  This paper studies the evolution of economic activities using a continuous
time-space aggregation-diffusion model, which encompasses competing effects of
agglomeration and congestion. To bring the model to the real data, a novel
discretization technique over time and space is introduced. This technique
effectively disentangles spatial effects into pure topography, agglomeration,
repulsion, and diffusion forces, which is crucial for developing robust
econometric methods in spatial economics. Our empirical analysis of personal
income across Italian municipalities from 2008 to 2019 validates the model's
primary predictions and demonstrates superior performance compared to the most
common spatial econometric models in the literature.
