Never-taker ($(D(0),D(1))=(0,0)$)

A never-taker is a unit whose potential treatment receipts are $D(0)=D(1)=0$: it receives no treatment under either value of a binary assignment or encouragement $Z$. This is the $(0,0)$ principal stratum, defined before observing which assignment actually occurs.

For example, a unit may decline participation whether or not it receives an invitation. Among units with observed $Z=0,D=0$, never-takers are mixed with compliers, so a single observation does not reveal the principal stratum. Under an exclusion restriction through treatment receipt, assignment has no outcome effect on a never-taker because receipt stays fixed; that is an additional causal assumption, not part of the definition.^[ref]