Causal Inference in Longitudinal Data Analysis

The focus of this dissertation is on developing new statistical methods for conducting causal inference in longitudinal data analysis and addressing real-world application problems. Chapter 1 provides an overview of causal inference from both the potential outcome and regression frameworks, together with a brief introduction to longitudinal data. It also summarizes the major contributions and outlines the overall organization of the dissertation. Chapter 2 introduces nuclear norm-penalized regression and its extensions, establishing foundational ideas that connect to the methodological developments in Chapters 3 and 4. In Chapter 3, we propose a new method that uses tensor completion to estimate causal effects with multivariate longitudinal data --- data in which multiple outcomes are observed for each unit and time period. Our motivation is to estimate the number of COVID-19 fatalities prevented by government mandates such as travel restrictions, mask-wearing directives, and vaccination requirements. In addition to COVID-19 fatalities, we observe related outcomes such as the number of deaths from other diseases. The proposed method arranges the data as a tensor with three dimensions --- unit, time, and outcome --- and uses tensor completion to impute the missing counterfactual outcomes. We first prove that, under general conditions, combining multiple outcomes using the proposed method improves the accuracy of counterfactual imputations. We then compare the proposed method to other approaches commonly used to evaluate COVID-19 mandates. Our reevaluation suggests these common approaches substantially overestimate the effect of mask-wearing directives in the United States but accurately characterize the effect of travel restrictions and vaccine mandates. Chapter 4 addresses the challenge of unobserved confounding in longitudinal data, where confounders often vary across both units and time periods. A common approach to account for these confounders is to use instrumental variables in combination with two-way fixed effects. However, this approach requires that any unobserved confounders correlated with the instrument vary solely by unit or time period, with no interactions between the two. In this chapter, we relax this assumption by proposing a novel method in which instrumental variable regression is estimated with interactive fixed effects. Our method leverages nuclear norm penalization to adjust for confounders that vary across both unit and time period, assuming the variation is low-rank. We first demonstrate that, under this assumption, the proposed estimator yields a consistent estimator of the average treatment effect. We then apply our method to investigate the relationship between traffic ticket issuance and car accident rates. The results of our analysis indicate that traffic tickets issued by police officers in New York City effectively reduce traffic collisions. Finally, we validate the efficacy and robustness of our approach by comparing it with competing methods. Chapter 5 concludes the dissertation and discusses future directions.

Author

• Zhang, Shixue

• Causal Inference
• Factor Model
• Longitudinal Data Analysis
• Machine Learning

Identifier

hdl:1920/15214

OAI identifier oai:identifier

oai:MARS:1920/15214