Capital spillovers and growth regime selection

Can capital accumulation sustain endogenous growth without imposing knife-edge linearity of aggregate technology in capital? This paper shows that it can, even when productivity is simultaneously shaped by diminishing-return capital spillovers.In a model with hybrid capital spillovers—a diminishing-return component and an AK-type component—the long-run dynamics exhibit growth regime selection in capital-based environments. The economy converges to fully endogenous growth if and only if the equilibrium saving rate exceeds a critical threshold; otherwise it converges to a semi-endogenous path tied to population growth.The result provides a tractable criterion for when an AK-type growth engine survives in the presence of diminishing spillovers, turning the AK versus semi-endogenous distinction into an equilibrium outcome governed by saving behavior and spillover structure. A calibration using U.S. national accounts data suggests that the economy operates in the endogenous regime, though relatively close to the regime boundary.