This paper proposes a new set of testable implications of the instrumen- tal variable (IV) independence assumption: generalized instrumental inequalities. In our leading case with a binary outcome, we show that the generalized instrumen- tal inequalities are necessary and sufficient to detect all observable violations of the IV independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and intersection bounds inferential methods. This idea allows one to easily implement the test using the Stata package of Chernozhukov, Kim, Lee, and Rosen (2015).We apply our pro- posed strategy to assess the validity of the IV independence assumption for various instruments used in the returns to college literature.