q F − 1 0 ( q ) F − 1 1 ( q ) F − 1 Δ ( q ) . 25 True − . 85 . 40 . 48 Worst [ − 1 . 70 , − . 85] [ − . 20 , . 90] [0 , 3 . 15] NSM [ − . 95 , − . 85] [ − . 20 , . 60] [0 , 2 . 60] MTR [ − 1 . 70 , − . 85] [0 , . 60] [0 , 3 . 05] NSM+MTR [ − . 95 , − . 85] [0 , . 60] [0 , 2 . 40] . 5 True 0 1 . 65 1 . 30 Worst [ − . 45 , . 05] [0 , 2 . 30] [0 , 5 . 50] NSM [ − . 15 . 05] [1 . 40 , 1 . 80] [0 , 4 . 20] MTR [ − . 45 , . 05] [1 . 40 , 1 . 80] [0 , 5 . 50] NSM+MTR [ − . 15 , . 05] [1 . 40 , 1 . 80] [0 , 4 . 20] . 75 True . 85 3 . 15 2 . 70 Worst [ . 40 , 1 . 20] [2 . 95 , 4 . 95] [ . 25 , ∞ ) NSM [ . 60 , 1 . 20] [2 . 95 , 3 . 30] [ . 25 , 7 . 40] MTR [ . 40 , 1 . 05] [2 . 95 , 3 . 30] [ . 25 , ∞ ) NSM+MTR [ . 60 , 1 . 05] [2 . 95 , 3 . 30] [ . 25 , 7 . 40] Table 1: True quantiles and bounds on the quantiles of Y$_{0}$ and Y$_{1}$ outcomes. I did not rely on rank similarity and the full support of IV, and furthermore I avoided strong distributional assumptions including a single factor structure, which contrasts with most of related work. The proposed bounds take the form of intersection bounds and lend themselves to existing inference methods developed in ? . 30