under NSM, for any ̂ p ( z ) ∈ ( p ( z ) , 1] , Since P $^{{}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) | p ( z ) < U ≤ ̂ p ( z ) $^{}}$is nondecreasing in ̂ p ( z ) by NSM, for z ∈ Z \ p − $^{1}$( p ) , the highest possible observable lower bound is obtained when ̂ p ( z ) = p . Therefore by NSM, for any z ∈ Z \ p − $^{1}$( p ) , NSM implies Obviously, P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) , U ≤ p ) and P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) , U ≤ p ( z ) ) are point-identified as lim p ( z ) → p P ( y, 1 | z ) and P ( y, 1 | z ) for any z ∈ Z . Similarly, P$_{0}$ ( y | 1 , z ) = P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) | U ≤ p ( z ) ) and by NSM, for any z ∈ Z \ p − 1 $^{(}$p) Also, P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) , p < U $^{)}$and P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) , p ( z ) < U $^{)}$are point-identified as lim p ( z ) → p P ( y, 0 | z ) and P ( y, 0 | z ), respectively, for any z ∈ Z . These bounds are tighter than bounds obtained without NSM. On the other hand, NSM has no additional identifying power on the upper bound on P$_{1}$ ( y | 0 , z ) and the lower bound on P$_{0}$ ( y | 1 , z ) , which means that these bounds under NSM are identical to those obtained without NSM . P $^{{}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) | p ( z ) < U } ≥ P $^{{}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) | p ( z ) < U ≤ ̂ p ( z ) $^{}}$. P$_{1}$ ( y | 0 , z ) = P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) | p ( z ) < U ) ≥ P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) | p ( z ) < U ≤ p ) = P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) , U ≤ p ) − P $^{(}$ε$_{1}$ ≤ m − $^{1}$(1 , y ) , U ≤ p ( z ) ) p − p ( z ) . P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) | U ≤ p ( z ) ≤ P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) | p < U ≤ p ( z ) ) = P $^{(}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) , p < U ) − P $^{{}$ε$_{0}$ ≤ m − $^{1}$(0 , y ) , p ( z ) < U } p ( z ) − p . 15