  We provide sufficient conditions for the identification of the heterogeneous
treatment effects, defined as the conditional expectation for the differences
of potential outcomes given the untreated outcome, under the nonignorable
treatment condition and availability of the information on the marginal
distribution of the untreated outcome. These functions are useful both to
identify the average treatment effects (ATE) and to determine the treatment
assignment policy. The identification holds in the following two general setups
prevalent in applied studies: (i) a randomized controlled trial with one-sided
noncompliance and (ii) an observational study with nonignorable assignment with
the information on the marginal distribution of the untreated outcome or its
sample moments. To handle the setup with many integrals and missing values, we
propose a (quasi-)Bayesian estimation method for HTE and ATE and examine its
properties through simulation studies. We also apply the proposed method to the
dataset obtained by the National Job Training Partnership Act Study.
