Sharp Instrumental Inequalities: Testing 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 sucient to detect all observable violations of the IV independence assumption. We propose a simple strategy to test the generalized instrumental inequalities, exploiting the intersection bounds framework. The test can therefore be easily implemented using Stata packages of Chernozhukov, Kim, Lee, and Rosen (2015) or Andrews, Kim and Shi (2016). We apply our proposed strategy to assess the validity of the IV independence assumption for the quarter of birth instrument used in Angrist and Krueger (1991).