Before revision:  I give a set of relaxed assumptions \tilde{A} that can never be rejected and always preserve the identified set of local average treatment effect (LATE ).
After revision:  I apply my methodology to the instrument monotonicity assumption in Local Average Treatment Effect (LATE) estimation and to the sector selection assumption in a binary outcome Roy model of employment sector choice. In the LATE application, I use my general method to construct a set of relaxed assumptions \tilde{A} that can never be rejected and always preserve the identified set of local average treatment effect (LATE ).