Table B1. Full Sample Results OLS/Probit

Transcription

1 Table B1. Full Sample Results OLS/Probit School Propensity Score Fixed Effects Matching (1) (2) (3) (4) I. BMI: Levels School 0.351* 0.196* 0.180* 0.392* Breakfast (0.088) (0.054) (0.060) (0.119) School 0.291* 0.187* 0.191* Lunch (0.082) (0.050) (0.057) (0.101) II. BMI: Logs School 0.018* 0.009* 0.009* 0.021* Breakfast (0.004) (0.003) (0.003) (0.006) School 0.015* 0.010* 0.010* Lunch (0.004) (0.003) (0.003) (0.005) III. BMI: Growth Rates School 0.010* 0.009* 0.009* 0.017* Breakfast (0.003) (0.003) (0.003) (0.004) School 0.011* 0.010* 0.010* 0.010* Lunch (0.003) (0.003) (0.003) (0.003) IV. Percentile BMI: Levels School 2.575* 1.366* 1.455* 3.229* Breakfast (0.687) (0.491) (0.551) (0.817) School 2.309* 1.713* 1.445* Lunch (0.639) (0.456) (0.520) (0.768) V. Percentile BMI: Changes School * 1.453* 2.267* Breakfast (0.527) (0.491) (0.551) (0.689) School 1.424* 1.712* 1.444* 1.598* Lunch (0.491) (0.456) (0.520) (0.612) VI. Probability of Being Overweight School * 0.031* 0.056* Breakfast (0.030) (0.034) (0.010) (0.014) School 0.090* 0.108* 0.031* Lunch (0.029) (0.033) (0.009) (0.011) VII. Probability of Being Obese School * 0.022* 0.035* Breakfast (0.034) (0.039) (0.008) (0.012) School * Lunch (0.034) (0.040) (0.007) (0.010) NOTES: p<0.10, p<0.05, * p<0.01. Standard errors in parentheses. Marginal effects reported in Panels VI and VII. Additional controls in each model: (1) age, gender dummy, child's birthweight, 4 race dummies, 2 city type dummies, 3 region dummies, 3 dummies for mother's age at first birth, dummies for whether mother received WIC benefits during pregancy, 5 mother's education dummies, 2 dummies for mother's current employment status, household income, number of children's books in the household, 3 dummies for the amount of food in the household, quadratic and cubic terms of all continuous variables, and the complete set of pairwise interactions among the continuous variables. (2) previous control set plus the lagged dependent variable (from the fall kindergarten wave), quadratic and cubic terms of the lagged dependent variable (Panels I -- V only), and the complete set of pairwise interactions between the lagged dependent variable and the continuous variables included in the previous control set; (3) previous control set plus school fixed effects. Specification (3) in Panels VI and VII are estimated using a linear probability model. Column (4) reports separate propensity score matching estimates for school breakfast and school lunch using the variables from model (2) in the propensity score model (estimated via probit). Standard errors from 100 bootstrap repetitions. N = 13,534. See text for more details.

2 Table B2. Results: Children by Risk Type Entering Kindergarten Normal Weight Range Overweight or Obese Entering Kindergarten OLS/Probit School Propensity OLS/Probit School Propensity Fixed Score Fixed Score Effects Matching Effects Matching (1) (2) (3) (1) (2) (3) I. BMI: Growth Rates School 0.010* 0.011* 0.020* Breakfast (0.003) (0.004) (0.005) (0.006) (0.007) (0.007) School 0.009* * 0.022* 0.023* Lunch (0.003) (0.003) (0.003) (0.006) (0.007) (0.007) II. Percentile BMI: Changes School * Breakfast (0.685) (0.730) (1.000) (0.538) (0.673) (0.669) School 1.621* Lunch (0.624) (0.672) (0.797) (0.535) (0.688) (0.610) III. Probability of Being Overweight School 0.129* 0.041* 0.064* Breakfast (0.041) (0.012) (0.017) (0.065) (0.021) (0.024) School * 0.056* Lunch (0.039) (0.010) (0.013) (0.062) (0.024) (0.020) IV. Probability of Being Obese School * 0.024* Breakfast (0.058) (0.007) (0.009) (0.057) (0.025) (0.029) School * 0.065* Lunch (0.059) (0.006) (0.006) (0.057) (0.023) (0.023) NOTES: p<0.10, p<0.05, * p<0.01. Standard errors in parentheses. N = 10,039 (Normal) and 3,495 (Overweight or Obese). Specification (1) is identical to Specification (1) in Table 1; Specifications (2) and (3) are analagous to Specifications (3) and (4) in Table 1. Specification (2) in Panels III and IV is estimated using a linear probability model; in addition, these models exclude lagged values of the dependent variable in Model A since there is no variation by construction. See Table 1 for additional details.

3 Table B3. Selection into School Nutrition Programs Full Sample I. Weight (lbs.) Normal Weight Entering Kindergarten Risk Type Overweight or Obese Entering Kindergarten OLS School Propensity OLS School Propensity OLS School Propensity Fixed Score Fixed Score Fixed Score Effects Matching Effects Matching Effects Matching (1) (2) (3) (1) (2) (3) (1) (2) (3) School * Breakfast (0.148) (0.167) (0.280) (0.087) (0.100) (0.159) (0.322) (0.401) (0.706) School Lunch (0.138) (0.158) (0.216) (0.079) (0.092) (0.152) (0.320) (0.410) (0.591) N II. Weight (lbs.): Change in Levels School * Breakfast (0.148) (0.168) (0.274) (0.087) (0.100) (0.154) (0.322) (0.400) (0.665) School Lunch (0.138) (0.159) (0.243) (0.080) (0.092) (0.147) (0.320) (0.410) (0.573) N III. Weight (lbs.): Logs School * Breakfast (0.003) (0.003) (0.005) (0.002) (0.002) (0.004) (0.005) (0.006) (0.010) School Lunch (0.003) (0.003) (0.005) (0.002) (0.002) (0.004) (0.005) (0.007) (0.009) N IV. Weight (lbs.): Growth Rates School 0.012* 0.012* 0.019* 0.012* 0.012* 0.019* Breakfast (0.004) (0.004) (0.007) (0.003) (0.004) (0.007) (0.007) (0.008) (0.014) School Lunch (0.003) (0.004) (0.006) (0.003) (0.004) (0.007) (0.006) (0.008) (0.013) N NOTES: p<0.10, p<0.05, * p<0.01. Standard errors in parentheses. Specification (1) is identical to Specification (1) in Table 1, except all terms involving child's birthweight are omitted in Panels II and IV; Specifications (2) and (3) are similarly analagous to Specifications (3) and (4) in Table 1. In addition, all regressions include controls for child's height in fall kindergarten (plus higher order and interaction terms). See Table 1 and text for details.

4 Table B4. Sensitivity Analysis: Bivariate Probit Results with Different Assumptions Concerning Correlation Among the Disturbances Correlation of the Disturbances Specification (1) Specification (2) ρ = 0 ρ = 0.1 ρ = 0.2 ρ = 0.3 ρ = 0.4 ρ = 0.5 ρ = 0 ρ = 0.1 ρ = 0.2 ρ = 0.3 ρ = 0.4 ρ = 0.5 A. Probability of Being Overweight School * * * * * 0.098* * * * * Breakfast (0.030) (0.030) (0.030) (0.030) (0.029) (0.028) (0.034) (0.034) (0.034) (0.033) (0.033) (0.032) School 0.090* 0.114* 0.139* 0.165* 0.192* 0.220* 0.108* 0.133* 0.158* 0.184* 0.212* 0.241* Lunch (0.029) (0.029) (0.029) (0.029) (0.029) (0.029) (0.033) (0.033) (0.033) (0.033) (0.033) (0.032) B. Probability of Being Obese School * * * * * 0.116* * * * * Breakfast (0.034) (0.034) (0.034) (0.033) (0.032) (0.031) (0.039) (0.039) (0.039) (0.038) (0.037) (0.036) School * 0.132* 0.162* 0.195* 0.230* * 0.152* 0.183* 0.215* 0.251* Lunch (0.034) (0.034) (0.034) (0.034) (0.033) (0.033) (0.040) (0.040) (0.039) (0.039) (0.039) (0.038) NOTES: p<0.10, p<0.05, * p<0.01. Standard errors in parentheses. Specifications (1) and (2) refer to control sets used in Table 1. See Table 1 and text for details.

5 Table B5. Sensitivity Analysis: Bivariate Probit Results with Different Assumptions Concerning Correlation Among the Disturbances by Risk Type Correlation of the Disturbances Specification (1) ρ = 0 ρ = 0.1 ρ = 0.2 ρ = 0.3 ρ = 0.4 ρ = 0.5 I. Normal Weight Entering Kindergarten A. Probability of Being Overweight School 0.129* * * * * Breakfast (0.041) (0.040) (0.040) (0.039) (0.038) (0.037) School * 0.143* 0.172* 0.204* 0.239* Lunch (0.039) (0.039) (0.039) (0.039) (0.039) (0.039) B. Probability of Being Obese School * * * * Breakfast (0.058) (0.058) (0.057) (0.056) (0.055) (0.053) School * 0.232* Lunch (0.059) (0.059) (0.059) (0.059) (0.058) (0.057) II. Obese or Overweight Entering Kindergarten A. Probability of Being Overweight School * * * * Breakfast (0.065) (0.065) (0.064) (0.063) (0.062) (0.060) School * 0.195* 0.215* 0.233* 0.248* Lunch (0.062) (0.062) (0.062) (0.062) (0.062) (0.062) B. Probability of Being Obese School * * * * Breakfast (0.057) (0.057) (0.056) (0.056) (0.054) (0.052) School * 0.191* 0.214* 0.236* Lunch (0.057) (0.057) (0.056) (0.056) (0.056) (0.056) NOTES: p<0.10, p<0.05, * p<0.01. Standard errors in parentheses. Specifications (1) refers to control set used in Table 1. See Tables 1, 4, and text for details.

6 Table B6. Sensitivity Analysis: Amount of Selection on Unobservables Relative to Selection on Observables Required to Attribute the Entire SBP Effect to Selection Bias Specification (1) Specification (2) Cov(ε,ν) τ 1 Implied Cov(ε,ν) τ 1 Implied Var(ν) Ratio Var(ν) Ratio BMI: Levels (0.088) (0.054) BMI: Logs (0.004) (0.003) BMI: Growth Rates (0.003) (0.003) Percentile BMI: Levels (0.687) (0.491) Percentile BMI: Changes (0.527) (0.491) Probability of Being Overweight (0.011) (0.009) Probability of Being Obese (0.009) (0.007) NOTES: Standard errors in parentheses. Specifications (1) and (2) refer to control sets used in Table 1, plus NSLP participation. Cov(ε,ν)/Var(ν) refers to the asymptotic bias of the unconstrained estimate under the assumption of equal (normalized) selection on observables and unobservables. 1 refers τ to the unconstrained estimate of the effect of SBP participation. The implied ratio is the latter divided by the former. See Table 1 and text for details.

7 Table B7. Sensitivity Analysis: Amount of Selection on Unobservables Relative to Selection on Observables Required to Attribute the Entire SBP Effect to Selection Bias by Risk Type Specification (1) Specification (2) Cov(ε,ν) τ 1 Implied Cov(ε,ν) τ 1 Implied Var(ν) Ratio Var(ν) Ratio I. Normal Weight Entering Kindergarten BMI: Levels (0.064) (0.056) BMI: Logs (0.004) (0.003) BMI: Growth Rates (0.003) (0.003) Percentile BMI: Levels (0.763) (0.640) Percentile BMI: Changes (0.685) (0.640) Probability of Being Overweight (0.010) Probability of Being Obese (0.006) II. Obese or Overweight Entering Kindergarten BMI: Levels (0.184) (0.128) BMI: Logs (0.008) (0.006) BMI: Growth Rates (0.006) (0.006) Percentile BMI: Levels (0.595) (0.536) Percentile BMI: Changes (0.538) (0.536) Probability of Being Overweight (0.018) (0.018) Probability of Being Obese (0.022) (0.019) NOTES: Standard errors in parentheses. Specifications (1) and (2) refer to control sets used in Table 1. See Tables 1 and 5 for details.

8 Table B8. Propensity Score Matching Sensitivity Analysis by Risk Type: Rosenbaum Bounds (SBP) I. Full Sample Γ = 1 Γ = 1.2 Γ = 1.4 Γ = 1.6 Γ = 1.8 Γ = 2 Γ = 2.5 Γ = 3 BMI: Levels p = p = p = p = p = p = p = p = BMI: Logs p = p = p = p = p = p = p = p = BMI: Growth Rates p = p = p = p = p = p = p = p = Percentile BMI: Levels p = p = p = p = p = p = p = p = Percentile BMI: Changes p = p = p = p = p = p = p = p = Prob. of Being Overweight p = p = p = p = p = p = p = p = Prob. of Being Obese p = p = p = p = p = p = p = p = II. Normal Weight Entering Kindergarten BMI: Levels p = p = p = p = p = p = p = p = BMI: Logs p = p = p = p = p = p = p = p = BMI: Growth Rates p = p = p = p = p = p = p = p = Percentile BMI: Levels p = p = p = p = p = p = p = p = Percentile BMI: Changes p = p = p = p = p = p = p = p = Prob. of Being Overweight p = p = p = p = p = p = p = p = Prob. of Being Obese p = p = p = p = p = p = p = p = III. Obese or Overweight Entering Kindergarten BMI: Levels p = p = p = p = p = p = p = p = BMI: Logs p = p = p = p = p = p = p = p = BMI: Growth Rates p = p = p = p = p = p = p = p = Percentile BMI: Levels p = p = p = p = p = p = p = p = Percentile BMI: Changes p = p = p = p = p = p = p = p = Prob. of Being Overweight p = p = p = p = p = p = p = p = Prob. of Being Obese p = p = p = p = p = p = p = p = NOTES: Rosenbaum critical p-values for test of the null of zero average treatment effect. For controls included in the propensty score, see Table 1.