Revealed Social Networks

The linear-in-means model is the standard empirical model of peer effects. Using choice data and exogenous group variation, we first develop a revealed preference style test for the linear-in-means model. This test is formulated as a linear program and can be interpreted as a no money pump condition with an additional incentive compatibility constraint. We then study the identification properties of the linear-in-means model. A key takeaway from our analysis is that there is a close relationship between the dimension of the outcome variable and the identifiability of the model. Importantly, when the outcome variable is one-dimensional, failures of identification are generic. On the other hand, when the outcome variable is multi-dimensional, we provide natural conditions under which identification is generic.