Unbiased Estimation and Sensitivity Analysis for Network-Specific Spillover Effects: Application to An Online Network Experiment

Online network experiments have become widely-used methods to estimate spillover effects and study online social influence. In such experiments, the spillover effects often arise not only through an online network of interest but also through a face-to-face network. Social scientists are therefore often interested in measuring the importance of online human interactions by estimating the spillover effects specific to the online network, separately from spillover effects attributable to the offline network. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers observe all relevant networks; they cannot observe the offline network in many applications. In this paper, we derive an exact expression of bias due to unobserved networks. Unlike the conventional omitted variable bias, this bias for the network-specific spillover effect remains even when treatment assignment is randomized and when unobserved networks and the network of interest are independently generated. By incorporating this bias into the estimation, we also develop parametric and nonparametric sensitivity analysis methods, with which researchers can examine the robustness of empirical findings to the possible existence of unmeasured networks. We analyze a political mobilization experiment on the Twitter network and find that an estimate of the Twitter-specific spillover effect is sensitive to assumptions about an unobserved face-to-face network.