  We develop a method to learn about treatment effects in multiple treatment
models with discrete-valued instruments. We allow selection into treatment to
be governed by a general class of threshold crossing models that permits
multidimensional unobserved heterogeneity. Under a semi-parametric restriction
on the distribution of unobserved heterogeneity, we show how a sequence of
linear programs can be used to compute sharp bounds for a number of treatment
effect parameters when the marginal treatment response functions underlying
them remain nonparametric or are additionally parameterized.
