  Interference arises when an individual's potential outcome depends on the
individual treatment level, but also on the treatment level of others. A common
assumption in the causal inference literature in the presence of interference
is partial interference, implying that the population can be partitioned in
clusters of individuals whose potential outcomes only depend on the treatment
of units within the same cluster. Previous literature has defined average
potential outcomes under counterfactual scenarios where treatments are randomly
allocated to units within a cluster. However, within clusters there may be
units that are more or less likely to receive treatment based on covariates or
neighbors' treatment. We define new estimands that describe average potential
outcomes for realistic counterfactual treatment allocation programs, extending
existing estimands to take into consideration the units' covariates and
dependence between units' treatment assignment. We further propose entirely new
estimands for population-level interventions over the collection of clusters,
which correspond in the motivating setting to regulations at the federal (vs.
cluster or regional) level. We discuss these estimands, propose unbiased
estimators and derive asymptotic results as the number of clusters grows.
Finally, we estimate effects in a comparative effectiveness study of power
plant emission reduction technologies on ambient ozone pollution.
