Identification and Estimation of Models with Endogenous Network Formation

This paper studies a linear model in which the regressors and errors covary with drivers of link formation in a large network. Neither the endogenous relationship between the regressors and errors nor the distribution of network links are restricted parametrically. Instead, the model is identified by variation in the regressors unexplained by the distribution of network links. I first demonstrate that 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, necessarily have a similar distribution of network links. I then propose a semiparametric estimator based on matching pairs of agents with similar columns of the squared adjacency matrix. I find sufficient conditions for the estimator to be consistent and asymptotically normal, and provide a consistent estimator for its asymptotic variance. While this paper focuses on cases in which the network is represented by a binary, symmetric, and square adjacency matrix, I also discuss extensions to weighted, directed, bipartite, multiple, sampled, and higher-order networks. Link to the online appendix here ∗Department of Economics, UC Berkeley. E-mail: [email protected]. I thank my advisors, James Powell and Bryan Graham for their advice and support. I also thank Aluma Dembo, Michael Jansson, Patrick Kline, Sheisha Kulkarni, Carl Nadler, Stephen Nei, Demian Pouzo, Mikkel Soelvsten and participants at the UC Berkeley Econometrics Seminar for helpful feedback.