Discovering the Temporal Evolution of Spatial Spillovers of Green Innovation: An Innovative Approach Using Dynamic Spatial-Temporal Weight Matrices

Understanding how spatial spillovers evolve over time—strengthening, weakening, or reversing—is a fundamental challenge in spatial econometrics, yet most empirical studies rely on static weight matrices that assume time-invariant spatial dependence. This article proposes a broadly applicable spatial-temporal weight matrix (STWM) framework in which temporal weights are derived from annual ratios of Moran’s I and Geary’s C, enabling the matrix to incorporate year-to-year changes in spatial autocorrelation without imposing ad hoc decay assumptions. The temporal and geographic-economic weight structures are integrated via the Kronecker product, and the resulting STWMs are formally shown to satisfy all admissibility conditions for spatial econometric estimation. Exogeneity is confirmed through Hausman tests, and Granger causality tests; finite-sample reliability is validated via Monte Carlo simulation. Applying the framework to green innovation across 276 Chinese cities from 2008 to 2021 reveals strong positive spillovers at the national level alongside substantial spatiotemporal heterogeneity: The Yangtze River Delta has entered the interactive stage, Beijing–Tianjin–Hebei is transitioning from polarization toward diffusion, and the Greater Bay Area, Chengdu–Chongqing, and the Yangtze River Middle Reaches remain in polarization or stalled transitions. A structural break in 2017 further documents a regime shift from intercity competition to nascent regional synergy in green innovation. The STWM methodology and all associated estimation and validation tools are released as an open-source Python package, providing researchers across disciplines with a replicable and theoretically grounded instrument for analyzing dynamic spatial dependence in any panel setting.