A Bayesian Approach to Inferring the Effects of Events Using Cohorted Data

Music City Center 

Researchers often wish to understand how an event affected individual behaviour (e.g., customer spending over time); oftentimes, such events affect the entire population of interest simultaneously, leaving no "control group" for comparison (e.g., the COVID-19 pandemic, a viral marketing campaign, or a national regulatory change).
In such settings, the researcher can infer causal effects by forecasting the counterfactual baseline (i.e., what would have happened without the event) based on pre-event trends. These inferences depend on accurate forecasts of baseline behaviour. In the customer base setting, researchers can observe multiple "cohorts" of customers who made their first purchase at differing times. Exploiting regularity in behavior across cohorts, data from older cohorts can be used to help predict behaviour of younger cohorts, enabling good forecasts of the baseline.
Recent work has proposed methods for such settings relying on an assumption that different cohorts follow parallel time trends. In this work, we develop an alternative method that relaxes the parallel trends assumption. Specifically, we propose a hierarchical Bayesian model that uses nonparametric Gaussian processes to model the spending over time of each cohort while pooling information across cohorts based on data-driven inferences of cohort similarity. We benchmark our approach against prior methods to show that it can achieve superior validity and precision of causal estimates, particularly when the parallel trends assumption is not exactly satisfied.