Identification of Nonconcave Aggregate Production Functions in Spatial Solow Models with Technology Diffusion

Abstract. Spatial Solow models seek to explain uneven regional economic development by accounting for spatiotemporal heterogeneity in the inputs of economic growth. Central to the Solow or perhaps any long-run economic growth model, the aggregate production function determines how inputs are transformed into outputs, and it shapes the convergence to a stable economic equilibrium in the long run. Identifying this function is therefore essential for understanding the true drivers of economic growth, and applying empirically validated spatial economic models can help develop effective strategies that promote economic progress and ensure sustainable development. We study the identification of spatial Solow models that treat capital mobility and technology diffusion as the primary sources of heterogeneity in a spatial economic market, where wealth flows from richer to poorer regions and technology spreads from more advanced to less innovative areas; the choice of S-shaped production functions enhances the model’s significance to capture poverty traps and economic agglomeration within a unified framework. The recovery of the resulting PDE system is then framed as an inverse problem for which we introduce a nonparametric approach. Numerical studies find that the presence of noise does not diminish computational accuracy or increase computational burden. While missing more data generally leads to larger errors in system recovery and wealth prediction, our approach demonstrates remarkable accuracy even when a majority of spatial data are unavailable. The resilience to data corruption and data loss underscores the practical utility of our method in real-world applications where imperfect measurement is often unavoidable.