# Identification and Estimation of a Partially Linear Regression Model using Network Data

## TL;DR

This paper introduces a novel nonparametric method for estimating a partially linear regression model with network data, leveraging the squared adjacency matrix to identify the unknown function of a latent network driver.

## Contribution

It proposes a new matching-based estimation approach that avoids specifying a parametric network formation model, using the squared adjacency matrix to capture all identifiable information.

## Key findings

- Consistent estimators for the regression parameters are developed.
- The method effectively captures latent network effects without parametric assumptions.
- Application to network peer effects demonstrates practical utility.

## Abstract

I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of the squared adjacency matrix characterize all of the identifiable information about individual linking behavior. In this paper, I describe the model, formalize this intuition, and provide consistent estimators for the parameters of the regression model. Auerbach (2021) considers inference and an application to network peer effects.