1.8.- RIESGOS Y ACCIONES PREVENTIVAS EN LA MAQUINARIA

The primary effect of interest for my study is the expected change in child weight caused by at-

tending a CEP participating school. Naturally, a threat to proper identification of this effect is that

CEP eligible schools serve higher numbers of students from disadvantaged backgrounds than their

CEP ineligible counterparts. Estimating a simple regression of child weight on CEP school atten-

dance would likely produce estimates which are biased by factors common to students who attend

CEP eligible schools. More specifically, children attending CEP schools have substantially higher

individual likelihoods of belonging to single parent households, having low household incomes,

living in poorer neighborhoods, etc. Furthermore, since a school’s ISP is largely determined by the

share of students enrolled in government assistance programs, attending a CEP school increases

CEP eligibility and child weight, then it is unlikely that estimates from a na¨ıve regression would

reflect the CEP’s causal effects on weight.

To account for these sources of potential bias in my estimates, I utilize the longitudinal structure

of the ECLS-K:2011 within a panel Difference-In-Differences framework. For child i attending

school j in year t, weight outcomes are modeled such that:

Yijt = Xijtβ + δCEPjt+ αi+ λt+ ijt (1.1)

where Yijt is either continuous child BMI percentile or binary indicators equal to 1 if a child is

underweight, healthy weight, overweight, or obese and 0 otherwise, Xijt is a vector of child- and

school-level time varying covariates, CEPjtis a binary indicator equal to 1 if the the child’s school

participated in the CEP during year t and 0 otherwise, αi is a child-level fixed effect, λtis a year

specific fixed effect, and ijtis the model’s idiosyncratic error term.

The effect of interest in equation (1.1) is δ which shows the expected change in each weight

outcome caused by attending a CEP participating school during a post-CEP year. Since the ECLS-

K:2011 is a longitudinal study, I am able to control for sources of time-invariant heterogeneity in

each child’s weight outcomes using my child fixed effects.13 _{In cases where a child’s level of dis-}

advantage is relatively constant across time, my child fixed effects will remove their bias from my

estimates of δ. In addition to my child fixed effects, I also control for observable covariates which

change across time. Since household income level can vary across time, I include an indicator

which is equal to 1 if a child’s household income is below 200% of the federal poverty line and

0 otherwise as a control variable in Xijt. This addition allows me to address the concern that my

primary estimates are driven by large shifts in household income which are correlated with CEP

participation rather than actual effect of CEP school attendance. Furthermore, while all students in

my sample started Kindergarten during the same year, I control for variation in weight outcomes

13_{It is also the case that time-invariant factors at the school level may be correlated with CEP participation and}

child weight. This school-level time-invariant heterogeneity could be controlled for using school fixed effects. Since I observe children from Kindergarten until fifth grade, however, most students attend a single school during the entire survey period and adding school fixed effects to the model has a largely trivial effect on my results. I also show that

related to differences in age by including child age in months in Xijt. I also include if a school

is Urban, if a school it Rural, and the percent of a school’s students who are non-white in Xijt

to control for potential effects of school demographic characteristics on child weight. My year

fixed effects account for potential changes in weight across time which are caused by unobserved

factors that equally affect all students at the same time. For example, the HHFKA imposed a set

of changes to minimum school meal nutrition standards prior to 2014 which took effect simultane-

ously for all schools across the country.

Estimating the causal effect of CEP school attendance on weight in my model relies on the

assumption that both the timing of the program’s introduction and each schools participation deci-

sion are independent of within-child variation in weight across time conditional on my child fixed

effects, year fixed effects, and set of control variables. There are three primary cases where this

assumption would not hold. The first is if the timing of the CEP’s introduction was in response

to differential trends in child weight among students attending CEP eligible schools. In this case,

my estimates would conflate the effect of the program’s introduction with pre-existing differences

in the change of average student weight across time. This concern is lessened by the fact that

I find generally similar unconditional pre-CEP period trends in the weight outcomes of children

attending CEP and non-CEP schools in my sample. Furthermore, since the timing of the CEP’s

introduction was set in place prior to students in my sample starting Kindergarten, it is unlikely

that relative trends in their weight would directly influence introduction timing.

The second threat is school migration in which families self-select into, or out of, CEP partici-

pating schools due to unobservable factors correlated with child weight. Given that the majority of

students in my sample do not change schools during the survey period, school migration is unlikely

to influence my results. The ECLS-K:2011 does provide information on if a child changes schools

between years as well as the reason for the move. I test the sensitivity of my results to student

migration in Section 1.7 by removing students who changed schools at any point during the survey

period from my sample.

choice during the post-CEP period is influenced by unobserved factors which are also related to

the weight of their students. For example, if schools are more likely to adopt the CEP because the

weight of their students is growing faster than neighboring schools, then the estimated effect of

attending a CEP school may be biased by the pre-existing differences weight trajectories. I use a

number of techniques to evaluate the potential sensitivity of my estimates to bias from school-level

self-selection on unobservables in Section 1.7. First, I follow Millimet and Tchernis (2013) and

use each school’s pre-CEP period observable characteristics to construct a sub-sample which mini-

mizes the potential bias of self-selection on unobservables in my estimates of the average treatment

effect on the treated. Second, I estimate my effects of interest using various specifications of CEP

eligibility and ISP as instruments for CEP school attendance in a two-stage regression model. This

approach allows me to estimate my results using the variation in CEP participation explained by

the plausibly exogenous timing of the provision’s introduction and ISP rather than self-selection

into the program.