  This paper estimates individual treatment effects in a triangular model with
binary--valued endogenous treatments. Following the identification strategy
established in Vuong and Xu (2014), we propose a two--stage estimation
approach. First, we estimate the counterfactual outcome and hence the
individual treatment effect (ITE) for every observational unit in the sample.
Second, we estimate the density of individual treatment effects in the
population. Our estimation method does not suffer from the ill--posed inverse
problem associated with inverting a non--linear functional. Asymptotic
properties of the proposed method are established. We study its finite sample
properties in Monte Carlo experiments. We also illustrate our approach with an
empirical application assessing the effects of 401(k) retirement programs on
personal savings. Our results show that there exists a small but statistically
significant proportion of individuals who experience negative effects, although
the majority of ITEs is positive.
