Industrial policies, while often aimed at domestic industries, can spur technological progress abroad. We document this mechanism in the case of rare earth elements (REE) – critical inputs for manufacturing and the green transformation, with low elasticity of substitution, inelastic supply, and high production and processing concentration in China. Using REE-related patents classified by a large language model, sectoral TFP data, and matched trade data, we show that the introduction of REE export restrictions led to a global surge in innovation and exports in REE-intensive downstream sectors outside of China. To quantify the global impact of the adverse REE supply shock, we develop a quantitative general equilibrium model of trade and directed technological change. Under endogenous technologies, input-supply restrictions shift the direction of innovation in downstream sectors toward scarce inputs when inputs are gross complements, which can lead to the expansion of these sectors.