  I study partial identification of distributional parameters in triangular
systems. This model consists of a nonparametric outcome equation and a
selection equation. This allows for general unobserved heterogeneity and
selection on unobservables. The distributional parameters considered in this
paper are the marginal distributions of potential outcomes, their joint
distribution, and the distribution of treatment effects. I investigate how
different types of plausible restrictions contribute to identifying these
parameters. The restrictions I consider include stochastic dominance and
quadrant dependence between unobservables and monotonicity between potential
outcomes. My identification applies to the whole population without a full
support condition on instrumental variables and does not rely on rank
similarity. I also provide numerical examples to illustrate the identification
power of each assumption.
