Evaluating the Effects of Childcare Policies on Children’s Cognitive Development and Maternal Labor Supply

Andrew S. Griffen

doi:10.3368/jhr.54.3.0315.6988R1

Abstract

To explore the role of childcare policies in the development of early cognitive skills, this paper jointly estimates a cognitive achievement production function and a dynamic, discrete choice model of maternal labor supply and childcare decisions. Using counterfactuals from the model, I investigate how the designs of two childcare programs, Head Start and childcare subsidies, affect the formation of cognitive skills through maternal work and childcare decisions. The results suggest large impacts on cognitive skills from expanding Head Start to current noneligibles and negligible impacts of subsidies on cognitive skills of current eligibles.

JEL Classification

I. Introduction

The formation of cognitive skills has been a source of renewed interest in recent years given the importance of early cognitive skills in predicting later life outcomes (Currie and Thomas 1999; Chetty et al. 2011) and work suggesting that cognitive skills are formed relatively early in life (Cunha and Heckman 2007, 2008). Human capital policies for children can take many forms (Almond and Currie 2011), but one area of focus is the childcare decisions of families. The reason for this focus in the United States is that children spend on average a substantial fraction of time outside their parents’ care, even at young ages. Among nine-month-old children, for example, 45.1 percent spent time in some form of nonparental childcare and those children were in care on average 31.4 hours/week.¹ Theories of child development emphasize the importance of stimulating environments for the development of skills (Case 2013; Piaget and Inhelder 1969), and empirical research consistently finds positive associations between a child’s test score and the quality of their environment, whether in the home or the childcare setting (Love, Schochet, and Meckstroth 1996). Therefore, improving childcare experiences is seen as a potentially effective means of improving cognitive skills in early childhood (Blau and Currie 2006).

To that end, I study how the design of two prominent childcare policies, Head Start and childcare price subsidies, affect mothers’ labor supply and childcare choices, and how those decisions in turn affect their children’s cognitive skills.² Head Start is a free, federally funded preschool program for poor children that aims to “promote school readiness by enhancing the social and cognitive development of children.”³ A randomized controlled trial of Head Start (Head Start Impact Study) demonstrated that the program has positive effects on cognitive achievement at kindergarten entry that fade out by first grade (Puma et al. 2005), which has led to calls to cut Head Start funding or to change how Head Start is implemented. In the face of budgetary pressure, understanding who should be eligible for Head Start and how to design Head Start to improve cognitive skills are important questions to answer in order to improve the program’s effectiveness.

I also study childcare price subsidies provided through the Child Care and Development Fund (CCDF). These subsidies lower the price of childcare services for income-eligible mothers conditional on the mothers working. Although childcare subsidies are designed primarily to support the labor force participation of women (Adams and Rohacek 2002), how to incorporate child development goals into the design of childcare subsidies has been an issue at least since the 1970s (Heckman 1974). Childcare subsidies have an ambiguous impact on child outcomes because subsidies can simultaneously increase the demand for childcare quality, which improves cognitive skills, and increase the use of childcare, which can lower cognitive skills if the home environment is more productive. Recent reduced form empirical research finds that subsidies have a negative effect on children’s cognitive outcomes (Herbst and Tekin 2010, 2016; Hawkinson et al. 2013). However, open questions are to understand the mechanisms through which childcare subsidies affect children’s cognitive achievement, to elucidate how childcare subsidy policy parameters affect choices, and to quantify the tradeoffs (if any) between impacts on maternal labor supply and cognitive achievement.

To investigate the design of these childcare policies, I embed a cognitive achievement production function into a dynamic discrete choice model of childcare and maternal labor supply decisions. In each model period (every six months), mothers receive a wage offer and a price-quality offer for childcare services. Fathers, when present, contribute to household income. Families eligible for Head Start have an additional Head Start specific quality offer in their choice set, and subsidy-eligible families also have the option to use the subsidies to reduce the price of childcare. The mother then makes decisions about whether to stay home, work part-time, or work full-time, and whether to keep her children at home, use childcare part-time, or use childcare full-time. The time spent in childcare, the quality of childcare, and the quality of the home environment are inputs into the cognitive achievement production function. The child’s cognitive skills and the mother’s labor market experience evolve endogenously, and the mother faces tradeoffs between consumption, leisure, the cognitive development of her children, and the accumulation of labor market experience. A mother in the model faces uncertainty in the form of shocks to wage offers, father’s income, divorce, fertility, the cognitive skills of her children, home quality, the price and quality of childcare, access to Head Start and subsidies, and preferences for leisure and childcare. Marital status and fertility are modeled as stochastic processes.

A dynamic structural model is a natural setting for examining the impact of alternative childcare policies for several reasons. First, cognitive skills develop over time, and a value-added cognitive achievement production function captures the dynamic nature of skill accumulation (Cunha and Heckman 2007, 2008). Second, a dynamic labor supply model captures the effect of childcare programs on the accumulation of maternal work experience, which can affect future labor supply and childcare use decisions.⁴ Third, the structural model allows a realistic representation of how different childcare policy parameters affect constraints, choice sets, and prices, which allows me to investigate both the channels through which the design of childcare policies affects outcomes and to perform out-of-sample counterfactuals. This is in contrast to most of the literature on Head Start and subsidies focused exclusively on treatment effects. Fourth, dynamic forward looking behavior allows mothers to forecast the impact of policy changes when making decisions. This forward looking behavior has been shown to generate more accurate out-of-sample predictions than myopic models or approximation decision rules (Keane and Wolpin 1997, 2007).

I estimate the model using indirect inference (Gourieroux, Monfort, and Renault 1993) with data from the Early Childhood Longitudinal Study–Birth Cohort (ECLS-B), a nationally representative panel of 14,000 children born in the United States in 2001. Children were followed until kindergarten entry, and extensive information was collected about the children’s home environments, childcare environments, and scores on cognitive assessments. I define and measure the “quality” of the child’s home and childcare environments in a way that is consistent with other early childhood research. The data also contain information on the wages and labor force participation decisions of mothers, fathers’ income, hours spent in childcare, prices paid for childcare services, marital status, and other characteristics of the child’s parents.

Using the estimated model, I study the effect of current and prospective Head Start and subsidy policies on the cognitive achievement of children and maternal labor supply. As a model validation exercise, I first evaluate the impact of Head Start in my model using the design of the Head Start Impact Study (HSIS), a randomized controlled trial of Head Start (Puma et al. 2005). The magnitude of the impacts of Head Start on cognitive skills in my model are consistent with those of the HSIS, which I take as evidence of the model’s validity. I then use the model to evaluate prospective out-of-sample changes to Head Start, such as expanding access by raising the income eligibility ceiling, increasing the age range of eligibility, increasing Head Start program hours, providing equivalent cash transfers to eligible families, and improving Head Start quality. These Head Start counterfactual exercises are motivated by specific policy proposals made directly in response to the HSIS findings (improving quality and increasing hours, proposed during the Obama administration), by calls for more research into tradeoffs and interactions of policy parameters both within and between different forms of government childcare policy (Blau 2003; Blau and Currie 2006), and by interesting differences among countries in the design of childcare policies (for example, universal government provided childcare).⁵

The counterfactual results show that Head Start is effective at increasing cognitive skills, even for currently noneligible children, which suggests a role for expanding access to Head Start. A universal offer of Head Start is predicted to increase cognitive skills by 0.13σ at age five. This is a consequence of the relatively poor quality of childcare in the United States (compared to Head Start) and the intensive use of childcare, even among higher income families. Another important result is a large impact from expanding hours of Head Start, which is consistent with proposed reforms aimed at Head Start. However, proposed quality improvements produce relatively small improvements compared to baseline because of the small variation in Head Start quality compared to the larger market for childcare services. Increasing the age eligibility range can increase cognitive skills, but at higher cost because the effects dissipate over time as some children are treated but cycle out of participation. Overall, the results imply that targeting Head Start and increasing its hours, rather than changing its quality or age range, would be more effective at improving cognitive skills. The fact that some of the counterfactuals, based on proposed or existing variation in Head Start policies, produce similar impacts at varying costs indicates that more attention should be paid to how Head Start funding is allocated across different program policies. Interestingly, Head Start has very little interaction with subsidies for reasons having to do with the design of the programs that show up clearly when modeling them. The programs appear to serve different populations in the data, and families select into each program accordingly.

I also use the model to study the effects of current and prospective childcare price subsidies. In contrast to recent research on childcare subsidies, I find that for the typical subsidy-eligible population that subsidies have negligible impacts on cognitive skills. The subsidies do, however, have fairly substantial impacts on maternal labor supply, demonstrating that subsidies can be an important work support. The estimated lack of a tradeoff between labor supply and child skills is an important practical policy finding because concern about a tradeoff for these competing objectives has been raised repeatedly in the design of subsides (Blau 2003; Blau and Currie 2006; Heckman 1974). The result is driven by the childcare quality and choice patterns observed in the data, and I connect the result to these patterns.

I also explore impacts of varying subsidy policy parameters. The purpose of these counterfactuals is both to unpack the mechanisms behind the impacts and to provide insight into the consequences of changes in subsidy policies.⁶ Moving beyond treatment impacts to mechanisms is important for reasons elucidated in Elango et al. (2016), especially for prospective policies. In general, the results show that, for the subsidy-eligible population, making the subsidies more generous induces more participation and has larger impacts on labor supply. However, there is interesting impact heterogeneity by subsidy design that suggests that mothers are more responsive to raising the price reimbursement rate than lowering family copayments. As predicted from the structural model, raising income eligibility cutoffs for subsidies does not increase participation, as the fixed copay rate creates a natural disincentive for higher income families. However, the main conclusion is that the current design of subsidies, although not improving cognitive skills, is not estimated to have harmful impacts either.

This paper contributes to a large literature in child development and education and an emerging literature in economics on childcare decisions and their impacts on children’s skills. Outside of economics, papers typically focus on measuring the quality of childcare environments and regressing child outcomes on childcare quality and other controls. Examples include NICHD Early Child Care Research Network (2001), Love et al. (2003), and Burchinal et al. (1996, 2000, 2008). Papers then consider whether there are statistically significant associations between childcare quality and children’s skills and sometimes assess the magnitude of impacts on children’s skills from improving childcare quality. Blau (1997, 1999) provides an extended discussion and criticism of the results from this literature. Essentially the papers tend to use small, nonrepresentative samples and do not address problems of sample selection, endogeneity of inputs, unobserved inputs, interpretation of parameters, or robustness to departures from linear functional forms. Another criticism is that while directly improving childcare quality is an interesting thought experiment, it is not actually a control variable for childcare policymakers. Instead, a more realistic set of policies operates through the choice sets, prices, and the constraints that families face for childcare services. Basically, it is difficult to determine which policies could conceivably induce the higher quality inputs that these papers consider in their counterfactuals.

Within economics, much more focus is put on the endogeneity of childcare decisions and developing a model of the formation of children’s skills. Papers have estimated production functions for cognitive achievement taking into account childcare decisions (Duncan 2003; Bernal and Keane 2010, 2011) and childcare characteristics (Blau 1999) and have jointly estimated behavioral models and production functions (Bernal 2008; Del Boca, Flinn and Wiswall 2014). The work most closely related to my paper is Bernal (2008).⁷ She also models work and childcare decisions in the context of a cognitive achievement production function but only considers time in childcare as an input and ignores differences in childcare quality experiences.⁸ This is a result of data limitations in the NLSY-79.⁹ Bernal (2008) actually suggests incorporating a quality decision as an important extension to her work and as a potential qualification to her findings. Interestingly, my results are broadly consistent with her findings, but what she attributes to differences in impact by unobserved heterogeneity I find to be driven by the childcare quality patterns in the data. This is relevant for policy because if variation in impact is driven by quality choices and not some other unobserved variable, such as mother’s ability, then it suggests a direct role for childcare policies. My model also extends her framework along several important dimensions by incorporating a Head Start option, a realistic representation in the budget constraint for both childcare subsidies and Head Start, an intensive margin for childcare and labor supply, and the potential for divorce and fertility.¹⁰

A limitation of the economics papers from a child development perspective is the lack of focus on childcare quality as an input into the production function.¹¹ Moreover, given the large variation and relatively poor quality of childcare quality in the United States (Lamb 1998; Vandell and Wolfe 2000; NICHD Early Child Care Research Network 2005), the intensive use of childcare, and the importance of a child’s environment in theories of child development, this is an important omission in the economics literature on childcare and child development. My paper incorporates insights from the child development literature into a behavioral model of childcare decisions and serves to bring the economics literature on child development closer to the literature on child development in education and psychology.

The rest of the paper is organized as follows. I present the model in Section I, the data in Section II, and the estimation in Section III. Section IV presents the parameter estimates and the model fit, Section V presents the counterfactual results, and Section VI concludes.

II. Model

The model begins when a mother first has a child and ends when she turns 45. Mothers can be married (or not), face the risk of divorce, and can have more children as they age. Every six months the mother makes a labor supply decision and a childcare decision for her children. For her labor supply decision, the mother receives a wage offer that depends on her characteristics, and she can either work full-time, work part-time, or stay home. For childcare, the mother chooses, for all her children younger than age five, whether they attend childcare full-time, part-time, or stay at home. Here I define “childcare” as any type of nonparental care, and I define “home care” as care given by one of the child’s parents in the child’s home.¹² In the model, childcare varies in both quality and price. Families make a draw from a price–quality distribution for childcare services and can then choose whether to use childcare at that price and quality. Children from eligible families also have the option to attend Head Start, which offers free childcare for children from poor families. In addition, conditional on eligibility, mothers can also use subsidies to help reduce the costs of childcare.

In the model, mothers face a skill production function with the quality of childcare, the time spent in childcare, and the quality of the home environment as inputs. The child’s cognitive skills and the mother’s labor market experience evolve endogenously, and the mother faces tradeoffs between consumption, leisure, the cognitive development of her children, and the accumulation of labor market experience. For the remainder of the model section, assume that I have univariate measures of both home quality and childcare quality. After the model section, I discuss how I measure home and childcare quality in a way consistent with other early childhood research. To facilitate exposition of the model, I present the model without some of the exact specifications, which are relegated to the Appendix.

A. Preferences

The mother’s contemporaneous utility function is given by

(1)

where her utility at time t, u(t), depends on her consumption , a vector of the cognitive skills of all her children less than age five θ_t, her hours of leisure h_lt, hours of childcare for her children h_ct, a permanent unobserved component η, a shock to the utility of hours of leisure ε_lt, and a shock to the utility of childcare hours use ε_cct.¹³ Other variables enter through the state space Ω_t, as marginal utility shifters by allowing some parameters to vary by marital status m_t, the number of younger children k_t, the number of older children o_t, mother’s race, and a vector with the ages of the younger children a_t.

B. Childcare

Each period the household receives a price–quality offer for childcare services. I assume the childcare quality offers are drawn from¹⁴

(2)

where the mean quality offer can depend on both observable, x_c, and unobservable characteristics, η, of the household. The price for the childcare quality draw is then given by the hedonic equation:

(3)

where the childcare price, p_ct, depends on the quality draw q_ct, observable characteristics x_p, unobservable characteristics η, and a shock ε_pt. The dependence of the price–quality draw on characteristics is intended to capture variation in the childcare choice sets across families. The child(ren) can then attend childcare of quality q_ct for hours h_ct ∈{0, 500, 1,000} at a price per hour of p_ct.¹⁵ I assume the mother makes the same childcare hours decision for all children in the household.¹⁶

C. Head Start

Families may be eligible for government provided care in the form of Head Start. I assume that a Head Start–eligible family makes a draw from the distribution of Head Start quality:

(4)

A child can then attend Head Start that offers childcare of quality q_hs,t.¹⁷ To be eligible for Head Start at time t, child i’s age, , must be between three and five, and family income must be below a federal threshold, , that depends on family size.¹⁸ The income eligibility cutoff potentially introduces labor disincentives because maternal employment may make children ineligible. Because Head Start is rationed, I assume that eligible families receive an offer of Head Start with probability π_hs. Let equal 1 if child i is eligible for Head Start at time t and 0 otherwise:

(5)

Further let be a choice variable that equals 1 if and the mother chooses Head Start for child i, and 0 otherwise.

D. Home Quality

Home quality at time t, q_ht, is modeled as a function of both observed variables, x_ht, a permanent unobserved component, η, and a transitory component, ε_ht:

(6)

E. Cognitive Achievement Production Function

Cognitive skills evolve endogenously according to the hours spent in childcare, the quality of the childcare arrangement, the quality of the home environment, the time spent at home, and previous skills. Initial cognitive skills, , are given by

(7)

where the observable and unobservable η contributions to initial skills capture either endowments or prenatal investments. The cognitive skill production function is given by

(8)

so that cognitive skills for child i at t + 1, , are formed through a value-added production function that depends on lagged cognitive achievement , inputs , and a shock . Inputs are a time weighted average of the home and childcare quality environments:¹⁹

(9)

Note that the input has a child i specific superscript. Children within the same family can receive different inputs through , which is a time-weighted average of the market childcare quality draw, q_ct, and the Head Start quality draw, q_hs,t, that depends on whether and how much time child i spends in Head Start (see the Appendix for a complete specification). The index assumption in Equation 9 naturally captures that the opportunity cost of using childcare is the foregone home quality, which has the interesting implication that childcare use can have differential impacts across children depending on their home environments. This is also the first place in the model where dynamics are potentially important, as initial skills and inputs both propagate through the value-added cognitive achievement production function.

F. Wages and Income

For married couples, the household enters the period knowing the father’s education, e_f, and years of experience, x_ft. The household then draws an income shock, ε_yt, to form the father’s earnings. Similarly, the household draws a wage shock, ε_wt, and uses the mother’s education, e_m, and years of experience, x_mt, to form the current wage offer. The income function for the father is given by

(10)

where I also have added a household specific permanent component, η. I assume that the father works full-time

(11)

so that his years of experience augments each period by 0.5 years (six months).²⁰ Analogously, the wage offer function for the mother is

(12)

which also depends on a household specific permanent component, η. Unlike the fathers, however, the mother’s years of experience evolves based on her hours of work choice, h_ct ∈{0, 500, 1,000}, according to²¹

(13)

If, for example, the mother works full-time, h_wt = 1,000, then her experience will increase by 0.5 years. This is the second place in the model where dynamics are important, as work today will increase wage offers (and the probability to work) in the future.

G. Childcare Subsidies

Childcare subsidies programs in the United States have three features: (i) an income cutoff above which families are ineligible, (ii) a rate ceiling that determines the marginal price that the family pays, and (iii) a copay that is a percentage of family income. If the price of childcare is less than the rate ceiling, then the effective price per hour is zero. If the price per hour is greater than the rate ceiling, then the family pays the difference between the price and the rate ceiling for each hour of childcare. Define the program features:

(14)

(15)

(16)

where m_t is an indicator variable that equals 1 if married and 0 otherwise, so that if married, the father contributes y_tm_t to family income. Then, the copay is a percentage ψ of family income y_tm_t + w_th_wt. For a given number of hours, h_ct, instead of paying p_cth_ct per child, the cost under the subsidy becomes

(17)

Families always pay the copay and pay zero marginal price per hour if the price of childcare is less than the rate ceiling and positive marginal price (p_ct – rc) if the price is greater than the rate ceiling. The subsidy program has an interesting feature that subsidy-eligible mothers may not always elect to use the subsidy. This can occur if the copay is large enough to outweigh the fall in the marginal price of childcare from the subsidy. This would particularly apply to families with low prices for childcare, few hours spent in childcare, or those having relatively higher incomes.²²

To allow for the possibility of rationing of the subsidies, I assume that eligible families receive a subsidy offer with probability π_s. Let equal 1 if the family is eligible for the subsidy and 0 otherwise,

(18)

which captures two main features of the program: (i) mothers must work, h_wt > 0, and (ii) family income, y_tm_t + w_th_wt, must be below an income threshold . Let equal 1 if and if the mother chooses to use the subsidy for child i and 0 otherwise.²³

H. Fertility and Divorce

In the model, the probability of a birth is given by , which depends on observable characteristics . At any given time, I do not permit mothers to have more than three children less than five years of age.²⁴ When a child turns five, the number of older children, o_t, increases by 1, and the number of younger children, k_t, decreases by 1. The probability of divorce is given by , which depends on observable characteristics . I do not permit women with young children to remarry or to cohabit with a nonbiological father.²⁵

I. Shocks and State Space

Before making labor force and childcare decisions, the mother makes a childcare quality draw q_ct, a childcare price draw p_ct, a draw for subsidy eligibility , a draw for Head Start eligibility , and, conditional on eligibility for Head Start, a Head Start quality draw q_hs,t. Let denote the vector of Head Start eligibility for each child i in the house. The household also draws shocks to cognitive skills for each child , home quality ε_ht, utility of leisure ε_lt, utility of childcare ε_cct, mother’s wage offer ε_wt, and father’s income ε_yt. Collecting the shocks in a vector ϵ_t, define the state space at time t:

(19)

J. Choices

The mother makes decisions about her hours of work and a childcare hours decision for all her children younger than age five. Let h_wt be a discrete variable that equals 0 at time t if the mother works 0 market hours, 500 if she works part-time, and 1,000 if she works full-time. Hours of childcare for child, h_ct, is assumed to be the same across all siblings and can also equal either 0, 500, or 1,000. Without considering Head Start or childcare subsidies, a family would have nine choices.²⁶ However, depending on the number of children, whether the family is eligible for childcare subsidies, and whether (at least one) of the children is eligible for Head Start, the childcare choice set can expand up to 33 choices.

K. Budget Constraint

The budget constraint is straightforward on the revenue side: the father’s income y_t enters if marital status m_t equals 1, and the mother’s wage, w_t, multiplies her hours of work, h_wt. On the expenditure side, both Head Start and childcare subsidies shift the marginal and fixed cost of childcare expenditures for each child. The programs can affect childcare costs independently or potentially interact. Let be an indicator for whether a child i is in the house at time period t. The budget constraint is then given by²⁷

(20)

I assume that mothers receive a share of family consumption that depends on family size and marital status according to

(21)

L. Mother’s Problem

At each period a, the mother makes labor supply and childcare decisions to maximize the expected present value of remaining lifetime utility,

(22)

subject to the within period budget constraint. The expectation is formed over the distribution of the value function given the optimal decision rule and the transitions induced by the evolution of experience and the production function.

M. Terminal Value

The model ends when mothers become 45 years old. Following Bernal (2008), I assume mothers have a terminal value that captures the remaining lifetime utility given by²⁸

(23)

N. Unobserved Heterogeneity

I assume the distribution of unobserved heterogeneity, f(η), follows a discrete distribution with J support points. The support points are sometimes called “types.” This treatment of unobserved heterogeneity follows Heckman and Singer (1984). Recall that there is unobserved heterogeneity over preferences, income, wages, home quality, cognitive skills, and the price/quality distribution. In the estimation I assume that there are J = 6 types.

O. Solution Method

The model is written recursively and solved backward from the last period. Given the state space, I draw from the distribution of shocks and calculate the optimal choice. I repeat this process and take the average over the optimal values. This simulated integration gives the expected maximum value at that particular state space point. I then pick a different state space point and repeat the simulated integration. The resulting function is known in the literature as the EMAX function. Instead of calculating the EMAX at every point in the state space, I use an approximation method developed by Keane and Wolpin (1994). First, I randomly select a subset of the state space points and calculate the EMAX at each point in the randomly drawn subset. Second, I use a regression polynomial in the state space points to approximate the EMAX function and then use the estimated polynomial to form the expected future value of utility given today’s choices when solving the model backwards or when simulating the model. For the evolution of marriage and number of children, I use exact integration because I have a closed form for the probabilities.

II. Data

I estimate the model using data from the Early Childhood Longitudinal Study–Birth Cohort (ECLS-B). The ECLS-B is a nationally representative panel of 14,000 children born in 2001. Researchers followed the children from birth until kindergarten entry and collected detailed information about their family background, home environments, childcare environments, maternal work decisions, childcare use decisions, maternal wages, family income, and cognitive achievement outcomes. Childcare providers were given questionnaires that asked detailed information about the care environment, care activities, qualifications, and questions designed to elicit information about their attitudes towards childcare. Families were also asked questions about the kinds of activities the child engaged in and the materials and toys to which the child had access. Before describing statistics from the data, I first detail how I measure home and childcare quality and how cognitive skills were assessed in the ECLS-B.

A. Measuring Quality

The quality of an environment, either in the home or in a childcare setting, is intended to capture the amount of stimulation that children receive in that environment.²⁹ Stimulation can come in the form of developmentally appropriate materials, whether the caregiver encourages the child and the kinds of activities that the classroom or child does during their time in childcare, such as reading books or singing songs (Love, Schochet, and Meckstroth 1996; Caldwell and Bradley 1984). In the childcare literature, researchers make a distinction between structural and process measures of quality (Vandell and Wolfe 2000). Structural measures include the student/caregiver ratio and the qualifications of the caregiver. Improved structural measures are thought to increase the likelihood of high quality care but do not guarantee improved care quality. On the other hand, process measures capture what actually occurs in the childcare environment and are the actual “quality” of the childcare environment.

One commonly used measure of childcare quality is the Early Childhood Environment Rating Scale (ECERS). The ECERS asks questions about the routines that occur in the classroom, the use of language by the caregiver toward the child, whether there is time for motor activities, whether the child engages in creative activities such as music or art, observer impressions of the “tone of interaction,” and more. Other scales, such as the Global Rating Scale, attempt to measure whether the relationship between the care provider and the child is “positive” by assessing how the caregiver speaks to the child, whether they enjoy the child, etc. (Lamb 1998). Although the scales have some overlap, there does not seem to be complete uniformity in questions that relate to quality. In general, measures of childcare quality can then be any variable that measures materials in the care environment and whether the interactions between child and caregivers are “stimulating.”

Analogous to issue of measuring childcare quality is the issue of measuring home quality. A commonly used measure is the Home Observation for the Measurement of the Environment (HOME). The HOME scale is based on direct observation and interviewer questions of the parent. The questions vary by the age of the child. Some subscales that span multiple ages are questions related to the learning environment, parental responsiveness, and learning materials. The HOME scale includes questions about whether the parent spontaneously spoke to the child, verbal responses to the child, whether the parent provided toys to the child, and whether the interviewer felt the play environment was safe. The goal is to capture whether the child lives in a stimulating environment both from the mother and from items that the family might buy.³⁰ Caldwell and Bradley (1984) argue that the HOME scale is consistent with “Piagetian notions about the development of sensorimotor and preoperational thinking.”

An advantage of using these scales is that both the ECERS and HOME have been extensively used and validated in the literature.³¹ However, Cunha and Heckman (2008) state that a disadvantage of these indexes is that they “often have an ad hoc quality about them and may be poor proxies for the true combination of inputs that enter the technology.” In my data, I have measures from the HOME scale and from the ECERS scale. However, a limitation is that the ECLS-B contains only a subset of questions from the HOME scale, and the ECERS was collected for only a small subset of children. The data also contain additional questions that could be considered inputs, and I risk losing information by focusing only on the HOME and ECERS scale.

Similar to the existing scales, I choose to combine all of the information on inputs into a single variable for the home environment and a single variable for the childcare environment. Specifically, for the measurements of home and childcare quality and for each data round, I use principle components analysis (PCA) to collapse the data into an index where the component is chosen to explain the maximize amount of variance in the measures of home and childcare quality. I treat the predicted component as data. Although using PCA does not address the criticism that the weights are arbitrary, PCA captures a component that explains the maximum amount of variance in the data and allows me to expand my sample and to incorporate all input information in the data. Moreover, given that questions vary across existing scales, it seems that there is no consensus on which measures should be used to capture the quality of children’s experiences.³² In the Online Appendix (available at http://jhr.uwpress.org/), Table A.1 has a list of questions and summary statistics for the measurements that I use to form the childcare quality measure. Table A.2 is an analogous table for the home quality measurements. The childcare quality measures are reported by the childcare providers. The home quality measurements are a mix of direct observations and self-reports by the parents. In the subsequent section when discussing statistics from the data, I demonstrate that both of the constructed indexes by PCA are statistically significant and quantitatively large predictors of cognitive skills in a value-added model with controls.

B. Measuring Cognitive Skills

For cognitive achievement measures, the ECLS-B contains the Bayley Short Form–Research Edition (BSF-R) in the first two rounds. The BSF-R uses a subset of the Bayley Scales for Infant Development, 2nd Edition (BSID-II), which is a widely used assessment to “monitor neurodevelopmental outcomes in young children up to three years of age” (Bos 2013) and which predicts later cognitive functioning (dos Santos et al. 2013). The BSF-R places infants in various situations and scores their responses and can be given to children from 2 to 30 months. The assessment contains both a mental and a motor score. I use the mental score for my analysis. Example situations from the BSF-R include ringing bells and checking whether the child turns their head in response and whether the child vocalizes at least once during the interview. Each situation contains a series of activities that are age and developmentally appropriate. The assessor checks the child’s responses in order to locate their basal and ceiling levels. For the ECLS-B, the interviewers gave children a core assessment and moved downward to the basal set for children for whom the core set was too difficult. The ceiling set was used for children who scored perfectly on the core set. Instead of reporting the BSF-R score, researchers used item response theory to predict a scale score on the BSID-II, which is what is reported in the data file.

For cognitive achievement at older ages, the ECLS-B administered math and early reading tests. The math and reading tests were adaptive tests derived from well-known early childhood assessments (Najarian et al. 2010). To encourage cross-study comparisons, the ECLS-B used questions previously developed for the ECLS-K, the Head Start Impact Study, and the Family and Child Experiences Study. In addition, questions were added from the Peabody Picture Vocabulary Test (PPVT, various forms), the Test of Early Mathematics Ability-3 (TEMA-3), the Preschool Comprehensive Test of Phonological and Print Processing (Pre-CTOPPP), and the PreLAS 2000.³³ Again, the ECLS-B contains scale scores and T-scores for both the math and early reading tests. I use the scale scores. To combine information, I simply average the math and early reading scores. Finally, because test scores do not have a metric, I standardize the scale scores by age.

C. Summary Statistics

Table 1 shows summary statistics from the ECLS-B disaggregated by marital status, race, and maternal education.³⁴ One of the most salient features is the gaps in cognitive achievement already present at young ages. Children from married households have 0.33σ higher test scores than children from single family households, and the average difference between black (Hispanic) and white children is 0.35 (0.44)σ.³⁵ There are similar gaps by maternal education: the average difference in children’s cognitive skills between a mother with a high school diploma versus a college degree is 0.39σ. These gaps are large. A one standard deviation gap corresponds to approximately one year of developmental delay, and gaps at school entry explain 60–70 percent of skill gaps in later school years (Bradbury et al. 2015). Given the importance of skills gaps at age 16 in explaining labor market outcomes (Neal and Johnson 1996; Keane and Wolpin 1997), the persistence of early skill gaps suggests that explaining their formation before school entry is clearly important.

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Table 1

Summary Statistics ECLS-B Estimation Sample^{^a}

The data also show standard human capital differences by mothers’ characteristics. Compared to single mothers, married mothers have more years of education (14.57 vs. 12.37 years) and higher wages ($18.77/hour vs. $10.61/hour). The same basic pattern holds for white (14.94 years and $19.27/hour) versus black (13.42 years and $13.79/hour) and Hispanic (12.30 years and $12.29/hour) mothers. Interestingly, higher observed wages do not necessarily translate into higher labor force participation as both single (62%) and black mothers (62%) work more than married (50%) or white mothers (54%). This could be a result of nonlabor income effects for married mothers, higher marriage rates for white mothers (92%) compared to black mothers (45%), and, conditional on being married, higher husband income for white versus black mothers ($29,913/6 months vs. $21,161/6 months).³⁶ Hispanic mothers, on the other hand, actually have lower labor force participation (50%), while more educated mothers have higher labor force participation (57% college vs. 47% high school). The childcare use patterns largely track the labor force patterns with a high correlation between the choices (Spearman’s ρ = 0.59), which is consistent with the notion that childcare is used primarily while mothers are working.

The income eligibility requirements for Head Start and subsidies clearly show up in the data, with higher participation rates in both programs among those likely from lower income households. Specifically, Head Start participation is higher among single (12.93%) versus married (4.07%), black (16.56%) and Hispanic (13.42%) versus white (2.28%), and by maternal education (12.21% high school vs. 3.80% college). Similar patterns hold for subsidy participation: single (8.37%) versus married (0.43%), black (8.02%) and Hispanic (1.82%) versus white (0.93%), and by education (3.01% high school vs. 1.34% college). Overall, Head Start has higher use than subsidies (5.74% vs. 1.82%), reflecting the larger scale of Head Start.

The home quality patterns largely follow the previous discussion. Measured home quality environments are higher for married than for single mothers (0.26 vs. −0.18), white (0.37) versus black (−0.16) and Hispanic mothers (−0.24), and for higher educated mothers (a 0.5 gap between high school and college graduates). However, the childcare quality patterns are fairly different. First, there is much less between-group variation in childcare quality. This can be seen in smaller differences in the means across maternal characteristics. Second, the children of single mothers do not have much lower quality childcare experiences compared to married mothers (0.03 vs. −0.06), and black children actually have higher childcare quality experiences (0.17) on average than white children (0.00).³⁷ Hispanic children, however, have lower childcare quality experiences (−0.02) than either white or black children. Another interesting feature is that the childcare quality experiences of the children of more highly educated mothers are not substantially higher; the difference in childcare quality between high school versus college is only 0.11, which is much smaller than the comparable gap for home quality. The exact reasons for these patterns are not clear. It might reflect differential access to higher quality Head Start by single, black, and lower educated mothers, but it could also reflect market substitution for the lower productivity of the home environments of these groups of mothers. These patterns are important because they will drive several of the counter-factual results below. I next present evidence that the home and childcare quality inputs translate the same way into skills.

Table 2 estimates reduced-form value-added cognitive achievement production functions.³⁸ The purpose is to demonstrate the importance of considering quality measures as inputs. In addition, the reduced form evidence helps guide some of the choice of specification of the production function in the structural model. Column 1 of Table 2 begins with a simple value-added model showing the importance of lagged cognitive skills in forming subsequent skills à la Cunha–Heckman. Column 2 adds as an input the quality index given in Equation 9, which shows up as statistically significant and large in magnitude.³⁹ A back-of-the-envelope calculation suggests that equalizing black (Hispanic)–white gaps in the quality index would decrease the black (Hispanic)–white skill gap by 21 (23) percent.⁴⁰ Column 3 allows the home quality index [(2,000 – h_ct)q_ht/ 2,000] and the childcare quality index [)/2,000] to have separate parameters. The parameters have very similar magnitudes, and there is no statistical difference between them. Finally, interactions between the inputs in Column 4 are quantitatively close to zero and not significant. The latter two findings provide support for the index assumption in Equation 9.

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Table 2

Reduced Form Cognitive Achievement Regressions (Dependent Variable: Cognitive Skills)

D. Timing, Attrition and Sample Selection

The ECLS-B consists of five rounds of data collection. The researchers visited the children when they were approximately nine months, two years, four years, and five years with a follow-up round for delayed kindergarten entrants. I use the first four rounds.⁴¹ Two issues complicate taking the model to the data. First, the spacing between rounds is irregular. Second, there is a large amount of variability in the age at assessment in each round. For example, in the nine-month round, the children actually ranged in age from six months to 18 months. Because of these features, I instead organize the data into six-month bins, with bins at 6–12 months, 12–18 months, 18–24 months, etc. For each round I will see some children in each age bin, and I will see each child four times (ignoring attrition). I treat the observations between rounds when I do not see the child as missing data. Because the amount of missing data is large, I do not estimate the model by maximum likelihood. Instead I use indirect inference where I simulate different paths and estimate auxiliary statistical models on the simulated data. The estimation procedure is described in more detail below.

Like any panel data, the ECLS-B experienced attrition across survey rounds. From an initial sample of 14,000, 10,700 respondents entered the first survey round. Each subsequent round lost approximately 3 percent of the sample for a total of 36,000 round × individual observations across the four rounds. This level of attrition is consistent with other large panel data sets (Fitzgerald, Gottschalk, and Moffitt 1998; Griffen, Nakamuro, and Inui 2015), and the ECLS-B provides weights to correct for this attrition that I use in my analysis. Further imposing that the children are measured at or before age five gives 29,150 observed round × individual observations, which is 80 percent of the nonattrited sample.

Finally, the structural model itself necessitates several sample selection restrictions. First, I focus on only whites, blacks, and Hispanics. This is because Asians are much less likely to use either Head Start or subsidies. This is also consistent with some literature that focuses on these three subgroups (Neal and Johnson 1996; Keane and Wolpin 1997, 2010; Todd and Wolpin 2007). Second, the ECLS-B also purposively oversampled several minority groups (Asian, Pacific Islander, American Indian, and Alaska Natives), low birth weight babies and twins, which was done to help power subgroup analyses for researchers. I exclude some of these oversampled groups because of concern about special institutional or labor market issues potentially affecting these groups. Third, I do not include teenage mothers in the model because of the likelihood of them still making education and parental coresidence decisions. In addition, blended families that consist of nonbiological parents and siblings or families that form, break up, and reform over the course of the family are difficult to model, so I exclude these. The complete list of exclusion restrictions is given in Table A.3 in the Online Appendix. The final estimation sample consists of 9,200 individual × round observations, which is 31.6 percent of the original nonattrited sample. However, these restrictions appear more severe than they are because of the oversampling, and accounting for these additional parts of the sample would involve much more complicated modeling, especially along dimensions of family formation and alternative labor markets. I save this for future work. Compared to the estimation sample, the main patterns and statistical differences in Table 1 and the reduced-form production functions results in Table 2 are all preserved in the full sample.⁴² However, the estimation sample on average has higher maternal education, higher home quality, is more likely to be married, has a smaller family, and earns more money.

III. Estimation

The structural model has 153 parameters that I estimate using indirect inference (Gourieroux, Monfort, and Renault 1993). The basic idea is to match parameters estimated using auxiliary statistical models on data simulated from the model to corresponding parameters from the same auxiliary statistical models estimated on the ECLS-B. The procedure works as follows. Given a guess for the structural parameter values, I solve the model by iterating backward from the terminal value. I then draw the family’s type from the discrete distribution of types and given the model solution, the type, and the initial conditions, I simulate a path of endogenous variables for each family in the data set. I repeat this procedure ten times to create ten “clones” of each family. I then estimate auxiliary statistical models on the simulated data using only the rounds where I actually observe the families in the ECLS-B.⁴³ The estimation procedure iterates between the model solution and the objective function, which is a weighted distance between auxiliary parameter estimates computed from the data and corresponding parameter estimates computed from the simulated data. For the weighting matrix, I use a diagonal matrix with the inverse of the variances of the auxiliary statistical model parameters estimated on the ECLS-B.

Let θ be the vector of parameters to estimate from the structural model, W be the weighting matrix, β^d be the vector of parameters from the auxiliary model estimated on the ECLS-B, and β^s(θ) be the vector of parameters from the auxiliary model estimated on the simulated data (which is a function of the structural parameters θ). The indirect inference estimator is given by

(24)

The auxiliary statistical models consist of a mixed logit model for childcare and work hours conditional on exogenous variables, the joint distribution of childcare and work hours choice, the transition of work and childcare decisions between rounds, correlations between all endogenous variables, regressions of wages, income, home quality, price, cognitive skills, childcare quality, labor force participation and childcare participation on exogenous variables, and autocorrelations across rounds for each of the previous variables. All together the auxiliary statistical models have 209 parameters.

There are several complications in the estimation. The first issue is that the model has multiple children per family, but I only observe one child per family in the ECLS-B. It is important to consider multiple children because restricting the estimation to single child families is a large sample restriction and because many policy-relevant families for these types of childcare programs come from larger and poorer families. I am able to identify the model with multiple children through assumptions about the mother’s utility over cognitive skills and through the estimation procedure. First, I assume that the children’s skills enter linearly and additively in the mother’s utility function, so that she cares about efficiency when making decisions.⁴⁴ Second, I use an unconditional simulations approach developed in Keane and Wolpin (2001), so that I never have to calculate conditional choice probabilities for unobserved state space elements, such as the cognitive skills of other children in the family. Although my assumption about the mother’s utility function is not directly testable because I never observe the cognitive skills of other children in the family, the model does have implications for how siblings’ cognitive achievement scores are correlated. In the Estimation Results section, I present simulated evidence from the model about the intrasibling correlation in cognitive skills and compare it with other studies to check the model’s predictions.

The second estimation issue is that the ECLS-B is not a random sample of children but a sample of children born in 2001. However, I assume that the model begins when the mother first has a child, which could be in or before 2001. In order for the mother to be selected in the ECLS-B, she must have a sequence of shocks such that she has a birth in 2001. I mimic the ECLS-B sample selection procedure by only keeping sequences of fertility shocks that result in a birth in 2001.

Finally, I estimate the model with the subsidy program in place and with the policy parameters (rate ceiling, copay, and income cutoff) calibrated to national averages.⁴⁵ Subsidy programs actually differ across U.S. states, but incorporating state-level variation in subsidy programs would require solving the model separately for each U.S. state, which is completely computationally infeasible.⁴⁶ The calibrated parameters that I use are $3.65 for the rate ceiling, $12,000 for the six-month income cutoff (based on $24,000 per year), and 7 percent of family income for the copay.

IV. Estimation Results

A. Parameter Estimates

The parameter estimates and associated standard errors are presented in Table 3. As the parameters of the cognitive achievement production function play an important role in tracing out the impact of different policy counterfactuals on the cognitive skills of children, I first highlight these estimates. Consistent with previous research, the parameters suggest the importance of lagged cognitive skills (δ₁ = 0.81) and of the quality index inputs (δ₂ = 0.29). Interestingly, gaps in initial skills are not statistically significant for any of the maternal characteristics, which suggests that inputs alone are driving the emergence of test score gaps at age five.⁴⁷

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Table 3

Model Parameter Estimates

A second important feature of the estimates is that for most children Head Start has a higher quality mean offer (μ_hs = 0.63) than most types of market childcare. This holds for every unobservable type . Of course, some individual families would receive higher quality offers depending on their observables and shock draws. Another notable difference is that the standard deviation of the Head Start quality offer distribution (σ_hs = 0.41) is smaller than the standard deviation of market childcare quality (σ_q = 0.93). This translates into much more variability in childcare quality experienced by children in the market. Prior research has highlighted similar qualitative differences in quality between Head Start and other forms of childcare (Zill et al. 2001). The other parameters have obvious signs and interpretations with the returns to education and experience for mothers and fathers both within ranges suggested by previous labor market studies. Most mothers receive positive utility from “leisure” (nonmarket work), which is higher for married mothers and mothers with larger numbers of children. Consumption and leisure are estimated to be complements, which is similar to previous work (Keane and Wolpin 2010) and quantitatively important to help fit the labor supply patterns for low versus high wage mothers. Both subsidies (π_s = 0.30) and Head Start (π_hs = 0.26) are estimated to be rationed.⁴⁸ Consistent with most research estimating dynamic discrete choice models, unobserved types play a critical role in helping the model fit the data, and the estimates show substantial variation across the types endowments and choice sets. Interestingly, however, unobserved heterogeneity appears to play a more important role in the labor market (wage and income) and the childcare market (quality and prices) than for the cognitive skill endowment and home quality (for which none of the types are significant).

Some features of the parameter estimates are difficult to understand without simulating the model, so I also compute wage elasticities and intrasibling correlation in cognitive skills to further highlight the features of parameter estimates. Computing the elasticities on data simulated from the model at the final parameter estimates, the intensive labor supply elasticity is 0.63, and the extensive labor supply elasticity is 0.59, which are consistent with previously high estimated wage elasticities for women and for dynamic models that feature human capital accumulation.⁴⁹ Comparing cognitive skills among siblings, I find 0.45 for the intrasibling correlation in cognitive achievement test scores, which is very close to the 0.5 intrasibling correlation for IQ scores among siblings reported in Scarr (1992).

B. Model Fit

The model fit is shown in Tables 4–6. The model captures well all the main features of the data in Table 1, and in general the model fit for the endogenous variables is not statistically different between the model and the data.⁵⁰ Table 4 shows the cognitive achievement inputs (childcare quality, home quality, and childcare participation) and cognitive achievement conditional on family covariates. Consistent with the data, home quality is higher on average for white children with married parents and mothers with higher education. Childcare quality also displays the patterns observed in the data, with black children having, on average, better childcare experiences than white and Hispanic children. In addition, there is much less between-group variation and the quality–education gradient is much flatter than for home quality, consistent with the data. These features are curious given the similar productivity of the childcare and home quality in Table 2.⁵¹ Such a pattern could reflect poor consumer knowledge of the quality of childcare experiences (Walker 1991) or limited knowledge of the cognitive achievement production function.⁵² However, mothers are estimated to have fairly large preferences over cognitive skills, so another channel is through level of quality offered by the market, which is estimated to be low quality for most types of mothers.

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Table 4

Cognitive Achievement Inputs and Output

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Table 5

Labor Market Outcomes

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Table 6

Distribution of Care/Work Decisions

The model also picks up the patterns of childcare hours, with higher childcare use for single versus married mothers and for black women compared to white and Hispanic women. White mothers have higher wage offers as a result of higher education and experience, which increases their likelihood to work, but they also are more likely to be married, which increases their demand for leisure through nonlabor (husband’s) income effects. The higher home quality of married/white mothers gives an additional incentive to stay home relative to black and Hispanic mothers because of higher productivity of their inputs in creating cognitive skills. These inputs differences acting through the estimated parameters of the cognitive achievement production function serve to capture well all the gaps in cognitive achievement in Table 4.

Finally, the model also captures different labor force participation and wage patterns by maternal characteristics (Table 5) and the distribution and transition of childcare, work, and program participation decisions (Table 6). The model also predicts very little joint use of subsidies and Head Start, which is consistent with the data. This feature is generated via the structural features of the programs discussed previously, where the use of subsidies is not likely to be worthwhile for part-time care given the copay costs, so that using Head Start part-time and subsidies for additional hours of care is unlikely to be optimal.

V. Counterfactuals

The main goal of the paper is to evaluate changes to Head Start and childcare subsidies and their effects on (i) children’s cognitive achievement and (ii) maternal labor force participation. For each kind of policy, I also document the per capita and total cost associated with different interventions relative to baseline costs.

A. Head Start

The results from the Head Start counterfactuals are given in Tables 7 and 8. As a model validation exercise, I first use the model to evaluate Head Start using the same design as the Head Start Impact Study (HSIS), a randomized controlled trial of Head Start.⁵³ The HSIS consisted of two interventions: a group of four-year-olds who were randomized to receive Head Start or not (HSIS four-year-olds) and a group of three-year-olds who were randomized into a treatment group and a delayed treatment control group that could apply again for Head Start at age four (HSIS three-year-olds). I implement these design features in the model simulations as follows. For the HSIS four-year-olds design, I remove Head Start from the choice set for four-year-olds in the control counterfactual. For the HSIS three-year-olds design, I remove Head Start from the choice set for three-year-olds at age three and reintroduce Head Start in the choice set at age four in the control counterfactual. The control counterfactual is “business as usual,” meaning a mix of whatever childcare choices they would experience in the absence of Head Start. In the HSIS experiment, the children were followed longitudinally to observe impact estimates over time. Consistent with the experiment, I measure impacts at age five for the HSIS four-year-old design. For the HSIS four-year-old design, I measure impact estimates at age four to again capture the first year impacts.

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Table 7

Model Validation Using HSIS Design

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Table 8

Head Start Counterfactuals

In Table 7, I report the effect sizes for two arms of the HSIS computed in my estimated model and from the report of the HSIS.⁵⁴ I report two kinds of estimates of the program’s effect. The first is an intent to treat (ITT) estimate, which is the average change in the outcome for all eligibles. The second estimate is a LATE, which is the average impact for those induced to switch into Head Start by the offer of the program.⁵⁵ The results of the HSIS validation exercise suggest that the structural model produces impact estimates of Head Start in line with the HSIS. In Table 7, the ITT estimate for the HSIS four-year-olds design is 0.06σ in the model and 0.11σ in the HSIS study. For the same design, the LATE estimate is 0.07σ in the model and 0.17σ in the HSIS. Although smaller in magnitude, both estimates are in the range of the sampling variation of the HSIS impact estimates. Using the HSIS three-year-olds design, I find an effect size of 0.04σ in the model, and the HSIS reports 0.13σ for the ITT estimate. The LATE estimate is 0.11σ versus 0.19σ in the HSIS. The former difference is statistically significant, whereas the latter is not. Although the HSIS was conducted on a different cohort of children, with a sample of oversubscribed Head Start centers, and could not prevent treatment cross-overs to other Head Start centers, the effect sizes simulated in my model and reported in HSIS are of a similar magnitude, which provides evidence of the validity of the structural model.⁵⁶

I next use the model to consider a series of prospective policy changes to Head Start: (i) reducing rationing, (ii) expanding access to Head Start by increasing the income eligibility cutoff, (iii) lowering the eligibility age range of Head Start⁵⁷, (iv) making Head Start a full-time program of 1,000 hours, (v) giving eligible mothers a cash transfer equivalent to the per capita funding of Head Start, (vi) improving Head Start quality by replacing below mean offers with mean quality offers, and (vii) evaluating Head Start in a world without childcare subsidies. These counterfactuals are based on either proposed or existing policies and are intended to understand policy tradeoffs within Head Start or more general policy interactions across childcare programs (Blau 2003; Blau and Currie 2006). For each counterfactual, I compare the counterfactual to a world without Head Start. This allows the counterfactual impacts to be benchmarked against the baseline Head Start impacts. I also keep track of total costs relative to the baseline Head Start to gauge the cost of different program configurations.

In Table 8, the first row illustrates that removing Head Start completely lowers cognitive achievement scores by 0.07σ at kindergarten entry.⁵⁸ Removing Head Start also has only a moderate impact on changing maternal labor force participation by −1.60 percentage points (pp). Although Head Start does impose income eligibility criteria, the result is perhaps not so surprising given that Head Start imposes no work requirement as a condition of participation. These relatively small impacts on labor supply are also consistent with the HSIS results (Griffen and Todd 2017).

I then consider reducing rationing by making a Head Start offer to every child from an income-eligible family. The impacts on cognitive skills are actually larger, 0.16σ, because reducing rationing allows the children to receive a higher dose of Head Start over time. However, this policy is predicted to lower labor force participation by 5.73 pp. This fairly large effect also comes from the dynamic effects as mothers accumulate less labor market experience. In addition, reducing rationing gives mothers a guaranteed option of using Head Start conditional on satisfying the income cutoff, which at the margin induces some mothers to lower their labor supply.

The next set of counterfactuals in Table 8 gradually increases access by raising the Head Start income eligibility cutoff. The ITT estimates are large even for higher income families, with a 0.13σ impact on cognitive achievement at age five. Because the impact estimates are ITT estimates of children ever eligible for Head Start, increasing the income eligibility cutoff will produce an even larger overall effect as the scale of the program is expanded. This policy finding is important because it suggests that even for higher income children there are nontrivial gains to be had in their cognitive achievement scores.⁵⁹ The reason for this finding is that children from higher income families tend to spend more time in childcare, and their childcare quality experiences are not particularly high, as documented in the data and estimation results. So providing a relatively higher quality Head Start option also increases the cognitive skills of noneligibles because of their extensive use of low quality childcare. The overall takeup rate is large in the universal offer, with 96 percent of children participating. Although this may seem high, it is consistent with the high participation rates in European countries with heavily subsidized childcare.⁶⁰ Note also that the overall change in labor force participation is small for a universal offer (0.15 pp), suggesting that an unconditional program is not inducing many mothers to enter the labor market. Finally, however, the costs are very large with a universal offer at 13.38 times the baseline Head Start program. Obviously such a costly expansion would need to be considered carefully against the benefits of the gains in cognitive skills.

Expanding the age range of Head Start by lowering the initial eligibility age from age two to age one to age zero has approximately the same impact as the baseline program (0.16–0.17σ). Although this is partly driven by lower takeup among younger children (the mother’s utility from using childcare is low for very young children, as she would rather stay home with them), another factor is that because income, wage, and childcare hours decisions change over time, mothers do not always satisfy the income eligibility cutoff even when there is no rationing. So one feature of this counterfactual is that the Head Start effects get dissipated because some children only participate briefly (which raises costs) before reverting to either home or other childcare choices, so the input quality improvements from Head Start do not accumulate over time. This dissipation is one reason that that lowering the age range is significantly more costly for approximately the same impact as reducing rationing.

The next counterfactual keeps the age eligibility from age three to five but expands Head Start from a part-time to a full-time program, as proposed during the Obama administration. This has a 0.31σ impact on cognitive achievement. Interestingly, this has a much larger impact on cognitive skills than lowering the age range and at a lower cost (4.8 times baseline costs). However, the full-time program is predicted to lower maternal labor force participation (−8.41 pp) because mothers are now more willing to reduce labor supply to satisfy the income cutoff to take advantage of the now more beneficial program. One way to mitigate these predicted labor disincentives would be to have separate income eligibility cutoffs depending on labor force status.

To assess the role of improvements in Head Start quality, I replace every below average Head Start quality offer with the mean Head Start quality offer. The idea of the counterfactual is to mimic Head Start quality improvements mandated under the Obama administration in response to the HSIS findings. This has an impact of 0.18σ on cognitive skills, which is similar to the baseline impact of 0.16σ. This is a result of the relatively low variation in Head Start quality offers. However, because the cost of such a quality improvement policy is unknown, it is difficult to directly compare it to the other policies.

I also consider the effect of removing Head Start and giving Head Start–eligible families a cash transfer equal to the per-child spending on Head Start ($3,611 per six months). The idea is to test whether in kind or cash transfers are a better method of achieving the aims of Head Start (through the parents perhaps making better decisions when provided the money directly). The results indicate that providing cash transfers lowers cognitive achievement scores by −0.02σ and labor force participation −13.98 pp. Although the decrease in cognitive skills is small relative to no Head Start, and mothers’ utility will clearly increase from the cash transfer, the result implies that if policymakers want to target improvements in cognitive skills, then such cash transfers would not be effective. In addition, the labor supply disincentives are quite large and would likely also be undesirable from a policymaker’s perspective. Finally, I consider the impact of Head Start in a world without subsidies, and, given the limited interaction of subsidies and Head Start, the results are quite similar to the baseline impact estimates.

B. Childcare Subsidies

In Table 9, I report the effects on cognitive achievement and labor supply of the subsidy program. I consider a series of counterfactuals: (i) a baseline impact of the subsidy program compared to a world without subsidies, (ii) numerical comparative statistics of varying each of the program policy parameters (copay, rate ceiling and income cutoff), (iii) reducing rationing, and (iv) the impact of subsidies in a world without Head Start. The goal of these counterfactuals is to understand potential tradeoffs between child skills and maternal labor supply but also to assess within-policy variation in the design of subsidies and potential interactions of subsidy design with Head Start, all of which have been raised as important policy and research issues (Blau 2003; Blau and Currie 2006). To be comparable with the Head Start counterfactuals, I report the change in cognitive skills at age five. For each counterfactual, I compare the counterfactual program to a world without subsidies. This again allows each counterfactual to be benchmarked against the impact of the baseline subsidy program.

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Table 9

Subsidy Counterfactuals

In Table 9, the first row shows that the baseline subsidy program has a fairly large impact on labor force participation (6.38 pp) but essentially zero impact on cognitive skills (−4.17E-03). The finding of a limited impact on cognitive skills carries over to all the subsidy counterfactuals. This is an important finding because a potential child skill–maternal labor supply tradeoff has been an ongoing policy concern in subsidy design (Blau 2003; Blau and Currie 2006; Heckman 1974). The result here suggests that for subsidy-eligible mothers childcare is no worse on average for their children than their home environments. The finding is partly driven by the fact that mothers care about cognitive skills, which induces a selection into subsidy use/employment for mothers who have particularly low home quality and/or access to relatively higher quality childcare draws. In addition, the relatively smaller variation in childcare versus home quality by observables, especially by characteristics that predict subsidy use, suggests that encouraging subsidy and childcare use is unlikely to have negative impacts. Another reason for the small impact estimates is that almost 80 percent of the subsidy users are predicted to be inframarginal, so that although they use subsidies they do not adjust their labor supply or childcare decisions. These findings are not consistent with much of the current literature on subsidies, which typically finds negative impacts on cognitive skills.⁶¹ However, the labor supply impacts presented here are very consistent in magnitude with results from a quasi-experiment (Lefebvre and Merrigan 2008), and the negligible impact estimates on cognitive skills are more consistent with positive impact estimates on cognitive skills from a randomized control trial of work supports and childcare assistance (Huston et al. 2005). The structural model also has the implication that the impact estimates will vary across households depending on their home environments and differential access to childcare quality, which implies that the particular sample or population being analyzed will potentially produce different impact estimates.

Another interesting feature of the simulations is that subsidy takeup among eligibles, defined as the percentage of income-eligible families that actually receive a (stochastic) offer and decide to use the subsidy, is 77 percent. This suggests that 23 percent of families elect not to use a subsidy for reasons related to the design of the program discussed in the model section, such as low price, higher income, or part-time hours. Among income-eligible families with working mothers, 23 percent use subsidies in the model, consistent with the statistics reported by Herbst (2008). Although direct rationing is the major factor that explains low takeup, optimal selection into subsidy nonuse is also not trivial.

I next vary each subsidy policy parameter holding the other two policy parameters constant at their calibrated values. The idea is to describe how changing the policy parameter affects the cognitive skills of children, the labor supply of mothers, the program coverage, and the cost per child. Each counterfactual is compared to a world without subsidies to ease comparison of the impact estimates across counterfactuals.

Increasing the copay from 0 percent to 20 percent in increments of 5 percent decreases the impact on labor force participation from 6.61 pp to 4.16 pp and reduces takeup from a high of 86 percent to a low of 66 percent, consistent with the discussion in the model that higher copays reduce participation. There are again very small impacts on cognitive skills, and, at a copay of 0 percent, the total cost is 16 percent higher than the baseline program.

Increasing the rate ceiling from $2 to $14 in increments of $4, while holding the other parameters constant, the impacts on labor force participation increase from 2.86 pp to 11.47 pp. This is also not surprising because the program is being made more generous, and, at a rate ceiling of $14, the total cost increases by 35 percent. Comparing to the previous set of counterfactuals, it seems that impacts on maternal labor supply are more sensitive to raising the rate ceiling than lowering the copay. This implies a group of mothers are not participating in the labor force because they face high childcare prices. One interesting dynamic feature is the higher rate ceiling helps insure mothers against future price increases, which may increase current participation. The changes in cognitive skills are quite small, which suggests that the design of the program can be made independently of its effects on cognitive skills.

I next vary the income cutoff from $5,000 to $20,000 in increments of $5,000. This counterfactual does something conceptually different by changing the pool of eligible families. Although initially higher income families begin to use the subsidy, this usage tapers off because the copay on a larger income is not worth the gain from lower childcare costs, which creates a natural barrier to subsidy use among higher income families.⁶² Specifically, takeup among eligibles falls from 85 percent to 75 percent, and the impact on labor force participation is roughly constant.

Given the extensive rationing of subsidies, I also consider a counterfactual where I set π_s = 1 so that only conditional on income eligibility the family can use a subsidy. This counterfactual has a larger impact on labor force participation (10.77 pp) than baseline but again very small impacts on cognitive skills. However, the cost is much higher at 3.60 times baseline. Finally, I also examine the impact of subsidies in a world without Head Start. The impacts look similar to the baseline subsidy program. Consistent with the analogous counterfactual for Head Start, there seems to be very little interaction between the programs.

VI. Conclusions

In this paper, I use a value-added cognitive achievement production function and a dynamic discrete choice model of maternal labor supply and childcare to explore the impact of current and prospective Head Start and childcare subsidy policies on the cognitive achievement of children and maternal labor supply. The structural model allows a rich characterization of policies through constraints, prices, and choice sets in order to understand the channels and magnitudes of different policy changes on outcomes. The main findings are a large impact on cognitive skills from expanding Head Start to current noneligibles (0.13σ), which is largely driven by their current extensive use of low quality childcare, and negligible impacts of childcare subsidy design on the cognitive skills of current eligibles. Some Head Start counterfactuals produce similar impact estimates, but at widely varying costs, which suggests more attention should be paid to within-program policy choices. There appears to be no tradeoff between cognitive skills and maternal labor supply outcomes in subsidy design and little interaction across subsidies and Head Start. The model predictions are consistent with external experimental evidence, and several qualitative predictions of the structural model are confirmed in the data and simulations. Future work could expand the current analysis to consider the interaction of these programs with other features of the policy and welfare landscape and to incorporate additional decisions of mothers (for example, fertility, marriage, and divorce) to provide a more comprehension picture of childcare policy design.

Appendix

The utility function is given by

where hours of leisure for the mother is h_lt = 2,000 – h_wt, which is the residual of the total hours in a six-month period (assumed to be 2000 hours) net of hours worked, h_wt. For hours of work, is an indicator that equals 1 if the mother stays home at time t and 0 otherwise. and are defined analogously for part-time and full-time work. For childcare, , , and are indicators for home, part-time, and full-time childcare. is an indicator that equals 1 if child i is present in the house (for up to three children under the age of five). This specification incorporates features from both Bernal (2008) and Keane and Wolpin (2010). In particular, differences in utility parameters by race, education, and marital status are important to capture differences in labor supply and program participation patterns across these subgroups even net of differences operating through other channels (wages, income, prices, marital status, fertility and program access). In addition, I add utility costs of working without childcare (α₂), complementarity between consumption and leisure (α₃), and transition costs in choices (α₆–α₁₁).⁶³

Unobserved heterogeneity for leisure (time-varying and permanent component) is given by

and analogously for childcare:

The distribution of utility shocks is given by

The childcare quality offer mean is

and the hedonic pricing equation is

with shock distributed according to

Observed prices follow

Head Start access is probabilistic and is given by

where the index is given by

and where the income eligibility cutoffs for Head Start are given by

Because the income cutoffs for eligibility are not strict (Besharov and Morrow 2007), I model eligibility probabilistically conditional on being above and below the cutoff. These cutoffs were constructed from the Health and Human Services Federal Poverty Guidelines for 2001. The guidelines are for a year, so I divided by two to be consistent with the six-month model period. I use the 2001 guidelines because I report all prices in 2001 dollars. The cutoffs vary by family size 1 + m_t + k_t + o_t and for each additional person above eight the cutoff increases by $1,510 (or $3,020 for a one-year period). Head Start eligibility is then drawn from the Bernoulli distribution:

I assume that , so that conditional on satisfying the eligibility criteria and not being rationed, all age-eligible children within a household are Head Start eligible. Subsidy access is also probabilistic and is given by

and then subsidy eligibility is drawn from the Bernoulli distribution:

Home quality is given by

where the shock is distributed

Although the childcare quality draw is the same for all children in a family, the chosen childcare quality, , is child specific because it can vary across children within the same household depending on whether the child is eligible and attends Head Start

The chosen child quality equals the market quality draw, q_ct, if Head Start is not chosen (). It equals the Head Start quality draw, q_hs,t, if Head Start () and 500 hours of care are chosen. It equals the average of the Head Start and market qualities, 0.5q_hs,t + 0.5q_ct, if Head Start and 1,000 hours of care are chosen, which assumes that a child in Head Start and full-time care spends half their time in Head Start and half their time using their market childcare draw (see Footnote 17). The initial cognitive skill endowment is given by

and subsequent cognitive skills evolve according to the production function:

where the input is given by

and the shock to cognitive skills is distributed according to

The mother’s wage offer is

with shock

The father’s income is

with shock

The probability of a birth, π_b, is given by

where the index is

The evolution of children’s age, the number of younger, and the number of older children follows

where a new birth b_t is drawn from the Bernoulli distribution:

The probability of a divorce, π_d, is given by

with the following index:

The evolution of marriage then follows

where the divorce random variable d_t is drawn from the Bernoulli distribution:

Type probabilities are given by

where t₀ is the period of the mother’s first birth and m_t0 is her initial marital status. The parameters for Type 6 are normalized to zero. I assume the continuous outcomes are observed with mean zero log-normal measurement error (wages, income, and prices),

or normal measurement error in levels (home quality, childcare quality, and cognitive skills),

with associated parameters (σ_wm, σ_ym, σ_pm, σ_hm, σ_ccm, σ_θm). Finally, following Keane and Wolpin (2010), I assume that the discrete hours of work h_w are subjected to unbiased classification error rate E_w. Let the probability of correctly reporting j hours of work be given by

where f (h_w = j) is the true aggregate choice frequency of j hours of work. The probability of incorrectly reporting j hours of work is then given by

Analogous equations are used to estimate the classification error rate E_c for childcare hours h_c.

Footnotes

* Supplementary materials are freely available online at: http://uwpress.wisc.edu/journals/journals/jhr-supplementary.html
↵1. Author’s calculation, Early Childhood Longitudinal Study–Birth Cohort (ECLS-B). Nonparental care includes any kind of care not given by a parent (center-based, informal care, relative care, home based nanny, etc.). One of the fundamental tradeoffs in the model I develop is between maternal childcare and maternal work. I discuss this more in the Model section.
↵2. Public provision through Head Start and changing the price of childcare through subsidies are not the only possible government interventions in the market for childcare. Another style of intervention tries to improve childcare quality through the regulation of childcare providers. Hotz and Xiao (2011) investigate the effects of accreditation regulations and find that they increase childcare quality but reduce the number of childcare providers. This result suggests that the cognitive skills for children in childcare would increase and the cognitive skills of children crowded out of using childcare could increase or decrease depending on the quality of their home or of an alternative childcare provider not affected by regulation (such as a relative). Previous research suggested that regulations affecting the child/caregiver ratio or teacher qualifications would have limited impact of childcare quality (Blau 1997) and no impact on children’s skills (Blau 1999).
↵3. For the quote, see the program description at the Office of Head Start http://www.acf.hhs.gov/programs/ohs/ (accessed September 24, 2018).
↵4. Lefebvre and Merrigan (2008) provide quasi-experimental evidence that short-term childcare policies can have exactly these kinds of long-term impacts on maternal labor supply decisions.
↵5. See the White House Press Releases “We Can’t Wait: President Obama Takes Action to Improve Quality and Promote Accountability in Head Start Programs” (November 8, 2011, http://www.presidency.ucsb.edu/ws/index.php?pid=104587, accessed September 24, 2018) and “More is Better: Expanding Learning Time in Head Start Programs” (April 25, 2016, https://obamawhitehouse.archives.gov/blog/2016/04/25/more-better-expanding-learning-time-head-start-programs, accessed September 24, 2018).
↵6. States actually vary widely in their subsidy design. Unfortunately the data used here are not powered for state-level differences, which is exacerbated by the low incidence of subsidy use in the general population. Because the data cannot be used to directly assess the impact of variation in subsidy policy, this is a good example where we need to rely on structural modeling to assess impact estimates. In this case, the subsidy design will affect choices through the budget constraint, so the structural model makes use of how existing wage and price variation affects choices in the data to infer the impact of subsidies. See the discussion in Keane, Todd, and Wolpin (2011).
↵7. The paper by Del Boca, Flinn, and Wiswall (2014) also explores the formation of children’s skills in a dynamic model. Their model includes the choice of time inputs in the home, which is certainly a potentially important source of variation in children’s inputs. However, their model ignores the extensive use of childcare and variation in children’s childcare quality experiences because of data limitations in the PSID. A synthesis of my paper, Del Boca, Flinn, and Wiswall (2014), and Bernal (2008) would allow for choice of childcare time inputs, home time inputs, and quality in both the home and the childcare setting. However, estimating such a model would require a kind of data set that, to my knowledge, does not exist. Other recent work also focusing on dynamic models analyzes childcare policy and the formation of skills in the context of Norway (Chan and Liu 2017) and intergenerational transmission of human capital (Gayle, Golan, and Soytas 2016a, 2016b).
↵8. Bernal (2008) also has maternal employment as an input into cognitive achievement, but maternal employment should not have any direct impact on cognitive development if the child’s quality and time inputs are all captured. In her case, it serves as a black box to capture differences in home time inputs and goods inputs. An earlier paper in economics, James-Burdumy (2005), also explored maternal employment as an input.
↵9. The NLSY-79 only asks whether children were in childcare for more than 10 hours a week and has no information on quality.
↵10. Bernal (2008) restricts the estimation to married mothers with a single child, which is not necessarily a target group for current childcare policies in the United States.
↵11. An important exception is Duncan (2003), who also bridges the economics and child development literatures by considering childcare quality inputs in a carefully modeled production function. My paper builds on his work by estimating childcare quality inputs in a skill production function jointly with a behavioral model for childcare and quality decisions.
↵12. Under this definition, childcare encompasses relative care in the child’s home, relative care outside the child’s home, nonrelative care in the child’s home, and nonrelative care outside the child’s home such as center based care, Head Start, and preschool. So any care not given by the child’s parent would be considered “childcare” even if the care occurred in the child’s home. For example, a live-in nanny would be considered childcare and not home care.
↵13. I assume here that the cognitive skills of older children do not enter the mother’s utility function. This is primarily because they are not observed in the data I use. However, an observationally equivalent model could have the cognitive skills of older children enter additively separable and the production function for older children’s skills not depend on the labor supply decisions of the mother. This could be the case if skills for older children were largely predetermined, school inputs are weakly related to skills, and home inputs depend more on fixed factors like learning expectations than on purchased inputs. These are all true to some extent.
↵14. An important point here is that search for different childcare options is not observed in the data. For computational considerations, I only permit one draw from the distribution of price and quality, so what I am trying to estimate is the envelope of the offer distribution from some unobserved search process. Then the usual selection issues arise in that I only observe accepted offers from the price–quality distribution. This same issue would come up in a labor supply model without search with only observed wages.
↵15. Because each period corresponds to six months, I assume that children can potentially attend childcare for up to 40 hours per week × 26 weeks = 1,040 hours. I round this to 1,000 hours, and I assume that part-time care corresponds to 500 hours and full-time care to 1,000 hours.
↵16. Most data sets collect information for a focal child only, so it is difficult to gather information on the joint decision hours decisions across children (Joesch, Maher, and Durfee 2006). However, the available evidence suggests that the vast majority of families put multiple children in the same type of childcare (Harris, Raley, and Rindfuss 2002).
↵17. Head Start is a part-time program, so I assume that if families choose Head Start but also want to have fulltime care they use their draw of price and childcare quality to provide so-called “wrap around care.”
↵18. This cutoff is not entirely strict (Besharov and Morrow 2007), so I allow families with incomes above the cutoff access but with a lower probability that I also estimate.
↵19. Here I am assuming that a child has 2,000 input hours available. Because each period corresponds to six months, 80 hours per week × 26 weeks = 2,080 hours, which I round to 2,000. Notice that this specification assumes that even a child in full-time care (1,000 hours) still receives half of their input from home quality hours. In the data section, I detail the features of the data that support these choices.
↵20. In the data y_t are fathers’ earnings, so instead of interpreting y( ) as an income offer function combined with an assumption of perfectly inelastic labor supply for fathers, an alternative interpretation would be as a process for the fathers’ earnings. Unemployment events would then be captured through a particularly low shock and/or a low value for unobserved heterogeneity. A difficulty with such an interpretation is that if fathers do not work every period, then the stock of experience should not augment every period as I assume. The data used in this paper do not have extensive labor market histories and are also too low frequency to capture unemployment spells, so it’s likely these two interpretations cannot be meaningfully distinguished given the current data.
↵21. Paralleling hours of childcare, I also assume that hours of work can also equal 0, 500 or 1,000 hours.
↵22. A standard explanation for the lack of takeup of CCDF subsidies is unfamiliarity with or difficulty navigating the program requirements (Herbst 2008). Explicitly modeling the subsidy system shows that there are structural features of the program that reduces participation. It also reveals a “catch-22” situation in that mothers need to work in order to be eligible, but working may put family income above the income eligibility cutoff, thus making the family ineligible. This feature can also obviously reduce participation.
↵23. Although all the children attend childcare for the same number of hours, if one child has the option to attend Head Start, it is possible the mother could choose not use the subsidy for that child, but still use the subsidy for her other children. Hence, the child i specific notation for the subsidy choice. However, unlike Head Start, eligibility for subsidies is family, not child, specific.
↵24. This covers 96.4 percent of the sample. In the event k_t = 3, then π_b is set to zero until at least one of her children turns ages five and “ages out,” at which point she can have additional children.
↵25. This selection criterion reduces the sample by 7.4 percent. I also define a “father” as the child’s biological father, and being “married” in the model conflates cohabitation and marriage. Divorce then refers to the child’s biological father exiting the household. Women who are “divorced” in the initial state space may have never been married or may have been cohabiting and then the father left before the child was six months old. I discuss this and other sample selection criterion used in the estimation in the Data section.
↵26. These nine choices come from the Cartesian product of the childcare hours and work hours choices sets. Similarly to Bernal (2008), I do not restrict the mothers to necessarily choose childcare even if they work because this would actually contradict the data (the choice is uncommon, however). Instead I estimate a utility cost for mothers working without childcare, which could have several interpretations, including a cost of having nonoverlapping work schedules with a spouse, working at night while children are sleeping, or working at home.
↵27. Note I assume here that the cost of older children does not enter the budget constraint because, given the specification of the utility function, it is not separately identified from the utility of older children interacted with hours of leisure (Eckstein and Wolpin 1989).
↵28. Specifically, predicted consumption and predicted hours of work are plugged into û(), which I assume has the same specification as u( ), except without any of the childcare hours terms (because the mothers no longer have any younger children). One difference with Bernal (2008) is that she also had a continuation value over the child’s skills, but in my case, because the mother can potentially have so many children over her life-cycle, I wanted to avoid carrying around all the children’s skills in the state space. So the mother’s flow utility over child skills will be used to capture any of her behavioral responses to producing skills. Moreover, computationally it seemed difficult to separately identify both flow utility and continuation value over cognitive skills because both controlled similar aspects of maternal behavior.
↵29. The word quality is typically used in reference to childcare settings. The quality of home environment might be called the HOME score (in reference to a particular scale) or home inputs. I use quality to define the amount of measured stimulation in any environment whether home or childcare. One of points I stress is that the foregone alternative of making a childcare quality choice is the quality of the home environment.
↵30. Bernal and Keane (2010) make a distinction between time and goods inputs, which I do not follow. Todd and Wolpin (2007) also discuss how the HOME scale conflates time and goods inputs and also combines items that could logically be considered inputs with items that instead seem to be proxies for inputs. Instead my approach is closer to Cunha and Heckman (2008), who model the inputs into the production function as a latent variable.
↵31. For a discussion about the use, reliability, and validity of ECERS see Clifford et al. (2010). The HOME was developed by Caldwell and Bradley (1984). Both Todd and Wolpin (2007) and Cunha and Heckman (2008) discuss its use.
↵32. See Layzer and Goodson (2006) for a discussion about the difficulties in defining and measuring childcare quality and relating childcare quality to child outcomes.
↵33. For additional information on the cognitive assessments see the ECLS-B publication “The ECLS-B Direct Assessment Choosing the Appropriate Score for Analysis” (https://nces.ed.gov/ecls/pdf/birth/ChoosingScores.pdf, accessed September 24, 2018).
↵34. Maternal education is classified as “high school” for 12 or less years of school and “college” for more than 12 years of school.
↵35. It is common in education research to report test scores in effect size units where the test scores have been standardized to have mean zero and standard deviation one.
↵36. A second hypothesis would be that the lower labor force participation of white mothers simply generates a higher sample selected wage mean because they are less likely to accept low wage offers.
↵37. Interestingly these positive gaps in childcare quality for blacks only appear around age three in the data, which suggests that access to services like Head Start is a driving force between the higher childcare quality.
↵38. The parameters of the production in Table 2 uses data between rounds whereas the estimated production in the structural model organizes data into six-month bins (see discussion below).
↵39. See Griffen and Todd (2017) for evidence that in the cognitive domain that nonexperimental value-added models can successfully uncover causal impacts.
↵40. This calculation simply multiplies the input coefficient from Table 2 by the racial input gap and divides by the racial achievement gap. It ignores any dynamic considerations such as the cumulative effect of input differences over time, the impact through the value-added production function, and potential behavioral responses to introducing differences in home quality or available of childcare quality that are all stressed in this paper. Using the current model to explore the sources of the racial achievement gap would be an interesting future line of research.
↵41. The fifth round of data collection is for the subset of children who are delayed kindergarten entrants.
↵42. These tables are available upon request.
↵43. This way of mimicking the missing data process in the simulated data to address attrition follows Yamaguchi (2012). In addition, I also use weights provided in the ECLS-B used to adjust for attrition.
↵44. Even when multiple children are observed estimates of the efficiency versus equity tradeoffs have produced different results. See the discussion and papers cited in Behrman (1997). Recently, Aizer and Cunha (2012) find evidence that parents engage in reinforcing investment behavior, which is consistent the assumptions of my model.
↵45. This calibration takes each state’s policy parameter from 2007 (Schulman and Blank 2007) and constructs an average policy parameter weighted by each state’s population. In addition, I adjusted the rate ceiling and income cutoff to 2001 dollars to be consistent with the treatment of the data.
↵46. For example, Keane and Wolpin (2010) allow welfare program differences across states but restrict the estimation to five large U.S. states. Another strategy would be to add the subsidy policy parameters to the state space. However, the ECLS-B actually cautions against interpreting state-level differences in something as simple as a mean because the data collection was not powered for state-level differences. Of course, the problem would be even worse for cross-state subsidies usage statistics or outcomes measures because participation is restricted to lower income families, which further lowers the power for state-level differences. Other recent work (Guner, Kaygusuz, and Ventura 2017; Kubota 2017) investigating macroeconomic effects of these subsidy programs also ignores cross state heterogeneity in subsidies.
↵47. This is consistent with recent work by Fryer and Levitt (2013) using the same data demonstrating that early racial gaps in cognitive skills disappear with controls. Interestingly, the calculation using the production function from Table 2 suggested input gaps could explain only 21 (23) percent of achievement gaps, which implies that some of the dynamic feature introduced in the model are important for the model to fit the achievement gaps in Table 4. Todd and Wolpin (2007) make a similar point about how the specification of the production function is important for whether inputs gaps accumulate over time.
↵48. The subsidy rationing probability is consistent with other work (Herbst 2008), and the Head Start rationing probability is consistent with the estimated 42 percent of eligible children who are served by Head Start (Schmit et al. 2013). In addition, I estimate that 5 percent of families above the Head Start cutoff in the estimation sample receive an offer of Head Start, which is consistent with the 10 percent children above the income cutoff who are eligible to enroll in Head Start.
↵49. Following other papers in this literature, this counterfactual considers a 5 percent increase in wages in every period and is consistent with those findings (Keane and Wolpin 2010).
↵50. The exception are the unconditional joint distributions in Table 6 where tests decisively reject the null hypothesis of equality between the data and the model. This is not completely surprising given the large sample size and well-known property of the test as a “test of sample size.” Generally papers would condition on age or time period, which shows a good fit but also has less power. Regardless, the qualitative fit of the model in Table 6 is quite good.
↵51. Blau and Hagy (1998) document a similar pattern for the demand for structural measures of quality. Their result is perhaps not as surprising given the lack of productivity of structural measures of quality (Blau 1999) and the weak relation between structural measures and process measures (Blau 1997).
↵52. Bernal (2008) discusses the assumption that the mothers know the functional form for the production of cognitive achievement. Cunha, Elo, and Culhane (2013) find evidence that some mothers do not understand the skill production function very well. In my model, this would appear as mothers not having utility over cognitive skills, so that even though the cognitive production function operates in the background to produce cognitive skills, the mothers do not purposely make decisions to change cognitive skills.
↵53. The HSIS results were actually fairly consistent with meta-analyses from previous nonexperimental findings. I use the experimental findings as a benchmark given its high internal validity and because the ECLS-B and HSIS were sampled from nearby age cohorts. For more about these issues, see the literature review and discussion in Griffen and Todd (2017).
↵54. The effect sizes from the HSIS were computed as follows. For the reading domain outcomes, I averaged effect sizes across all of the reading outcomes. For the math domain, I averaged across the effect sizes for all of the math outcomes. I then averaged the separate math and reading effect sizes, which most closely approximates my treatment of the data in the ECLS-B. The LATE impacts estimates were derived by using the random assignment to Head Start as an instrument for Head Start participation.
↵55. See Griffen and Todd (2017) for further details about always-takers and no-shows in the HSIS and comparability with the ECLS-B.
↵56. Todd and Wolpin (2006) use experimental data to validate a structurally estimated economic model. They estimate their model using data from an experimental evaluation of PROGRESA, a conditional cash transfer program in Mexico. They limit their estimation sample to data in the control group and use the estimated model to predict the experimental impacts of PROGRESA. The difference in my case is that I estimate the model using a completely different data set and only mimic the design of the experiment for the model validation. However, the spirit of the exercise is the same.
↵57. There is an existing program called “Early Head Start,” although the scale is smaller than Head Start as it serves less than 4 percent of eligible children (Schmit et al. 2013). In addition, in the model the idea of Head Start for the younger children should simply be thought of as changing the quality input offer distribution for the younger children to have the same relative distribution as between Head Start and non-Head Start as for the older children.
↵58. This was an experimental arm that HSIS did not estimate because the three-year-old control group received a delayed treatment offer. The magnitude of the impact of this counterfactual are larger but in line with the HSIS experimental results.
↵59. An important caveat for this counterfactual is the assumption that Head Start can be scaled up.
↵60. See “PF3.2: Enrolment in childcare and pre-school” from the OECD Family Database (https://www.oecd.org/els/soc/PF3_2_Enrolment_childcare_preschool.pdf, accessed September 24, 2018).
↵61. However, Hawkinson et al. (2013) conduct a sensitivity analysis and report that their negative impact estimates are sensitive to unobserved confounders.
↵62. One very important caveat to these counterfactuals is the exogeneity of divorce and fertility. It is possible that making childcare less expensive could, by reducing the cost of children, induce mothers to have additional children. Or, perhaps it could increase the divorce rate if, for example, mothers were staying married because of financial resources provided by their husband. The impact on the results seems ambiguous because some of the channels would likely increase childcare use (divorce), whereas others would likely reduce childcare use (additional children). These pathways are shut down in this model, but I leave them open for future work to incorporate the design of these programs in a model with endogenous marriage, divorce, and fertility.
↵63. In the estimation, of course, the parameter could capture either complementarity or substitutability. However, consistent with Keane and Wolpin (2010), the estimation finds complementarity between consumption and leisure, which is needed to explain the relatively small differences in labor force participation between women with large wage differences.

Received March 2015.
Accepted October 2017.

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Keywords

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Rohacek Monica
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[3] Rohacek Monica

[4] ↵
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Cunha Flavio
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[5] Aizer Anna,

[6] Cunha Flavio

[7] ↵
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[12] ↵
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[14] ↵
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[16] Keane Michael P.

[17] ↵
Bernal Raquel,
Keane Michael P.
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[19] Keane Michael P.

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Morrow Jeffrey S.
2007. “Nonpoor Children in Head Start: Explanations and Implications.” Journal of Policy Analysis and Management 26(3):613–31.
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[22] Morrow Jeffrey S.

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Blau David
. 2003. “Child Care Subsidy Programs.” In Means-Tested Transfer Programs in the United States, ed. Moffitt Robert, 443–516. Chicago, IL: University of Chicago Press.

[24] Blau David

[25] ↵
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[26] Blau David M.

[27] ↵
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[31] Currie Janet

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[33] Blau David M.,

[34] Hagy Alison P.

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[37] ↵
Bradbury Bruce,
Corak Miles,
Waldfogel Jane,
Washbrook Elizabeth
. 2015. Too Many Children Left Behind: The US Achievement Gap in Comparative Perspective. New York: Russell Sage Foundation.

[38] Bradbury Bruce,

[39] Corak Miles,

[40] Waldfogel Jane,

[41] Washbrook Elizabeth

[42] ↵
Burchinal Margaret,
Howes Carollee,
Pianta Robert,
Bryant Donna,
Early Diane,
Clifford Richard,
Barbarin Oscar
. 2008. “Predicting Child Outcomes at the End of Kindergarten from the Quality of Pre-Kindergarten Teacher–Child Interactions and Instruction.” Applied Developmental Science 12(3):140–53.
OpenUrl CrossRef

[43] Burchinal Margaret,

[44] Howes Carollee,

[45] Pianta Robert,

[46] Bryant Donna,

[47] Early Diane,

[48] Clifford Richard,

[49] Barbarin Oscar

[50] ↵
Burchinal Margaret R.,
Roberts Joanne E.,
Nabors Laura A.,
Bryant Donna M.
1996. “Quality of Center Child Care and Infant Cognitive and Language Development.” Child Development 67(2):606–20.
OpenUrl CrossRef PubMed

[51] Burchinal Margaret R.,

[52] Roberts Joanne E.,

[53] Nabors Laura A.,

[54] Bryant Donna M.

[55] ↵
Burchinal Margaret R.,
Roberts Joanne E.,
Riggins Rhodus Jr.,
Zeisel Susan A.,
Neebe Eloise,
Bryant Donna
. 2000. “Relating Quality of Center-Based Child Care to Early Cognitive and Language Development Longitudinally.” Child Development 71(2):339–57.
OpenUrl CrossRef PubMed

[56] Burchinal Margaret R.,

[57] Roberts Joanne E.,

[58] Riggins Rhodus Jr.,

[59] Zeisel Susan A.,

[60] Neebe Eloise,

[61] Bryant Donna

[62] ↵
Caldwell Bettye M.,
Bradley Robert H.
1984. “Home Observation for Measurement of the Environment.” Little Rock, AR: University of Arkansas.

[63] Caldwell Bettye M.,

[64] Bradley Robert H.

[65] ↵
Case Robbie
. 2013. The Mind’s Staircase: Exploring the Conceptual Underpinnings of Children’s Thought and Knowledge. London, UK: Psychology Press.

[66] Case Robbie

[67] Chan Marc K.,
Liu Kai
. “Life-Cycle and Intergenerational Effects of Child Care Reforms.” Quantitative Economics 9(2):659–706.

[68] Chan Marc K.,

[69] Liu Kai

[70] ↵
Chetty Raj,
Friedman John,
Hilger Nathaniel,
Saez Emmanuel,
Schanzenbach Diane Whitmore,
Yagan Danny
. 2011. “How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project Star.” The Quarterly Journal of Economics 126(4):1593–660.
OpenUrl CrossRef PubMed

[71] Chetty Raj,

[72] Friedman John,

[73] Hilger Nathaniel,

[74] Saez Emmanuel,

[75] Schanzenbach Diane Whitmore,

[76] Yagan Danny

[77] ↵
Clifford Richard M.,
Reszka Stephanie S.,
Rossbach Hans-Guenther
. 2010. “Reliability and Validity of the Early Childhood Environment Rating Scale.” Working Paper. Chapel Hill, NC: Frank Porter Graham Child Development Institute.

[78] Clifford Richard M.,

[79] Reszka Stephanie S.,

[80] Rossbach Hans-Guenther

[81] ↵
Cunha Flavio,
Heckman James
. 2007. “The Technology of Skill Formation.” American Economic Review 97(2):31–47.
OpenUrl CrossRef

[82] Cunha Flavio,

[83] Heckman James

[84] ↵
Cunha Flavio,
Heckman James
. 2008. “Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formation.” Journal of Human Resources 43(4):738–82.
OpenUrl Abstract/FREE Full Text

[85] Cunha Flavio,

[86] Heckman James

[87] Cunha Flavio,
Elo Irma T.,
Culhane Jennifer
. 2013. “Eliciting Maternal Expectations about the Technology of Cognitive Skill Formation.” NBER Working Paper 19144. Cambridge, MA: NBER.

[88] Cunha Flavio,

[89] Elo Irma T.,

[90] Culhane Jennifer

[91] ↵
Currie Janet,
Thomas Duncan
. 1999. “Early Test Scores, Socioeconomic Status and Future Outcomes” NBER Working Paper 6943. Cambridge, MA: NBER.

[92] Currie Janet,

[93] Thomas Duncan

[94] ↵
Del Boca Daniela,
Flinn Christopher,
Wiswall Matthew
. 2014. “Household Choices and Child Development.” The Review of Economic Studies 81(1):137–85.
OpenUrl CrossRef

[95] Del Boca Daniela,

[96] Flinn Christopher,

[97] Wiswall Matthew

[98] ↵
dos Santos Elsa S.,
Luttikhuizen,
de Kieviet Jorrit F.,
Königs Marsh,
van Elburg Ruurd M.,
Oosterlaan Jaap
. 2013. “Predictive Value of the Bayley Scales of Infant Development on Development of Very Preterm/Very Low Birth Weight Children: A Meta-analysis.” Early Human Development 89(7):487–96.
OpenUrl CrossRef PubMed

[99] dos Santos Elsa S.,

[100] Luttikhuizen,

[101] de Kieviet Jorrit F.,

[102] Königs Marsh,

[103] van Elburg Ruurd M.,

[104] Oosterlaan Jaap

[105] ↵
Duncan Greg J.
2003. “Modeling the Impacts of Child Care Quality on Children’s Preschool Cognitive Development.” Child Development 74(5):1454–75.
OpenUrl CrossRef PubMed

[106] Duncan Greg J.

[107] ↵
Eckstein Zvi,
Wolpin Kenneth I.
1989. “Dynamic Labour Force Participation of Married Women and Endogenous Work Experience.” The Review of Economic Studies 56(3):375–90.
OpenUrl CrossRef

[108] Eckstein Zvi,

[109] Wolpin Kenneth I.

[110] ↵
Elango Sneha,
García Jorge Luis,
Heckman James J.,
Hojman Andrés
. 2016. “Early Childhood Education.” In Economics of Means-Tested Transfer Programs in the United States, Volume II. ed. Moffitt Robert, 235–98. Chicago, IL: University of Chicago Press.
OpenUrl FREE Full Text

[111] Elango Sneha,

[112] García Jorge Luis,

[113] Heckman James J.,

[114] Hojman Andrés

[115] ↵
Fitzgerald John,
Gottschalk Peter,
Moffitt Robert
. 1998. “An Analysis of Sample Attrition in Panel Data: The Michigan Panel Study of Income Dynamics.” The Journal of Human Resources 33(2):251–99.
OpenUrl CrossRef

[116] Fitzgerald John,

[117] Gottschalk Peter,

[118] Moffitt Robert

[119] ↵
Fryer Roland G. Jr.,
Levitt Steven D.
2013. “Testing for Racial Differences in the Mental Ability of Young Children.” The American Economic Review 103(2):981–1005.
OpenUrl CrossRef

[120] Fryer Roland G. Jr.,

[121] Levitt Steven D.

[122] ↵
Gayle George-Levi,
Golan Limor,
Soytas Mehmet A.
2016a. “What Accounts for the Racial Gap in Time Allocation and Intergenerational Transmission of Human Capital?” Unpublished.

[123] Gayle George-Levi,

[124] Golan Limor,

[125] Soytas Mehmet A.

[126] ↵
Gayle George-Levi,
Golan Limor,
Soytas Mehmet A.
2016b. “What is the Source of the Intergenerational Correlation in Earnings?” Unpublished.

[127] Gayle George-Levi,

[128] Golan Limor,

[129] Soytas Mehmet A.

[130] ↵
Gourieroux Christian,
Monfort Alain,
Renault Eric
. 1993. “Indirect Inference.” Journal of Applied Econometrics 8(S1):S85–S118.
OpenUrl CrossRef

[131] Gourieroux Christian,

[132] Monfort Alain,

[133] Renault Eric

[134] ↵
Griffen Andrew S.,
Nakamuro Makiko,
Inui Tomohiko
. 2015. “Fertility and Maternal Labor Supply in Japan: Conflicting Policy Goals?” Journal of the Japanese and International Economies 38:52–72.
OpenUrl CrossRef

[135] Griffen Andrew S.,

[136] Nakamuro Makiko,

[137] Inui Tomohiko

[138] ↵
Griffen Andrew S.,
Todd Petra E.
2017. “Assessing the performance of nonexperimental estimators for evaluating Head Start.” Journal of Labor Economics 35(S1):S7–S63.
OpenUrl CrossRef

[139] Griffen Andrew S.,

[140] Todd Petra E.

[141] ↵
Guner Nezih,
Kaygusuz Remzi,
Ventura Gustavo
. 2017. “Child-Related Transfers, Household Labor Supply and Welfare.” Unpublished.

[142] Guner Nezih,

[143] Kaygusuz Remzi,

[144] Ventura Gustavo

[145] ↵
Harris Kathleen Mullan R.,
Raley Kelly,
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Evaluating the Effects of Childcare Policies on Children’s Cognitive Development and Maternal Labor Supply

Abstract

I. Introduction

II. Model

A. Preferences

B. Childcare

C. Head Start

D. Home Quality

E. Cognitive Achievement Production Function

F. Wages and Income

G. Childcare Subsidies

H. Fertility and Divorce

I. Shocks and State Space

J. Choices

K. Budget Constraint

L. Mother’s Problem

M. Terminal Value

N. Unobserved Heterogeneity

O. Solution Method

II. Data

A. Measuring Quality

B. Measuring Cognitive Skills

C. Summary Statistics

D. Timing, Attrition and Sample Selection

III. Estimation

IV. Estimation Results

A. Parameter Estimates

B. Model Fit

V. Counterfactuals

A. Head Start

B. Childcare Subsidies

VI. Conclusions

Appendix

Footnotes

References

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