Title: Efficient conditional instrumental set selection
Authors: Leonard Henckel - ETH Zurich (Switzerland) [presenting]
Marloes Maathuis - ETH Zurich (Switzerland)
Abstract: Instrumental variable estimators are a popular tool for causal effect estimation in the presence of unmeasured or latent confounding. However, it is well known that they tend to suffer from low accuracy. We consider ways to improve the 2SLS estimator's accuracy by improving the conditional instrumental set (CIS) selection. Presupposing knowledge of the underlying causal structure in the form of an acyclic directed mixed graph (ADMG), we develop three graphical tools to aid in the selection of more efficient CISs. First, we reformulate the asymptotic variance formula for the 2SLS estimator in a way that in particular provides new insights into how the choice of conditioning set, commonly referred to as the exogenous variables, affects the asymptotic variance. Second, we derive a graphical criterion allowing us to compare the asymptotic variance of certain pairs of CISs. Third, we construct a near-optimal valid CIS, that is, a CIS with an efficiency guarantee that cannot be improved without additional non-graphical information. We also use the first two results to derive guidelines that are helpful even in the absence of precise graphical knowledge and can be applied using only instrumental validity checks.