Methods to identify linear network models: a review

Abstract

In many contexts we may be interested in understanding whether direct connections between agents, such as declared friendships in a classroom or family links in a rural village, affect their outcomes. In this paper, we review the literature studying econometric methods for the analysis of linear models of social effects, a class that includes the ‘linear-in-means’ local average model, the local aggregate model, and models where network statistics affect outcomes. We provide an overview of the underlying theoretical models, before discussing conditions for identification using observational and experimental/quasi-experimental data.

Causal network effect models

“…That is, one-by-one, I introduce the issue and then review proposed solutions to the problem. I focus on causally identifying regression coefficients and disregard the largely unresolved problem of correcting standard errors for network dependence (Advani and Malde 2018b;Lee and Ogburn 2020). I also omit a growing literature on the nonparametric identification of network effects (Egami 2020;Ogburn et al 2017;Ogburn, Shpitser, and Lee 2020;Zeleneev 2020).…”

Partial identification of nonlinear peer effects models with missing data

“…In models of social interactions, the individual behavior depends both on individual characteristics and on aggregate characteristics of members of the group of which the agent is a member (Advani & Malde, 2018), integrating sociological concepts and economic thinking (Blume et al 2010). Important applications of peer effects models have been developed for education (Sacerdote, 2001, Cipollone & Rosolia, 2007, Lalive & Cattaneo, 2009, Sojourner, 2013, Ammermueller & Pischke, 2009, Madeira, 2018, health behaviors (Bruhin et al, 2020, Bailey et al, 2021, employment (Roth, 2020) or migration (Slotwinski et al, 2019).…”

“…In the linear case, Manski (1993Manski ( , 2000 showed that it is difficult to distinguish between the effects of endogenous social interactions and the impact of measures of exogenous group quality. Several works analyze identification of peer effects in the linear case (Advani & Malde, 2018, Sojourner, 2013, Ammermueller & Pischke, 2009. These works analyze partial and point identification of the linear peer effects model with missing data on outcomes.…”

Conformism, Social Norms and the Dynamics of Assimilation

“…See,Boucher and Fortin (2016),Chandrasekhar (2016),Advani and Malde (2018) for overviews of this literature.…”