  This paper studies treatment effect models in which individuals are
classified into unobserved groups based on heterogeneous treatment rules. Using
a finite mixture approach, we propose a marginal treatment effect (MTE)
framework in which the treatment choice and outcome equations can be
heterogeneous across groups. Under the availability of instrumental variables
specific to each group, we show that the MTE for each group can be separately
identified. Based on our identification result, we propose a two-step
semiparametric procedure for estimating the group-wise MTE. We illustrate the
usefulness of the proposed method with an application to economic returns to
college education.
