  This paper studies a specific inference problem for a partially-identified
parameter of interest with an interval identified set. We consider the
favorable situation in which a researcher has two possible estimators to
construct the confidence interval proposed in Imbens and Manski (2004) and
Stoye (2009), and one is more efficient than the other. While the literature
shows that both estimators deliver asymptotically exact confidence intervals
for the parameter of interest, their inference in terms of statistical power is
not compared. One would expect that using the more efficient estimator would
result in more powerful inference. We formally prove this result.
