This seminar features a paper presentation by Erin Evelyn Gabriel (University of Copenhagen).
Nonparametric partial identification methods, particularly in the context of instrumental variable (IV) models, have recently attracted substantial attention. Nevertheless, few existing approaches extend naturally to settings involving high-dimensional covariates, as most methods are restricted to discrete and finitely supported variables. Scalable methodologies for symbolic partial identification, in particular, remain limited. One potential approach involves post hoc conditioning and averaging of bounds derived for discrete variables over high-dimensional auxiliary covariates. However, this procedure need not yield sharp bounds when additional information about the covariates is available. The recent Levis et al. 2025 paper, which is primarily concerned with estimation of bounds, establishes a theorem demonstrating that, in the fully binary IV setting, averaging bounds over high-dimensional auxiliary covariates produces sharp bounds. Crucially, this result rests on the assumption that no information about the covariates is available beyond the fact that conditioning on them preserves the IV conditions.
This work investigates how the incorporation of auxiliary covariates affects the sharpness of bounds when some information about these covariates is known or assumed. It provides formal definitions of pointwise and uniform sharpness for covariate-conditional bounds and establish both general and IV-specific results about when covariate-averaged bounds are sharp based on these concepts. As demonstrated, general and easy to verify conditions are more difficult to establish. Consequently, this work emphasises the importance of transparency when incorporating ancillary covariates through conditioning, particularly regarding the underlying assumptions and the inferential context to which the resulting bounds apply. For more details please see Jonzon et al. 2025. (joint with G. Jonzon, A. Sjolander and M. C. Sachs).
Additional reference:
Alexander W Levis, Matteo Bonvini, Zhenghao Zeng, Luke Keele, Edward H Kennedy, covariate-assisted bounds on causal effects with instrumental variables: 'Series B: Statistical Methodology', 2025, Journal of the Royal Statistical Society.