Social Learning With State-Dependent Observations

In this note, I study a variant of the canonical binary-state binary-choice social learning model (Bikhchandani et al., 1992). An individual would like to choose an action only in the high state. When making her own decision, she observes previous decision-makers who chose the action. Importantly, the likelihood of observing the action of previous decision-maker depends on the state. I show that when observing the action is more likely in the low state, the individual faces an inference problem: does she observe many actions because the state is high and previous decision-makers had private information about this or because the state is low and previous actions are more visible. In this situation, learning is confounded (Smith and Sorensen, 2011).