# Heterogeneous Endogenous Effects in Networks

## TL;DR

This paper introduces a new method to identify influential leaders in networks by allowing for individual-specific effects, overcoming limitations of traditional centrality measures, and provides consistent estimation and inference procedures validated through simulations and real data.

## Contribution

Develops a novel two-stage LASSO approach for identifying influential individuals with heterogeneous effects in networks, extending to multiple connection types and providing robust inference.

## Key findings

- Estimator shows good finite sample performance in simulations.
- Method successfully identifies leaders and influential networks in real data.
- Extends analysis to multiple network types with sparse group LASSO.

## Abstract

This paper proposes a new method to identify leaders and followers in a network. Prior works use spatial autoregression models (SARs) which implicitly assume that each individual in the network has the same peer effects on others. Mechanically, they conclude the key player in the network to be the one with the highest centrality. However, when some individuals are more influential than others, centrality may fail to be a good measure. I develop a model that allows for individual-specific endogenous effects and propose a two-stage LASSO procedure to identify influential individuals in a network. Under an assumption of sparsity: only a subset of individuals (which can increase with sample size n) is influential, I show that my 2SLSS estimator for individual-specific endogenous effects is consistent and achieves asymptotic normality. I also develop robust inference including uniformly valid confidence intervals. These results also carry through to scenarios where the influential individuals are not sparse. I extend the analysis to allow for multiple types of connections (multiple networks), and I show how to use the sparse group LASSO to detect which of the multiple connection types is more influential. Simulation evidence shows that my estimator has good finite sample performance. I further apply my method to the data in Banerjee et al. (2013) and my proposed procedure is able to identify leaders and effective networks.