Abstract: We extend the continuity-based framework to Regression Discontinuity Designs (RDDs) to identify and estimate causal effects in the presence of interference when units are connected through a network. In this setting, assignment to an “effective treatment”, which comprises the individual treatment and a summary of the treatment of interfering units (e.g., friends, classmates), is determined by the unit’s score and the scores of other interfering units, leading to a multiscore RDD with potentially complex, multidimensional boundaries.

We characterize these boundaries and derive a set of assumptions to identify the proposed causal estimands, i.e., point and boundary causal effects.

Additionally, we develop a distance-based nonparametric estimator, derive its asymptotic properties under restrictions on the network degree distribution, and introduce a novel variance estimator that accounts for network correlation.

Finally, we apply our methodology to the PROGRESA/Oportunidades dataset to estimate the direct and indirect effects of receiving cash transfers on children’s school attendance.