Before revision:  Then, we consider two strategies to build confidence intervals on the AME. In the first, we estimate the sharp bounds with a semiparametric two-step estimator involving a first-step nonparametric estimator. We derive the asymptotic distributions of these bounds under, mostly, a restriction on the cardinality of the support of the unobserved heterogeneity.
After revision:  Then, we consider two strategies to build confidence intervals on the AME. In the first, we estimate the sharp bounds with a semiparametric two-step estimator .