Random Assignment with Nonrandom Peers: A Structural Approach to Counterfactual Treatment Assessment

Abstract

Efforts to leverage peer effects by changing assignment have often fallen short due to endogenous peer choice. To address this, I build a two-part model: agents form networks via continuous linking decisions; conditional on realized networks, outcomes are determined. I provide results on identification of both parts of the model. Using data from a randomized study in India, I estimate the model, assess its performance in out-of-sample prediction, and simulate outcomes under preferential assignment rules. This paper contributes new methodology for identifying effects of alternative assignments in the presence of network endogeneity, as well as identification of network formation models.

A model of weighted network formation

“…First, note that in both reciprocal and nonreciprocal equilibria, two agents' investments in the link between them are predicted to be positively correlated. Griffith (2017) finds support for this property in his analysis of a weighted social network among school girls. He shows that the weights assigned by two girls to their relationship are positively (though not perfectly) correlated.…”

“…The most closely related articles are Salonen (2015), Griffith (2017), and Brueckner (2006), which analyze the formation of weighted social networks, and Goyal et al (2008), which analyzes a two‐stage game in which firms first form weighted links in research and development (R&D) networks and then compete in a market. These authors focus on symmetric equilibria.…”

A continuous model of strong and weak ties

“…Proposition 2 is an important result that may have empirical implications, which a companion paper (Griffith, 2022) explores further. With DRS, we can rationalize any set of binary links.…”

“…In this sense, the model here shares the goals of Graham (2017), which seeks to develop a tractable model to rationalize common features of network data, in contrast to the bulk of the theory literature that seeks to make sharp predictions on the types of networks that arise in equilibrium. A companion paper demonstrates the usefulness of the DRS case in empirical work accounting for endogenous network formation (Griffith, 2022).…”