Linear Social Interactions Models

Abstract

This paper provides a systematic analysis of identification in linear social interactions models. This is both a theoretical and an econometric exercise as the analysis is linked to a rigorously delineated model of interdependent decisions. We develop an incomplete information game that describes individual choices in the presence of social interactions. The equilibrium strategy profiles are linear. Standard models in the empirical social interactions literature are shown to be exact or approximate special cases of our general framework, which in turn provides a basis for understanding the microeconomic foundations of those models. We consider identification of both endogenous (peer) and contextual social effects under alternative assumptions on a priori information about network structure available to an analyst, and contrast the informational content of individual-level and aggregated data. Finally, we discuss potential ramifications for identification of endogenous group selection and differences between the information sets of analysts and agents.

Conformism and Self-Selection in Social Networks

“…This contrasts with part of the literature on social interactions (e.g. Blume et al (2011)). In an economy where individuals are not ex-ante connected in a network, it seems unlikely that all of the individuals' characteristics are common knowledge.…”

“…The identification of β, σ ε and λ, given G, follows from standard results for linear models (see Blume et al (2011) or Lee et al (2010)). …”

The Economic Consequences of Social Network Structure

“…Although the reflection problem was an important issue in the early peer-effects literature, since it prompted researchers to think carefully about model specification and identification, it has since become clear that it applies mostly to a sort of simple reduced-form model, and is not an issue in many other micro-founded models. For instance, as emphasized by Blume, Brock, Durlauf, and Ioannides (2011) and Blume, Brock, Durlauf, and Jayaraman (2015), the reflection problem is functional form dependent -not applying to many nonlinear models, and being even nongeneric in linear models. An additional, complemetary, insight is that network information, rather than only group-level information, can enable identification, as then the full feedback patterns pointed out by Manski (1993) can be disentangled by taking advantage of the fact that different individuals have different sets of peers, and therefore different exposures and net effects, as shown by Bramoullé, Djebbari, and Fortin (2009).…”

Econometrics of network models

“…Finally, I should also point out that this special structure delivers a direct dependence of the outcome variable y on the KatzBonacich centrality index for each individual atβ, listed in the vector (I −βW ) −1β W 1 if the "peer effect" effort depends on the degree of the individual (i.e., α = 0). Blume, Brock, Durlauf, and Jayaraman (2015) focus their analysis on a different payoff structure corresponding to a narrative where individuals have preference for conformity. As they point out, the models are observationally equivalent.…”

“…One way in which that condition is satisfied is if W is block-diagonal with at least two blocks of different order. Suppose, for example, that the social network is comprised of two complete subgraphs of size N 1 and N 2 such that 14 Exogenous covariates x l and (observed) contextual effects on those can be accomodated (see Blume, Brock, Durlauf, and Jayaraman (2015)), but are ommitted as in Graham (2008).…”