I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify or fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of this matrix characterize all of the identifiable information about individual linking behavior. In the paper, I first describe the model and formalize this intuition . I then introduce estimators for the parameters of the regression model and characterize their large sample properties .
I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of the squared adjacency matrix characterize all of the identifiable information about individual linking behavior. In this paper, I describe the model , formalize this intuition , and provide consistent estimators for the parameters of the regression model . Large sample approximations suitable for inference, potential extensions to the framework, simulation evidence, and an application to network peer effects can be found in an online appendix .
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