Primary Submission Category: Instrumental Variables
The Instrumental Variable Model with a Binary Outcome and Categorical Instrument and Treatment
Authors: Yilin Song, Kwun Chuen Gary Chan, Thomas Richardson,
Presenting Author: Yilin Song*
Instrumental variable models are central to the inference of causal effects in many settings, including Mendelian randomization and clinical trials with non-compliance. Richardson and Robins (2014) studied the instrumental variable model with binary exposure (X) and binary outcome (Y) with an instrument (Z) that takes k states where k≧2. In our work, we consider the instrumental variable model allowing X to be categorical with p≧2 states, while Y still being binary and Z taking k states. We assume that the instrument is randomized and that there is no direct effect of Z on Y so that Y(x,z) = Y(x). We first provide a simple characterization of the set of joint distributions of the potential outcomes p(Y(x=1),…, Y(x=p)) compatible with a given observed probability distribution p(X, Y|Z). We then characterize the resulting constraints on the margins p(Y(x=1)), …, p(Y(x=p)). We find that, in contrast to the case where p=2, these margins are not variation-independent when p>2. We discuss the implications for partial identification of average causal effect contrasts such as E[Y(x=i) – Y(x=j)].