Identification and Estimation of a Semiparametric Logit Model using Network Data

TL;DR

This paper develops a method to identify and estimate semiparametric logit models with endogenous social networks, using network data to correct bias without fully specifying the network formation process.

Contribution

It introduces a novel identification strategy leveraging network similarity for semiparametric models with endogenous networks, along with consistent estimators and empirical validation.

Findings

Network data can correct endogeneity bias in social network models.

Proposed estimators are consistent and asymptotically normal.

Accounting for endogenous networks significantly alters covariate effect estimates.

Abstract

This paper studies identification and estimation in semiparametric logit 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 a parametric structure on the link formation process. Although the outcome equation is semiparametric in this social component and the network formation process is left unspecified, the logistic distribution assumption is crucial for identification. I show that slope parameters are point identified by pairwise comparisons of agents who share identical network formation behavior. I propose feasible estimators based on matching agents using network similarity measures and establish their consistency and asymptotic normality. 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.