Generalized Instrumental Inequalities: Testing the IV Independence Assumption

Abstract

This paper proposes a new set of testable implications of the instrumental variable (IV) independence assumption: generalized instrumental inequalities. In our leading case of binary outcome, we show that the generalized instrumental 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 packages of Chernozhukov, Kim, Lee, and Rosen (2015). We apply our proposed strategy to assess the validity of the IV independence assumption for various instruments used in the return to college literature.

Keywords: Instrumental variable, Independence assumption, Sharp inequalities, Intersection bounds, Quarter of birth

JEL Classification: C12, C15, C21, C24