Instrumented Nuclear Norm-Penalized Regression for Longitudinal Data

Conducting reliable causal inference in observational longitudinal data analysis encounters challenges when unmeasured confounding is present. Inspired by two influential methodologies, instrumental variables and nuclear norm-penalized regression, we propose a novel method called instrumented nuclear norm-penalized regression. This method aims to estimate average causal effects of exposure on outcome for longitudinal data while accounting for potential unmeasured confounding. Our method handles confounding variables with low-rank structures and provides flexibility by relaxing the exclusion restriction linked with instrumental variables. We develop the identification assumptions utilizing the potential outcome framework and provide theoretical results demonstrating the consistency of the proposed estimator. We also conduct simulation studies and apply the method to estimate the number of collisions deterred by the issuance of traffic tickets by police officers in New York City, validating its efficacy and robustness in comparison with competing methods.

Mid-Level

Knowledge

Women in Statistics and Data Science 2024