Social Interactions Models with Latent Structures

TL;DR

This paper introduces a novel estimation method for heterogeneous social interaction models with latent group structures, utilizing classifier-Lasso for clustering and a bootstrap approach for bias correction, validated through simulations and real data.

Contribution

It adapts the classifier-Lasso algorithm for discovering latent structures and proposes a bootstrap method to address bias in binary social interaction models.

Findings

Successfully detects latent clusters in social interaction data

Identifies significant peer effects within specific clusters

Demonstrates practical applicability in real-world behavioral data

Abstract

This paper studies estimation and inference of heterogeneous peer effects featuring group fixed effects and slope heterogeneity under latent structure. We adapt the Classifier-Lasso algorithm to consistently discover latent structures and determine the number of clusters. To solve the incidental parameter problem in the binary choice model with social interactions, we propose a parametric bootstrap method to debias and establish its asymptotic validity. Monte Carlo simulations confirm strong finite sample performance of our methods. In an application to students' risky behaviors, the algorithm detects two latent clusters and finds that peer effects are significant within one of the clusters, demonstrating the practical applicability in uncovering heterogeneous social interactions.