Principal Covariates Regression for Causal Case Studies - Weibin Ding; Jie Li; Dian Jin; Jiayang Kong (Journal of Mathematics)
Researcher and analyst are often interested in estimating the effect of an intervention or treatment, which takes place at the aggregate level and affect one single unit, such as country and region. Thus, comparative case studies would be their first choice in practice. However, comparative case studies could fail to yield an estimate in the effect that is unbiased and consistent, as in some contexts; there are not suitable control units that are similar to the treated. The econometric literature has taken synthetic control methods and panel data approaches to this problem. In this study, we developed a principal covariate regression estimator, which exploits the cross-sectional correlation, as well as the temporal dependency, to reproduce the dynamics of the treated in the absence of an event or policy. From a theoretical perspective, we introduce the statistical literature on dimensional reduction to make a causal inference. From a technique perspective, we combine the vertical regression and the horizontal regression. We constructed an annual panel of 38 states, to evaluate the effect of Proposition 99 on beer sales in California, using the principal covariate regression estimator proposed here. We find that California’s tobacco control program had a significant negative and robust effect on local beer consumption, suggesting that policymakers could reduce the use of cigarette and alcohol in the public using one common behavioral intervention.