Figure 1: Makarov bounds Y$_{1}$ attains its upper bound, the improved lower bound on F ( y$_{0}$, y$_{1}$ ) does not affect the lower bound on the DTE. Similarly, the Makarov upper bound is obtained from the upper bound on 1 − P ( Y$_{0}$ ≤ y ′ − δ, Y$_{1}$ ≥ y $^{′}$) for y ′ ∈$_{R}$ , which is in turn obtained from the Fr´echet-Hoeffding lower bound on P ( Y$_{0}$ ≤ y ′ − δ, Y$_{1}$ ≥ y $^{′}$) . Therefore by the same token, the improved lower bound on F ( y$_{0}$, y$_{1}$ ) does not affect the upper bound on the DTE either. The specific forms of sharp bounds on marginal distributions of Y$_{0}$ and Y$_{1}$, their joint dis- tribution, and the DTE under M. 1 − M. 5 and CPQD are provided in Theorem 2 in Appendix. In this subsection, I maintain M. 1 − M. 4 on the model (1) and additionally impose MTR, which is written as P ( Y$_{1}$ ≥ Y$_{0}$ ) = 1. As illustrated in Figure 2, MTR is a restriction imposed on the support of ( Y$_{0}$, Y$_{1}$ ), while NSM and CPQD directly restrict the sign of dependence between unobservables. I show that MTR has substantial identifying power for the marginal distributions, the joint distribution, and the DTE. Start with bounds on marginal distributions. Remember that NSM as well as M. 1 − M. 4 has no additional identifying power for the upper bound on P$_{1}$ ( y, 0 | z ) and the lower bound on P$_{0}$ ( y, 1 | z ). Interestingly, MTR improves both the upper bound on P$_{1}$ ( y, 0 | z ) and the lower bound on P$_{0}$ ( y, 1 | z ) . On the other hand, unlike NSM, MTR does not have any identifying power on the 19 3.4 Monotone Treatment Response