Households with children in the United States are more likely to experience food insecurity than households with no children. However, households with children are less likely to experience hunger. This finding suggests that food insecure households with children may be drawing on personal and/or public resources to help them avoid hunger. In this paper, we use data from the April Food Security Supplements of the Current Population Survey to evaluate whether federal food assistance programs play a role in helping households with children avoid hunger. The problem of the endogeneity of a household's participation decision is addressed in two ways. First, for the Food Stamp Program, we use exogenous state-level policy variables that affect participation but not food security. Second, for households that experienced hunger during a given year, we study whether participation in any of the three largest federal food assistance programs was associated with lower levels of food insecurity during the last 30 days of that year. The paper also studies whether one personal resource, household employment circumstances, helps households with children avoid hunger. We find that by using better income data from the March Demographic Survey and by using a 10-item adult-referenced food security scale that excludes child-referenced items, we are able to control for the observed differences between households with and without children under 5 years old. For households with school-age children, only participation in the National School Lunch Program appears able to explain why they are able to avoid hunger. (Contains 10 tables and 20 footnotes.)