Identification and Estimation of a Semiparametric Logit Model using Network Data

This paper studies identification and estimation in semiparametric binary choice models when social networks are endogenous. In many applications, unobserved individual traits shape both the outcome of interest and the formation of social ties, so standard logit specifications, including those augmented with common network controls, can be biased. I show how network data can be used to address this endogeneity without imposing parametric structure on the link formation process. The key insight is that agents who are observationally equivalent in their network formation behavior share the same latent social influence, even if the underlying individual traits remain unobserved. Exploiting this equivalence, I establish point identification of the slope parameters in a binary response model by comparing matched pairs of agents with identical network types. I propose feasible estimators based on nonparametric matching using codegree information derived from the adjacency matrix and establish their consistency and asymptotic normality. Monte Carlo simulations demonstrate that the proposed estimator performs well in finite samples across a range of network designs. An empirical application to microfinance adoption in rural Indian villages illustrates how the method can be implemented in a canonical network dataset and shows that accounting for endogenous network formation affects estimated covariate effects, both with and without village fixed effects.