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:  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 . I illustrate my findings in an application to causal effects of college education using the college proximity instrument. The benchmark estimates suggest that college attendance yields earnings gains of about 60 log points, which is well outside the range of estimates in the recent literature. I demonstrate that this result is driven by the existence of defiers and the presence of negative weights. Corrected estimates indicate that attending college causes earnings to be roughly 20\% higher .