I will discuss a general class of testable implications for the instrumental variable models when the treatment is discrete, but the outcome and instruments are unrestricted: generalized instrumental inequalities (GIV). This class generalized the Pearl instrumental inequalities. I will discuss the complexity of proving the sharpness of the GIV when the support of the outcome is large. Discuss the importance of sharpness results for a correct interpretation of the bounds on the average causal effect under the IV model.

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