Asymptotic Inference in High Dimensional Instrumental Variable Models

Music City Center 

In this project, we look into high-dimensional Instrumental Variables (IV) models, which have a wide range of applications ranging from econometrics to genomics. Specifically, we focus on the case of many weak IVs and high dimensional exposures and derive a minimax rate for optimal estimators of linear and quadratic functionals in the model. This allow us to infer causal effects and gain information about the signal-to-noise ratio. To obtain a complete picture, we explore versions of the problem in ultra-high dimensional regimes, under suitable notions of sparsity, and proportional asymptotic regimes, without requiring sparsity assumptions. Our analyses rely on a combination of results from causal inference, high dimensional statistics, random matrix theory, and semiparametric inference.

High Dimensional Statistics

Instrumental Variables Models

Asymptotic Inference

Causal Inference

Minimax Optimality 

ENAR