SMaC: Spatial Matrix Completion method

Synthetic control methods are commonly used in panel data settings to evaluate the effect of an intervention. In many of these cases, the treated and control time series correspond to spatial areas such as regions or neighborhoods. Synthetic control methods can be used to evaluate the effect that the treatment had in the treated area, but it is often unclear how far the treatment’s effect propagates, as this approach ignores the spatial structure of the data, and can lead to efficiency loss in spatial settings. We propose to deal with these issues by developing a Bayesian spatial matrix completion framework that allows us to predict the missing potential outcomes in the different areas around the intervention point while accounting for the spatial structure of the data. Specifically, the missing time series in the absence of treatment for the treated areas of all sizes are imputed using a weighted average of control time series, where the weights are assumed to vary smoothly over space according to a Gaussian process.