Cultural Transmission with Incomplete Information: Parental Perceived Efficacy and Group Misrepresentation

This paper introduces incomplete information in the standard model of cultural transmission (Bisin and Verdier, 2001). We allow parents to ignore own group size and the efficiency of their cultural transmission technology, while receiving a feedback from their children. Using the selfconfirming equilibrium concept, parents may end up to sustain, and be confirmed about, wrong conjectures. We show that in equilibrium optimal socialization efforts display cultural complementarity with respect to own population share, while the standard substitution result holds with respect their own conjectured population shares. Considering the population dynamics, if conjectures about population shares are shaped by cultural leaders who want to maximize the presence of own traits in the next period, then conjectures are characterized by negative biases. Our main finding is that, depending on the magnitude of the bias, the dynamics can display stable or unstable polymorphic equilibria, or just a stable homomorphic equilibrium, potentially reverting standard predictions.