From AI Capability Growth to Real-Economy Growth: A Semi-Endogenous Model of Physical and Institutional Bottlenecks

Modern growth theory is often organized into three benchmark families: exogenous-growth models (Solow–Swan), endogenous-growth models (e.g., Romer; Aghion Segerstrom; Young; Bloom et al.). Building on the semi-endogenous tradition, this paper refines growth modeling for the AI era by explicitly separating (i) potential progress in “information space” from (ii) realized progress in the real economy, and by quantifying the translation-speed gap between them. The information layer models coupled dynamics of algorithmic knowledge, AI-augmented research effort, and installed compute. Realization is governed by two reflection channels: a physical channel that maps installed compute into deployable compute through electricity, interconnection, materials, cooling/water, and permitting/construction throughput; and an institutional channel capturing social acceptance, regulatory readiness, institutional readiness, and operational maturity. The system is formulated as a hybrid ODE–jump model with predictable controls, bounded deployment-adjustment flows, and ordered event handling. Analytical results include: (i) global existence, uniqueness, positivity, and boundedness under primitive regularity conditions; (ii) pathwise decomposition and event attribution of the information-to-reality gap; (iii) deterministic and stochastic bottleneck-switch timing results; (iv) reflection-adjusted long-run growth formulas, including a semi-endogenous balanced-growth-path expression; and (v) allocation rules under both affine-response and diminishing-return control regimes. An estimation and simulation protocol is provided, including block identification under event exclusions, jump-consistent speed-ratio measurement, and bias control for smooth minimum approximations. The paper also maps source-grounded calibration anchors from energy, infrastructure, and compute datasets into concrete numerical growth and speed-ratio predictions. JEL: O33, O41, C61, C63, D83.