1 Introduction In this paper, I consider partial identification of distributional parameters in triangular systems as follows: Here Y denotes a continuous observed outcome, D a binary selection indicator, Z instrumental variables (IV), ε$_{D}$ a scalar unobservable, and U a scalar unobservable. Let Y$_{0}$ and Y$_{1}$ denote the potential outcomes without and with some treatment, respectively, with Y$_{d}$ = m ( d, ε$_{d}$ ) for d ∈ { 0 , 1 } . Note that I suppress covariates included in the outcome equation and the selection equation to keep the notation manageable. The analysis readily extends to accoount for conditioning on these covariates. The distributional parameters that I am interested in are the marginal distributions of Y$_{0}$ and Y$_{1}$ , their joint distribution, and the distribution of treatment effects (DTE) P (Δ ≤ δ ) with the treatment effect Δ = Y$_{1}$ − Y$_{0}$ and δ ∈$_{R}$ . In the context of welfare policy evaluation, various distributional parameters beyond the average effects are often of fundamental interest. First, changes in marginal distributions of potential outcomes induced by policy are one of the main concerns when the impact on total social welfare is calculated by comparing the distributions of potential outcomes. Examples include inequality measures such as the Gini coefficient and the Lorenz curve with and without policy (e.g. ? ), and stochastic dominance tests between the distributions of potential outcomes (e.g. ? ). Second, information on the joint distribution of Y$_{0}$ and Y$_{1}$ , and the DTE beyond their marginal distributions is often required to capture individual specific heterogeneity in program evaluation. Examples of such information include the distribution of the outcome with treatment given that the potential outcome without treatment lies in a specific set P ( Y$_{1}$ ≤ y$_{1}$ | Y$_{0}$ ∈ Υ$_{0}$) for some set Υ$_{0}$ in $_{R}$, the fraction of the population that benefits from the program P ( Y$_{1}$ ≥ Y$_{0}$ ) , the fraction of the population that has gains or losses in a specific range P $^{(}$δ L ≤ Y$_{1}$ − Y$_{0}$ ≤ δ U ) for $^{(}$δ $^{L}$, δU ) ∈$_{R}$ 2 with δ L ≤ δ $^{U}$, and the q quantile of the impact distribution inf { δ : F$_{Δ}$ ( δ ) > q } . The triangular system considered in this study consists of an outcome equation and a selection 2 Y = m ( D, ε$_{D}$ ) , D = 1 [ p ( Z ) ≥ U ] .