favorably shifted the noncognitive ability distributions of participants.77

Estimates of the Technology of Skill Formation

Cunha and Heckman and Cunha, Heckman, and Schennach estimate recursive multistage technology (6) with cognitive and noncognitive skills, generating adult outcomes, such as schooling, earnings, and occupational choice.53,78,ff I refer to those reports for econometric details and discussions of the rich panel data on child development that makes such estimation possible.

They find strong evidence of self-productivity and complementarity. Their evidence is consistent with the literature, demonstrating malleability of the prefrontal cortex governing executive function and socioeconomic development as well as the stability of IQ measures after age 10 cited in this chapter's first section. They find higher substitutability of early and late investment in producing noncognitive skills and lower substitutability of early investment in producing cognitive skills. Higher stocks of noncognitive skills promote the self-productivity of cognitive skills; cognitive skill stocks promote the self-productivity of noncognitive skills. Higher levels of both cognitive and noncognitive skills raise the productivity of subsequent investment. There is evidence of sensitive periods for parental investment. The productivity of parental investment is higher in early stages for cognitive skills, with a falloff in its productivity in later years. The productivity of parental investment is higher at later stages for noncognitive skills. This evidence is consistent with greater malleability of the prefrontal cortex governing socioemotional development into the early 20s, documented by Dahl.33

Cunha, Heckman, and Schennach estimate a strong interaction between initial endowments and parental investments that questions the conventional additive model of nature versus nurture.78 This evidence is consistent with the modern literature on epigenetics. Nature and nurture interact to produce child outcomes and environmental effects that last across generations. Even θ1, endowment at birth, is affected by environmental factors, as a large literature documents.60

Lessons for the Design of Policies

Cunha and Heckman simulate the nonlinear model of skill formation estimated by Cunha, Heckman, and Schennach to show the importance of self-productivity and complementarity for designing policies to reduce inequality.37,78 They focus their analysis on children from disadvantaged backgrounds because at current levels of social inequality they benefit the most from policies that supplement early Disadvantaged children are at risk of being permanently poor and uneducated and of participating in crime. In the simulation presented, disadvantaged children come from a background where mothers are in the first (lowest) decile in the distribution of parental skills. If no intervention occurs, the children receive investments equivalent to the first decile of the distribution of parental investments.

Consider three different policies. The first policy is a Perry Preschool–like policy. It provides investment at early ages that moves children from the first decile of child cognitive skills at entry age to the fourth decile of child skills at the age of exit from the program. This gain can be achieved by moving parental investment from the bottom decile to around the seventh decile of the family investment distribution. In this policy, there is no follow-up investment. Cunha and Heckman also consider a second policy for the same target population that postpones remediation until adolescence.24 It compensates for early shortfalls by investing larger amounts in adolescent stages of the life cycle to produce approximately the same high school graduation rates that are observed in the Perry program.

College tuition programs, adolescent literacy programs, and mentoring programs are examples of such a policy. To achieve Perry-like outcomes for this population through adolescent investment, it is necessary to move adolescent investment to the ninth decile of the parental investment distribution. The present value of the costs of the investment in this adolescent remediation program is more than 35% larger than in the Perry Preschool program. Late remediation is possible, but it is costly. The correct case for early childhood intervention is based more on the importance of sensitive periods in the life cycle of the child than on the importance of irreversible critical periods, although many advocates of early childhood programs suggest that the early years are critical periods.60 One can contrast early-only and late-only investment policies with a third policy that optimally distributes the resources spent in the second policy over the full life cycle of the child. A balanced investment strategy is the most efficient.

The first column in Table 1 reports high school graduation, college enrollment, conviction, probation, and use of welfare if no intervention is made. The Cunha–Heckman model predicts a 41% high school graduation rate for this group, compared with 41.4% found in the Perry control group. Only 4.5% of the control group ever enrolls in college. Around 22% of them will be convicted of a crime or be on probation at some point in their adult lives. About 18% will use welfare programs in their adult years.

Table 1.  Comparison of different investment strategies
StatusBaselineEarly childhood intervention: moving children from the first decile of family investment to the seventh decileAdolescent intervention: moving investments in adolescence from first to ninth decileChanging initial conditions and performing a balanced intervention
  1. Disadvantaged children: first decile in the distribution of cognitive and noncognitive skills at age 6.

  2. Mothers are in first decile in the distribution of cognitive and noncognitive skills at ages 14–21.

  3. Note: The adolescent-only and balanced intervention programs cost 35% more than the Perry program intervention.

  4. Source: Cunha and Heckman (2006).37

High school graduation0.41090.65790.63910.9135
Enrollment in college0.04480.12640.11650.3755

The second column in Table 1 reports the performance of the Perry-like early intervention policy. This policy increases high school graduation and college enrollment rates to more than 65% and 12%, respectively. It reduces participation in crime. It makes the children more productive when they are adults. It cuts in half the probability that the child collects welfare benefits in his or her early adult years. These effects are comparable to those reported in the Perry preschool intervention.50 Thus, with their estimated technology, Cunha and Heckman can rationalize the results found in the Perry program as an intervention that boosts parental investments (but not parental characteristics) from the first decile of investment in children to the seventh decile.

The third column in Table 1 presents the performance of a 35% more costly policy that produces comparable educational outcomes for those obtained from a Perry-like intervention. Adolescent interventions can be effective, but they are more costly than early interventions. The greater cost associated with later remediation arises from lost gains in self-productivity and dynamic complementarity from early investment, which are key features of our model.

The empirical importance of dynamic complementarity—that the marginal productivity of investment depends on the level of skills produced by previous investments—generates an important insight for the design of policies. For a fixed expenditure, policies that are balanced increase returns and are more productive than policies tailored to one segment of the life cycle of the child. The returns to later investment are greater if high levels of early investment are made. Perry children made less use of remedial education than peers who did not receive treatment. The intervention made later schooling more effective. If early interventions are followed up with later interventions optimally, outcomes can be considerably improved.

The fourth column in Table 1 presents the results from a balanced policy intervention based on the analysis of Section 3. It displays the outcomes that can be produced by an intervention that distributes the funds spent on the adolescent-only intervention optimally. For a balanced program, high school graduation and college enrollment rates are, respectively, 91% and 37%. The reductions in conviction and probation rates are better than what is obtained from an adolescent-only policy, and welfare use is reduced to a low 2.6% rate.

Complementarity implies that early investment is more productive if it is followed up with late investment. And late investment is more productive if it is preceded by early investment. The mechanism that makes the balanced intervention more effective has a simple economic interpretation. When adolescent-only interventions are made, baseline skills are low and, consequently, so is the marginal productivity of later investment. A balanced investment program increases the stock of skills of the child coming into adolescence. Because the marginal productivity of later investment depends on the level of skills acquired before adolescence, the investment in the last period is more productive. Thus, the same amount of total investment distributed more evenly over the life cycle of the child but front-loaded toward the early years produces more adult skills than a policy that concentrates attention on only one part of the child's life cycle. Advantaged children are showered with parental investments in the early years. Disadvantaged children are not.


A technology of cognitive and noncognitive skill formation that features self-productivity, dynamic complementarity, and skill multipliers explains a variety of findings established in the child development and child intervention literatures. Although I have focused on cognitive and noncognitive skills in this chapter, the analysis also applies to the formation of physical health capital.79 The evidence on the importance of early childhood environments on adult health can be rationalized by our technology.80,81 Stocks of cognitive and noncognitive skills facilitate the accumulation of health capital through self-regulation and choices. Stocks of health skills also raise the productivity of schooling.82

Family resources play an important role in explaining child development. The ultimate constraint on a child is the accident of birth and the inability of the child to choose its parent. Additional constraints are the inability of parents to borrow against the future earnings of a child to finance investment in the child and the inability of parents to borrow against their own future income to finance investments in their children. The recent literature suggests that the truly scarce resource facing disadvantaged children is parenting, which may be only loosely related to measures of parental family well-being.


  • a

    For example, Becker contrasts the implications for the earnings distribution of ability models of earnings and human capital models, claiming that the latter are more consistent with the empirical evidence on earnings.12 The implicit assumption in his analysis and the literature it spawned is that ability is determined by nature, that is, is genetic, and outside the influence of family investment strategies.

  • b

    A special issue of Twin Research and Human Genetics edited by Jennifer Harris provides many concrete studies.13

  • c

    There is some evidence that gene expression affected by environment is heritable.10,20

  • d

    Some recent evidence on gene–environment interactions resulting from child maltreatment is presented in Caspi, McClay, et al.17 Rutter surveys this evidence.10

  • e

    Permanent income is the measure of socioeconomic status in this figure. See CHLM for the source of this figure and the precise definition of permanent income.

  • f

    Head Start is a national program targeted to low-income preschool-aged children (ages 3-5) that promotes school readiness by enhancing their social and cognitive development through providing educational, health, nutritional, social, and other services to enrolled children and families. There is a new program, Early Head Start, that begins at age 1.

  • g

    Currie and Thomas present additional analyses of the Head Start Program.40

  • h

    The Perry preschool experiment was an intensive family enhancement preschool program administered to randomly selected disadvantaged black children enrolled in the program over five different waves between 1962 and 1967. Children were enrolled 2½ hours per day, 5 days a week, during the school year and there were weekly 1½-hour home visits. They were treated for 2 years, at ages 3 and 4. A control group provides researchers with an appropriate benchmark to evaluate the effects of the preschool program.

  • i

    CHLM briefly discuss the evidence on this point and suggest a model of comparative advantage in occupational choice to supplement their model of skill formation.

  • j

    Cunha and Heckman develop a formal overlapping generations (OLG) model in section C of their Web site.24

  • k

    A sketch of such a model is discussed in Carneiro, Cunha, et al.59

  • l

    Cunha and Heckman ignore investments in the child's adult years to focus on new ideas in their analysis.24

  • m

    These conditions are sufficient. There is no need for a differentiability requirement for h, and the differentiability requirement with respect to θt can be weakened.

  • n

    Examples are developed in section A of the Web site in Cunha and Heckman.24

  • o

    The Abecedarian Project recruited children born between 1972 and 1977 whose families scored high on a “high risk” index. It enrolls and enriches the family environments of disadvantaged children beginning a few months after birth and continuing until age 5. At age 5—just as they were about to enter kindergarten—all the children were reassigned to either a school-age intervention through age 8 or to a control group. The Abecedarian program was more intensive than the Perry program. Its preschool program was a year-round, full-day intervention.

  • p

    The CPC was started in 1967, in selected public schools serving impoverished neighborhoods of Chicago. Using federal funds, the center provided a half-day preschool program for disadvantaged 3- and 4-year-olds during the 9 months that they were in school. In 1978, state funding became available, and the program was extended through third grade and included full-day kindergarten.

  • q

    See CHLM for a definition of critical and sensitive periods in terms of technology (1). These definitions are developed further in Appendix B of Cunha and Heckman.24

  • r

    This technology applies to in utero and postnatal investments as well. See Shonkoff and Phillips for evidence on the importance of such investments.60

  • s

    CHLM analyze the vector case.

  • t

    Both periods are critical. Here the production function is not strictly differentiable as required in the definition. The definition can be extended to deal with this limit case.

  • u

    I offer another explanation of the apparently weak Head Start effects below.

  • v

    Consider an example in which inline image for t= 1, 2; ρ1= 1,  ρ2 < 1; and η1,t2,t3,t= 1. Then, substituting for θ2, one obtains inline image. The parameter φ2 describes how easy it is to compensate early neglect with second-period investment. The parameter φ1 describes the compensation possibilities for overcoming adverse initial conditions θ1 with first-period investment. The technology in the text is obtained by setting φ12,  η3,13,21,1= 0, so that γ=η1,2η2,1 and η2,2= 1 −γ. See Section A.1 of Cunha and Heckman.24

  • w

    At their Web site, Cunha and Heckman develop an overlapping generations model.24

  • x

    Table A1 on the Web site for Cunha and Heckman concisely summarizes this analysis.24

  • y

    I refer to parental resources specific to a given generation.

  • z

    This thought experiment is whimsical. If parents create the child, through genes and environment, the child is not an independent actor. Under a homunculus theory, the child would have an identity independent of the parent.

  • aa

    Of course, other reasons why skill gaps open up early and are perpetuated are variation in h and θ1, the parental environmental and initial endowment variables, respectively.

  • bb

    This type of constraint is also analyzed by Caucutt and Lochner.62

  • cc

    Belley and Lochner show that, in recent years, the effect of family income in the adolescent years on college attendance has increased and may play a quantitatively more important role in affecting college enrollment than it has in the past.45

  • dd

    The Abecedarian early intervention program permanently boosted adult IQ. See CHLM.

  • ee

    The exact mechanism by which noncognitive skills are boosted is not yet established. It could be that noncognitive skills are created directly in the early years and persist. It could also be that the higher early cognitive skills that fade out foster noncognitive skills that persist. Both channels of influence could be in operation.

  • ff

    Anchoring test score outcomes in behavior avoids reliance on arbitrarily scaled test scores as a measure of output.53,78

  • gg

    This is fact three of Section 1.


This research was supported by National Institutes of Health Grant R01-HD043411, National Institute of Child and Health Development Grant R01 HD054702, National Institute on Aging Grant P01 AG029409-01, National Science Foundation Grant SES-024158, National Science Foundation Grant BCS-0433990, Buffett Early Childhood Fund at the Susan T. Buffett Foundation, the Nemours Foundation, the Committee for Economic Development with a grant from the Pew Charitable Trusts and the Partnership for America's Economic Success, and the Pritzker Family Foundation's Children's Initiative's support of the Pritzker Consortium on Early Childhood Development at the Harris School of Public Policy, University of Chicago. The views expressed in this article are those of the author and not necessarily those of the funders listed here.

Conflicts of Interest

The author declares no conflicts of interest.