The New School Food Standards and Nutrition of School Children: Direct and Indirect Effect Analysis

Abstract

The Healthy, Hunger-Free Kids Act (HHFKA) of 2010 made sweeping changes to school nutritional standards. We estimate the impacts of shifts in school nutritional standards on dietary quality as well as dietary quantity of children’s food intakes from school and away-from-school food sources. We find the average effect of consuming school food, rather than away-from-school food, on children’s overall dietary quality significantly increased from the pre- to post-HHFKA implementation period. This effect was solely driven by substantial improvements in the dietary quality of foods acquired at school, mainly among older and higher-income children. Our indirect effect analysis indicated that children shifted towards consuming lower-quality diets at home in the post-HHFKA period, thereby partially offsetting the positive effects of the HHFKA on their overall dietary quality. Indirect impacts were primarily driven by a subset of children consuming more than a third of their daily calories from school food. Additionally, we find suggestive evidence of a modest decrease in daily calorie intake, particularly among older and higher-income children. Together, our findings imply that the HHFKA, despite its unintended negative indirect effects, led children to consume more-nutritious, less-energy-dense diets.

1. Introduction

Healthy dietary quality in childhood is essential for proper physical and cognitive development of children (Glewwe and King 2001, Marshall et al. 2014, Frisvold 2015) as well as for preventing a variety of adverse health outcomes such as childhood obesity (Epstein et al. 2001, Epstein et al. 2008, Nunn et al. 2009). To promote adequate nutrition among school children, particularly those from low-income households, federally subsidized school lunch and breakfast programs serve about 30 million lunches and 15 million breakfasts to students each school day (USDA 2019).

The Healthy, Hunger-Free Kids Act (HHFKA) of 2010 marked the most sweeping changes to the school nutritional standards in 15 years. The new rules officially went into effect in the 2012–13 school year for school lunches and in the 2013–14 school year for breakfasts, resulting in the increased availability of whole grains, fruits, and vegetables, while decreasing sodium and saturated fats and allowing only fat-free/low-fat milk (Marcason 2012, USDA-FNS 2012). The primary purpose of this paper is to examine how changes in school nutritional standards affected dietary quality (measured by the Healthy Eating Index 2010) as well as dietary quantity (i.e., calorie intake) of school children’s food intakes from different food acquisition sources (e.g., school vs. away-from-school food sources).

Previous evaluations of the dietary impacts of the HHFKA, typically small localized studies, showed that the new nutritional standards were associated with improvements in the quality of school foods offered (Terry-McElrath et al. 2015), selected and consumed (Bergman et al. 2014, Cohen et al. 2014, Cullen et al. 2015, Schwartz et al. 2015, Johnson et al. 2016, Smith et al. 2016, Cohen et al. 2019), while not having an adverse impact on the plate waste (Schwartz et al. 2015) or school meal program participation rates (Johnson et al. 2016, Vaudrin et al. 2018). Recently, using national-level data, Gearan and Fox (2020) documented significant improvements in the quality of school food offerings after implementation of the HHFKA.¹ However, they did not investigate the impact on the dietary quality of children’s food intakes (the amount and kinds of foods children actually eat at school). More recently, Smith et al. (2020) estimated the effects of the HHFKA across the distribution of the overall dietary quality of students’ food intakes and found significant gains were made across the entire spectrum from low- to high-quality diets.

Yet, earlier studies have not examined whether the improvements in the overall dietary quality of students were merely driven by direct effects of HHFKA on the quality of foods obtained at school or whether the away-from-school dietary quality of students was also affected. On any given school day, children consume 30%−50% of their daily calories from school foods (Schanzenbach 2009). As such, the school food environment accounts for a major part of the overall food environment that children experience (Frisvold and Price 2019). Thus, substantial changes in the quality and types of foods offered at school may influence the away-from-school consumption behaviors of children or their parents. For instance, the dietary habit formation that can occur through repeated exposure to school food may lead children to be more receptive to some foods (e.g., fruits and vegetables) at home (see, e.g., Birch 1999, Benton 2004, Dovey et al. 2008). Alternatively, children may choose to lower at-home consumption of some foods (e.g., whole grains) that have already been consumed at school. It is also possible that parents may let their children consume less-healthy foods when they eat healthy school foods. Therefore, it is essential to examine changes in dietary quality of children across food acquisition sources.

Additionally, no study has examined the differential effects of the HHFKA on dietary quality of children acquiring different shares of their daily calories from school foods. Allowing for this kind of heterogeneity is important because some children rely more heavily on school foods than others. Furthermore, to our knowledge, no national-level study has investigated the impacts of the HHHKA on children’s calorie intake. This is a limitation because, as we will discuss below, the HHFKA, among other changes, specified new calorie guidelines for schools to further address concerns about childhood obesity (USDA-FNS 2012).

This study advances what we know about the HHFKA in three ways. First, using a nationally representative sample of children from the National Health and Nutrition Examination Survey (NHANES), we examine the overall, direct, and indirect effects of the HHFKA on dietary quality of children’s food intake. The overall effect analysis explores the impacts on the dietary quality of food intakes from all food acquisition sources (i.e., both school and away from school). The direct effect analysis focuses on the dietary quality of foods obtained from the school cafeteria. The indirect (spillover) effect analysis investigates the impacts on the diet quality of foods acquired from the away-from-school food sources (e.g., home, restaurants, fast food establishments). Although Smith et al. (2020) analysis of changes in the overall dietary quality accounts for the notion of indirect effects, their approach can neither identify the presence nor the direction (i.e., positive or negative) of potential indirect effects.

Second, we allow for heterogeneity in the effects of HHFKA based on the share of daily calories received from school foods, to assess if there was a “dose-response” relationship. Here, we explore if children consuming less than one-third of their daily calories (roughly one meal) from school food were affected differently from those receiving more than one-third of their daily calories, compared to those not consuming school foods.² Third, we examine changes in caloric intake. To draw a more comprehensive picture of the extent of the nutritional effects of HHFKA, in addition to analyzing the full sample of school children, we explore heterogeneity by school grade (i.e., K-5 vs. 6–12) as well as income status (i.e., low income vs. high income).

Our main identification strategy focuses on comparing the effects of consuming school food, rather than away-from-school food, on children’s dietary outcomes before and after the HHFKA implementation. To account for endogeneity of school food participation (Bhattacharya et al. 2006, Millimet et al. 2010), we use two-day dietary intake data from the 2009–2016 NHANES and exploit within-child variation to control for fixed unobserved and observed confounders associated with school food consumption and dietary outcomes (e.g., food preferences, parental characteristics, school environment, income, age, gender), as done elsewhere (Gleason and Suitor 2003, Bowman et al. 2004, Mancino et al. 2009, Powell and Nguyen 2013, Smith 2017, Smith et al. 2020).

Consistent with Smith et al. (2020), we find that the average effect of consuming school food, relative to away-from-school food, on the overall dietary quality of students significantly increased from the pre-HHFKA (2009–12) to post-HHFKA period (2013–16). This improvement was solely driven by HHFKA’s direct effects on the quality of foods acquired from school, primarily among older and higher-income students. The indirect effect analysis indicated a shift towards the consumption of lower quality diets at home in the post-HHKA period, mostly among children eating more than one school meal. However, the negative indirect effects were not large enough to completely offset the direct impact of the HHFKA. We also find suggestive evidence of a reduction in daily calorie consumption, mainly among older and higher-income children. Overall, our findings suggest that, despite its unintended negative consequences, the HHFKA helped children consume more-nutritious, less-energy-dense diets.

2. Background: School Food and the HHFKA of 2010

The school lunch and breakfast programs serve federally subsidized meals at public and private schools and other qualifying institutions to provide children with adequate nutrition. Schools receive federal reimbursements for all meals offered or served, provided that they meet minimum nutritional standards. Federal payments made to schools are determined by a three-tiered system (free, reduced price, full price) based on a child’s household income. This system also typically determines the student’s price category unless a school has adopted a universal free-meal plan. Students from households with income up to 130% and 185% of the federal poverty line (FPL) can receive free and reduced-price meals, respectively, while higher-income students may purchase the full-price (paid) meals (USDA 2019).

The HHFKA made substantial changes to both school lunch and breakfast programs, aligning them with the 2005 Dietary Guidelines for Americans. In particular, it specified new calorie guidelines that set calorie ranges with both minimum and maximum levels and used narrower defined age/grade groups (see Appendix Table A1). The updated standards required schools to ensure that no more than 10% of total calories are from saturated fats. There were also requirements for minimum daily and weekly servings of fruits, vegetables, grains, meats, and milk by age/grade group (see Appendix Table A2). Additionally, the HHFKA provided stronger requirements for weekly servings of various vegetable subgroups and imposed restrictions on the fat content of milk. It also specified a phased-in requirement to use only whole grain-rich grains and reduce the sodium content of meals.

Moreover, under the “offer versus serve” (OVS) requirement, students were not allowed to decline more than two food items at lunch and more than one item at breakfast and must select at least half a cup of fruits or vegetables as part of each subsidized meal. The HHFKA also mandated all other nonsubsidized foods sold in school (i.e., competitive foods), including food items in vending machines, school stores, and á la carte lunch items, to meet minimum nutritional standards. This provision officially went into effect in the 2014–15 school year (Marcason 2012, USDA-FNS 2012). Lastly, to increase program access, schools were allowed to provide free meals to all students if at least 40% of their students were categorically eligible for free meals. This Community Eligibility Provision (CEP) was phased in in the 2011–12 school year and became available nationwide in the 2014–15 school year.

3. Data

We draw our sample from four cycles of the National Health and Nutrition Examination Survey (NHANES) covering 2009–10 to 2015–16. Each cycle is an independently drawn, nationally representative sample, collected over 12 months from November 1 of the odd year to October 31 of the even year. NHANES collects data about individuals’ food intake as well as food acquisition sources on two non-consecutive 24-hour dietary recalls (Day 1 and Day 2). Day 1 recall was collected in-person during the standardized medical examination at a mobile examination center (MEC). Day 2 recall was conducted randomly 3–10 days after the MEC visit in a follow-up telephone interview.³ Respondents did not know in advance when Day 2 recall would be collected or that it would not be conducted on the same day of the week as Day 1. Trained dietary interviewers administered both interviews with the help of three-dimensional instruments such as measuring cups. All interviews used computer-assisted, automated multi-pass data collection methods to reduce misreporting/underreporting of energy intakes (Moshfegh et al. 2008, Foster and Bradley 2018). Dietary interviews were conducted by proxy (typically a parent or other caregiver) by the age of five and by proxy assistance through the age of 11.⁴

We restrict our sample to school-age children (4–19 years old) who had complete dietary intakes on both Day 1 and Day 2 and reported attending a K-12 grade school during the school year. We further limit the sample to children whose schools offered a lunch, as done elsewhere (Gleason and Suitor 2003, Schanzenbach 2009, Millimet et al. 2010, Gundersen et al. 2012, Smith 2017). This full sample includes n=7,341 children and N=14,682 observations. To conduct heterogeneity analysis by a child’s current school grade, we group children into K-5 graders (kindergarteners and elementary schoolers; n=3,534) and 6–12 graders (middle and high schoolers; n=3,807). Further, we classify children as low income if their household income is less than or equal to 185% of federal poverty guidelines (n=4,250) and as high income otherwise (n=3,091).

We consider the period from 2009 to 2012 as the pre-HHFKA implementation period and from 2013 to 2016 as the post-HHFKA implementation period.⁵ As mentioned earlier, the first phase of the HHFKA was implemented at the beginning of the school year 2012–13. Thus, our pre-HHFKA observations may contain two to three months of the post-policy implementation period, depending on a school district’s start date.⁶ This could bias our estimates towards finding no effects, leading to conservative estimates of the HHFKA impacts.⁷

Table 1 presents the sociodemographic characteristics of the sample. Briefly, the average child is about 11 years old. About 43%−45% of children attend a K-5 grade school. 50–55% of children are Non-Hispanic White. Roughly half of the children are from low-income households (income <185% FPL). The average household size is less than five people. About 26%−28% of household reference persons are college-educated, and 67%−70% are married.

Table 1.

Summary statistics: sociodemographic characteristics

	Pre-HHFKA (2009–12)		Post-HHFKA (2013–16)
Child’s Characteristics:
Age (years)	11.4	(3.8)	11.6	(3.8)
Female (%)	51.7	(50.0)	49.5	(50.0)
School grade
K-5 (%)	44.6	(49.7)	42.8	(49.5)
6–8 (%)	23.4	(42.3)	23.2	(42.2)
9–12 (%)	32.0	(46.7)	34.0	(47.4)
Race/ethnicity
Non-Hispanic White (%)	54.8	(49.8)	49.9	(50.0)
Non-Hispanic Black (%)	14.3	(35.0)	15.4	(36.1)
Hispanic (%)	23.3	(42.3)	24.5	(43.0)
Other (%)	7.6	(26.5)	10.2	(30.3)
Household’s and Reference Person’s Characteristics:
Percent poverty <130 (%)	35.8	(47.9)	33.6	(47.2)
Percent poverty 130–185 (%)	11.9	(32.4)	12.1	(32.7)
Percent poverty >185 (%)	52.3	(50.0)	54.3	(49.8)
Household size	4.5	(1.3)	4.7	(1.3)
College grad+ (%)	26.5	(44.1)	28.0	(44.9)
Age (years)	41.9	(9.8)	42.2	(9.8)
Married (%)	67.4	(46.9)	69.9	(45.9)
Number of Children	3818		3523

Notes: Standard deviations are in parentheses. All calculations use survey weights.

3.1. Construction of Variables

Using the reported food acquisition sources in NHANES, we divide daily food intake of children into “school food” and “away-from-school food,” including “at-home” and “away-from-home-and-school food” (e.g., restaurants, fast food establishments). Following Smith (2017), our school food category consists of all foods acquired from the “cafeteria in a K-12 school.” At-home food primarily contains food items purchased at grocery stores. Food away from home and school (FAFHS) broadly includes full-service restaurants, fast foods, and vending machine items (see Appendix Table A3 for more details).

It is important to note that respondents do not differentiate between subsidized (i.e., free, reduced-priced price, and paid) meals and competitive foods sold at school and simply report if a food item was acquired from the school cafeteria. Therefore, our analysis examines the effects of all foods from school and not just subsidized school breakfasts and lunches. This is not problematic because the HHFKA regulated all foods offered at school, including competitive foods.

Further, we use the information on self-reported daily calorie intakes of children to define three sets of variables, which we will use in the empirical methods section. First, we define a binary (dummy) variable that equals one if a child consumed any calories from school food on an interview day and zero otherwise. We then define a continuous variable as the share of daily calories from school food on an interview day. Third, we construct a categorical variable, grouping children into three categories by shares of daily calories received from school food: children who did not consume any school foods, those who got up to 33% of their daily calories, and those obtaining more than 33% of calories. We derive dummy variables from this variable.

Table 2 provides summary statistics for the child’s food source selection for each interview day in pre- and post-HHFKA periods. Panel A presents the average participation rates into different food acquisition sources in a typical food intake day. About 30% of children eat school food (including subsidized school meals and competitive foods). A closer look at children consuming school food suggests that about half of them acquire up to 33% of their daily calories from school food, while the other half get more than 33% of calories. Almost all children (98%) consume home-prepared foods. Roughly 63% of children participate in the FAFHS market on Day 1. This rate is lower on Day 2 (49%), which is most likely associated with the NHANES’s fewer intake records on Thursday-Saturday on Day 2 (Panel B), when children are perhaps more likely to eat outside the home (see, also, Smith 2017).⁸ Panel C shows the average allocation of daily calories across food sources. On a typical day of the year, children receive a small share (10%−11%) of their daily calories from school food and acquire the majority of daily calories (63%−70%) from home-prepared foods. The remaining calories (19%−27%) are obtained from FAFHS locations. In Panel D, we see that the school food’s share of daily calories is higher at about 33% (or roughly one meal) when children report consuming school foods.⁹

Table 2.

Summary statistics: child’s food acquisition source selection

	Pre-HHFKA (2009–12)		Post-HHFKA (2013–16)
	Day 1	Day 2	Day 1	Day 2
Panel (A). Average Participation Rates into Food Acquisition Sources (%):
School	31.3	30.5	29.1	31.0
Calories from school ≤33%	16.6	15.4	15.0	14.7
Calories from school >33%	14.7	15.2	14.1	16.4
Away from school	100.0	100.0	100.0	99.8
Home	98.5	98.5	97.5	97.9
Away from home and school	63.4	49.1	62.5	51.0
Panel (B). Proportions of Dietary Recalls across Days of the Week (%):
Sunday	13.7	25.1	14.6	26.3
Monday	13.3	20.1	13.6	16.6
Tuesday	12.5	14.1	10.2	14.9
Wednesday	14.0	15.7	14.2	11.1
Thursday	14.5	7.1	10.3	11.8
Friday	14.4	14.7	17.4	14.3
Saturday	17.7	3.2	19.6	4.9
Panel (C). Average Allocation of Daily Calories across Food Acquisition Sources (%):
School	10.4	10.7	9.9	11.2
Away from school	89.6	89.3	90.1	88.8
Home	64.0	70.3	63.3	69.4
Away from home and school	25.6	19.0	26.7	19.4
Panel (D). Average Allocation of Daily Calories Conditional on Food Source Participation (%):
School	33.2	35.0	34.2	36.1
Away from school	89.6	89.3	90.1	89.0
Home	65.0	71.4	65.0	70.8
Away from home and school	40.4	38.7	42.8	38.1
Number of Children	3818	3818	3523	3523

Notes: All calculations use two-day survey weights.

3.2. Measurement of Dietary Quality and Dietary Quantity

We assess dietary quality using the Healthy Eating Index (HEI), which measures adherence to dietary guidelines outlined in the Dietary Guidelines for Americans (DGA). The HEI was first developed in 1995 and has been revised multiple times since then to reflect key changes in the DGA. In this study, we use the 2010 HEI (HEI-2010) corresponding to the 2010–2015 DGA, the most current dietary guidelines available at the time of our sampling period.¹⁰

The HEI-2010 is a continuous score on a 0–100 range, calculated as the sum of 12 components (nine adequacy and three moderation components), based on the per-calorie consumption of different foods and nutrients. For the adequacy components (total fruit, whole fruit, total vegetables, greens and beans, whole grains, dairy, total protein foods, seafood and plant proteins, and fatty acids) higher scores indicate higher consumption. For moderation components (refined grains, sodium, and empty calories) higher scores imply lower intake. Each component assigns a score ranging from 0–5, 0–10, or 0–20, adding up to the maximum total score of 100.

We use reported dietary intake data from NHANES to calculate the HEI-2010 (hereafter, HEI) scores for each child, on each interview day, and from each food acquisition source, according to Guenther et al. (2013). Because HEI is calculated on a per calorie basis (e.g., quantities per 1,000 calories), it measures the relative quality of foods independent of quantity (i.e., calories), making it comparable across ages.

We measure diet quantity using the number of daily calories (kcal) consumed. To account for differences in calorie consumption by age, gender, and anthropometric measures (e.g., weight and height), we standardize the self-reported calorie intake using the Institute of Medicine’s estimated energy requirements (EER) (Gerrior et al. 2006).¹¹

Table 3 presents summary statistics for nutritional outcomes of interest. Standard deviations are in parentheses. Panel A shows the average total HEI score for food intakes from all sources (i.e., the overall dietary quality) remained almost unchanged at 47–49 HEI points over the sampling period. Among the sample of children in this analysis, HEI for school food substantially increased from 44–46 HEI points before the HHFKA to 53–54 HEI points after the HHFKA (i.e., about 19% increase). However, there is evidence of a slight decrease in the away-from-school diet quality, which seems to be driven by a minor reduction in the dietary quality of home-prepared foods. Further, consistent with earlier studies (Guthrie et al. 2002, Bowman et al. 2004, Mancino et al. 2009, Mancino et al. 2010, Powell and Nguyen 2013), we see that FAFHS has a substantially lower quality than home-prepared and school foods.¹² Panel B shows that children, on average, consumed between 1906–1990 calories on a typical day of food intake before the HHFKA implementation. The number of calories was slightly smaller in the post-HHFKA period at 1850–1939 calories per day. This decrease seems to be mainly driven by a reduction in calories consumed from home-prepared foods.

Table 3.

Summary statistics: child’s mean nutritional outcomes, overall and across food sources

	Pre-HHFKA (2009–12)		Post-HHFKA (2013–16)
	Day 1	Day 2	Day 1	Day 2
Panel (A). HEI-2010 (HEI points):
All food sources	47.0	48.2	47.6	48.9
	(12.9)	(13.0)	(13.8)	(14.2)
School	44.3	45.8	53.6	53.3
	(13.3)	(12.8)	(13.8)	(14.0)
Away from school	46.0	47.2	45.2	46.6
	(13.5)	(13.4)	(13.9)	(14.4)
Home	46.2	47.2	45.4	47.0
	(15.1)	(14.3)	(15.2)	(15.3)
Away from home and school	36.4	36.8	36.4	35.9
	(12.1)	(12.1)	(12.3)	(12.7)
Panel (B). Calorie Intake (kcal):
All food sources	1998.0	1913.1	1950.8	1850.7
	(796.3)	(792.9)	(854.9)	(770.7)
School	198.6	195.7	191.1	198.9
	(362.7)	(361.9)	(373.4)	(363.3)
Home	1270.8	1331.0	1211.7	1272.7
	(786.6)	(787.2)	(792.0)	(768.3)
Away from home and school	528.6	386.4	548.0	379.1
	(658.3)	(573.2)	(707.0)	(565.9)

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. Standard deviations are in parentheses. All calculations use two-day survey weights.

3.3. Descriptive Analysis

Figure 1 compares the two-intake-day average dietary quality of children by their reports of school food consumption. Panel A indicates that children, on average, had a higher overall dietary quality when they reported consuming school food, with a larger difference after the HHFKA implementation (denoted by the vertical line). Panel B suggests that consuming any school food was associated with a lower away-from-school HEI in the post-HHFKA implementation period. We observe a similar pattern in Panel C for at-home food HEI. Panel D shows that consuming school food was also associated with a lower FAFHS diet quality, but the difference did not change over time.

Figure 1. Dietary quality of children by school food consumption, overall and across food sources.

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. Two-day sampling weights are applied. Source: Author’s calculations of the 2009–16 National Health and Nutrition Examination Survey (NHANES).

Similarly, Figure 2 compares the two-intake-day average calorie intake of children by reports of school food consumption. In Panel A, we see that total daily calorie consumption does not vary meaningfully by children’s school food consumption status. Panel B suggests that the number of calories received from school food (i.e., the gap between dashed and solid lines) remained fairly stable over time. Panels C and D indicate that calories acquired from away-from-school food sources also remained relatively unchanged over time.

Figure 2. Daily calorie intake of children by school food consumption, overall and across food sources.

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. Two-day sampling weights are applied. Source: Author’s calculations of the 2009–16 National Health and Nutrition Examination Survey (NHANES).

None of the descriptive findings mentioned above, however, account for the endogeneity of food source choices. Additionally, observable confounders (e.g., days of the week) further cast doubt on drawing causal inferences from Figures 1 and 2. In the following section, we employ regression methods to first identify the effects of consuming school food on children’s dietary outcomes, separately before and after the HHFKA implementation. We then examine how these effects changed over time (i.e., a pre-post analysis).

4. Empirical Methods

4.1. The Overall and Indirect Effect Analysis

Consider the following conditional mean regression specification:

$$Y_{it}^{(S)}=W_{it}^{{(\tau )}^{\prime }}{\beta }^{(\tau )}+X_{it}^{\prime }\gamma +c_i+{\epsilon }_{it}$$ (1)

where $Y_{it}^{(S)}$ is the dietary outcome (i.e., HEI or EER-standardized calorie intake) of child i, on interview day t, from the food acquisition source S ∈ [all sources; away from school; home; away from home and school]. $W_{it}^{(\tau )}$ is either a binary, continuous, or categorical treatment variable, as defined earlier based on children’s intakes of calories from all school foods (subsidized meals and competitive foods). We discuss the interpretations of the coefficients for these treatment variables (i.e., ${\beta }^{(\tau )}$) momentarily. The matrix X_it includes 13 indicator variables for days of the week interacted with interview day to control for confounding effects of the days of the week, as done elsewhere (Smith 2017). c_i is the time-invariant child-specific unobserved heterogeneity and ${\epsilon }_{it}$ is an idiosyncratic error term.

We are concerned that omitted variables in c_i (e.g., food preferences, food environment, and parental characteristics) in equation (1) are correlated with $W_{it}^{(\tau )}\text{and}{Y}_{it}^{(S)},$ thereby rendering estimates of school food effects on dietary outcomes biased and inconsistent. Following previous studies (Gleason and Suitor 2003, Bowman et al. 2004, Mancino et al. 2009, Powell and Nguyen 2013, Smith 2017), we overcome this endogeneity problem by leveraging two-day dietary intake data from NHANES using a child fixed-effects approach. Put differently, we exploit within-child variation over interview days to control for fixed observed and unobserved child characteristics associated with non-random selection into school meal programs. To do so, we estimate an algebraic equivalence of equation (1) mentioned in Mundlak (1978):

$$Y_{it}^{(S)}=W_{it}^{{(\tau )}^{\prime }}{\beta }^{(\tau )}+X_{it}^{\prime }\gamma +{\overline{W}}_i^{{(\tau )}^{\prime }}\delta +{{\overline{X}}^{\prime }}_i\vartheta +{ϵ}_{it}$$ (2)

Where ${\overline{W}}_i^{(\tau )}\text{and}{\overline{X}}_i$ are the averages, over two interview days, for child i of the time-varying regressors in $W_{it}^{(\tau )}\text{and}{X}_{it},$ respectively.

Equation (2) thus models the dependence between c_i and model’s regressors according to $c_i={\overline{W}}_i^{{(\tau )}^{\prime }}\delta +{{\overline{X}}^{\prime }}_i\vartheta +{\eta }_i\text{where}{\eta }_i$ is a zero-mean projection error, which by definition is uncorrelated with model’s regressors (Wooldridge 2010, p. 332), and ${ϵ}_{it}={\epsilon }_{it}+{\eta }_i.$ By controlling for c_i in this manner, a causal interpretation of the effect of $W_{it}^{(\tau )}\text{on}{Y}_{it}^{(S)}$ is reached if we assume all observed and unobserved confounders associated with school food choices and dietary outcomes are fixed over the sampling period. Although the NHANES’s short recall period (3–10 days) could make this identifying assumption more plausible, we acknowledge that it may not fully hold in our application. This is because dietary choices could vary from day to day among children. For instance, children might be more (less) hungry on one dietary recall day than the other, making them more (less) likely to consume school food on that particular day. Thus, to the extent that there are time-varying confounders associated with children’s school food consumption, some bias may remain.

Before proceeding, it is important to note that one advantage of the algebraic equivalence in equation (2) over other fixed-effects estimation approaches¹³ is that it provides a simple regression-based Hausman (1978) test of exogeneity of $W_{it}^{(\tau )}.$ This can be done by simply testing the null hypothesis $H_0:\delta =\vartheta =0$ via a fully robust joint Wald test (Wooldridge 2019). Rejecting this null hypothesis provides evidence for the endogeneity of school food consumption. Moreover, comparing test results from before and after the HHFKA samples could provide some evidence of whether the HHFKA implementation changed the school food participation patterns.

Turning back to the alternative treatment variables, our binary treatment variable $W_{it}^{(binary)}$ is defined to take a value of one if child i consumed any school food on interview day t and zero otherwise. Thus, β^(binary) captures the effects of consuming any school food, rather than away-from-school food, on children’s dietary outcomes from food acquisition source S. One limitation of this binary treatment variable is that it treats children consuming a large proportion of their daily calories from school food in the same manner as those getting a small proportion of daily calories from school food.

Our continuous treatment variable $W_{it}^{(continuous)}$ is defined as the share of daily calories from school food and ranges from 0% to 100%. Therefore, it captures the extent to which a child is exposed to school food. For interpretation purposes, we rescale this variable to a 0–3 range such that a one-unit change in β^(continuous) captures the dietary quality effects of a 33% shift in the share of daily calories from away-from-school food sources to school food.¹⁴ Put differently, β^(continuous) captures the impact of substituting an away-from-school meal for a school meal on dietary outcomes (in short, “one school meal effect”). The latter assumes each daily meal (e.g., breakfast, lunch, dinner) provides one-third of the child’s daily calorie requirement.

Finally, our categorical treatment $W_{it}{}^{(categorical)}$ includes three indicator variables for children who do not consume any school foods, those obtaining up to 33% (roughly one meal) of their daily calories from school foods, and those receiving more than 33% of their daily calories from school food. This specification allows us to explore how/if the effects of consuming school food on dietary outcomes vary across children getting different shares of their daily calories from school food.¹⁵

For each dietary outcome, we estimate equation (2) for each possible combination of food source S and treatment variable type τ (i.e., 4 food sources × 3 treatment types = 12 combinations), separately before and after the implementation of HHFKA. To aid interpretation of the results, in particular those for changes in dietary quality, in addition to reporting estimates of β from equation (2) in HEI points, we provide results expressed as a percentage of the conditional baseline HEI score for each source calculated as:

$${\widehat{Y}}_{it}^{(S)}=X_{it}^{\prime }\widehat{\gamma }+{\overline{W}}_i^{{(\tau )}^{\prime }}\widehat{\delta }+{{\overline{X}}^{\prime }}_i\widehat{\vartheta }.$$ (3)

This predicted baseline HEI score/calorie intake is the dietary quality/quantity of food source S when children do not consume any school food.

The HHFKA impacts on dietary outcomes are then estimated as the change in the effects of school food from the pre- to post-HHFKA period. We do this by estimating the following conditional mean regression specification:

$$\begin{gathered} Y_{it}^{(S)}=W_{it}^{{(\tau )}^{\prime }}{\beta }^{(\tau )}+X_{it}^{\prime }\gamma +{\overline{W}}_i^{{(\tau )}^{\prime }}\delta +{{\overline{X}}^{\prime }}_i\vartheta +POS{T}_{it}\times W_{it}^{{(\tau )}^{\prime }}{\alpha }^{(\tau )}+POS{T}_{it}\times X_{it}^{\prime }\theta \\ +POS{T}_{it}\times {\overline{W}}_i^{{(\tau )}^{\prime }}\psi +POS{T}_{it}\times {{\overline{X}}^{\prime }}_i\xi +u_{it} \end{gathered}$$ (4)

where $POS{T}_{it}$ is an indicator variable taking a value of one in the post-HHFKA period (2013–16) and zero otherwise (2009–2012). That is, we interact all regressors in equation (2) with the post-HHFKA indicator, thereby letting their impacts vary by the implementation of the HHFKA. If the coefficient α^(τ) in equation (4) is significantly different from zero, then the effect of consuming school food on children’s dietary outcomes in the post-HHFKA period is different from the pre-HHFKA period. One limitation of this estimation strategy is that it does not account for the potential changes in school food participation rate over time. However, as we showed in Table 2, Panel A, and is documented elsewhere (Johnson et al. 2016, Vaudrin et al. 2018), school food participation remained almost unchanged over the sampling period.

4.1.1. FAFHS Participation and Consumption Decisions

To examine the impact of the HHFKA on FAFHS dietary outcomes of children, we need to take an additional step. A substantial fraction of children do not report consuming any FAFHS. These zero consumptions are likely to be the results of the corner solution decisions of children or their parents. In other words, FAFHS consumption corresponds to a two-step decision-making process (Byrne et al. 1996, Mancino et al. 2009). In the first step, known as the participation step, a decision is made on whether or not to consume FAFHS. In the second step, a decision is made as to the amount of consumption.

A straightforward estimation of equation (2), ignoring the two-step nature of the FAFHS consumption decision, could lead to biased and inconsistent estimates. We address this problem via a two-step estimation strategy developed in Wooldridge (1995), which can be considered an extension of the Heckman’s (1976) two-step model to an unobserved effects framework. We provide a detailed description of this method in the Appendix. Briefly, this approach involves a separate estimation of FAFHS participation and consumption decisions. The first step estimates the probability of participation based on both observed (e.g., income, age, gender, educational attainment of parents) and unobserved (e.g., personal preferences, time constraints, availability, price) determinants of eating away from home and school. The predicted participation probabilities are then used to construct the so-called inverse Mills ratio (see Appendix for details). The second step incorporates the inverse Mills ratio in equation (2), which is then estimated using a truncated sample, omitting zero consumption observations. Without this adjustment, the fixed effects estimation of equation (2) using the truncated sample could result in sample selection bias, defined as an omitted variable problem (Heckman 1976). Put differently, the inverse Mills ratio approximates a variable representation of the unobserved determinants of the participation decision. Thus, including it in equation (2) as the omitted variable for the truncated sample could address sample selection bias, if present.

4.2. The Direct Effect Analysis

Following the discussion above, we are also concerned about potential bias and inconsistency due to the prevalence of zero school food consumption observations. In our sample, 47% of children (n=3430) do not report consuming school foods on either interview days, 38% (n=2807) report consuming school food either on Day 1 or Day 2, and 15% (n=1104) report eating school food on both days. Overall, the sample includes 9667 (66%) zero observations for school food intake. Therefore, we estimate the direct effects of the HHFKA using the two-step estimation approach outlined above. However, because in the truncated sample the vast majority of children (72%) have one day of positive school food consumption, the second step estimation is conducted via pooled OLS for a regression model based on equation (1):¹⁶

$$Y_{it}^{(School)}=W_{it}^{{(continuous)}^{\prime }}\beta +X_{it}^{\prime }\gamma +Z_{it}^{\prime }\omega +MILL{S}_{it}^{\prime }P+e_{it}$$ (5)

where $Y_{it}^{(School)}$ is either dietary quality or calorie content of foods acquired from the school cafeteria, W_it and X_it are defined as before, Z_it is a vector of control variables, including log child’s age, dummies for child’s gender and race/ethnicity, dummies for household income level, log reference person’s age, dummies for reference person’s educational attainment, log household size, an indicator variable for dietary recalls conducted between May and October, and dummies for NHANES cycles. MILLS_it is a vector including two variables driven based on the inverse Mills ratio observations for Day 1 and Day 2 (see Appendix for details). e_it is an idiosyncratic error term. We conduct our direct effect analysis using the regression specification with the continuous treatment variable. We note that since the truncated sample only includes children consuming school food, endogeneity of school food participation is no longer an issue in equation (5).

5. Results

5.1. Changes in the Overall Dietary Quality (Overall Effect)

Table 4 presents the average effects of consuming school food, relative to away-from-school food, on the overall dietary quality of children. ¹⁷ Starting with Model (1), which uses the binary treatment variable, we see that before the HHFKA, consuming any school food increased the overall dietary quality by 2.39 HEI points (or 5.10% of the predicted baseline HEI score of 46.83 points). Post-HHFKA, this effect was larger at 4.5 HEI points (9.58%). The last column shows this 2.11 HEI point (4.48 percentage point) increase in the effect of school food, from the pre- to post-HHFKA period, is statistically significant. Additionally, we see that the baseline overall dietary quality of children (i.e., diet quality in the absence of school food) remained unchanged at 47 HEI points from the pre- to post-HHFKA period. Consistently, Model (2), which uses the continuous treatment variable, suggests that before the HHFKA, a 33% shift in the share of daily calories from the away-from-school food sources to school food (i.e., one-school-meal effect) improved the overall dietary quality of children by 2.10 HEI points (4.48%). This effect more than doubled after HHFKA implementation, resulting in a 4.28 HEI point (9.13%) increase in overall dietary quality. The last column indicates that this 2.18 HEI point dietary quality improvement is statistically significant.

Table 4.

Average effect of school food consumption on child’s overall dietary quality, all children

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre
Model (1). Any School Food Effect (Binary Treatment)
Any school food (HEI points)	2.39***	4.50***	2.11*
	(0.76)	(0.86)	(1.15)
Predicted baseline HEI	46.83	46.90	0.07
Any school food (%)	5.10	9.58	4.48
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	2.10***	4.28***	2.18***
	(0.62)	(0.61)	(0.87)
Predicted baseline HEI	46.91	46.90	−0.01
One school meal (%)	4.48	9.13	4.65
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	1.49	3.18***	1.69
	(0.93)	(0.93)	(1.31)
Calories from school (>33%) (HEI points)	3.43***	6.02***	2.59*
	(0.94)	(1.05)	(1.41)
Predicted baseline HEI	46.82	46.87	0.04
Calories from school (≤33%) (%)	3.18	6.79	3.61
Calories from school (>33%) (%)	7.32	12.84	5.52
P-values for the Hausman Test of Exogeneity of School Food Participation
Model (1)	0.01	0.58
Model (2)	0.01	0.68
Model (3)	0.01	0.43
N	7636	7046	14682

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

Comparing results from Models (1) and (2) in Table 4 suggests that ignoring the extent to which children are exposed to school food tends to overestimate the impact of school food on the overall diet quality. This result is expected because censoring the school food consumption into a binary variable could induce the problem of upward biased estimates, known as “expansion bias” (Rigobon and Stoker 2007). Since this upward bias is slightly larger in the pre-HHFKA period, the relative (pre-post) difference in Model (1) slightly underestimates the effects of HHFKA. Further, results from Model (3) that uses the categorical treatment variable imply that the HHFKA led to a larger improvement in the dietary quality of children consuming more than 33% of their daily calories from school-prepared food than children getting less than a third of daily calories. This difference, however, is not statistically significant (2.59 vs. 1.69 HEI points; p=0.54).

The bottom panel of Table 4 reports p-values for the Hausman test of the exogeneity of school food participation. Consistent with the literature, there is evidence of endogenous participation before the HHFKA. However, we cannot reject the null hypothesis of exogeneity of school food consumption post-HHFKA. One possible explanation is that perhaps the notion of improvements in the quality of school foods along with the CEP changed program participation patterns after HHFKA. In terms of the former, there is evidence of a significant positive association between the school lunch program participation rate and the quality of school lunches (USDA 2019).

Table 5 reports overall effect estimates by school grade. As before, the (naive) Model (1) provides biased estimates of the impact of school food, as compared to Model (2), and subsequently of the HHFKA effect. Thus, we focus on discussing the results from Model (2). Among K-5 graders, the impact of a school meal on the overall dietary quality increased from 2.29 (4.73%) to 3.96 HEI points (8.20%) over time. This 1.66 HEI point increase, however, is not statistically significant. On the other hand, 6–12 graders experienced a larger gain of 2.49 HEI points in their overall diet quality from the pre- to post-HHFKA. The reported p-value in the last column (p=0.63), however, suggests that the HHFKA’s effect on the overall diet quality of 6–12 graders is not statistically different from the impact on younger children. Predicted baseline HEI scores indicate that while the overall diet quality decreases with the child’s age/grade (48 vs. 46 HEI points for K-5 and 6–12 graders, respectively), it remained relatively stable over the sampling period within each age group.

Table 5.

Average effect of school food consumption on child’s overall dietary quality, by school grade

	K-5			6–12
Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Model (1). Any School Food Effect (Binary Treatment)
Any school food (HEI points)	2.05**	5.00***	2.94*	2.77***	4.12***	1.35	0.49
	(1.06)	(1.22)	(1.61)	(1.08)	(1.20)	(1.61)
Predicted baseline HEI	48.64	48.04	−0.60	45.36	46.01	0.64
Any school food (%)	4.22	10.40	6.18	6.10	8.95	2.86
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	2.29***	3.96***	1.66	2.00**	4.49***	2.49**	0.63
	(0.79)	(0.82)	(1.14)	(0.94)	(0.89)	(1.29)
Predicted baseline HEI	48.53	48.26	−0.27	45.56	45.88	0.32
One school meal (%)	4.73	8.20	3.47	4.38	9.79	5.41
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	0.49	4.11***	3.62**	2.27*	2.56**	0.29	0.20
	(1.26)	(1.34)	(1.84)	(1.30)	(1.28)	(1.83)
Calories from school (>33%) (HEI points)	3.63***	6.10***	2.47	3.43**	5.84***	2.41	0.98
	(1.21)	(1.41)	(1.85)	(1.41)	(1.52)	(2.07)
Predicted baseline HEI	48.63	47.99	−0.64	45.36	46.00	0.64
Calories from school (≤33%) (%)	1.00	8.56	7.56	5.01	5.57	0.56
Calories from school (>33%) (%)	7.47	12.70	5.24	7.55	12.69	5.14
P-values for the Hausman Test of Exogeneity of School Food Participation
Model (1)	0.07	0.67		0.15	0.42
Model (2)	0.04	0.67		0.15	0.49
Model (3)	0.05	0.43		0.19	0.52
N	3806	3262	7068	3830	3784	7614

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. P-values in the last column represent a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

Moving down in Table 5 to Model (3), we observe that K-5 graders who received up to 33% of their daily calories from school food experienced a significant increase of 3.62 HEI points in overall dietary quality due to HHFKA. Other K-5 graders who got more than 33% of daily calories from school food also experienced a statistically indistinguishable (p=0.53) gain of 2.47 HEI points. The point estimate of the impact, however, is not precisely estimated. Turning to the results for 6–12 graders, we find suggestive evidence that the significant increase in the impact of school food among older children (i.e., in Model [2]) was driven mostly by those consuming more than one-third of their daily calories from school food. However, the point estimate of the effect (2.41 HEI points) is neither accurately estimated nor statistically different from the impact on other 6–12 graders getting smaller shares of daily calories from school food (p=0.33). Lastly, the Hausman test results indicate endogeneity of school food participation only among K-5 graders pre-HHFKA.

Table 6 summarizes heterogeneity analysis for the overall effect estimates by income level. Briefly, Model (2) implies that all children along the income distribution benefited from the updated nutritional standards. Results suggest that higher-income children experienced a greater improvement in overall dietary quality than their low-income counterparts (2.88 vs. 1.77 HEI points, respectively). This difference, however, is not statistically significant (p=0.55). In terms of heterogeneity pattern by shares of daily calories from school food, we observe similar patterns to those found in Table 5, Model (3). Moreover, the Hausman test results provide evidence of endogenous school food participation within low-income students before the HHFKA implementation, but not after.

Table 6.

Average effect of school food consumption on child’s overall dietary quality, by income

	Low Income			High Income
Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Model (1). Any School Food Effect (Binary Treatment)
Any school food (HEI points)	3.93***	6.62***	2.68**	0.75	2.53*	1.77	0.70
	(0.88)	(0.97)	(1.31)	(1.34)	(1.38)	(1.93)
Predicted baseline HEI	45.55	45.56	0.02	47.90	47.84	−0.05
Any school food (%)	8.64	14.52	5.88	1.57	5.28	3.71
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	3.27***	5.05***	1.77*	0.58	3.45***	2.88*	0.55
	(0.73)	(0.68)	(0.99)	(1.07)	(1.12)	(1.54)
Predicted baseline HEI	45.68	45.90	0.22	47.95	47.66	−0.29
One school meal (%)	7.17	11.00	3.83	1.20	7.25	6.05
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	2.42***	5.59***	3.17**	0.56	0.95	0.39	0.29
	(0.97)	(1.06)	(1.44)	(1.62)	(1.48)	(2.19)
Calories from school (>33%) (HEI points)	5.21***	7.59***	2.38	1.09	4.91***	3.82	0.62
	(1.08)	(1.16)	(1.59)	(1.63)	(1.80)	(2.42)
Predicted baseline HEI	45.55	45.54	−0.01	47.89	47.79	−0.10
Calories from school (≤33%) (%)	5.31	12.27	6.95	1.16	1.99	0.83
Calories from school (>33%) (%)	11.44	16.66	5.23	2.27	10.28	8.01
P-values for the Hausman Test of Exogeneity of School Food Participation
Model (1)	0.01	0.23		0.45	0.59
Model (2)	0.00	0.57		0.40	0.57
Model (3)	0.01	0.09		0.49	0.63
N	4494	4006	8500	3142	3040	6182

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines. P-values in the last column represent a statistical difference test of the pre-post estimates between low income and high income.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

5.2. Indirect Effects on Away-from-School Dietary Quality

Results from Models (1) and (2) in Table 7 consistently suggest that the HHFKA implementation led students to consume lower quality diets at away-from-school food acquisition sources. Model (2) implies that before the HHFKA, consuming a school meal, rather than an away-from-school meal, had no significant impact on the quality of children’s away-from-school diets. Contrarily, after the HHFKA, consuming one school meal decreased the away-from-school dietary quality of children by 2.97 HEI points (6.35%). The last column shows that this negative indirect effect is statistically significant. Perhaps not surprisingly, Model (3) indicates that students consuming larger shares of their daily calories from school food drove this unintended negative consequence (4.47 vs. 0.45 HEI point decrease; p=0.01).

Table 7.

Average effect of school food consumption on child’s away-from-school dietary quality, all children

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre
Model (1). Any School Food Effect (Binary Treatment)
Any school food (HEI points)	−0.56	−2.88***	−2.31**
	(0.85)	(0.81)	(1.17)
Predicted baseline HEI	46.77	46.74	−0.03
Any school food (%)	−1.20	−6.15	−4.95
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	−0.08	−2.97***	−2.89***
	(0.68)	(0.64)	(0.94)
Predicted baseline HEI	46.62	46.82	0.20
One school meal (%)	−0.18	−6.35	−6.17
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−1.29	−1.74*	−0.45
	(1.08)	(0.94)	(1.43)
Calories from school (>33%) (HEI points)	0.28	−4.19***	−4.47***
	(0.98)	(0.99)	(1.39)
Predicted baseline HEI	46.76	46.77	0.02
Calories from school (≤33%) (%)	−2.76	−3.73	−0.97
Calories from school (>33%) (%)	0.61	−8.95	−9.55
N	7636	7046	14682

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects.

^***p<0.01

^**p<0.05

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

Table 8 presents the indirect effect estimates by school grade (Panel A) and income (Panel B). For brevity, we only report results measured in HEI points from Models (2) and (3).¹⁸ First, results imply that all children across the school grade and income distributions consumed lower quality diets at away-from-school food sources post-HHFKA. For instance, the away-from-school dietary quality for K-5 and 6–12 graders on average decreased by statistically indifferent 2.53 and 3.56 HEI points in the post-HHFKA period, respectively (Panel A, Model [2]). Consistent with Table 7, we observe that indirect effects are driven mostly by children consuming more than one-third of their daily calories at school (Panels A and B, Model [3]). Interestingly, we see that younger and low-income children consuming up to one school meal do not shift towards lower quality diets away from school. These results could help explain the observed heterogeneity patterns in their overall diet quality changes found in Model (3) in Tables 5 and 6.

Table 8.

Average effect of school food consumption on child’s away-from-school dietary quality, by school grade and income

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). School Grade	K-5			6–12
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	−0.74	−3.26***	−2.53**	0.73	−2.82***	−3.56***	0.58
	(0.92)	(0.87)	(1.27)	(0.99)	(0.90)	(1.34)
Predicted baseline HEI	48.49	48.24	−0.25	45.09	45.76	0.67
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−2.78**	−1.73	1.06	−0.08	−1.51	−1.42	0.37
	(1.27)	(1.45)	(1.93)	(1.57)	(1.25)	(2.01)
Calories from school (>33%) (HEI points)	−0.65	−4.74***	−4.09**	1.55	−4.02***	−5.56***	0.59
	(1.34)	(1.50)	(2.01)	(1.35)	(1.33)	(1.89)
Predicted baseline HEI	48.83	48.16	−0.68	45.11	45.72	0.61
Panel (B). Income	Low Income			High Income
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	−0.10	−3.04***	−2.93***	0.25	−2.37**	−2.62*	0.87
	(0.80)	(0.81)	(1.14)	(1.20)	(1.03)	(1.58)
Predicted baseline HEI	45.52	46.07	0.55	47.55	47.34	−0.21
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−1.46	−0.25	1.21	−1.08	−3.09**	−2.01	0.26
	(1.01)	(1.13)	(1.52)	(1.90)	(1.47)	(2.40)
Calories from school (>33%) (HEI points)	0.19	−4.10***	−4.29***	0.74	−3.26**	−4.01*	0.92
	(1.16)	(1.23)	(1.69)	(1.66)	(1.58)	(2.29)
Predicted baseline HEI	45.69	45.68	−0.02	47.69	47.56	−0.14
N (Panel A)	3806	3262	7068	3830	3784	7614
N (Panel B)	4494	4006	8500	3142	3040	6182

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines. P-values in the last column represent a statistical difference test of the pre-post estimates between K-5 and 6–12 grades (panel A) and similarly, between low income and high income (Panel B).

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

5.3. Indirect Effects on At-Home and Away-from-Home-and-School Dietary Quality

Appendix Table A4 summarizes indirect effect estimates of school food consumption on children’s at-home dietary quality in the full sample. Consistent patterns to the school food impacts on the away-from-school dietary quality (i.e., Table 7) were observed. In short, the negative effect of consuming one school meal in lieu of an away-from-school meal on the at-home diet quality of children increased by 3.19 HEI points from the pre- to post-HHFKA era. As before, this result was mostly driven by children consuming more than one school meal (4.22 vs. 0.99 HEI point decrease; p=0.08).

Appendix Table A5 reports indirect effect estimates by school grade and income. Overall, results indicated that all children along the school grade and income distributions shifted towards consuming lower quality diets at home in the post-HHFKA implementation period. There was some evidence of larger indirect effects among older and low-income children consuming more than a third of daily calories from school food. These differences, however, were not statistically significant.

In terms of the HHFKA impacts on the FAFHS dietary quality, results for sample selection tests indicated non-random selection in the full sample before and after HHFKA (see Appendix Table A6). Appendix Tables A7 and A8 present the selection-bias-corrected estimates from models with continuous and categorical treatment variables, respectively. Briefly, findings suggested that consuming one school meal was associated with 3.38 HEI point (9%) reduction in the FAFHS dietary quality of students before HHFKA. After the HHFKA, the effect was slightly smaller but statistically indifferent at 1.98 HEI points (5%), leading to a null indirect effect on students’ dietary quality from this food source (Appendix Table A7, Panel A).

In sum, the results discussed in this section indicate that the unintended adverse effects of the HHFKA on the away-from-school dietary quality of children were driven by a shift towards lower quality diets at home, mainly among children consuming more than a third of their daily calories from school food. Despite the negative ‘spillover’ effects, we observed a significant improvement in the overall quality of the average student’s diet. Together, these findings imply that children must have experienced a substantial increase in their at-school dietary quality (i.e., for foods acquired at school), as shown below.

5.4. Direct Effect on At-School Dietary Quality

Table 9 reports estimates for the impact of the HHFKA on the quality of children’s intakes of school food (i.e., federally subsidized school meals and competitive foods).¹⁹ In panel A, we see that the effect of a 33% increase (one school meal) in the share of daily calories from school food significantly went up by 3.97 HEI points from the pre- to post-HHFKA period. Our heterogeneity analyses by school grade and income indicate that 6–12 graders and higher-income students mainly drove this direct impact. We, however, see that younger and low-income students also gained nontrivial benefits.

Table 9.

Average effect of school food consumption on child’s at-school dietary quality

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). All Children
One school meal (HEI points)	0.17	4.14***	3.97***
	(0.89)	(0.92)	(1.29)
Predicted baseline HEI	44.90	48.96	4.07
Panel (B). K-5 Grade
One school meal (HEI points)	2.41**	3.63***	1.21
	(1.05)	(1.06)	(1.51)
Predicted baseline HEI	43.96	50.95	6.99
Panel (C). 6–12 Grade
One school meal (HEI points)	−1.76	3.67***	5.42***	0.09a
	(1.35)	(1.30)	(1.91)
Predicted baseline HEI	45.23	48.16	2.92
Panel (D). Low Income
One school meal (HEI points)	−0.15	2.71**	2.86*
	(1.04)	(1.13)	(1.54)
Predicted baseline HEI	46.43	50.57	4.13
Panel (E). High Income
One school meal (HEI points)	0.14	6.59***	6.46***	0.19b
	(1.51)	(1.58)	(2.21)
Predicted baseline HEI	43.48	46.45	2.97
N (Panel A)	2614	2401	5015
N (Panel B)	1483	1217	2700
N (Panel C)	1131	1184	2315
N (Panel D)	1721	1510	3231
N (Panel E)	893	891	1784

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Bootstrapped standard errors (1000 replications) are in parentheses. All regressions include days of the week and interview day dummies as well as control variables for child characteristics. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.

5.5. Changes in Calorie Intake

Table 10 presents the effects of the HHFKA implementation on the total daily calorie intake of children. Panel A shows that before the HHFKA, consuming a school meal, rather than an away-from-school meal, did not lead to a significant change in total calorie consumption of the average student. This suggests that school food had a similar calorie content to food acquired from away-from-school food sources before HHFKA. After HHFKA, consuming a school meal resulted in an 87-kcal (4%) reduction in daily calorie intake. However, the relative pre-post difference estimate in the last column (60 kcals) is not precisely estimated. In Panels C and D, we observe significant declines in calorie intakes among older and higher-income children are driving this result.

Table 10.

Average effect of school food consumption on child’s total daily calorie intake

Dependent Variable: Calorie Intake	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). All Children
One school meal (kcal)	−27.37	−87.23**	−59.86
	(40.16)	(35.59)	(53.66)
Predicted baseline calorie intake	2053.59	2007.29	−46.29
Panel (B). K-5 Grade
One school meal (kcal)	−31.17	23.70	54.87
	(38.13)	(45.26)	(59.17)
Predicted baseline calorie intake	1914.90	1853.88	−61.02
Panel (C). 6–12 Grade
One school meal (kcal)	−33.84	−207.75***	−173.92*	0.04a
	(76.28)	(53.32)	(93.05)
Predicted baseline calorie intake	2095.84	2070.87	−24.97
Panel (D). Low Income
One school meal (kcal)	−92.64**	−54.13	38.51
	(44.06)	(43.33)	(61.79)
Predicted baseline calorie intake	2034.75	1936.71	−98.04
Panel (E). High Income
One school meal (kcal)	34.91	−124.21**	−159.12*	0.08b
	(73.48)	(58.43)	(93.87)
Predicted baseline calorie intake	2079.69	2065.89	−13.80

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Calorie intake is standardized to reflect differences in energy intake by age, gender, weight, and height of children. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.

Table 11 shows the results for changes in the away-from-school daily calorie consumption of students. When children eat school food, they need to consume a smaller number of calories from away-from-school-prepared food to meet daily calories requirement. Thus, as shown in panel A, before the HHFKA, consuming a school meal resulted in lower calorie intake from away-from-school food sources by about 660 kcals (or roughly one-third of the average daily calorie intake). This effect did not significantly change by the implementation of HHFKA, leading to the null indirect effect in the last column. Heterogeneity analyses provide evidence of offsetting effects within subpopulations based on school grade (Panels B and C) and income (Panels D and E). Similar patterns were observed for at-home calorie consumption (see Appendix Table A10). We also did not find a significant change in the FAFHS calorie intake.²⁰ Finally, the HHFKA’s direct effect estimates in Table 12, Panel A, provide evidence of a modest decrease (61 kcals per one school meal) in calorie consumption from school food, mainly driven by low-income children (Panel D). Together, results in this section imply a modest decrease in total daily calorie intake of the average child following the HHFKA implementation due to a reduction in calorie intake from school food.

Table 11.

Average effect of school food consumption on child’s away-from-school calorie intake

Dependent Variable: Calorie Intake	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). All Children
One school meal (kcal)	−661.24***	−654.00***	7.24
	(32.51)	(31.39)	(45.19)
Panel (B). K-5 Grade
One school meal (kcal)	72.54	−624.32***	−551.78***
	(31.47)	(39.06)	(50.15)
Panel (C). 6–12 Grade
One school meal (kcal)	−81.91	−643.76***	−725.67***	0.09a
	(60.08)	(48.57)	(77.25)
Panel (D). Low Income
One school meal (kcal)	−709.81***	−597.04***	112.77**
	(35.53)	(34.17)	(49.29)
Panel (E). High Income
One school meal (kcal)	−614.22***	−719.02***	−104.80	0.02b
	(59.83)	(57.98)	(83.30)

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Calorie intake is standardized to reflect differences in energy intake by age, gender, weight, and height of children. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.

Table 12.

Average effect of the HHFKA implementation on child’s calorie intake from school food

Dependent Variable: Calorie Intake	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). All Children
One school meal (kcal)	590.19***	529.39***	−60.80*
	(28.26)	(22.80)	(36.91)
Panel (B). K-5 Grade
One school meal (kcal)	−35.34	575.91***	540.56***
	(27.57)	(30.82)	(42.27)
Panel (C). 6–12 Grade
One school meal (kcal)	−51.32	512.47***	461.14***	0.81a
	(45.07)	(27.14)	(52.84)
Panel (D). Low Income
One school meal (kcal)	581.33***	492.58***	−88.75*
	(35.81)	(30.42)	(47.89)
Panel (E). High Income
One school meal (kcal)	574.72***	566.30***	−8.41	0.27b
	(42.25)	(33.55)	(54.73)

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Calorie intake is standardized to reflect differences in energy intake by age, gender, weight, and height of children. Two-day sampling weights are applied. Bootstrapped standard errors (1000 replications) are in parentheses. All regressions include days of the week and interview day dummies as well as control variables for child characteristics. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.

6. Discussion and Conclusions

The HHFKA of 2010 updated nutritional standards for all school foods (i.e., federally subsidized school meals and competitive foods) to “provide nutrient-dense meals (high in nutrients and low in calories) that better meet the dietary needs of school children” (USDA-FNS 2012). Using nationally representative data from NHANES (2009–2016), we examine how substantial changes in school nutritional standards affected the dietary quality as well as the dietary quantity of school-age children’s food intakes from different food acquisition sources. First, we estimate the overall effects of the HHFKA, defined as the impacts on dietary quality/quantity of food intakes from all food acquisition sources (i.e., both school and away from school). We then examine whether the overall effects were solely driven by the HHFKA’s direct (intended) impacts through school food or perhaps the away-from-school dietary outcomes of children were also indirectly affected.

We document a significant increase in the overall dietary quality of the average student from the pre- to the post-HHFKA implementation period. Our analysis by food acquisition source indicates that a significant increase in the quality of children’s intakes of school food drove this impact. Our indirect effect analysis finds a negative effect on the away-from-school dietary quality of the average student. We show that school children shifted towards consuming lower-quality diets away from school. The observed negative unintended consequences of the HHFKA, however, were not strong enough to fully offset its direct effects on dietary quality. Yet, these results suggest that students could have achieved more substantial improvements in overall dietary quality if they had maintained their away-from-school diet quality at the pre-HHFKA period.

Further, we find that the direct effect of the HHFKA was primarily driven by improvements in the at-school diet quality of older (6–12 graders) and higher-income children. The higher at-school dietary quality gains among older students might be explained by the HHFKA’s differential requirements across grades/ages. For instance, the updated meal standards required schools to serve more fruits and vegetables to 9–12 graders than K-8 graders (see Appendix Table A2). Moreover, the HHFKA required all students to select at least half a cup of fruit or vegetable components of the subsidized meals under the OVS (USDA-FNS 2012). Before the HHFKA, middle and high schoolers were provided with a broader range of foods in terms of healthfulness than elementary schoolers, allowing them more autonomy in selecting foods (Briefel et al. 2009).

The larger direct effects among higher-income children might be attributed to increased regulation for both subsidized and competitive school foods. There is evidence that higher-income children are more likely to purchase competitive foods sold at school (USDA 2019). As we discussed, NHANES respondents do not distinguish between federally subsidized meals and competitive foods sold at the school cafeteria and only report whether a food item was acquired at the school cafeteria. Thus, to the extent that our analysis evaluates the effects of consuming all school foods, not just federally subsidized school breakfasts and lunches, the greater dietary quality gains among higher-income children might be expected.

Our more detailed analysis of the negative indirect (spillover) effects implied that this result was driven by consuming lower quality diets at home. We did not find a significant change in the FAFHS (e.g., restaurants, fast foods) diet quality. One explanation is that parents may be inclined to let their children consume less-healthy foods (e.g., snacks) at home if they eat healthy foods at school. Indeed, our heterogeneity analysis based on the share of daily calories consumed at school revealed that HHFKA’s unintended impacts were mostly driven by children getting more than one-third of their daily calories from school food. It is also possible that children or perhaps their parents might have lowered the consumption of some foods (e.g., whole grains, fruits, vegetables) that had already been consumed at school. Future research will investigate how the consumption of the HHFKA-targeted (and non-targeted) food categories were affected by the policy to provide a better understanding of the mechanisms behind the indirect effects.

We do not find strong evidence that a particular subset of children based on school grade or income were causing the indirect effects. The magnitudes of reductions in the away-from-school dietary quality were not statistically different between younger and older, and likewise among low-and higher-income children. As a result, the larger direct effects among older and higher-income children translated into greater improvements in their overall dietary quality. In terms of the impacts on the daily calorie intake of children, we find evidence of a modest reduction in daily calorie intake of the average student in the post-HHFKA implementation period. We show older and higher-income children primarily drove this result. Our results based on food acquisition sources revealed how different subpopulations changed their calorie consumption differently across food acquisition sources.

The empirical evidence from this study could inform contemporary policy discussions related to making changes to school meal standards. In December 2018, USDA published the most recent changes to nutritional standards for school foods, rolling back some key nutritional guidelines. The new rules (effective February 11th, 2019) allowed schools to offer low-fat flavored milk, provided them with more time for gradual sodium reduction, and required only half of the weekly grains in meals to be whole grain-rich (USDA-FNS 2018). Our analysis, using data from the period before the implementation of these rollbacks, indicates that school children consumed more-nutritious, less-energy-dense diets in the post-HHFKA implementation. Thus, rolling back nutrition standards could harm children, particularly those from disadvantaged households, by once again leaving them at higher risk of obesity and lowering their dietary quality.

Appendix: Methods for Testing and Correcting for Sample Selection

The procedure for testing for sample selection involves estimating a selection (participation) equation:

$$S_{it}=\varphi D_{it}+{Z^{\prime }}_{it}\varnothing +\omega {\overline{D}}_i+{{\overline{Z}}^{\prime }}_i\phi +v_{it}$$ (A1)

where S_it is a selection indicator taking a value of one if children obtain a non-zero proportion of their daily calories from FAFHS locations on interview day t and zero otherwise. D_it is the share of daily calories received from home-prepared foods; we expect individuals consuming larger shares of their daily calories from home-prepared food to have lower preferences for FAFHS. Z_it is a vector including indicators for days of the week; clearly, there are variations in the probability of eating away from home across the days of the week. ${\overline{D}}_i\text{and}{\overline{Z}}_i$ are child-level time averages, and v_it is an idiosyncratic error. As pointed out in Wooldridge (1995), the selection equation “need not be correctly specified in any sense; it is simply a vehicle for obtaining a sensible test.” Moreover, although exclusion restrictions, if available, could be helpful, they do not technically affect one’s ability to test and correct for selection bias (Wooldridge 1995).

We estimate equation (A1) separately for each interview day t using the standard Probit model. We then compute the inverse Mills ratio (IMR), defined as ${\widehat{\mathrm{\Lambda }}}_{it}=\mathrm{\Psi }\left({\mathcal{B}}^{\prime }G\right)/\mathrm{\Phi }\left({\mathcal{B}}^{\prime }G\right)\text{for}{S}_{it}=1$ where G includes all right-hand-side variables in equation (A1), Ψ(.) represents the standard normal density function, and Φ(. ) denotes the cumulative distribution function. The last step is to include ${\widehat{\mathrm{\Lambda }}}_{it}$ as an additional regressor in the nutritional outcome equation (2) and conduct a fully robust Wald test of H₀: ρ = 0 where ρ is the IMR’s coefficient in the modified version of equation (2). Rejecting H₀ provides evidence of non-random selection into FAFHS market (see, Wooldridge 1995 for details).

The procedure for correcting for sample selection bias testing for non-random sample selection. After computing the IMR, we construct two additional variables ${\widehat{\lambda }}_{\text{it}}^{\text{j}}=\{\begin{array}{l}{\widehat{\mathrm{\Lambda }}}_{it},t=j\\ 0,t\ne \text{j}\end{array}$ where j=1,2. Including ${\widehat{\lambda }}_{\text{it}}^1\text{and}{\widehat{\lambda }}_{\text{it}}^2$ in equation (2) for the truncated sample alleviates the selection-bias, if present. Statistical inferences from this modified version of equation (2) are drawn from bootstrapped standard errors (see, Wooldridge 1995 for details).

Figure A1. Probability density functions of HEI-2010 scores, overall and by food acquisition sources.

Notes: Two-day sampling weights are applied. Source: Author’s calculations of the 2009–16 National Health and Nutrition Examination Survey (NHANES).

Table A1.

School meal caloric standards before and after the HHFKA implementation

	Pre-HHFKA		Post-HHFKA
Grade	Minimum	Maximum	Grade	Minimum	Maximum
Panel (A): School Breakfast:
K-12	554	None	K-5	350	500
			6–8	400	550
			9–12	450	600
Panel (B): School Lunch:
K-3	633	None	K-5	550	650
4–12	785	None	6–8	600	700
7–12 (Optional)	825	None	9–12	750	850

Source: “Nutrition Standards in the National School Lunch and School Breakfast Programs; Final Rule” (USDA-FNS 2012) and “Nutrition Standards and Meal Requirements for National School Lunch and Breakfast Programs: Phase I. Proposed Approach for Recommending Revisions” (Institute of Medicine 2008).

Table A2.

New school meal dietary specifications: weekly and daily serving requirements

	Breakfast			Lunch
	School Grade			School Grade
	K-5	6–8	9–12	K-5	6–8	9–12
Fruits in cups	5 (1)	5 (1)	5 (1)	2½(½)	2½(½)	5 (1)
Vegetables in cups	0	0	0	3¾(¾)	3¾(¾)	5(1)
Dark green	0	0	0	½	½	½
Red/Orange	0	0	0	¾	¾	¾
Beans/Peas	0	0	0	½	½	½
(Legumes)
Starchy	0	0	0	½	½	½
Other	0	0	0	½	½	½
Additional Veg to Reach Total	0	0	0	1	1	4
Grains in oz eq.	7–10 (1)	8–10 (1)	9–10 (1)	8–9(1)	8–9(1)	10–12(1)
Meats/Meat Alternates in oz eq.	0	0	0	8–10(1)	8–10(1)	10–12(1)
Fluid milk in cups	5(1)	5(1)	5(1)	5(1)	5(1)	5(1)

Notes: Daily serving sizes are in parentheses.

Source: “Nutrition Standards in the National School Lunch and School Breakfast Programs; Final Rule” of January 26, 2012, available at: https://www.govinfo.gov/content/pkg/FR-2012-01-26/pdf/2012-1010.pdf.

Table A3.

Definition of food acquisition sources

NHANES Source Codes	Food “Where did you get (this/most of the ingredients for this) [FOODNAME]?”	Food Source
1	Store - grocery/supermarket	Home
2	Restaurant with waiter/waitress	Away
3	Restaurant fast food/pizza	Away
4	Bar/tavern/lounge	Away
5	Restaurant no additional information	Away
6	Cafeteria NOT in a K-12 school	Away
7	Cafeteria in a K-12 school	School
8	Child/Adult care center	Away
9	Child/Adult home care	Away
10	Soup kitchen/shelter/food pantry	Away
11	Meals on Wheels	Away
12	Community food program - other	Away
13	Community program no additional information	Away
14	Vending machine	Away
15	Common coffee pot or snack tray	Away
16	From someone else/gift	Away
17	Mail order purchase	Away
18	Residential dining facility	Away
19	Grown or caught by you or someone you know	Home
20	Fish caught by you or someone you know	Home
24	Sport, recreation, or entertainment facility	Away
25	Street vendor, vending truck	Away
26	Fundraiser sales	Away
27	Store - convenience type	Home
28	Store - no additional info	Home
91	Other, specify	Away
99	Don’t know	Home/Away/Missing
.	Missing	Home/Away/Missing

Notes: The NHANES cycle 2009–2010 does not provide the store-type breakdown as in food source codes [1], [27], and [28]. For consistency across all cycles, we consider foods from all store types as food from home. Food source codes for a few items are missing (~6%). These items are primarily non-caloric products (e.g., beverages) with zero nutrients (e.g., protein, fiber, whole grain, added sugar). When possible, we classified these items as food at home, if they were consumed at home (~4.5%) or as school food and away from home (~1.5%), based on intake day of the week (e.g., weekend versus weekday), eating time, and whether students had consumed school food on a given day.

Table A4.

Average effect of school food consumption on child’s at-home dietary quality, all children

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre
Model (1). Any School Food Effect (Binary Treatment)
Any school food (HEI points)	−0.63	−3.11***	−2.49*
	(1.08)	(0.94)	(1.43)
Predicted baseline HEI	46.17	46.08	−0.10
Any school food (%)	−1.36	−6.76	−5.40
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	−0.39	−3.58***	−3.19***
	(0.93)	(0.84)	(1.25)
Predicted baseline HEI	46.10	46.28	0.17
One school meal (%)	−0.84	−7.74	−6.89
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−0.86	−1.85*	−0.99
	(1.23)	(1.08)	(1.64)
Calories from school (>33%) (HEI points)	−0.36	−4.58***	−4.22**
	(1.34)	(1.17)	(1.78)
Predicted baseline HEI	46.17	46.11	−0.06
Calories from school (≤33%) (%)	−1.86	−4.01	−2.15
Calories from school (>33%) (%)	−0.78	−9.93	−9.15
N	7636	7046	14682

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

Table A5.

Average effect of school food consumption on child’s at-home dietary quality, by school grade and income

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). School Grade	K-5			6–12
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	−0.98	−3.76***	−2.79**	0.41	−3.49***	−3.91**	0.65
	(0.97)	(1.07)	(1.44)	(1.61)	(1.18)	(2.00)
Predicted baseline HEI	48.36	47.70	−0.65	44.24	45.20	0.96
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−2.52*	−1.57	0.95	0.77	−1.88	−2.65	0.26
	(1.39)	(1.61)	(2.13)	(1.87)	(1.45)	(2.36)
Calories from school (>33%) (HEI points)	−1.36	−4.71***	−3.36	1.07	−4.64***	−5.71**	0.52
	(1.40)	(1.74)	(2.23)	(2.42)	(1.54)	(2.87)
Predicted baseline HEI	48.69	47.41	−1.28	44.11	45.11	1.00
Panel (B). Income	Low Income			High Income
Model (2). One School Meal Effect (Continuous Treatment)
One school meal (HEI points)	0.14	−3.45***	−3.59***	−0.69	−3.24***	−2.55	0.69
	(0.91)	(1.06)	(1.40)	(1.85)	(1.26)	(2.23)
Predicted baseline HEI	44.56	44.93	0.37	47.38	47.30	−0.08
Model (3). Differential Effects by Shares of Daily Calories from School Food (Categorical Treatment)†
Calories from school (≤33%) (HEI points)	−1.49	0.05	1.54	−0.21	−3.83**	−3.62	0.11
	(1.30)	(1.37)	(1.89)	(2.12)	(1.59)	(2.65)
Calories from school (>33%) (HEI points)	0.55	−4.24***	−4.79**	−1.31	−3.86**	−2.55	0.55
	(1.33)	(1.46)	(1.97)	(2.61)	(1.80)	(3.18)
Predicted baseline HEI	44.76	44.34	−0.43	47.39	47.48	0.10
N (Panel A)	3806	3262	7068	3830	3784	7614
N (Panel B)	4494	4006	8500	3142	3040	6182

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines. P-values in the last column represent a statistical difference test of the pre-post estimates between K-5 and 6–12 grades (panel A) and similarly, between low income and high income (Panel B).

^***p<0.01,

^**p<0.05,

^*p<0.10.

^†The omitted category is zero calories from school food on a dietary recall day.

Table A6.

Sample selection test results: child’s away-from-home-and-school dietary quality equation

	Pooled OLS		Fixed-Effects OLS
Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)
One school meal (HEI points)	−3.12***	−3.14***	−3.30**	−1.84
	(0.78)	(0.73)	(1.30)	(1.45)
Day1, Monday	−0.64	1.02	7.15**	1.83
	(1.57)	(1.61)	(3.26)	(2.83)
Day1, Tuesday	1.67	2.33	9.87***	1.67
	(1.94)	(1.67)	(3.68)	(3.63)
Day1, Wednesday	1.06	2.72*	0.90	5.21
	(1.61)	(1.62)	(3.12)	(3.28)
Day1, Thursday	−1.29	2.93*	−1.97	6.24**
	(1.40)	(1.51)	(2.73)	(2.77)
Day1, Friday	−1.21	0.64	1.94	0.34
	(1.20)	(1.18)	(2.48)	(2.29)
Day1, Saturday	−2.16*	−0.54	−1.51	−1.58
	(1.16)	(1.09)	(2.26)	(2.14)
Day2, Sunday	−0.73	0.16	−1.26	1.02
	(1.35)	(1.26)	(2.55)	(2.34)
Day2, Monday	2.27	1.57	3.25	2.97
	(1.57)	(1.60)	(2.43)	(2.76)
Day2, Tuesday	2.84*	3.01*	5.97**	1.08
	(1.62)	(1.58)	(2.81)	(2.26)
Day2, Wednesday	1.15	2.95	4.87**	3.39
	(1.47)	(1.94)	(2.47)	(2.35)
Day2, Thursday	2.14	0.43	2.83	−1.91
	(1.61)	(1.86)	(3.19)	(2.31)
Day2, Friday	−0.74	1.88	1.80	0.16
	(1.49)	(1.41)	(2.45)	(2.37)
Day2, Saturday	−1.00	1.41	−2.54	0.46
	(1.79)	(2.21)	(4.80)	(3.29)
Inverse Mills ratio	−6.03***	−5.11***	−7.60***	−2.91*
	(0.83)	(0.88)	(1.50)	(1.67)
Log child’s age	0.01	−1.89**
	(0.83)	(0.86)
Female	1.11**	1.00*
	(0.56)	(0.59)
Hispanic	−1.65*	1.49
	(0.93)	(1.02)
Non-Hispanic White	−2.74***	−0.13
	(0.91)	(0.99)
Non-Hispanic Black	−0.95	2.19**
	(0.97)	(0.98)
Percent poverty (130–185)	0.73	−0.68
	(1.00)	(0.87)
Percent poverty (>185)	0.19	0.12
	(0.69)	(0.69)
Log household size	−1.12	−2.21**
	(1.02)	(1.05)
Some college	−1.44*	−0.88
	(0.74)	(0.71)
College grad+	−0.52	−0.55
	(0.83)	(0.89)
Log reference person’s age	−0.12	0.69
	(1.25)	(1.22)
May-October	−0.80	0.07
	(0.61)	(0.59)
NHANES cycle 2011–12	0.48
	(0.58)
NHANES cycle 2015–16		1.57***
		(0.58)
Constant	44.22***	41.84***	39.03***	36.83***
	(4.86)	(4.94)	(1.82)	(1.58)
Number of Observations	4158	3961	4158	3961
Number of Children	2967	2769	2967	2769

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level.

^*p < 0.10,

^**p < 0.05,

^***p < 0.01.

Table A7.

Average effect of school food consumption on child’s away-from-home-and-school dietary quality

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre	P-values
Panel (A). All Children
One school meal (HEI points)	−3.38**	−1.98	1.41
	(1.47)	(1.51)	(2.08)
Predicted baseline HEI	37.30	36.61	−0.69
Panel (B). K-5 Grade
One school meal (HEI points)	−4.59**	−1.77	2.82
	(1.93)	(2.10)	(2.88)
Predicted baseline HEI	37.62	37.03	−0.59
Panel (C). 6 −12 Grade
One school meal (HEI points)	−2.24	−2.08	0.16	0.52a
	(2.13)	(2.03)	(2.91)
Predicted baseline HEI	37.13	36.27	−0.87
Panel (D). Low Income
One school meal (HEI points)	−3.97**	−1.66	2.31
	(1.68)	(1.80)	(2.47)
Predicted baseline HEI	38.07	36.81	−1.25
Panel (E). High Income
One school meal (HEI points)	−3.56	−2.39	1.18	0.79b
	(2.37)	(2.52)	(3.49)
Predicted baseline HEI	36.88	36.48	−0.40
N (Panel A)	4158	3961	8119
N (Panel B)	1993	1798	3791
N (Panel C)	2165	2163	4328
N (Panel D)	2269	2130	4399
N (Panel E)	1889	1831	3720

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Two-day sampling weights are applied. Clustered bootstrapped standard errors (1000 replications) are in parentheses. All regressions include days of the week, interview day, child fixed effects, and sample-bias correction variables. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.

Table A8.

Differential effects of school food consumption on child’s away-from-home-and-school dietary quality, by shares of daily calories from school food

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post – Pre
Panel (A). All Children
Calories from school (≤33%) (HEI points)	−2.22	−1.72	0.51
	(1.71)	(1.60)	(2.33)
Calories from school (>33%) (HEI points)	−4.40**	−4.86**	−0.46
	(1.84)	(2.00)	(2.72)
Panel (B). K-5th Grade
Calories from school (≤33%) (HEI points)	−0.21	−1.03	−0.83
	(2.38)	(2.45)	(3.42)
Calories from school (>33%) (HEI points)	−5.24**	−5.19	0.05
	(2.29)	(3.29)	(4.12)
Panel (C). 6th–12th Grade
Calories from school (≤33%) (HEI points)	−3.78*	−2.34	1.44
	(2.31)	(2.08)	(3.08)
Calories from school (>33%) (HEI points)	−2.08	−4.48*	−2.41
	(2.58)	(2.34)	(3.45)
Panel (D). Low Income
Calories from school (≤33%) (HEI points)	−2.89	−0.89	2.00
	(2.30)	(1.91)	(2.95)
Calories from school (>33%) (HEI points)	−4.65*	−4.43	0.22
	(2.45)	(2.75)	(3.68)
Panel (E). High Income
Calories from school (≤33%) (HEI points)	−1.98	−2.44	−0.46
	(2.27)	(2.46)	(3.33)
Calories from school (>33%) (HEI points)	−4.86**	−5.40*	−0.55
	(2.48)	(2.82)	(3.74)

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. The omitted category is zero calories from school food on a dietary recall day. Two-day sampling weights are applied. Clustered bootstrapped standard errors (1000 replications) are in parentheses. All regressions include days of the week, interview day, child fixed effects, and sample-bias correction variables. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

Table A9.

Sample selection test results: child’s at-school dietary quality equation

Dependent Variable: HEI-2010	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)
One school meal (HEI points)	0.09	4.15***
	(0.91)	(0.93)
Day1, Monday	−9.62*	2.87
	(5.72)	(5.38)
Day1, Tuesday	−7.66	−1.75
	(5.44)	(5.58)
Day1, Wednesday	−9.07*	−0.36
	(5.32)	(5.45)
Day1, Thursday	−7.41	−2.88
	(5.37)	(5.39)
Day1, Friday	−8.78*	−2.57
	(5.25)	(5.26)
Day1, Saturday	−7.82	9.50**
	(7.95)	(3.90)
Day2, Sunday	−3.09	−8.51
	(7.56)	(5.23)
Day2, Monday	−8.02	0.01
	(5.19)	(5.06)
Day2, Tuesday	−6.16	−0.62
	(5.40)	(5.28)
Day2, Wednesday	−6.34	−0.00
	(5.33)	(5.90)
Day2, Thursday	−6.79	−2.44
	(5.74)	(5.54)
Day2, Friday	−6.97	−4.09
	(5.31)	(5.32)
Day2, Saturday	0.00	0.00
	(.)	(.)
Inverse Mills ratio	−2.04	−0.86
	(1.62)	(1.87)
Log child’s age	−4.34***	−2.73**
	(1.25)	(1.31)
Female	0.34	−1.47
	(0.85)	(0.96)
Hispanic	2.73	0.44
	(1.78)	(1.38)
Non-Hispanic White	0.57	−1.01
	(1.85)	(1.49)
Non-Hispanic Black	2.97*	−0.31
	(1.77)	(1.41)
Percent poverty (130–185)	−1.89	1.20
	(1.19)	(1.40)
Percent poverty (>185)	−1.52	−0.02
	(1.02)	(1.21)
Log household size	0.69	1.48
	(1.56)	(1.41)
Some college	−1.04	0.91
	(1.06)	(1.13)
College grad+	−0.93	2.01
	(1.41)	(1.73)
Log reference person’s age	0.59	0.23
	(1.64)	(1.76)
May-October	−0.09	−0.33
	(1.01)	(1.04)
NHANES cycle 2011–12	3.74***
	(0.88)
NHANES cycle 2015–16		2.35**
		(0.91)
Constant	58.57***	53.51***
	(8.54)	(10.71)
Number of Observations	2614	2401
Number of Children	2048	1863

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Sampling weights are applied. Robust standard errors are in parentheses.

^***p<0.01

^**p<0.05

^*p<0.10.

Table A10.

Average effect of school food consumption on child’s calorie intake from home-prepared food

Dependent Variable: Calorie Intake	Pre-HHFKA (2009–12)	Post-HHFKA (2013–16)	Difference: Post-Pre	P-values
Panel (A). All Children
One school meal (kcal)	−462.85***	−452.75***	10.10
	(38.49)	(29.87)	(48.72)
Panel (B). K-5th Grade
One school meal (kcal)	−479.68***	−416.90***	62.78
	(38.47)	(39.64)	(55.23)
Panel (C). 6th −12th Grade
One school meal (kcal)	−392.06***	−459.49***	−67.43	0.17a
	(69.21)	(43.08)	(81.51)
Panel (D). Low Income
One school meal (kcal)	−535.35***	−445.69***	89.66*
	(38.94)	(34.37)	(51.93)
Panel (E). High Income
One school meal (kcal)	−343.50***	−415.11***	−71.60	0.11b
	(72.88)	(51.51)	(89.23)

Notes: School food includes all federally subsidized meals and competitive foods acquired from the cafeteria in a K-12 school. “One school meal effect” is defined as the impact of a 33% shift in the share of daily calories from away-from-school food sources to school food. Calorie intake is standardized to reflect differences in energy intake by age, gender, weight, and height of children. Two-day sampling weights are applied. Standard errors in parentheses are clustered at the child level. All regressions include days of the week, interview day, and child fixed effects. Low versus high income corresponds to 185% of the federal poverty guidelines.

^***p<0.01,

^**p<0.05,

^*p<0.10.

^aP-value represents a statistical difference test of the pre-post estimates between K-5 and 6–12 grades.

^bP-value represents a statistical difference test of the pre-post estimates between low income and high income.