Heterogeneous Synthetic Learner for Panel Data

Evaluating the treatment effect from panel data has become an increasingly important problem in numerous areas including public health (Cole et al. 2020, Goodman-Bacon & Marcus 2020), politics (Abadie et al. 2010, Sabia et al. 2012), economics (Cavallo et al. 2013, Dube & Zipperer 2015), etc. During the past decades, a number of methods have been developed to estimate the average treatment effect (ATE) from panel data, including the celebrated Difference-in-Differences (DiD) (Abadie 2005) and the Synthetic Control (SC) method (Abadie & Gardeazabal 2003, Abadie et al. 2010). Yet, due to the heterogeneity of individuals in response to treatments, there may not exist one single uniformly optimal treatment across individuals. Thus, one major focus in causal machine learning is to access the Heterogeneous Treatment Effect (HTE) (see e.g., Athey & Imbens 2015, Shalit et al. 2017, Wager & Athey 2018, Künzel et al. 2019, Farrell et al. 2021) that measures the causal impact within a given group. Detecting such a heterogeneity in panel data hence becomes an inevitable trend in the new era of personalization. However, estimating HTE in panel data is surprisingly underexplored in the literature. On the one hand, despite the fact that there are many methods for the HTE estimation (see e.g., Athey & Imbens 2016, Johnson et al. 2019, Künzel et al. 2019, Nie & Wager 2021, and the reference therein), most of these works focus on independently and identically distributed (i.i.d.) observations and thus are infeasible to handle the non-stationarity and temporal dependency in the common panel data setting. On the other hand, in contrast to the popularity of estimating ATE in panel data as mentioned above, limited progress has been achieved for HTE.