Within-family differences in Head Start participation and parent investment

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Within-family differences in Head Start participation and parent investment Kathryn E. Gonzaleza,

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a

Harvard Graduate School of Education, 243 Gutman, Cambridge, MA 02138, United States

ARTICLE INFO

ABSTRACT

Keywords: Educational economics Early childhood education Family economics

There is limited understanding of how parents’ allocation of investments across their children are affected by differences in their children's participation in programs that promote early development. I use data from the National Longitudinal Survey of Youth to examine whether parents reinforce or compensate for differences in their children's access to an early education program, Head Start. I use a family fixed effects approach to contrast measures of parental investment, when children were age 5 through 14, for children who attended Head Start relative to their siblings who did not attend preschool. I find that parents provided lower levels of cognitive stimulation and emotional support to children who attended Head Start relative to their siblings who did not attend preschool. Although impacts are relatively small in magnitude (0.05 SD), results suggest that parent compensate for differences in access to early childhood educational opportunities.

JEL codes: I21 I28 J13

1. Introduction Founded in 1965 as part of the War on Poverty, Head Start is the first and largest federally-funded early childhood education program, enrolling roughly 900,000 low-income children and their families as of FY 2017 (U.S. Department of Health and Human Services, 2017). In recent decades, there has also been a large increase in the number of children and families participating in other types of center-based preschool programs, particularly state-funded prekindergarten programs often thought to be a close substitute to Head Start (Barnett, Lamy, & Jung 2005; Barnett, Carolan, Squires, & Brown, 2014; FriedmanKrauss et al., 2018). The growing availability of alternatives to Head Start highlights the importance of understanding the influence of Head Start on the behaviors and outcomes of participating children and their families. A large literature has focused on the short- and long-term impacts of participation in Head Start on children's outcomes (Deming, 2009; Ludwig & Miller, 2007; U.S. Department of Health and Human Services, 2010). There is also a growing focus on how children's participation in Head Start affects the behavior of their parents, including parents’ engagement with their children's early education and development (e.g., Gelber & Isen, 2013) and parents’ investment in their own education and human capital formation (e.g., Sabol & Chase-Landsdale, 2015; Sommer et al., 2018). Most of the research that considers the impacts of children's participation in Head Start on parent outcomes focuses on identifying these effects by comparing children across different households who did and did not have access to the program.

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At the same time, research also suggests that parents respond to differences in their children's prenatal endowments, skills, and academic achievement by reallocating time and resources across siblings (e.g., Datar, Kilburn & Loughran, 2010; Del Bono, Ermisch, & Francesconi, 2012; Dizon-Ross, 2018). Differences in children's access to opportunities and resources to promote development in early childhood may similarly impact the dynamics of parental investment within the household. One such opportunity includes participation in early education programs such as Head Start. Yet there is less understanding of how children's participation in formal early education programs such as Head Start affects their parents’ decision-making and investment behavior when some or all of the child's siblings do not have the same access to the program. On the one hand, parents may seek to maximize overall achievement among their children by investing more in children who have had early opportunities to build human capital (i.e., reinforcing behavior; Becker & Tomes, 1976). Alternatively, if parents value equality of outcomes for their children they may seek to provide more resources to children who did not participate in the program (i.e., compensating behavior; Behrman, Pollak, & Taubman, 1982). The influence of Head Start on the intra-household dynamics of parent investments is of particular interest, as Head Start is distinct from other early education programs based on the range of wraparound services and supports provided to participating children, the extent to which the program encourages parental involvement, and the quality of Head Start as compared with alternative types of care. In this paper, I use data from the National Longitudinal Survey of Youth 1979 (NLSY79) and the National Longitudinal Survey of Youth

Corresponding author E-mail address: [email protected].

https://doi.org/10.1016/j.econedurev.2019.101950 Received 14 December 2018; Received in revised form 7 December 2019; Accepted 13 December 2019 0272-7757/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Kathryn E. Gonzalez, Economics of Education Review, https://doi.org/10.1016/j.econedurev.2019.101950

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1979 Child and Young Adult (NLSY79-C) to examine the extent to which parent investment behavior varies across children in the same household based on children's differing participation in Head Start. I examine the extent to which parents compensate for (or reinforce) differences in their children's access to Head Start by investing less (or more) in their children who participated in Head Start relative to their siblings who did not attend preschool, when children are age 5 through 14. I use a family fixed effects approach similar to Currie and Thomas (1993), Garces, Thomas, and Currie (2002), and Deming (2009). This approach utilizes within-family differences in Head Start participation to compare levels of parental investment among siblings with differing access to Head Start. Under the assumption that within-family differences in Head Start participation are due to factors unrelated to how parents decide to allocate time and resources across their children when children are older, this approach identifies the effect of Head Start attendance on relative levels of parental investment across siblings. A positive impact of Head Start attendance on later parental investment indicates that parents tend to reinforce differences in access to early childhood resources by investing more in children who attended Head Start relative to their siblings. In contrast, a negative impact of Head Start attendance on later investment suggests that parental investments serve to compensate for differing access to these programs by investing more in children who did not have access to the program. I find evidence that parents reallocated time and resources across their children in order to compensate for differences in Head Start participation. Results suggest that parents provided lower levels of cognitive stimulation and emotional support, when children were age 5 through 14, to their children who attended Head Start relative to their siblings who did not attend preschool. Specifically, scores on a combined measure of cognitive stimulation and emotional support provided by children's home environments were 0.05 SD lower for children who attended Head Start relative to their siblings who did not attend preschool. Impacts are driven by lower levels of both emotional support and cognitive stimulation in the years following children's transition into Kindergarten through early adolescence. These findings indicate that parents compensate for, rather than reinforce, perceived differences in access to early childhood development resources and opportunities. Moreover, these findings indicate that evidence on the long-term impacts of Head Start based on withinfamily comparisons (e.g., Bauer & Schanzenbach, 2016; Deming, 2009; Garces et al., 2002) reflect not only the direct effects of Head Start participation, but also the effect of changes in later parental investment behavior induced by differences in Head Start access across siblings. Findings suggest that compensating parental behavior may be a potential mechanism for impact fade-out documented in earlier studies of Head Start, and that existing research relying on within-family comparisons may understate the benefits of Head Start.

on parents’ investment behavior. Evidence from the Head Start Impact Study indicates that parents of children who attended Head Start were more likely to read to their children and more likely to be involved in cultural enrichment activities (U.S. Department of Health and Human Services, 2010). Children's participation in Head Start also increased the amount of time parents invested in their children's education and development (Gelber & Isen, 2013), and increased parents’ investments in their own education (Sabol & Chase-Landsale, 2015). However, less is known about the effect of Head Start attendance on parents’ allocation of time and resources across their children, particularly when some children in the household participate in the program and others do not. Research also suggests that estimated impacts of Head Start attendance are dependent on the alternative types of care available – that is, whether children would otherwise use home-based care, attend statefunded Pre-K or attend another preschool program (Kline & Walters, 2016; Walters, 2015). Feller, Grindal, Miratrix, and Page (2016) find that Head Start attendance had a positive impact on early learning outcomes among children who would otherwise have used home-based care, but had little impact among children who would otherwise attend another center-based preschool program. This suggests that in studies of the impacts of Head Start, the largest impacts on both child and parent outcomes are likely to be observed for children who would otherwise utilize home-based care. The present study builds most directly on a body of literature that utilizes within-family variation in Head Start participation to identify the causal effect of Head Start by comparing the outcomes children who attended Head Start with their siblings who did not attend preschool. Using this approach, Currie and Thomas (1995) find large, positive test score gains for Head Start participants. Similarly, Garces et al. (2002) find evidence of positive effects of program participation on longerterm outcomes, including high school completion, college attendance, and criminal activity. More recently, Deming (2009) finds evidence of positive, long-term effects on a summary index of young adult outcomes, including education and health outcomes. But little research using this approach to date has considered how this type of intrahousehold variation in Head Start attendance relates to parents’ later investment behaviors. 2.2. Within-household allocations of parent investments Parents must decide how to allocate time and resources across their children. The theoretical model proposed by Becker and Tomes (1976) suggests that parents will invest more in the human capital development of higher-ability children relative to their siblings, in order to maximize overall utility (i.e. parents will demonstrate reinforcing behavior). A contrasting view, proposed by Behrman, Pollak, and Taubman (1982), suggests that parents’ aversion to inequality of outcomes across their children may lead parents to invest more in their relatively less-able children (i.e. parents will demonstrate compensating behavior). Empirical evidence on parental investment across siblings has yielded different findings across varied contexts. Some studies have found evidence to suggest that parents make child-specific investment that reinforce, rather than compensate, for differences in early endowments among siblings (Aizer & Cuhna, 2012; Almond & Muzumder, 2013; Dizon-Ross, 2018; Kim, 2005). Using data from the NLSY, Datar, Kilburn, and Loughran (2010) find that parents make child-specific investments (including breastfeeding and doctor visits) that reinforce differences in birth weight across siblings. Similarly, Frijters, Johnston, Shah, and Shields (2013) find that parents reinforce cognitive differences in their children by investing more in higherability children relative to their lower-ability siblings. However, other research has found evidence of compensating parent behavior in response to differences in children's early endowments driven by idiosyncratic birth endowments and prenatal human capital shocks (Del Bono et al., 2012; Halla & Zweimuller, 2014). Yi, Heckman, and

2. Review of the literature 2.1. Evidence on the effectiveness of Head Start Head Start is founded on a “whole-child” approach that emphasizes children's cognitive and non-cognitive development, as well as parents’ engagement with their children's learning (U.S. Department of Health and Human Services, 2010). Evaluations of Head Start have largely focused on the impacts of program attendance on children's cognitive and non-cognitive outcomes. Experimental and quasi-experimental studies of the program have found short-term impacts on test scores (Currie and Thomas, 1995; U.S. Department of Health and Human Services, 2010), and quasi-experimental studies have found evidence of positive effects on longer-term outcomes, such as health and educational attainment (Bauer & Schanzenbach, 2016; Deming, 2009; Garces et al., 2002; Ludwig & Miller, 2007). There is also growing literature regarding the effects of Head Start 2

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Zhang (2015) find that while parents make compensatory investments in response to early health shocks, educational investments tend to reinforce these early shocks. Other research suggests that the extent to which parental investments serve to compensate for or complement (and therefore exacerbate) perceived differences in ability depends on the level of resources available to parents. Hsin (2012) and Restrepo (2011) both find that more advantaged families demonstrate compensating behavior in response to differences in birth weight across siblings, while families with fewer resources demonstrate reinforcing behavior. In contrast, other research finds little evidence of differences in whether parents demonstrate reinforcing or compensating behavior based on socioeconomic status (Figlio, Guryan, Karbownik, & Roth, 2014; Oreopolous, Stabile, Walld, & Roos, 2008). However, parents’ allocation of investments in response to differences in their children's access to early childhood education programs may differ from their responses to differences in early health outcomes or birth endowments. If parents perceive that participation in Head Start does not have direct benefits (e.g., that the primary purpose of Head Start is to allow parents to enter the labor force), parents may not reallocate resources in response to differences in Head Start participation. On the other hand, if parents perceive Head Start as an opportunity to build human capital, parents may allocate investments in order to compensate or reinforce those differences. If parents perceive that human capital investments compound (i.e., dynamic complementary; Cuhna & Heckman, 2007) and if parents seek to maximize achievement across their children, parents may investment more in children who participated in Head Start as compared with their siblings who did not. Alternatively, if parents value equality of achievement across their children, parents may allocate investments in order to compensate for children's access to Head Start. Yet little evidence exists on how parents respond to differences in access to programs and resources that promote in development early childhood. This study seeks to fill this gap in the literature by providing evidence of how parents allocate childhood investments across siblings in response to differences in children's participation in Head Start. The influence of Head Start on the intra-household dynamics of parent investments is of particular interest, as it is possible that parents’ perceptions of the benefits that accrue to children as a result of attending Head Start differ as compared with their perceptions of the benefits of other types of preschool programs. First, Head Start is distinct from other programs based on the range of wrap-around services and supports provided to participating children, including a range of health, nutrition and other services. The benefits that children receive from participating in Head Start may therefore be particularly salient to parents, as compared to participation in other preschool programs that lack these services. Second, the benefits of attending Head Start for children's early development may also be particularly salient to parents due to the emphasis that Head Start places on parental involvement while their children are in the program. This includes encouraging parents to volunteer in centers and classrooms, and providing direct services to parents and families (Administration for Children and Families, 2009). As a result, parents may have considerable information about the types of services their children are receiving while they are enrolled in Head Start (e.g., through volunteering in the classroom). In contrast, parents may have fewer interactions with other types of preschool programs. Finally, there may be substantial differences in quality between Head Start programs and alternative available preschool programs. Historically, the quality requirements and observed quality among Head Start programs have often exceeded those of many other types of center-based preschool programs (Bassok, Fitzpatrick, Greenberg, & Loeb, 2016; Currie, 2001; Resnick & Zill, 1999)1. Furthermore, studies 1

looking at within-family differences in Head Start and preschool participation find that impacts on social and behavioral outcomes are higher for Head Start as compared with preschool, suggesting that Head Start may be of higher quality than non-Head Start alternatives (Bauer & Schanzenbach, 2016). If parents view Head Start as providing more direct benefits to participating children as compared with other preschool programs, parents may respond differentially to children's enrollment in Head Start as compared to other types of preschool. Alternatively, if parents view Head Start and other preschool programs as providing comparable benefits, parents may respond similarly to children's participation in Head Start and other preschool programs. 3. Data and sample In the present study, I utilize data from the National Longitudinal Survey of Youth 1979 (NLSY79), and National Longitudinal Survey of Youth 1979 Child and Young Adult Sample (NLSY79-C). The original NLSY79 included 12,686 individuals between the ages of 14 and 22 in 1979. In 1986, the NLSY79-C began following mothers from the NLSY79 and their children. In the present study, I focus on the biannual waves of the NLSY79-C from 1986 and 2012. Each survey wave collected information on a wide range of family, child, and parent characteristics for all children of mothers from the NLSY79, including information on various measures of parental investment. Beginning in 1988, surveys also collected information on children's participation in Head Start and other preschool programs. To create the analysis sample for the present study, I first restrict the sample to children who had information on Head Start or other preschool attendance in any wave of the survey, and were eligible for Head Start on or before 20022. I further restrict the sample to families with two age-eligible children where at least one child, but not all children, participated in Head Start or another preschool program. All analyses are conducted at the child-year (i.e., child-survey wave) level, and include all available waves of data from the time each child was age 5 through age 14 where at least one of the outcome measures is available. I also exclude families where all children with outcome information used the same type of care (Head Start, other preschool, or neither). In total, the analysis sample includes 3766 children and 14652 child-year observations. Children's participation in Head Start was determined based on parents’ retrospective reports across multiple waves of the NLSY79-C surveys. In each survey wave, parents reported whether each child ever attended Head Start or ever attended another preschool program. I classified children as attending Head Start (or another preschool program) based on parents’ responses to surveys administered when children were age four or older. If there was inconsistent information about whether the child had attended Head Start (or another preschool program) in these survey waves, children were classified as attending the program if parents reported that they had ever been enrolled in at least half of the surveys. If the parent reported that the child attended both Head Start and another preschool program, I classified the child as having attended Head Start. If parents did not report information on Head Start or other preschool attendance across any of the surveys administered when the children were age four or older, I assumed that the child did not attend either (footnote continued) states, these programs have quality standards comparable to those of Head Start. As of 2002, approximately 15 percent of four-year-olds were enrolled in state-funded prekindergarten (Barnett et al., 2003). Therefore, the alternative to Head Start for many children in the present analytic sample is unlikely to have been a highly-regulated state-funded program. 2 This includes children who were at least 4 years old in 2002 and at least 14 years old in 2012 (the most recent survey wave). If a child did not have age information or did not appear in the 2002 or 2012 survey, his or her age was imputed based a survey from an immediately adjacent year.

A notable exception is state-funded prekindergarten programs. In many 3

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subscores, and 3.5 cognitive stimulation scores7. The fourth outcome of interest is a summary index of child- and parentreported measures of parent investment. In addition to the HOME-SF measure, the NLSY79-C also collects child-reported measures of parent investment such as the following: how often parents check or help with the child's homework; how often parents discuss the child's studies, grades, school activities, selecting courses, going to college, the child's troubles, or current events; and whether the parents attend parent-teacher conferences, volunteer in the classroom, volunteer to supervise lunch or chaperoned school trips, and participate in parent-teacher organizations. Each of these variables was reported on a Likert scale, and the items included in the surveys varied based on child age. To create the summary index, I constructed binary indicators based on the reported frequency of each parent behavior and took the average of these binary variables, using the subset of items that was available for each child age group. The average of these items was then standardized to have mean zero and a standard deviation of one within each age group to form the summary index8. These measures were first collected in 1996. Therefore, the sample size for this analysis is smaller than the analyses using the HOME-SF inventory.

program. I also confirm that my results are robust to using alternative criteria to determine whether children had attended Head Start or another preschool program. 3.1. Outcome measures In the present study, I focus on four outcomes of interest related to parents’ investment behavior. The first three outcomes include scores from the Home Observation Measurement of the Environment-Short Form (HOME-SF) inventory, which provide a measure of parental investment for each individual child based on the child's home environment, parental traits, and parental behaviors. The HOME-SF inventory was completed biannually at each wave of the NLSY79-C between 1986 and 2012, for each child under the age of 15. The HOME-SF includes four sets of parent- and observer-reported items that capture the quality of cognitive stimulation and emotional support provided to the child in his or her home, and is a modification of the larger and widely-used HOME inventory (Bradley et al., 1992; Caldwell & Bradley, 1984). The specific items in the most recent version of the HOME-SF inventory by the NLSY are listed in Appendix A3. Although some of the HOME-SF items are measures of the household environment which may be constant across siblings within the household at a given point in time (e.g. “Family gets a daily newspaper” and “Home is not dark”) the majority of items are child-specific and would likely vary both across individual children and over time (e.g. “Mother reads to child 3 times a week or more” and “Child receives lessons or belongs to sports/music/art/ dance/drama organization”)4. In the present analysis, I focus on the overall HOME-SF scores as well as the cognitive stimulation and emotional support subscores, using the internally-normed standard scores provided by the NLSY79C5. The cognitive stimulation and emotional subscores represent the amount of cognitive and emotional resources parents provide to their children. The cognitive stimulation subscores capture information about the provision of learning opportunities in the home, such as whether parents encourage the child to read at home and the extent to which parents provide opportunities for children to participate in extracurricular activities. The emotional support subscores capture information about whether children's home environments have positive and nurturing parenting practices and mother-child interactions, such as the types of disciplinary practices used in the home and characteristics of verbal interactions between mothers and children (Barber & East, 2009; Caldwell & Bradley, 1984)6. For all analyses, I standardized the HOME-SF scores with respect to the overall sample (i.e., across ages) such that each score has a mean of zero and standard deviation of one. As HOME-SF scores were collected in each biannual wave of the survey for children age 14 or younger, an individual child had up to five sets of HOME-SF scores from surveys administered when the child was between 5 and 14 years old. Children had an average of 3.8 HOME-SF overall scores, 3.3 emotional support

3.2. Evidence of selection bias in Head Start participation The present analysis relies on the fact that among households included in the NLSY79-C, there are differences across siblings in terms of whether children attended Head Start, attended other preschool programs, or used neither form of care (i.e., used home-based care). However, it is possible parents’ decisions to enroll one child in Head Start but to utilize an alternative form of care for the child's sibling(s) could reflect differences between children. For example, parents’ decisions to enroll one child but not another in Head Start could also have been based on their perceptions of their children's early abilities and skills, or based on factors such as children's early health or special education needs. Alternatively, differences in Head Start attendance may have been driven by time-varying family or household characteristics such as changes in household socio-economic status over time. In these cases, a comparison of siblings who did and did not attend Head Start would likely yield a biased estimate of the effect of attending the program on relative levels of parental investment. Additionally, Head Start funding and enrollment increased between the late 1990s and early 2000s (see Fig. 1). Funded enrollment increased from 376,300 in 1980 to 912,345 in 2002 (U.S. Department of Health and Human Services), while the percentage of three- and four-year-olds enrolled in Head Start rose from 7% in 1990 to 11% in 2000 (Barnett, Robin, Hustedt, & Schulman, 2003). Importantly, many of the children in the analysis sample were eligible to attend Head Start during this same time period (see Fig. 2). Therefore, younger siblings may have had more access to Head Start relative to their older siblings. Although differences in access due to expansion in Head Start over time may be plausibly unrelated to many time-varying family and child characteristics (e.g., child health or family socioeconomic status), expanding access to Head Start over time could lead to children who attended Head Start being systematically younger, on average, relative to their siblings. As there is evidence that younger children receive, on average, lower levels of parental investment relative to their older siblings (Price, 2010), differences in sibling age based on Head Start participation could lead to concerns of bias.

3 There have been some changes to the administration of the HOME-SF since 1986. Currently, the exact items included in the HOME-SF vary based on the child's age: a separate set of items are provided if children are under the age of 3, if children are age 3 to 5, 6 to 9, and 10 to 14. In 1986, a single set of items was used for children age six and above; separate items for children age 6 to 9 and 10 to 14 were added in 1988. Items were also added to and removed from the inventory in various waves of the survey. (U.S. Bureau of Labor Statistics, 1998) 4 See Appendix Table A.1 for the complete list of items included in the most recent wave of the survey. 5 According to the U.S. Bureau of Labor Statistics, children were normed by year of age where each age group was assigned a standard score mean of 100 and standard deviation of 15. The standard scores in the present sample are presented by age in Appendix Figure A.1. 6 A complete list of items included in each subscore is presented in Appendix Table B.1.

7

The oldest children in the cohort (i.e., children who were age 7 to 14 in 1986) have fewer HOME-SF scores due to the fact that a smaller number of the 1986 to 2012 survey waves were administered before they turned 15. I choose not to exclude these children from the analysis, as children born prior to 1980 comprise a large fraction of the all children in the NLSY79-C data (approximately 15 percent). However, I confirm that results are robust to restricting the sample to children who were born between 1980 and 1998, and could therefore have five HOME-SF scores from five survey waves (see Appendix Table B.1). 8 See Appendix Table A.2 for details on construction on the summary index of outcomes 4

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Fig.1. Head Start Funded Enrollment Over Time. Notes: Includes Head Start funded enrollment, 1976 to 2014. Excludes American Recovery and Reinvestment Act (ARRA) funded enrollment in 2010. Based on data from the U.S. Department of Health and Human Services, Administration for Children and Families.

health and parent investment (HOME-SF scores) in the years prior to children's eligibility to enroll in Head Start or other preschool programs (i.e. ages zero to three). For consistency with the prior literature, I use largely the same child, family, and maternal characteristics as Deming (2009). Table 1 presents the results of this analysis. The first three columns report the sample means for children in the analytic sample who attended Head Start, attended other preschool programs, or did not attend preschool. The fourth column includes the result of a regression of the row variable on the indicators for Head Start and other preschool attendance, as well as family fixed effects. I observe no significant differences in child health, maternal employment, family income, and a range of additional time-invariant and pretreatment household characteristics between the Head Start sample and their siblings who were not enrolled in preschool. Reassuringly, there are also no significant differences in parent investment behavior, as measured by scores on the HOME-SF inventory from birth through age three, between children in Head Start and their siblings who were not enrolled in preschool. Prior work examining within-family differences in Head Start participation in the NLSY have found that children in Head Start had higher birth weights relative to their siblings who were not enrolled in preschool (e.g., Deming, 2009). Although I do not observe a statistically significant difference between children who attended Head Start and their siblings who used home-based care in the present sample, point estimates do suggest similar differences in birthweight. The implications of birthweight differences with regards to the direction of bias are unclear. Some evidence indicates that parents reinforce differences in birth weight, which would lead to positive bias (Datar et al., 2010), while other studies indicate that parents demonstrate compensatory behavior that would lead to negative bias (Del Bono et al., 2012) or found no differences in parent behavior based on birth weight (Kelly, 2011; Lynch & Brooks, 2013). But regardless of bias direction, it is unlikely that these minor differences in birth weight are driving the results presented here due to the small magnitude of these differences. Another concern is that there may be differences in age or birth order among children who attended Head Start relative to their siblings. As shown in Table 1, children enrolled in Head Start were slightly younger as of 2012 and slightly less likely to be first-born children, on average, than their siblings who were not enrolled in preschool, although neither of these differences are not statistically significant. On the one hand, this suggests that expanding access to Head Start over time, which may have led to increased enrollment in Head Start among

Fig.2. Year of Head Start Eligibility in NLSY Analysis Sample. Notes: Includes all children in the analysis sample. Year of eligibility is the year in which the child turned four year old.

However, it is also possible that differences in Head Start participation arose from idiosyncratic factors that affected children's access to Head Start. For example, Head Start centers are often over-subscribed (U.S. Department of Health and Human Services, 2010). Differences in enrollment among families may have arisen if one child was able to enroll in Head Start, but his or her sibling was not able to enroll due to lack of availability in the year in which they were eligible to attend. Alternatively, it may be the case that the number of Head Start centers proximal to the child's neighborhood changed in the years between when siblings were eligible to attend Head Start. As noted above if changes in availability are correlated with children's year of birth this could lead to concerns of bias. But differences in the presence of a local Head Start center may also be due to other factors less likely to be related to parents’ later investment, such as the closure of an existing center or families’ movement between similar neighborhoods that differed in terms of whether there was a Head Start center. Therefore, I first examine whether there are systematic differences in child or family characteristics that predict participation in Head Start. Specifically, I examine whether children who attended Head Start differ from their siblings who did not attend preschool on a range of child, family, and maternal characteristics, as well as measures of child 5

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younger siblings, was not the primary driver of within-family differences in Head Start attendance in the analytic sample. However, even small differences in birth order raise concerns about potential bias, as first-born children tend to spend more time with their parents relative to their younger siblings (Price, 2010). Therefore, differences in birth order based on Head Start participation in the present sample could present a potential source of downward bias. As discussed below, differences in birth order are similarly unlikely to drive results presented here. To account for missing data, I impute the mean of the analysis sample and include an indicator for missingness in all subsequent analyses.

heterogeneity. To examine the extent to which the effect of attending Head Start on parent investment behavior differs over the course of childhood, I estimate the following model with interactions by child age:

Yijt = +

1 HSij

+

2 Preschoolij

+ Xij +

j

+

t

+

k

+

itj

3 AgeGroupitj

+

+ Xij +

2 Preij *AgeGroupitj j

+

t

+

itj

(2)

5. Results

Because children in the NLSY79-C were not randomly assigned to Head Start, a simple comparison of parent investment behavior for children who attended Head Start and children who were not enrolled in preschool is likely to be biased. However, the direction of this bias is uncertain. Parents who enroll their children in Head Start are typically low income and may have fewer resources and less time to spend with their children, relative to parents who are not eligible for Head Start. Therefore, a simple comparison of children who were and were not enrolled in Head Start could yield estimates that are biased downwards. Alternatively, if unobserved characteristics are positively correlated both with parents’ decisions to enroll their children in Head Start as well as parents’ investment behavior when their children are older, a simple comparison of parent behavior for children who did and did not attend Head Start could be biased upwards. Therefore, I use family fixed effects to control for all time-invariant parent and family characteristics that are constant within a family, following the examples of Deming (2009), Currie and Thomas (1995), Garces et al. (2002), and others. The critical identifying assumption is that within a single family, parents’ decisions to enroll their children in Head Start is uncorrelated with unobserved variables that affect parent investment behavior later in childhood, which is the key outcome of interest. If differences in Head Start participation within a given family are due to idiosyncratic factors uncorrelated with later parent investment behavior, such as whether there was availability at a local Head Start center, then using family fixed effects will recover the unbiased estimate of the effect of Head Start participation on parent investment behavior. Therefore, I estimate the following primary model for child i, in family j, at year t:

+

1 HSij *AgeGroupitj

where AgeGroupitj is an indicator for child i in family j being in one of the following age groups in year t: age 5 or 6 (early primary school), ages 7 to 10 (primary school), and ages 11–14 (early adolescence). To examine whether impacts differ by birth order, I estimate analogous models that include interactions between Head Start enrollment and a series of indicators for birth order category.

4. Methodology

Yijt =

+

5.1. Impact of within-family differences in Head Start participation on parent investment behavior The results of estimating the primary model are presented in Panel A of Table 2, and suggest that parents compensated for differences in access to early childhood educational opportunities. The fixed effects estimates suggest that overall, Head Start attendance had a small, negative effect on parent investment behavior as measured by the HOMESF inventory. That is, parents appeared to have provided less cognitive stimulation and emotional support to their children who attended Head Start, relative to their siblings who were not enrolled in preschool. Overall HOME-SF standard scores were approximately 0.05 SD lower for children enrolled in Head Start relative to their siblings, and estimated impacts across the two subscales are similarly negative. Cognitive stimulation scores were 0.04 SD lower for children who attended Head Start relative to their siblings, while the impact on emotional support scores is similarly negative although less precisely estimated (−0.04 SD). In contrast, I find little impact of Head Start attendance on the parent index. The estimated impact is negative in sign, but small in magnitude and imprecisely estimated. I discuss the effects on the parent index in greater detail below. Additionally, I find little evidence to suggest that levels of parental investment differed across siblings who attended other types of preschool programs relative to their siblings who did not attend either Head Start or other preschool programs. Point estimates are generally positive in sign, but small in magnitude and not statistically significant. Differences in children's access to early education opportunities and resources may have been more salient to parents when their children were closer in age, or where there were fewer children in the household. I therefore also estimate the primary model for households with only two eligible children, which I refer to as the sibling pair subsample. These results are presented in Panel B of Table 2. Results show that the estimates of Head Start participation on parent investment for this sample are similar to results for the full sample and are, in fact, generally larger in magnitude. Head Start participants had overall HOME-SF scores 0.11 SD lower relative to their siblings who did not attend preschool, relative to an effect of −0.05 SD in the full sample. The negative effect on emotional support scores is similarly larger (−0.11 SD). The effect of on cognitive stimulation scores, while similarly negative, is not statistically significant. As above, I see little evidence of differences in levels of parental investment among children who attended preschool programs other than Head Start as compared with their siblings who did not attend preschool or Head Start.

(1)

where Xij is a vector of pre-treatment child and family characteristics listed in Table 19, γj are family fixed effects, ωt are year fixed effects, and δk are age-at-outcome fixed effects. HSij and Preschoolijt are indicators for whether child i attended Head Start or another preschool program, respectively. Therefore, HSij can be interpreted as the effect on parent investment outcome, Yijt, of attending Head Start relative to having not attended preschool. Specifically, a positive sign on β1 would indicate that parents invest relatively more in children who attended Head Start relative to their siblings who did not attend preschool (i.e., that parents reinforce differences in children's attendance of early childhood education programs). In contrast, a negative sign on β1 would indicate that parents invest relatively more in children who did not attend preschool relative to their siblings who attended Head Start (i.e., that parents compensate for differences in children's access to early childhood education programs). I also consider several sources of potential treatment effect

5.2. Differences in the impact of Head Start on parent investment by child age

9 Variable selection and construction was done following the example of Deming (2009). In all analyses I also include indicator variables for birth order (2, 3, 4, 5+) with firstborn as the omitted category.

I also consider whether impacts of Head Start on within-household dynamics of investment vary based on child age, in order to examine 6

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Table 1 Sample characteristics by preschool type.

Sample size Male Age in 2012 First born Birth order Birth weight (ln) Premature birth Pre-existing health condition Regular doctor's visit, age 0–3 Ever visited dentist, age 0–3 Illness in first year In mother's household, age 0–3 In maternal care, age 0–3 In relative care, age 0–3 In non-relative care, age 0–3 Family income, age 3 (ln) Family income, age 0–3 (ln) Father in household, age 0–3 Grandmother in household, age 0–3 Maternal Characteristics Hours worked in year prior to birth Hours worked in year after birth Smoked before birth Drank alcohol before birth Breastfed Weight change during pregnancy Insurance, age 0–3 Medicaid, age 0–3 HOME-SF Standard Scores, Age 0–3 Overall HOME-SF score, age 0–3 Cognitive stimulation standard score, age 0–3 Emotional support standard score, age 0–3

Head Start

Other Preschool

None

Sibling Difference: Head Start vs. None

942 0.511 (0.500) 26.817 (5.763) 0.301 (0.459) 2.293 (1.185) 4.721 (0.211) 0.224 (0.417) 0.054 (0.227) 0.478 (0.500) 0.264 (0.441) 0.541 (0.499) 0.937 (0.244) 0.634 (0.408) 0.189 (0.330) 0.177 (0.309) 10.132 (0.871) 10.161 (0.738) 0.591 (0.458) 0.200

1285 0.500 (0.500) 25.801 (5.324) 0.358 (0.480) 2.082 (1.073) 4.737 (0.252) 0.211 (0.408) 0.026 (0.158) 0.453 (0.498) 0.259 (0.438) 0.556 (0.497) 0.960 (0.197) 0.567 (0.416) 0.197 (0.321) 0.236 (0.346) 10.613 (0.969) 10.607 (0.815) 0.769 (0.388) 0.141

1539 0.500 (0.500) 26.634 (5.886) 0.323 (0.468) 2.234 (1.161) 4.736 (0.219) 0.223 (0.416) 0.038 (0.190) 0.452 (0.498) 0.247 (0.431) 0.536 (0.499) 0.948 (0.221) 0.651 (0.409) 0.177 (0.322) 0.172 (0.318) 10.454 (0.972) 10.470 (0.849) 0.732 (0.422) 0.163

0.020 [0.026] -0.325 [0.281] -0.028 [0.030] 0.058 [0.065] 0.017 [0.011] -0.012 [0.021] 0.003 [0.013] -0.048 [0.036] 0.041 [0.033] 0.009 [0.025] -0.006 [0.012] -0.009 [0.015] 0.006 [0.013] 0.003 [0.013] -0.040 [0.043] -0.010 [0.027] -0.005 [0.020] -0.002

(0.333)

(0.288)

(0.309)

[0.015]

28.550

30.552

29.764

-1.480

(14.208) 33.568 (12.492) 0.368 (0.482) 0.083 (0.276) 0.302 (0.459) 29.760 (15.496) 0.472 (0.457) 0.443 (0.462)

(13.838) 34.045 (12.248) 0.294 (0.456) 0.074 (0.262) 0.483 (0.500) 30.794 (13.826) 0.702 (0.429) 0.188 (0.364)

(14.140) 33.318 (12.320) 0.327 (0.469) 0.066 (0.249) 0.422 (0.494) 31.009 (14.797) 0.660 (0.443) 0.261 (0.414)

[1.159] -1.820 [1.113] 0.008 [0.016] -0.003 [0.012] -0.004 [0.016] -0.765 [0.685] -0.002 [0.023] 0.021 [0.022]

89.920 (15.993) 90.647

96.436 (14.395) 96.201

94.297 (15.812) 94.350

-0.090 [0.874] -0.363

(16.499) 92.704

(14.800) 97.842

(16.158) 96.326

[0.850] -0.020

(15.742)

(14.365)

(14.891)

[1.026]

Notes: The first three columns contain sample means with standard deviations in parentheses. The fourth column contains the coefficient on Head Start from a regression of the row variable on an indicator for Head Start, an indicator for other preschool, and family fixed effects. Standard errors in brackets and clustered at the family level. Sample sizes in the top row of each column indicate overall sample size for type of childcare used (Head Start, other preschool, none). Exact sample sizes for each column vary across rows. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

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Table 2 The effect of Head Start on parent investment behavior. (1) Overall HOME-SF Scores A. Family Fixed Effects Estimates Head Start

−0.052* (0.021) Other Preschool 0.016 (0.016) Observations 14443 Sample Size 3763 B. Family Fixed Effects Estimates – Sibling Pair Subsample Head Start −0.106** (0.033) Other Preschool −0.032 (0.025) Observations 4039 Sample Size 1077

(2) Cognitive stimulation scores

(3) Emotional support scores

(4) Parent index

−0.042* (0.021) 0.008 (0.015) 13536 3715

−0.044+ (0.025) 0.014 (0.019) 12598 3703

−0.010 (0.037) 0.007 (0.026) 7048 2508

−0.052 (0.035) −0.046+ (0.025) 3802 1061

−0.111** (0.039) −0.000 (0.031) 3585 1055

−0.097 (0.079) 0.082+ (0.048) 1977 706

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Table 3 The effect of Head Start on parent investment behavior by child age.

Head Start Age 5–6 Age 7–10 Age 11–14 Other Preschool Age 5–6 Age 7–10 Age 11–14 Observations Sample Size p-value from F test that HS coefficients. are equal

(1) Overall HOME-SF scores

(2) Cognitive stimulation scores a

(3) Emotional support scores

(4) Parent index

−0.105** (0.038) −0.041 (0.027) −0.042 (0.031)

−0.060 (0.042) −0.046 (0.028) −0.035 (0.030)

−0.102* (0.045) −0.015 (0.033) −0.051 (0.037)

0.152 (0.097) −0.029 (0.051) −0.023 (0.048)

0.044 (0.030) 0.029 (0.022) −0.024 (0.024)

0.061+ (0.031) 0.006 (0.022) −0.030 (0.024)

0.020 (0.037) 0.032 (0.028) −0.019 (0.029)

0.113 (0.078) 0.028 (0.039) −0.034 (0.038)

14,443 3763 0.273

13,536 3715 0.883

12,598 3703 0.255

7,048 2508 0.201

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age category fixed effects (5–6, 7–10, 11–14), and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.; a Results from Wald tests comparing coefficients across models cannot reject the null hypothesis that the coefficients on the impacts of Head Start on the cognitive stimulation and emotional support scores are the same at age 5–6 (p = 0.474), age 7–10 (p= 0.425), or age 11–14 (p = 0.710).

the ages at which impacts emerge and persist throughout childhood. Patterns of parental investment likely change throughout childhood, and it is possible that the effect of Head Start on parents’ allocation of time and resources across children similarly vary with child age. Furthermore, the items specified on the HOME-SF inventory vary based on the child age (ages 3–5, 6–9, and 10–14), as do the items included the in parent index (ages 5–7, 8–9, 10–14), and may therefore capture somewhat different aspects of parental behavior10. The results of estimating the models with interactions by child age

are shown in Table 3 and show only limited evidence of differential impacts by child age-at-outcome group. The first column of Table 3 suggests that the effects were strongest in the years immediately following children's eligibility for Head Start. I observe a negative effect on overall HOME-SF scores of 0.11 SD for children previously enrolled in Head Start at ages five and six, relative to their siblings who did not attend preschool. Although estimated impacts are negative in later years, I observe no statistically significant differences in parental investment between children who attended Head Start and their siblings at ages 7–14. However, I cannot reject that impacts across the three age groups are the same. Turning to the HOME-SF subscales, I also observe a negative impact on emotional support scores of 0.10 SD at ages five and six with smaller impacts at later ages, although, as above, I cannot

10 I use the age groups of 5-6, 7-10, and 11-14 for analyses in order to have relatively similar sample sizes in each age group.

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Table 4 The effect of Head Start on parent investment behavior by birth order.

Head Start Birth Order 1 2 3 4 5+ Observations Sample Size p−value from F test that HS coefficients. are equal

(1) Overall HOME-SF scores

(2) Cognitive stimulation scores

(3) Emotional support scores

(4) Parent index

−0.053 (0.036) −0.079* (0.032) −0.012 (0.040) −0.058 (0.060) −0.026 (0.084) 14443 3763 0.716

−0.050 (0.037) −0.047 (0.032) −0.027 (0.040) −0.009 (0.065) −0.059 (0.078) 13536 3715 0.969

−0.058 (0.044) −0.046 (0.037) −0.005 (0.048) −0.130+ (0.069) 0.041 (0.114) 12598 3703 0.478

−0.045 (0.086) −0.067 (0.064) 0.008 (0.068) 0.120 (0.086) −0.004 (0.122) 7048 2508 0.461

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

reject that impacts across the age groups are the same. Effects on cognitive stimulation scores are similar in magnitude across age groups, but not statistically significant. I also cannot reject that impacts at each age range on the two HOME-SF subscores are the same, suggesting that the patterns of effects by age did not differ across the cognitive stimulation and emotional support outcomes. As above, I observe no statistically significant impacts on the parent index across the age ranges. However, in contrast to the negative impact estimates on the overall HOME-SF scores, the estimated impact on the parent index at ages five and six is positive and substantively large in magnitude. This may indicate an increase in parental investments among children who attended Head Start as compared with their siblings in areas captured by the parent index but not aligned with the HOME-SF inventory. An alternative possibility is that the positive effect may reflect the fact that some five- and six-year-olds were not yet enrolled in Kindergarten, and may still have been enrolled in Head Start, at the time of the survey. In this case, a positive impact may capture parents’ involvement with their children's Head Start program. To disentangle these possible explanations, I construct an index of “school engagement” items that includes four measures of school engagement, including how often parents attend parent-teacher conferences, volunteer in the classroom, volunteer to supervise lunch or chaperone school trips, and participate in parent-teacher organizations. As these are the only four items included in the parent index for children age five and six, the positive impact effect of Head Start observed for this age group is driven by impacts on these items11. Next, I reestimate the models with interactions by child age with this school engagement index as the outcome of interest. Finally, I re-estimate these models after restricting the sample to children who were reported in being enrolled in K-12 at the time of the survey12. Consistent with the

results in Table 3, the estimated impact of Head Start on the school engagement index at ages five and six is substantively large and statistically significant (see Appendix Table B.2). However, this effect is largely attenuated, albeit still positive, after restricting the sample to children enrolled in K-12 (see Appendix Table B.3). These findings suggest that the pattern of results for the parent index presented in Table 3 may be driven in part, but not entirely, by some children still being enrolled in Head Start at ages five and six. Nevertheless, the fact that the positive point estimate at ages five and six persists after restricting the sample to children in K-12 suggests that Head Start participation may have led to short-lived increases in parents’ school engagement in the years immediately after children entered Kindergarten. 5.3. Differences in the impact of Head Start on parent investment by birth order Birth order may have also played a role with regards to how differences in Head Start attendance affected parents’ allocation of time and resources. Having an older child participate in Head Start may have affected parents’ investment behavior across siblings differently than if a younger child was the first child in the household to the program. For example, the presence of positive spillover effects from an older child's participation in Head Start on a younger sibling's outcomes may have affected how parents perceived the differences of siblings’ experiences. This may have subsequently affected the degree to which they compensated for or reinforced those differences. Research also suggests first-born children also tend to have more parent investment relative to their later-born siblings (Price, 2010). Therefore, if the results presented in Table 2 are driven by the minor differences in birth order observed in Table 1, we would expect the effects to be largest for younger siblings and to see little effect on first-born siblings. As shown in Table 4, the effects of Head Start attendance on the total HOME-SF scores are similar in magnitude across birth order groups. First-born children who attend Head Start had total HOME-SF

11

As noted above, the parent index includes different sets of items based on child age; see Appendix Table B.2 for the full list of items included in the parent index for each age range. To calculate the school engagement index, I calculated the average of the four variables; average values were then standardized with respect to the full sample. 12 In the full sample, 93 percent of children were reported as being enrolled in K-12 schooling at the time of the survey. An additional 3 percent were reported as being enrolled in preschool or nursery school; this includes almost exclusively five- and six-year-olds. Grade enrollment information was missing for the remaining 4 percent. Among five-year-olds, 49 percent were enrolled in K-

(footnote continued) 12 and 31 percent were in preschool or nursery school; information was missing for 21 percent. Among six-year-olds, 95 percent were enrolled in K-12 and 3 percent were in preschool or nursery school; information was missing for 2 percent. 9

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Table 5 The effect of Head Start on parent investment behavior by household preschool usage.

A. Head Start vs. Other Preschool Head Start Observations Sample Size B. Head Start vs. Home-Based Care Head Start Observations Sample Size

(1) Overall HOME-SF scores

(2) Cognitive stimulation scores

(3) Emotional support scores

(4) Parent index

−0.027 (0.032) 2621 643

−0.023 (0.032) 2428 637

−0.019 (0.038) 2275 638

0.030 (0.057) 1329 469

−0.086** (0.027) 3245 900

−0.045 (0.027) 3036 888

−0.094** (0.033) 2813 882

−0.050 (0.056) 1316 497

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

scores 0.05 SD lower relative to children who did not attend preschool (although imprecisely estimated) while I observe the largest impacts for second-born children (−0.08 SD). However, I cannot reject that the coefficients across age groups are equal. A similar pattern of consistently negative impacts across different birth order categories holds for the cognitive stimulation and emotional support subscores, although none of the estimates are statistically significant.

perceived that their children who attended Head Start and those who attended other preschool programs have similar access to early educational opportunities and services outside the home. This could be the case if some children who did not attend Head Start attended highquality programs such as state-funded prekindergarten, as a growing body of evidence suggesting that state-funded preschool programs can have positive short-term effects similar or larger than those found for Head Start (Barnett et al., 2005; Gormley & Gayer, 2005; Henry, Gordon, & Rickman, 2006; Weiland & Yoshikawa, 2013). However, it is important to note that I only observe the childcare programs that were utilized by the parents. Parents who chose to enroll their children in a non-Head Start preschool program may have differed from parents who used only home-based care along unobserved dimensions related to how they allocate time and resources across their children. If the children in Panel B who did not attend Head Start were instead enrolled in other preschool programs (and analogously for the children in Panel A), observed impacts might be larger or smaller.

5.4. Differences in the impact of Head Start on parent investment by household preschool usage The main results presented in Table 2 can be interpreted as the effect of attending Head Start on the level of parental investment program participants received at ages 5 through 14, relative to their siblings who did not attend preschool. However, it is important to note that families may have used any combination of Head Start, other preschool programs, and home-based care (i.e. not attending preschool), including the use of all three types of care. It is possible that parents who used all three forms of childcare may have perceived the differences between Head Start and home-based care differently than parents who used only two forms of childcare. For example, parents who used only homebased care and Head Start may perceive the benefits of Head Start to be greater relative to parents who used home-based care, Head Start and another type of preschool. To more explicitly examine the role of the alternative to Head Start, I first restrict the sample to families who only used a combination of Head Start and other preschool programs. Using this sample, I estimated a version of the primary model without the indicator for other preschool usage, with the results presented in Panel A of Table 5. Therefore, the coefficient on Head Start can be interpreted as the effect of Head Start on parent investment behavior for Head Start participants relative to their siblings who attended another preschool program. I then conduct the same analysis on the sample of parents who use only Head Start and home-based care, with the results presented in Panel B of Table 5. Similarly, the coefficient on Head Start can be interpreted as the effect on parent investment behavior for participants, relative to their siblings who did not attend preschool. Consistent with the results in Table 2, I observe negative impacts of Head Start enrollment on overall HOME-SF scores behavior among households that use only Head Start or home-based case (−0.09 SD). Impacts on the HOME-SF subscales and parent index are negative in sign, but mixed in magnitude and precision. In contrast, I observe little effect of Head Start on parent investment among households where all siblings who did not attend Head Start attended other preschool programs. One explanation for these findings is that parents may have

5.5. Robustness checks An interpretation of the results described above is that parents compensate for perceived differences to children's access to early opportunities to promote human capital. Specifically, results indicate parents compensate for differences in Head Start attendance by providing more resources in the home, at ages 5–14, for children who did not attend preschool as compared with their siblings who attended Head Start. This interpretation relies on the assumption that parents perceive Head Start as having sustained, positive impacts. Earlier studies of the medium- and long-term effects of Head Start that similarly use family fixed effects and data from the NLSY79-C find evidence of impacts on cognitive test scores, with larger impacts at younger ages (Deming, 2009; Currie & Thomas, 1998). These studies have also found evidence of sustained, long-term impacts of Head Start on young adult and adult outcomes (Bauer & Schanzenbach, 2016; Deming; 2009). These results provide support for this assumption, as parents may recognize and respond to these positive impacts of Head Start that emerge early and persist into young adulthood. However, these prior family fixed effects studies rely on smaller samples of older children as compared with the sample used in the present analysis. Therefore, I examine whether there are impacts of Head Start on parental investment among older cohorts of children in the NLSY79-C for whom studies have found evidence of positive, longterm impacts of Head Start. Specifically, I restrict the sample to include students who were age 27 or older in 2012 (comparable to the sample used by Deming, 2009) and among students who were age 22 or older

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in 2012 (comparable to the sample used by Bauer & Schanzenbach, 2016)13. In both cases, results similarly suggest a negative impact of Head Start on parent investment as measured by HOME-SF scores, and indicate little impact on the parent index (see Appendix Table B.4). I also test the sensitivity of the results to the use of alternative decision rules to determine whether children attended Head Start or other preschool programs. As described above, there were inconsistencies in some parents’ retrospective reporting of whether their children attended Head Start or other preschool programs. I therefore test the sensitivity of my results to alternative specifications of the sample selection, including using whether parents ever reported that their children attended Head Start or another preschool program to determine the child's classification, dropping observations with inconsistent reporting in surveys when the child was age 4 or older, dropping observations with missing information on Head Start or other preschool attendance from surveys when the child was age 4 or later, and retaining children who were missing information on both Head Start and other preschool attendance in all waves of the survey and assuming that these children attended neither program. The main results are robust to these alternative classification criteria (see Appendix Table B.5). I also confirm that results are not sensitive to the inclusion of covariates (see Appendix Table B.6–B.8). As noted above, the exact items included in the HOME-SF vary based on child age. I therefore also present results separately for individual age, based on the results of models that include separate interactions between the indicator for Head Start attendance and each individual age (and the interactions for other preschool attendance and each individual age). Results suggest impacts are generally negative, although imprecisely estimated, from age 5 through age 14 (see Appendix Figs. B.1–B.3). Finally, a limitation of the family fixed effects approach is that due to the selection of households into the analytic sample, the estimated impacts do not necessarily represent the average treatment effect (ATE) for broader populations of interest. Miller, Shenhav, and Grosz (2019) note that while the family fixed approach can provide an internally valid estimate of the effect of Head Start attendance among households with variation in Head Start participation, this approach may not uncover an unbiased estimate of the ATE for larger populations of interest such as Head Start participants. If the sample of children and households included in the fixed effects sample differ from the target population sample, and if there are heterogeneous impact of Head Start participation across different households, the fixed effects estimate of Head Start attendance may be a biased estimate of the ATE. For example, if households with a larger number of siblings are more likely to have within-household variation in Head Start participation, and if effects are larger for larger households, then the fixed effects approach will provide an estimate of the ATE that is biased away from zero. I follow a two-step reweighting approach similar to that outlined by Miller, Shenhav, and Grosz (2019) to obtain an estimate of the ATE for a policy-relevant target population: households with at least one child in Head Start. This approach reweights family-specific estimates of Head Start participation based on observable child and family characteristics to recover an estimate of the ATE for the target population. Details of this approach and results of the reweighted estimation are presented in Appendix C. In general, estimates of the ATE for the overall HOME-SF scores and HOME-SF subscores outcomes are between 2 percent and 27 percent smaller than the fixed effects estimates presented in Table 2. However, the estimated impact of Head Start participation on overall HOME-SF scores and cognitive stimulation scores remain statistically significant and marginally significant, respectively (see Appendix Table C.1).

5.6. Limitations I recognize several limitations in the present study. First, I only observe differences in parents’ investment in their children who attended Head Start relative to other children in their household. Therefore, I cannot observe whether children's participation in Head Start impacted overall levels of investment. For example, it is possible that one child's participation in Head Start raised levels of parental investment among all children in the household, but that this increase was particularly targeted at those children who did not attend Head Start. Thus, the results of the present study may not be inconsistent with other research showing positive impacts of Head Start attendance on parent behaviors (e.g., Gelber & Isen, 2013). Second, all analyses are unweighted and do not incorporate sampling weights provided by the NLSY79-C. Therefore, these results are only generalizable to the analytic sample in the present study, and do not provide evidence on the impact of within-family differences in Head start attendance among a broader population of children and families. In addition, while the present findings are consistent with the theory that parents compensate for children's differential access in resources to promote development in early childhood, an important limitation is that I do not have direct information on parents’ perceptions of the value of Head Start. If parents perceive that Head Start is less valuable relative to not attending preschool, these estimates would in fact support the explanation that parents reinforce differences in access to resources to support development in early childhood. Additionally, I am unable to examine the quality of children's K-12 schooling. It is possible that differences in parental investments may be driven by differences in the quality of K-12 schools attended by children who participated in Head Start as compared with their siblings. Some evidence suggests that children who attended Head Start subsequently attend lower-quality K-12 schools as compared with children with similar family backgrounds and demographic characteristics (Bailey, Duncan, Odgers, & Yu, 2017; Currie & Thomas, 1998; Lee & Loeb, 1995). If children in the present sample who attended Head Start subsequently enrolled in lower (or higher) quality elementary or secondary schools, the pattern of results could be evidence of parents reinforcing (or compensating) for differences in the quality of their children's later schooling experiences. Although the data do not have direct information about school quality, I examine two proxies for whether children who attended Head Start may have had different K-12 schooling experiences as compared with their children who did not attend preschool: whether children attended public schools, and children's reported satisfaction with their schools. In general, I find little evidence to suggest that children who attended Head Start were more likely to attend public school in K-12 (See Appendix Table B.9)14. Children who attended Head Start also reported similar levels of satisfaction with their school as compared with their siblings who did not attend preschool (See Appendix Table B.10). However, I cannot rule out the possibility that the quality of K-12 schooling experiences differed for children who attended Head Start as compared with their siblings based on other, unobserved aspects of quality.

14

When I examine impacts on the likelihood of attending public school by age, results indicate that children who attended Head Start were more likely to attend public school at ages 5 to 6 as compared with their siblings. However, after excluding children who were reported as not yet being enrolled in Kindergarten at the time of the survey, the impact of Head Start is small in magnitude and not statistically significant. Therefore, this suggests that the difference in public school attendance at ages 5 and 6 for children who attended Head Start (a public program) as compared with their siblings is based the presence of children still enrolled in Head Start at these ages rather than differences in the type of schools attended for Kindergarten or first grade.

13 Deming (2009) includes children who were 19 or older by 2004; Bauer & Schanzenbach (2016) include children who were eligible to participate in Head Start between 1974 and 1994.

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6. Discussion

emerge at ages 5 and 6, but fade out in later ages. In the present study, I find suggestive evidence that declines in parental investment are concentrated during this time period, in the years immediately following children's Head Start attendance. This suggests that the fade out of Head Start impacts observed in prior studies may be explained, in part, by within-family reallocation of resources that provide more cognitive stimulation and emotional support to children who did not attend preschool as compared with their siblings who attended Head Start. Finally, studies using the family fixed effects approach have found positive impacts on high school graduation, college attendance and other outcomes (Bauer & Schanzenbach, 2016; Deming, 2009; Garces et al., 2002). One implication of the present results – that parents reallocate investments away from children who attended Head Start and towards their siblings – is that the findings from these longterm studies capture both the effect of the direct benefits from children's participation in the program as well as the downstream effects on parental investment behavior. This suggests that Head Start may have had positive impacts on long-term outcomes despite potential declines in parent investment, and that these estimates of the long-term effects of Head Start may understate the impacts of these programs.

This paper provides evidence that parents allocate time and resources across their children based on within-family differences in Head Start attendance. I find that parents provide lower levels of cognitive stimulation and emotional support resources to siblings who attended Head Start later in childhood when children are age 5–14, relative to their siblings who did not attend preschool. Specifically, I find that children who attended Head Start had lower scores on an inventory measure of cognitive stimulation and emotional support provided by the child's home environment, a difference of about 0.05 SD, as compared with their siblings who did not attend preschool. These impacts are driven by lower levels of emotional support and cognitive support between the years children transitioned to Kindergarten through early adolescence. I find no clear evidence of systemically differential impacts based on child age, nor do I find evidence of systematic differences in impacts based on child birth order. This provides evidence to help rule out the possibility that impacts are driven by factors unrelated to Head Start attendance such as differential investment between older and younger siblings (Price, 2008, 2010). Overall, as Head Start provides a wide range of services to which children who do not attend preschool may not have access, these findings are consistent with the explanation that parents compensate for perceived differences in access to resources to promote development in early childhood. These findings also have implications for the interpretation of the results from a large number of studies that have used the family fixed effects approach to examine the long-term impacts of Head Start. For example, recent evidence finds that Head Start impacts on long-term outcomes are smallest among households with two children (Miller, Shenhav, & Grosz, 2019). In the present study, I find that the negative effects of Head Start on parental investment are largest among these types of households. This suggests that parents’ compensating behavior may explain, in part, the lack of long-term impacts among these families. Additionally, results from the present study suggest compensating parental behavior may be a potential mechanism for the fade-out of program impacts documented in earlier studies of Head Start. Deming (2009) finds that early impacts of Head Start attendance

CRediT authorship contribution statement Kathryn E. Gonzalez: Conceptualization, Methodology, Formal analysis, Writing - original draft, Writing - review & editing. Declaration of Competing Interest None. Acknowledgments The research reported here was supported in part by the Institute of Education Sciences, U.S. Department of Education, through grant R305B150010 to Harvard University. The opinions expressed are those of the authors and do not represent the views of the Institute or the U.S. Department of Education. I would also like to thank Felipe BarreraOsorio, Dana McCoy, and Lawrence Katz for their helpful comments on this work.

Appendix A: Details of the HOME inventory and parent index

Table A.1 Measures included in the HOME-SF inventory.

Child gets out of house 4 times a week or more Child has 3 children's books Mother reads to child 3 times a week or more Child taken to grocery store (once/week or 2–3 times a month) Child has one or more cuddly, soft or role-playing toys Child has one or more push or pull toys Mother believes parents should usually or always spend time teaching kids Child eats meal with both mother and father(-figure) once a day or more Mom often talks with child while working Mom reports no more than 1 spank during past week Mom spontaneously vocalize to/conversed with child at least twice Mom responded verbally to child Mom showed physical affection to child Mom did not spank child

0–2

3–5

6–9

10–14

Subscale

1 1 1

– 1 1

– 1 1

– 1 –

C C C

1

1

–

–

C

1 1

– –

– –

– –

C C

1

–

–

–

C

1 1

1 –

1 –

1 –

E E

1

1

1

–

E

1 1 1 1

1 – 1 1

1 – 1 –

1 – 1 –

E E E E

(continued on next page) 12

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Table A.1 (continued)

Mom did not interfere/restrict child more than 3 times Mom provided appropriate toys/activities to child Mom kept child in view Play environment is safe (home or building for ages 36 mos +) Family subscribes to at least one magazine Child has use of record/CD player and at least 5 records/CDs/tapes Child helped to learn numbers at home Child helped to learn alphabet at home Child helped to learn colors at home Child helped to learn shapes and sizes at home Child has some choice in foods for breakfast and lunch Non-harsh discipline if child hits Child taken to museum in past year Child expected to make his/her bed Child expected to clean his/her room Child expected to clean up after spills Child expected to bathe him/herself Child expected to pick up after himself/herself Child expected to keep shared living areas clean and straight Child expected to do routine chores such as lawn, help w/ dinner, dishes Child expected to help manage his/her own time Musical instrument in home child can use Family gets a daily newspaper Child reads several times a week for enjoyment Family encourages child to start and do hobbies Child receives lessons or belongs to sports/music/art/dance/drama org Child taken to musical or drama performance in past year Family visits with family or friends 2–3 times a month Child spends time with father(-figure) 4 times a week Child spends time with father(-figure) in outdoor activities once a week When watching TV, parent discusses program with child Mom encouraged child to contribute to conversation Mom answered child's questions or requests verbally Mom introduced interviewer to child by name Mom's voice conveyed positive feeling about child Home is not dark Home is reasonably clean Home is minimally cluttered

0–2

3–5

6–9

10–14

Subscale

1

–

–

–

E

1 1

– –

– –

– –

C E

1 –

1 1

1 –

1 –

C C

– – – – –

1 1 1 1 1

– – – – –

– – – – –

C C C C C

– – – – – – – –

1 1 1 – – – – –

– 1 1 1 1 1 1 1

– 1 1 1 1 – – 1

E E C E E E E E

–

–

–

1

E

– – – – – –

– – – – – –

– – 1 1 1 1

1 1 1 1 1 1

E E C C C C

–

–

1

1

C

–

–

1

1

C

–

–

1

1

E

–

–

1

1

E

–

–

1

1

E

–

–

1

1

C

–

–

1

1

E

– – – – – –

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

E E E C C C

Note: C = “Cognitive Stimulation,” E = “Emotional Support.”

Construction of parent behavior index The items included below were used to construct the parent behavior index. The items children responded to in the survey varied based on the child age; the table below lists the ages for which each item was used in the parent behavior index. The construction of the parent index was as follows: First, a binary indicator for each item was constructed following the rules in the table listed below. Second, the average of the binary indicators for each item was calculated. This sum was set to missing if more than half of the items were missing in a given wave of the survey (based on the relevant items for the child's age group). Finally, the sum of the binary items was standardized across all observations (i.e., across all ages and survey waves) within each age range (5–7, 8–9, 10–14) to have mean zero and a standard deviation of one. The standardization as done separately by age range to account for the fact that the specific items included in the parent index varied across the age ranges.

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Table A.2 Parent index – indicator measures. Child-reported

Coding rule

Ages

How often parents check homework How often parents help with homework

1 if 1–2 times a week, almost every day, or every day; 0 if never, less than once a month, or 1–2 times a month 1 if 1–2 times a week, almost every day, or every day; 0 if never, less than once a month, or 1–2 times a month 1 if often; 0 if sometimes, rarely, or never 1 if often; 0 if sometimes, rarely, or never 1 if often; 0 if sometimes, rarely, or never 1 if often; 0 if sometimes, rarely, or never

8–14

1 if often; 0 if sometimes, rarely, or never 1 if often; 0 if sometimes, rarely, or never 1 if often; 0 if sometimes, rarely, or never 1 if 1–2 a month or once a week or more; almost never 1 if 1–2 a month or once a week or more; almost never 1 if 1–2 a month or once a week or more; almost never 1 if 1–2 a month or once a week or more; almost never Coding rule 1 if Yes; 0 if No

0 if once a month, less than once a month, or never/

8–14 10–14 10–14 10–14

0 if once a month, less than once a month, or never/

10–14

0 if once a month, less than once a month, or never/

10–14

0 if once a month, less than once a month, or never/

10–14

How often parents How often parents How often parents How often parents troublesa How often parents How often parents How often parents How often parents

discuss discuss discuss discuss

things studied in school grades or report card school events or activities child's

discuss community, national or world events discuss going to college discuss selecting courses or programs at school attend a school meetinga

How often parents phone or speak to teacher or counselor

a

How often parents attend a school event in which child participates

a

How often parent acts a volunteer at schoola Parent-reported Do often parents attend parent-teacher conferences Do often parents volunteer in the classroom Do parents volunteer supervise lunch or chaperone school trips Do parents participate in parent-teacher organizations

8–14 8–14 8–14 8–14 10–14

Ages 5–14

1 if Yes; 0 if No

5–14

1 if Yes; 0 if No

5–14

1 if Yes; 0 if No

5–14

a These items were also asked for children ages 8 and 9 starting in the 1998 or 2000 survey waves; responses to these items for children age 8 or 9 were not included in the present analysis.

Fig.A.1. Distribution of HOME-SF Overall Standard Scores by child age, for selected ages

Appendix B: Robustness checks Sensitivity of results to excluding children born prior to 1980 The sample for the present analysis includes children who were at least 4 years old as of 2002 and at least 14 years old as of 2012. The primary outcomes for the present analysis are measures of parental investment collected from the 1986 through 2012 survey waves, including surveys administered when children were age 5 through 14. As a result of this sample selection, the oldest children in the sample (i.e., children age 7 or older as of 1986) have outcome data from a small number of waves, due to the fact that a smaller number of the 1986 through 2012 surveys were administered prior to when the children turned 15. As shown in Table B.1, after dropping children born in 1980 or later from the analysis sample the magnitude of estimated impacts are similar to those from the main results. However, results are less precisely estimated, likely due to the substantial decrease in sample size.

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Table B.1 Effect of within-family differences in Head Start participation on overall HOME-SF scores, excluding children born before 1980.

Head Start Other Preschool Observations Sample Size

(1) Overall HOME-SF scores

(2) Cognitive stimulation scores

(3) Emotional support scores

(4) Parent index

−0.050* (0.024) 0.015 (0.017) 11487 2846

−0.040+ (0.024) 0.013 (0.016) 10783 2811

−0.039 (0.029) 0.013 (0.021) 10001 2795

−0.010 (0.037) 0.008 (0.026) 6616 2322

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Fig.B.1. Impacts of Head Start on HOME-SF Overall Standard Scores by child age, point estimates and standard errors. Notes: Point estimates and standard errors based on a regression of HOME scores on age fixed effects, and a series of interactions between indicators for Head Start attendance and preschool attendance, and each age indicator. The model also includes family, year, and birth order fixed effects and the child and family pretreatment covariates included in Table 1.

Fig. B.2. Impacts of Head Start on Cognitive Stimulation Standard Scores by child age point estimates and standard errors. Notes: Point estimates and standard errors based on a regression of HOME scores on age fixed effects, and a series of interactions between indicators for Head Start attendance and preschool attendance, and each age indicator. The model also includes family, year, and birth order fixed effects and the child and family pretreatment covariates included in Table 1.

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Fig. B.3. Impacts of Head Start on Emotional Support Standard Scores by child age point estimates and standard errors. Notes: Point estimates and standard errors based on a regression of HOME scores on age fixed effects, and a series of interactions between indicators for Head Start attendance and preschool attendance, and each age indicator. The model also includes family, year, and birth order fixed effects and the child and family pretreatment covariates included in Table 1.

Impacts on school engagement items in the parent index and sensitivity of results to restricting the sample to children in K-12 Table B.2 Effect of within-family differences in Head Start participation on parent investment behavior, separately by parent investment type. (1) Overall HOME-SF scores Head Start Other Preschool Impacts separately by child age Head Start Age 5–6

−0.052* (0.021) 0.016 (0.016)

Age 7–10 Age 11–14 Other Preschool Age 5–6 Age 7–10 Age 11–14 Observations

(2)

14443

(3) Parent index

(4)

−0.010 (0.037) 0.007 (0.026)

(5) (6) Parent index: school engagement 0.014 (0.034) −0.003 (0.023)

−0.105** (0.038) −0.041 (0.027) −0.042 (0.031)

0.152 (0.097) −0.029 (0.051) −0.023 (0.048)

0.181* (0.091) −0.002 (0.049) −0.003 (0.043)

0.044 (0.030) 0.029 (0.022) −0.024 (0.024) 14443

0.113 (0.078) 0.028 (0.039) −0.034 (0.038) 7048

0.085 (0.074) 0.047 (0.037) −0.057+ (0.033) 6,902

7048

6,902

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age or age group fixed effects, and year fixed effects. Analyses of parent index outcomes include information from the 1996 through 2012 survey waves. Items included in the school engagement index include the following subset of items from the parent appendix: how often parents attend parentteacher conferences, volunteer in the classroom, volunteer to supervise lunch or chaperone school trips, and participate in parent-teacher organizations. +p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

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Table B.3 Effect of within-family differences in Head Start participation on parent investment behavior, excluding children still enrolled in preschool. (1) Overall HOME-SF scores Head Start Other Preschool Impacts separately by child age Head Start Age 5–6

−0.056* (0.022) 0.009 (0.016)

(3) Parent index

(4)

(5) (6) Parent index: school engagement

−0.005 (0.038) 0.005 (0.027)

Age 7–10 Age 11–14 Other preschool Age 5–6 Age 7–10 Age 11–14 Observations Excludes Children not in K-12a

(2)

0.010 (0.035) -0.011 (0.023)

−0.124** (0.043) −0.044 (0.028) −0.047 (0.031)

0.096 (0.105) −0.016 (0.052) −0.009 (0.049)

0.076 (0.097) 0.009 (0.050) 0.005 (0.043)

0.007 (0.035) 0.032 (0.022) −0.024 (0.024)

0.016 (0.089) 0.038 (0.040) −0.027 (0.039)

−0.015 (0.082) 0.052 (0.037) −0.056+ (0.033)

13,455

13,455

6783

6783

6701

6701

Yes

Yes

Yes

Yes

Yes

Yes

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age or age group fixed effects, and year fixed effects. Analyses of parent index outcomes include information from the 1996 through 2012 survey waves. Items included in the school engagement index include the following subset of items from the parent appendix: how often parents attend parentteacher conferences, volunteer in the classroom, volunteer to supervise lunch or chaperone school trips, and participate in parent-teacher organizations. +p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.; aAlso excludes cases where grade information was not reported.

Differences in the impact of Head Start on parent investment by age cohort Table B.4 Effect of within-family differences in Head Start participation on overall home-sf scores, separately by age cohort.

A. Main Specification Head Start Other Preschool Observations Sample Size B. Age 27 or older in 2012 Head Start Other Preschool Observations Sample Size C. Age 22 or older in 2012 Head Start Other Preschool Observations Sample Size

(1) Overall HOME-SF scores

(2) Cognitive stimulation scores

(3) Emotional support scores

(4) Parent index

−0.052* (0.021) 0.016 (0.016) 14443 3763

−0.042* (0.021) 0.008 (0.015) 13536 3715

−0.044+ (0.025) 0.014 (0.019) 12598 3703

−0.010 (0.037) 0.007 (0.026) 7048 2508

−0.049+ (0.028) −0.001 (0.022) 4456 1256

−0.011 (0.027) −0.025 (0.021) 4,214 1246

−0.049 (0.035) −0.009 (0.028) 3925 1244

0.083 (0.174) −0.078 (0.146) 574 397

−0.058* (0.023) 0.011 (0.018) 9495 2523

−0.046* (0.023) 0.000 (0.018) 8934 2499

−0.047+ (0.027) 0.010 (0.022) 8343 2493

0.025 (0.052) −0.011 (0.039) 3130 1378

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Sensitivity of results to alternative approaches of determining whether children attended Head Start or other preschool As shown in Table B.5, results are not sensitive to alternative classifications of Head Start and other preschool enrollment. Estimates are comparable in magnitude and precision when Head Start and other preschool enrollment are based on whether parents reported that the child was 17

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Table B.5 Effect of within-family differences in Head Start participation on overall HOME-SF scores. (1) Overall HOME-SF scores

(2)

(3)

(4)

(5)

Head Start

−0.047* (0.021) 0.012 (0.016) 14407 3751 Ever reported Head Start, preschool enrollment

−0.047+ (0.024) 0.022 (0.018) 11226 2987 Drop children with inconsistent reporting at age 4 or older

−0.050* (0.021) 0.017 (0.016) 14316 3711 Drop children missing Head Start and other preschool information at age 4 or older

−0.051* (0.021) 0.020 (0.015) 14910 3947 Assume no information on Head Start and other preschool attendance across all survey waves means child attended neither program

Other Preschool Observations Children Sample

−0.052* (0.021) 0.016 (0.016) 14443 3760 Main results

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

enrolled in the program in any wave (column 2), dropping children that had inconsistent reporting in Head Start or other preschool use in surveys administered when the child was age 4 or older (column 3), and dropping children that had missing Head Start and preschool information in all surveys administered when the child was age 4 or older (column 4). Results are also robust to including observations that have no information on Head Start or other preschool attendance across all survey waves (regardless of child age when the survey was administered) and assuming that in these cases the child attended neither program (column 5). Sensitivity of results to inclusion of covariates As shown in Table B.6 through B.8, results are not sensitive to the inclusion of covariates that are shown to be slightly imbalanced between siblings who did and did not attend Head Start within the same family, nor to the inclusion of measures of parent investment at ages zero to three. Estimates are nearly identical in models that do and do not include controls for birth order, birth weight, HOME-SF scores collected in ages 0 to 3, and other covariates. Table B.6 Effect of within-family differences in Head Start participation on overall HOME-SF score, showing sensitivity to model specification.

Head Start Other Preschool Observations Birth order Birth weight HOME-SF scores, age 03 Other covariates

(1) Overall HOME-SF scores

(2)

(3)

(4)

(5)

−0.051* (0.022) 0.020 (0.016) 14443 No No No

−0.052* (0.021) 0.017 (0.016) 14443 Yes No No

−0.051* (0.022) 0.021 (0.016) 14443 No Yes No

−0.050* (0.022) 0.021 (0.016) 14443 No No Yes

−0.052* (0.021) 0.016 (0.016) 14443 Yes Yes Yes

No

No

No

No

Yes

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Table B.7 Effect of within-family differences in Head Start participation on emotional support scores.

Head Start Other Preschool Observations Birth order Birth weight HOME-SF scores, age 0-3 Other covariates

(1) Emotional support scores

(2)

(3)

(4)

(5)

−0.043+ (0.026) 0.016 (0.019) 12598 No No No

−0.044+ (0.025) 0.014 (0.019) 12598 Yes No No

−0.044+ (0.026) 0.018 (0.019) 12598 No Yes No

−0.042+ (0.026) 0.017 (0.019) 12598 No No Yes

−0.044+ (0.025) 0.014 (0.019) 12598 Yes Yes Yes

No

No

No

No

Yes

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

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Table B.8 Effect of within-family differences in Head Start participation on cognitive stimulation scores.

Head Start Other Preschool Observations Birth order Birth weight HOME-SF scores, age 0–3 Other covariates

(1) Cognitive stimulation scores

(2)

(3)

(4)

(5)

−0.043* (0.021) 0.014 (0.016) 13,536 No No No

−0.043* (0.021) 0.012 (0.015) 13,536 Yes No No

−0.043* (0.021) 0.015 (0.016) 13,536 No Yes No

−0.043* (0.021) 0.014 (0.016) 13,536 No No Yes

−0.042* (0.021) 0.008 (0.015) 13,536 Yes Yes Yes

No

No

No

No

Yes

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Impact of Head Start on public school attendance and school satisfaction Table B.9 Effect of within-family differences in Head Start participation on whether children are enrolled in public school. (1) Child is enrolled in public school Head Start Other Preschool Impacts separately by child age Head Start Age 5–6

(3)

0.089** (0.030) 0.004 (0.010) −0.001 (0.009)

−0.029 (0.023) −0.001 (0.010) −0.002 (0.009)

0.061* (0.029) 0.014 (0.009) 0.011 (0.008) 9,678 No

−0.041+ (0.023) 0.007 (0.009) 0.008 (0.008) 9,327 Yes

0.008 (0.007) 0.015* (0.007)

Age 7–10 Age 11–14 Other Preschool Age 5–6 Age 7–10 Age 11–14 Observations Excludes children not enrolled in K-12a

(2)

9,678 No

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age or age category fixed effects, and year fixed effects. Includes information from the 1988 through 2012 survey waves; information on type of school children attended was only collected for children age 10 or older in some survey waves. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001;aAlso excludes cases where grade information was not reported.

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Table B.10 Effect of within-family differences in Head Start participation on children's school satisfaction. Child satisfaction with school: Very satisfied Head Start

−0.029 (0.021) 0.004 (0.018) 6145 3297

Other Preschool Observations Children

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. Includes information from the 1988 through 2012 survey waves. Includes children age 10 or older. + p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

Appendix C: Details and results of the reweighted approach I follow the two-step “post-regression weighting” approach similar to that outlined by Miller, Shenhav and Grosz (2019) to recover an unbiased estimate of the average treatment effect (ATE) for a policy-relevant target population. In this case, the target population includes families with at least one child enrolled in Head Start. First, I classify households into one of three categories: households included in the Head Start fixed effects sample (i.e., families with some but not all children attending Head Start), families included in the target population but not the fixed effects sample (i.e., families with all children attending Head Start, including families with only one child), and families not included in either the fixed effects sample or target population (i.e., families with no children attending Head Start)15. Then, I estimate a multinomial logistic regression predicting membership in these categories as a function of the baseline covariates included in Table 1 as well as a series of indicators for the number of children in the household (1–2, 3, 4, and 5+). Next, based on the results of this model, for each child I obtain the predicted probability for each child of being in a household in the fixed effects sample, and the predicted probability of being in the target population (calculated as the sum of the predicted probability of being in the fixed effects sample and the predicted probability of being in the target population but not the fixed effects sample). I then use these probabilities to obtain weights for child i in household j:

Tx *Pr(Sj = 1)

^ j (i ) = w

(B.1)

Sx *Pr(Tj = 1)

Where Tx is the estimated probability that child i in household j is in the target population and Sx is the estimated probability that child is in the Head Start fixed effects sample. Pr(Sj = 1) and Pr(Tj = 1) represent the overall proportions of households in the Head Start fixed effects sample and target population, respectively. Next, I aggregate these weights to the household level:

1 w^j = nj

nj

w^j (i )

(B.2)

i=1

where nj is the number of children in household j. Next, I perform a normalization to obtain final weights based on the following:

w^j *nj

s^j = j

wj ^*nj

GS

(B.3)

where GS is the set of households in the Head Start fixed effects sample. Next, I obtain household-specific estimates of the effect of Head Start based on estimating a version of Eq. (1) that replaces the Head Start indicator with a series of interactions between the Head Start indicators and group-specific dummy variables for all households included in the fixed effects sample. Specifically, I estimate a model of the following form for child i in household j, including all households that were included in the main analysis (i.e., households with variation across siblings in the use of Head Start and/or other preschool): J

Yijt =

+

1j Householdj *HSij

+

2 Preschoolij

+ Xij +

j

+

t

+

k

+

itj

j =1

(B.4)

where Householdj is an indicator for whether child i is in household j. This yields estimates of the impact of Head Start for each household in the fixed effects sample, ^1j . Finally, I obtain the 2-step ATE by the following:

^

1,2 step

s^j * ^1j

=

(B.5)

j GS

And obtain a cluster-robust variance estimate by the following:

15

There are only three categories due to the fact that the fixed effects sample is a subset of the target population. 20

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^ (^ Var 1,2

step)

(s^j ) *( ^1j 2

=

^

1,2 step)

2

(B.6)

j GS

Table C.1 The effect of Head Start on parent investment behavior using reweighting.

A. Family Fixed Effects Estimates Head Start B. Reweighted ATE Head Start

(1) Overall HOME-SF Scores

(2) Cognitive Stimulation Scores

(3) Emotional Support Scores

(4) Parent Index

−0.052* (0.021)

−0.042* (0.021)

−0.044+ (0.025)

−0.010 (0.037)

−0.046* (0.021)

−0.041* (0.021)

−0.032 (0.025)

0.027 (0.036)

Notes: Standard errors clustered at the family level in parentheses. All regressions include pretreatment covariates listed in Table 1, family fixed effects, birth order indicators (2, 3, 4, 5+), age fixed effects, and year fixed effects. Target population for reweighted ATE includes all households with at least one child attending Head Start. Reweighted ATE estimates are based on the two-step post-regression weighting procedure described by Miller, Shenhav & Grosz (2019). +p < 0.10; * p < 0.05; ⁎⁎ p < 0.01; ⁎⁎⁎ p < 0.001.

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