The impact of the National School Lunch Program on child health: A nonparametric bounds analysis

Children in households reporting the receipt of free or reduced-price school meals through the National School Lunch Program (NSLP) are more likely to have negative health outcomes than observationally similar nonparticipants. Assessing causal effects of the program is made difficult, however, by missing counterfactuals and systematic underreporting of program participation. Combining survey data with auxiliary administrative information on the size of the NSLP caseload, we extend nonparametric partial identification methods that account for endogenous selection and nonrandom classification error in a single framework. Similar to a regression discontinuity design, we introduce a new way to conceptualize the monotone instrumental variable (MIV) assumption using eligibility criteria as monotone instruments. Under relatively weak assumptions, we find evidence that the receipt of free and reduced-price lunches improves the health outcomes of children.