Estimating Spillover Effects in the Presence of Isolated Nodes

TL;DR

This paper investigates the bias introduced when estimating spillover effects in networks with isolated nodes, highlighting issues with common practices and providing theoretical and simulation evidence.

Contribution

It reveals the bias caused by imputing zero for isolated nodes in spillover regressions and offers causal interpretations of the coefficients.

Findings

Imputing zero for isolated nodes introduces bias.

Theoretical derivations demonstrate the bias.

Simulations confirm the impact of the bias.

Abstract

In estimating spillover effects under network interference, practitioners often use linear regression with either the number or fraction of treated neighbors as regressors. An often overlooked fact is that the latter is undefined for units without neighbors (``isolated nodes"). The common practice is to impute this fraction as zero for isolated nodes. This paper shows that such practice introduces bias through theoretical derivations and simulations. Causal interpretations of the commonly used spillover regression coefficients are also provided.