Primary Submission Category: Instrumental Variables
Manipulating a Continuous Instrumental Variable: Algorithm, Partial Identification Bounds, and Inference under Randomization and Biased Randomization Assumptions
Authors: Min Haeng Cho, Zhe Chen, Bo Zhang,
Presenting Author: Min Haeng Cho*
An instrumental variable (IV) can be thought of as a random nudge towards accepting a treatment. With a continuous IV, Baiocchi et al. (2010) strengthened the original IV using non-bipartite matching and proposed a valid test for the effect ratio estimand, an analog of the sample average treatment effect (SATE) among compliers. Their key insight is to shift focus from the entire study cohort to a possibly smaller cohort amenable to being paired with a larger separation in the IV dose, inducing a higher compliance rate. Three elements change as one switches from one design to the other. First, the study cohort changes. In this article, we show it can be avoided using a template matching algorithm. Second, the compliance rate changes. Third, the latent complier subgroup changes as a person’s principal stratum status in a matched design is defined with respect to the two IV doses within each pair. In this article, we study partial identification bounds for the SATE for the entire matched cohort. Unlike the effect ratio, the SATE estimand does not depend on who is matched to whom in the design, although a strengthened-IV design may narrow its partial identification bounds. We derive valid statistical inference for the partial identification bounds under a randomization assumption and an IV-dose-dependent, biased randomization scheme in a matched-pair design, with applications to a study of the effect of neonatal intensive care units on the mortality rate of premature babies.