We address a gap in the literature on causal inference in connected populations: while there is a growing body of work on estimating causal effects in connected populations, little is known about how contagion and other network processes impact causal effects and inference. Contagion and other network processes imply that the outcomes of units affect the outcomes of other units, which enables the effects of interventions to propagate throughout connected populations and complicates insight into causal effects and inference. We offer novel insight into how contagion and other network processes impact causal effects and inference based on closed-form expressions for causal effects under spillover and contagion. These closed-form expressions reveal that the main effects of interventions, spillover, and contagion are intertwined even in the simplest possible settings, and that contagion can decrease or increase causal effects. We discuss statistical implications, including asymptotic bias of model-based estimators ignoring contagion, the violation of neighborhood exposure assumptions by unrestricted contagion and its effect on design-based estimators, and possible remedies.

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