Endogenous Interference in Randomized Experiments

TL;DR

This paper develops methods to identify and estimate treatment effects in social network experiments, accounting for endogenous network formation and changes induced by interventions, using IV and eigendecomposition techniques.

Contribution

It introduces a framework for distinguishing direct and indirect treatment effects in networks, and proposes estimators that handle endogeneity and network density issues.

Findings

Establishes consistency and asymptotic normality of OLS estimators without endogeneity.

Proposes shift-share IV estimators for sparse networks with endogeneity.

Introduces a denoised eigendecomposition estimator for dense networks.

Abstract

This paper investigates the identification and inference of treatment effects in randomized controlled trials with social interactions. Two key network features characterize the setting and introduce endogeneity: (1) latent variables may affect both network formation and outcomes, and (2) the intervention may alter network structure, mediating treatment effects. I make three contributions. First, I define parameters within a post-treatment network framework, distinguishing direct effects of treatment from indirect effects mediated through changes in network structure. I provide a causal interpretation of the coefficients in a linear outcome model. For estimation and inference, I focus on a specific form of peer effects, represented by the fraction of treated friends. Second, in the absence of endogeneity, I establish the consistency and asymptotic normality of ordinary least squares estimators. Third, if endogeneity is present, I propose addressing it through shift-share instrumental variables, demonstrating the consistency and asymptotic normality of instrumental variable estimators in relatively sparse networks. For denser networks, I propose a denoised estimator based on eigendecomposition to restore consistency. Finally, I revisit Prina (2015) as an empirical illustration, demonstrating that treatment can influence outcomes both directly and through network structure changes.