Identification and Estimation of a Partially Linear Regression Model Using Network Data

Author:

Auerbach Eric1

Affiliation:

1. Department of Economics, Northwestern University

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.

Publisher

The Econometric Society

Subject

Economics and Econometrics

Reference21 articles.

1. Semiparametric estimation of censored selection models with a nonparametric selection mechanism

2. Arduini, T., E. Patacchini, and E. Rainone (2015): “Parametric and Semiparametric iv Estimation of Network Models With Selectivity,” Technical report, Einaudi Institute for Economics and Finance (EIEF).

3. Auerbach, E. (2021): “Identification and Estimation of a Partially Linear Regression Model Using Network Data: Inference and an Application to Network Peer Effects,” arXiv preprint arXiv:2105.10002.

4. Identification of peer effects through social networks

5. Peer Effects in Networks: A Survey

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