Estimating spillover effects in the presence of isolated nodes

In estimating spillover effects under network interference, practitioners often use linear regression with either the number or fraction of treated neighbours as regressors. An often overlooked fact is that the latter is undefined for units without neighbours (‘isolated nodes’). The common practice is to impute the fraction of treated neighbours 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.