Inference Theory for Quasi-experimental Methods when Data are Non-stationary with Unknown Structure : Does the Lifting of Shelter-in-Place Keep Covid-19 Manageable?

Increasingly, marketers and policy makers are interested in estimating the average treatment effect on the treated (ATT) in settings where a randomized experiment is infeasible. Furthermore, in marketing and policy contexts, the data are often non-stationary and the precise structure of nonstationarity is unknown. The causal effect of general data protection regulation (GDPR) on consumer search and purchases and that of communicating a COVID-19 policy change on consumer health outcomes are two examples of such contexts. Quasi-experimental methods such as the synthetic control (SC) method (e.g., Abadie et al. 2010), the modified synthetic control (MSC) method (e.g., Doudchenko and Imbens 2016), and the ordinary least squares (OLS) method (Hsiao, Chin, and Wang, HCW 2012) are emerging as powerful ways to estimate the ATT. Inference theory for these methods exists when the data are stationary but not when the data are non-stationary and of unknown structure, precluding researchers from correctly estimating or quantifying the ATT. We fill the research void by deriving inference theory for the ATT estimates from these methods. We apply our approach in an important public health context to estimate the causal effect of communicating the lifting of the shelter-in-place order on the number of COVID-19 patients in Texas. We conclude that the lifting was premature as it exacerbated the spread of COVID-19. We quantify the causal effect by showing that the number of COVID-19 patients in the 60 days following the lifting spiked by about 38 percent more than what would have been the level had the shelter-in-place order continued. The results offer valuable insights and lessons to marketers and policy makers in communicating policy decisions