  Synthetic control (SC) models are widely used to estimate causal effects in
settings with observational time-series data. To identify the causal effect on
a target unit, SC requires the existence of correlated units that are not
impacted by the intervention. Given one of these potential donor units, how can
we decide whether it is in fact a valid donor - that is, one not subject to
spillover effects from the intervention? Such a decision typically requires
appealing to strong a priori domain knowledge specifying the units, which
becomes infeasible in situations with large pools of potential donors. In this
paper, we introduce a practical, theoretically-grounded donor selection
procedure, aiming to weaken this domain knowledge requirement. Our main result
is a Theorem that yields the assumptions required to identify donor values at
post-intervention time points using only pre-intervention data. We show how
this Theorem - and the assumptions underpinning it - can be turned into a
practical method for detecting potential spillover effects and excluding
invalid donors when constructing SCs. Importantly, we employ sensitivity
analysis to formally bound the bias in our SC causal estimate in situations
where an excluded donor was indeed valid, or where a selected donor was
invalid. Using ideas from the proximal causal inference and instrumental
variables literature, we show that the excluded donors can nevertheless be
leveraged to further debias causal effect estimates. Finally, we illustrate our
donor selection procedure on both simulated and real-world datasets.
