Aporetic Conclusions When Testing the Validity of an Instrumental Variable

Validity of an Instrumental Variable Fan Yang, José R. Zubizarreta, Dylan S. Small, Scott Lorch, Paul R. Rosenbaum1 University of Pennsylvania and Columbia University Abstract: An instrument or instrumental variable is often used in an effort to avoid selection bias in inference about the effects of treatments when treatment choice is based on thoughtful deliberation. An instrument is a haphazard nudge to accept one treatment or another, where the push can affect outcomes only to the extent that it alters the treatment received. There are two key assumptions here: (i) the push is haphazard or essentially random once adjustments have been made for observed covariates, (ii) the push affects outcomes only by altering the treatment, the so-called “exclusion restriction.” These assumptions are often said to be untestable; however, that is untrue if testable means checking the compatibility of assumptions with other things we think we know. A test of this sort may result in an aporia, that is, a collection of claims that are individually plausible but mutually inconsistent, without clear indication as to which claim is culpable for the inconsistency. We discuss this subject in the context of our on-going study of the effects of delivery by cesarean section on the survival of extremely premature infants of 23-24 weeks gestational age.