Inference on Causal Effects of Interventions in Time using Gaussian Processes

Recently, many applications have been devoted to understanding and revealing causal rather than associative relations among variables. One approach in the context of time series is that of synthetic controls (Abadie and Gardeazabal, 2003) and various extensions. This is based on the idea of recovering the counterfactual outcome that would have been observed had an intervention not taken place. This article contributes to expanding and generalizing this class of models, allowing for non-linearity in a nonparametric manner through Gaussian Processes. These models have high degree of flexibility in building the counterfactual outcome, using all types of information and without any limitations on the functional form. They also make it possible to assess the robustness of the synthetic controls, as we can use the posterior distributions of the Gaussian Processes to quantify uncertainty stemming from the functional form estimation. Lastly, as the models learn the relationships which prevail amongst all associated variables, there is no need to match the time series on a calendar basis, making the most of the available data.