Identification and Estimation of Network Models with Nonparametric Unobserved Heterogeneity

TL;DR

This paper develops methods to identify and estimate network models with complex unobserved heterogeneity, addressing issues of bias and inconsistency caused by latent fixed effects.

Contribution

It introduces nonparametric techniques to identify and estimate network effects while controlling for unobserved heterogeneity without specifying fixed effects.

Findings

Proposes estimators with desirable large sample properties

Numerical experiments validate the effectiveness of the methods

Addresses bias issues caused by unobserved heterogeneity in networks

Abstract

Homophily based on observables is widespread in networks. Therefore, homophily based on unobservables (fixed effects) is also likely to be an important determinant of the interaction outcomes. Failing to properly account for latent homophily (and other complex forms of unobserved heterogeneity) can result in inconsistent estimators and misleading policy implications. To address this concern, we consider a network model with nonparametric unobserved heterogeneity, leaving the role of the fixed effects unspecified. We argue that the interaction outcomes can be used to identify agents with the same values of the fixed effects. The variation in the observed characteristics of such agents allows us to identify the effects of the covariates, while controlling for the fixed effects. Building on these ideas, we construct several estimators of the parameters of interest and characterize their large sample properties. Numerical experiments illustrate the usefulness of the suggested approaches and support the asymptotic theory.