Shapley Instruments

Abstract

When multiple valid instrumental variables are available, researchers must decide which instruments to include in their model to achieve optimal finite sample performance. We propose a novel instrument selection method based on the Shapley value. Our approach is examined under two different settings.

In the first, there are many potentially weak instruments, and the goal is to select a subset that meets certain regularity conditions. In the second, we consider a heterogeneous treatment effect model and estimation of the Combined Compliers Local Average Treatment Effect (CC-LATE), where adding instruments entails a trade-off between improving precision and increasing the size of the Combined Compliers share.

Preliminary simulation results demonstrate that our Shapley-based instrument selection method performs well in the many-weak-instruments setting.