Identifying instrumental variables for causal inference

Abstract

We propose a procedure for identifying instrumental variables to be used in causal analyses that can preclude the effects of unobserved confounders and reverse causality. Being based on graphical models, our novel approach employs four sequential regressions to infer the role of endogenous variables (potential cause) as colliders or complete mediators in the relationship between candidates for instruments and the explained variable (potential effect). The inclusion restriction condition is met by the fact that the instruments are, by definition, determinants of the endogenous variables while compliance with the exclusion restriction condition is deduced from the role (e.g. complete mediation) of the endogenous variables with respect to the other variables analyzed. Given an underlying data generating process, we consider not only cases where all relevant variables are included in the analyses but also situations when some of them are omitted (e.g. due to data unavailability or because analysts are not aware of them). Simulation results support our method’s ability to identify statistically valid instruments that lead to correct causal conclusions. An empirical case illustrating the application of our method is presented in an online appendix.