  In the context of a binary outcome, treatment, and instrument, Balke and
Pearl (1993, 1997) establish that adding monotonicity to the instrument
exogeneity assumption does not decrease the identified sets for average
potential outcomes and average treatment effect parameters when those
assumptions are consistent with the distribution of the observable data. We
show that the same results hold in the broader context of multi-valued outcome,
treatment, and instrument. An important example of such a setting is a
multi-arm randomized controlled trial with noncompliance.
