is different from theirs: I use this condition to bound the counterfactual marginal distributions for the whole population, while they use this condition to identify a particular structure in the outcome equation for individuals who change their selection by variation in IV. Another type of restriction that I discuss is conditional positive quadrant dependence (CPQD) for the dependence between ε$_{0}$ and ε$_{1}$ conditional on U . CPQD means that ε$_{0}$ and ε$_{1}$ are positively dependent conditionally on U . Finally, I consider monotone treatment response (MTR) P ( Y$_{1}$ ≥ Y$_{0}$ ) = 1, which assumes that each individual benefits from the treatment. Unlike other two restrictions, MTR restricts the support of potential outcomes. Interesting conclusions emerge from the results of this paper. First, NSM has identifying power on the marginal distributions only. CPQD improves the bounds on the joint distribution only. On the other hand, MTR yields substantially tighter identification regions for all three distributional parameters. In the next section, I give a formal description of my problem, define the parameters of interest, and discuss assumptions considered for the identification. In Section 3, I establish sharp bounds on the distributional parameters. Section 4 discusses testable implications and considers bounds when some of the restrictions are jointly imposed. Section 5 provides numerical examples to illustrate the identifying power of each restriction and Section 6 concludes. Technical proofs are collected in Appendix. Consider the triangular system: where Y is an observed scalar outcome, D is a binary indicator for treatment participation, ε$_{D}$ is a scalar unobservable in the outcome equation , and U is a scalar unobservable in a selection variable. However, his setting does not allow for the binary selection. 5 Y = m ( D, ε$_{D}$ ) , (1) D = 1 [ p ( Z ) ≥ U ] , 2 Basic Model and Assumptions 2.1 Model