Investigating Treatment Effects of Participating Jointly in SNAP and WIC when the Treatment is Validated Only for SNAP

USDA operates several food assistance programs aimed at alleviating food insecurity. We study whether participation in both SNAP and WIC alleviates food insecurity compared with participation in SNAP alone. We bound underlying causal effects by applying nonparametric treatment effect methods that allow for endogenous selection and underrepresented program participation when validation data are available for one program (treatment) but not the other. We estimate average treatment effects using data from the National Household Food Acquisition and Purchase Survey (FoodAPS). FoodAPS includes administrative data to validate SNAP participation. Information on local food prices allows us to construct a food expenditure-based monotone instrumental variable that does not require a typical IV exclusion restriction. Under relatively weak monotonicity assumptions, we identify that the impact of participating in both programs relative to SNAP alone is strictly positive, suggesting that the programs are nonredundant. This evidence can support improved design and targeting of food programs.