Air Pollution and Climate-Mitigation Innovation: A Spatial Optimal Control Approach

We develop a spatial optimal-control model in which air pollution and climate-mitigation innovation evolve jointly through a coupled reaction–diffusion system. We characterize stability and optimal policy, derive closed-form controls under spatial homogeneity, and obtain bounds for nonlinear dynamics. Using data from 1,181 European NUTS 3 regions over 2005–2020, we estimate the reaction–diffusion dynamics and simulate the optimal policy mix under alternative welfare valuations of pollution-generating activities. Pollution exhibits strong spatial diffusion, whereas innovation diffusion is limited. Innovation is associated with lower subsequent pollution growth, while higher pollution is followed by stronger innovation growth. The optimal policy mix combines environmental regulation and innovation support, but their timing and persistence differ. Abatement may be immediate or delayed depending on the net welfare contribution of pollution-generating activities, while sustained innovation support depends on the value assigned to the terminal innovation stock.