Identification and Estimation of a Semiparametric Logit Model using Network Data

Abstract

This paper studies identification and estimation of a semiparametric logit model in which an unobserved individual characteristic affects both a binary outcome and the formation of social links. In this setting, the endogeneity of the network is informative rather than a nuisance: because the same latent trait drives linking behavior, observed network data can be used to control for unobserved heterogeneity in the outcome equation without imposing a parametric model of link formation. Slope parameters are point identified by a conditional likelihood argument applied to pairs of agents with identical network formation behavior. I propose a kernel-weighted conditional logit estimator that matches agents using codegree distances and establish its consistency. I then derive two asymptotic normality results: an exact root-$n$ result when network types have finite support, and a general result centered at a pseudo-true value whose bias I characterize and remove with a jackknife bias correction. Variance estimators that account for matching on estimated network distances are provided. Monte Carlo simulations demonstrate good finite-sample performance, and an empirical application to microfinance adoption demonstrates that accounting for endogenous network formation materially affects estimated covariate effects.