Household Food Expenditures, Parental Time Allocation, and Childhood Obesity

The increased prevalence of childhood obesity is a major concern for society. This study aims at exploring the influence of the parents (especially parental time allocation choices) on children's obesity-related health outcomes and examining the potential differences between the fathers' and the mothers' marginal effects. A household with two parents and one child is modeled. The household production theory and the collective household modeling structure are combined. The model treats the mother, the father and the child as three separate agents with individual preferences. The two parents' interaction is modeled within the collective model framework by assuming that they will reach Pareto efficient resource allocation between them. In order to capture the dynamics between parents and the child, parents-child interaction is modeled in a two-stage Stackleberg game structure where the child is allowed to have certain decision choices of his/her own. This game structure allows us to explore the parental influence on the child's health outcomes while allowing the child to have influencing power in the household decision-making process. Based on this theoretical model, a general triangular system with one child's health production equation and five health inputs demand equations is derived and estimated. The empirical estimation is performed for three systems: pooled model, the younger children model (of age 9 to 11), and the older children model (of age 13 to 15). The empirical results shows positive relationship between total household monthly food expenditure and the child's BMI outcome. Both parents' time spent with the child are important and both show negatively significant impact on the child's BMI outcomes in all models and the pool model confirms the statistical difference between paternal and maternal time spent with the child. Other mother-related variables show more influence on the children's BMI. There exists a complementary relationship between mothers' income and fathers' time allocation. Fathers have more significant influence on household food expenditure compared to mothers. In general, mothers' show more significant influence on the parental time allocation compared to fathers. The main contribution of this study is that it develops a general theoretical framework to capture the dynamics in parents-child interaction. Based on this theoretical model, empirical analysis and future work can be conducted in a theoretically consistent way.