Compute as Capital: Measuring the Macroeconomic Impact of Frontier AI Compute Constraints

This paper introduces a novel theoretical and empirical framework for analyzing frontier AI compute as a distinct form of productive capital. Extending standard semi-endogenous growth models, we formalize a "compute capital" stock separate from general ICT capital and demonstrate that AI productivity is a joint function of compute capacity, data availability, and human expertise. Using a newly constructed cross-country panel dataset of effective AI compute capacity covering 42 economies from 2016 to 2024, we document substantial and widening global compute inequality: the top five economies account for over 82 percent of estimated global frontier AI compute, while the bottom quartile shares less than 1.2 percent. Exploiting quasi-natural experiments, including the October 2022 U.S. semiconductor export controls on China, regional data center openings, and cloud provider expansion events, we identify causal effects of compute access on firm-level productivity, AI-related research and development, and labor-market outcomes. A one-standard-deviation increase in effective compute access is associated with a 3.7 percentage point gain in sectoral total factor productivity and a 12 percent increase in AI-related patent filings. We then develop a structural industrial organization model of the cloud computing and semiconductor supply chain to evaluate welfare implications of market concentration, finding that the current oligopolistic structure generates deadweight losses equivalent to 0.3 to 0.8 percent of GDP in advanced economies. Policy counterfactuals suggest that targeted compute subsidies for research institutions yield higher social returns than broad-based industrial subsidies, while overly restrictive export controls accelerate indigenous chip development in targeted economies without proportionally reducing their AI capabilities. Our findings have direct implications for competition policy, industrial strategy, AI governance, and the design of international technology agreements.