Tensor Completion for Causal Inference with Multivariate Longitudinal Data: A Reevaluation of COVID-19 Mandates

TL;DR

This paper introduces a tensor completion method for causal inference in multivariate longitudinal data, specifically applied to evaluating COVID-19 mandates, improving counterfactual estimates and challenging prior overestimations of mask effectiveness.

Contribution

The paper presents a novel tensor completion approach that leverages multiple outcomes to enhance causal effect estimation in longitudinal data, with a focus on COVID-19 policy evaluation.

Findings

Other methods overestimate mask effectiveness

Mask mandates were not a substitute for travel restrictions

Tensor completion improves counterfactual accuracy

Abstract

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 fatalities from other diseases and injuries. 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 main finding is that other approaches overestimate the effect of masking-wearing directives and that mask-wearing directives were not an effective alternative to travel restrictions. We conclude that while the proposed method can be applied whenever multivariate longitudinal data are available, we believe it is particularly timely as governments increasingly rely on longitudinal data to choose among policies such as mandates during public health emergencies.