This paper presents an empirical analysis of a choice-theoretic model of cultural transmission. In particular, we use data from the General Social Survey to estimate the structural parameters of a model of marriage and child socialization along religious lines in the United States. The observed intermarriage and socialization rates are consistent with Protestants, Catholics, and Jews having a strong preference for children who identify with their own religious beliefs and making costly decisions to influence their children's religious beliefs. Our estimates imply dynamics of the shares of religious traits in the population that are in sharp contrast with the predictions obtained by linear extrapolations from current intermarriage rates.