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Spillover Effects in the Presence of Unobserved Networks

Published online by Cambridge University Press:  18 November 2020

Naoki Egami*
Department of Political Science, Columbia University, New York, NY10027, USA. Email:, URL:
Corresponding author Naoki Egami


When experimental subjects can interact with each other, the outcome of one individual may be affected by the treatment status of others. In many social science experiments, such spillover effects may occur through multiple networks, for example, through both online and offline face-to-face networks in a Twitter experiment. Thus, to understand how people use different networks, it is essential to estimate the spillover effect in each specific network separately. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers observe all relevant networks. We show that, unlike conventional omitted variable bias, bias due to unobserved networks remains even when treatment assignment is randomized and when unobserved networks and a network of interest are independently generated. We then develop parametric and nonparametric sensitivity analysis methods, with which researchers can assess the potential influence of unobserved networks on causal findings. We illustrate the proposed methods with a simulation study based on a real-world Twitter network and an empirical application based on a network field experiment in China.

© The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Edited by Betsy Sinclair


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