Revealed Social Networks

TL;DR

This paper develops a revealed preference test for the linear-in-means peer effects model using choice data, and analyzes the conditions under which the model is identifiable depending on the outcome dimension.

Contribution

It introduces a new test for the linear-in-means model based on choice data and explores the model's identification properties relative to outcome dimensionality.

Findings

The test is formulated as a linear program with an incentive compatibility constraint.

Identification is generally possible when the outcome is multi-dimensional.

Failures of identification are common when the outcome is one-dimensional.

Abstract

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.