Primary Submission Category: Instrumental Variables
The Multiplicative Quasi-Instrumental Variable Model
Authors: Jiewen Liu, Eric Tchetgen Tchetgen, Chan Park, David Richardson,
Presenting Author: Jiewen Liu*
We introduce the Quasi-Instrumental Variable (QIV) model, a framework for causal inference with unmeasured confounding that leverages an instrument that may be imperfectly exogenous. We allow the candidate instrument to have a direct effect on the outcome not mediated by the treatment, thus violating the standard IV exclusion restriction. Despite this, we establish nonparametric identification of the population average treatment effect on the treated (ATT) under a multiplicative treatment model, in which the QIV and the hidden confounder combine multiplicatively to govern treatment uptake. This multiplicative structure arises naturally, when treatment occurs only if both two independent instrument-driven and confounder-driven causal mechanisms are present, or when uptake follows a class of latent index model. Importantly, the QIV model is agnostic to treatment-effect heterogeneity with respect to hidden confounders. Identification is achieved via a modified Wald ratio estimand, which corrects the bias due to the exclusion restriction violation, and we propose a new class of estimators that are multiply robust and semiparametric efficient. Finally we propose a straightforward falsification test for the proposed QIV model, and we evaluate the approach in extensive simulations and an application to evaluate the causal effect of having three or more children on mothers’ labor-market engagement.