The instrumental variable method relies on a strong "no-defiers" condition, which
requires that the instrument affect every subject's treatment decision in the same
direction. This paper shows that "no-defiers" can be replaced by a weaker "compliers-
defiers" condition, which requires that a subgroup of compliers have the same size and
the same distribution of potential outcomes as defiers. This condition is necessary and
sufficient for IV to capture causal effects for the remaining part of compliers. In many
applications, "compliers-defiers" is a very weak condition. For instance, in Angrist &
Evans (1998), 94% of DGPs compatible with the data satisfy "compliers-defiers", while
0% satisfy "no-defiers"
