Having obtained estimates of γ
, γ
1
, γ
2
, γ
3
, γ
4
, and γ
5
using the SHPSSNCES Census county-level data, we then use these estimates to predict food policies in indi-
vidual-level data from the NLSY97. Because the independent variables in the first step vary only at the county and state level, and since we know the county of residence
for the NLSY97, we can append the appropriate fiscal, legal, and population change variables to the individual data and create predicted food policies based on the
first–step estimates. This prediction can then serve as our proxy for exposure to unhealthful food in school, and we can then estimate the effect of food policy on indi-
vidual weight status, controlling for additional covariates.
To do so, we use a model of the following form: 2
ln bmi
i
= α + β
1
predicted policy
c
+ β
2
X
i
+ β
3
F
i
+ β
4
R
i
+ ε
i
where lnbmi is the log of the individual’s Body Mass Index; X is a set of individual- level covariates, including age, race, sex, and cigarette use; F is a set of family back-
ground covariates, including family income, mother’s and father’s education, and the log of the responding parent’s BMI; and R is a set of region dummies. Finally, we
adjust the standard errors for arbitrary forms of heteroskedasticity and within county correlation. In addition, in order to adjust for the fact that the food policy is estimated,
we calculate the standard errors following Murphy and Topel 1985. In brief, all of the standard errors are adjusted by adding a term that depends on both the variance-
covariance matrix from the first step and the second-step parameter on the estimated food policy variable.
16
For the key variable in our main model, the result is a standard error that is about 20 percent higher than would be obtained from OLS.
B. The Relationship between School Food Policies and Finances
The results from the first step, in which we estimate Equation 1, are shown in Table 2. The first column gives the means of the independent variables while the first row gives
the means for the dependent variables across the 180 counties represented in the SHPPS. First, note that all of the estimated effects for the models in this step are of
the predicted sign. Because higher values for each independent variable represent a higher level of local budgetary pressure, our hypothesis predicts a positive coefficient.
For both junk food and pouring rights, the fraction of total revenues that come from the state is significantly positive. For both junk food and school advertising, the tax
and expenditure limit indicator is significant. Thus, at least one of the variables is sig- nificant in each case. The overall F-statistics and F-statistics for just those variables
excluded from the second step are reported at the bottom of the table. They indicate that the overall models are highly significant in each case, and that the excluded vari-
ables are jointly significant at better than the 1 percent level for both junk food and pouring rights, but are not significant at conventional levels for school advertising.
Note that the standard errors are corrected for arbitrary forms of heteroskedasticity and within state correlation.
17
Anderson and Butcher 475
16. See Equation 15’ in Murphy and Topel 1985. 17. In this stage, the data are already at the county level, but we allow for within-state correlation. In the
second stage, the data are at the individual level, but we allow for within-county correlations because the pre- dicted policy will only vary at the county level.
Table 2 Step One Predictions of Food Policies
Fraction of Fraction of
Fraction of Mean of
Schools in Schools in
Schools in Independent County
in County
with County Variable
which can “Pouring
that allow Standard Purchase Rights” Food
Ads Deviation
Junk Food Contracts
at School Mean of dependent
Variable standard 0.748
0.671 0.441
deviation 0.352
0.405 0.406
Share of total revenue 0.495
0.350 0.502
0.371 from state sources
0.142 0.157
0.239 0.241
State has tax and 0.472
0.113 0.077
0.119 expenditure limits
0.501 0.061
0.059 0.061
1990 to 2000 relative 0.939
0.0003 −0.0004
0.0020 growth rate in county
10.18 0.0016
0.0025 0.0020
population aged 5–17 State has school
0.856 0.070
0.113 −0.042
accountability rules 0.353
0.100 0.073
0.102 Northeast
0.156 0.102
−0.061 −0.102
0.363 0.089
0.139 0.122
Midwest 0.261
−0.156 0.212
0.130 0.440
0.068 0.071
0.095 South
0.372 0.047
0.140 0.233
0.485 0.071
0.075 0.077
Constant 0.469
0.193 0.131
0.121 0.151
0.167 Sample size
180 180
179 180
R -squared
0.1334 0.1058
0.1344 Overall F-statistic
10.07 5.20
5.23 p
-value for overall 0.0000
0.0003 0.0003
F -test
F -statistic for excluded
3.88 4.91
2.04 variables
p -value for excluded
0.0094 0.0026
0.1069 variables F-test
Notes: Dependent variables come from public middle and high schools sampled in the 2000 wave of the School Health Policy and Programs Study SHPPS. SHPPS school weights are used to aggregate the data
to the county level. Revenues come from the NCES Common Core Data for each district. District enrollment is used to aggregate the data to the county level. Growth in county population of children aged 5–17 relative
to total county population growth from 1990 to 2000 comes from the U.S. Census. See Data Appendix for more details. See Data Table A4 for information on which states have property tax revenue limits and which
have accountability laws. “Junk Food Available” means that the students can buy chocolate, candy, cakes, ice cream, or salty snacks that are not fat free from a machine or school store. “Pouring Rights” contracts
means the school has agreed to sell one brand of soft drinks. “Soda or Snack Food Advertisements” means that advertisements are allowed at least at one type of school related activity or in one or more places at the
school—for example, on a school bus, at a school sporting event, on school grounds, or school textbooks etc. Standard errors in parentheses unless noted otherwise are adjusted for arbitrary correlation within the state.
C. The Effect of Predicted School Policies on Obesity
