Spatial vertical regression for spatial panel data: evaluating the effect of the florentine tramway’s first line on commercial vitality

Synthetic control methods are commonly used in panel data settings to evaluate the effect of an intervention. In many cases, the treated and control units correspond to spatial units such as regions or neighborhoods. Our approach addresses the challenge of understanding how an intervention applied at specific locations influences the surrounding area. Traditional synthetic control applications do not address how to define the effective area of impact, the extent of treatment propagation across space, and how effects vary with distance from the treatment sites. To address these challenges, we introduce spatial vertical regression (SVR) within the Bayesian paradigm. SVR predict the missing potential outcomes in varying proximities to the treatment sites, while accounting for the spatial structure inherent in the data. Rooted in the vertical regression framework of the synthetic control method, SVR employs a Gaussian process to ensure that the imputation of missing potential outcomes is spatially coherent, reflecting the expectation that nearby treated areas have similar relationships to control areas and experience similar outcomes. This approach is particularly pertinent to our study on the Florentine tramway’s first line construction. We study its influence on the local commercial landscape, focusing on how business prevalence varies at different distances from the tram stops.