Teaching by example and induced beliefs in a model of cultural transmission

We augment standard models of cultural transmission with an explicit account of social learning, grounded in the information transmission literature. Youngsters observe the behavioral trait of a role model and form beliefs about the desirability of that trait. Adults have better information about each trait and have a paternalistic attitude toward their children. This makes them reluctant to adopt myopic behavior to avoid setting a negative example to their children. This signaling distortion increases in the influence parents have over their offspring. We extend the model to allow parental influence to depend on the population frequency of each trait and show that cultural complementarity does not imply convergence to a homogeneous population. We find empirical support for a positive relationship between parental influence and propensity to exert self-restraint by looking at alcohol and tobacco consumption.