Before revision:  Even if monotonicity holds unconditionally , the IV estimand  is not interpretable as the unconditional LATE parameter unless the groups with different values of the instrument are roughly equal sized  .
After revision:  The problem of negative weights disappears in the overidentified specification of Angrist and Imbens (1995) and in an alternative method, termed "reordered IV," that I also develop. Even if all weights are positive , the IV estimand is not interpretable as the unconditional LATE parameter unless the groups with different values of the instrument are roughly equal sized .