Selection and Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem

We address the estimation of sample selection and endogenous treatment models with social interactions. To model the interaction between individuals in an internally consistent matter we employ a game theoretic approach based on the use of a discrete Bayesian game. We overcome the substantial computational burden this introduces through a sequential version of the nested fixed point algorithm. We describe how our methodology can be applied to a large class of commonly employed models. We employ our approach to examine the impact of an individual's frequency of exercise on her level of self esteem in a setting where an individual's exercise frequency is treated as endogenous and is potentially influenced by her belief of her friends' exercise frequency.