Using novel firm-level microdata and leveraging a natural experiment, this paper provides causal evidence for the role of trade and multinational firms in the cross-country transmission of shocks. Foreign multinational affiliates in the U.S. exhibit substantial intermediate input linkages with their source country. The scope for these linkages to generate cross-country spillovers in the domestic market depends on the elasticity of substitution with respect to other inputs. Using the 2011 Tohoku earthquake as an exogenous shock, we estimate this elasticity for those firms most reliant on Japanese imported inputs: the U.S. affiliates of Japanese multinationals. These firms suffered large drops in U.S. output in the months following the shock, roughly one-for-one with the drop in imports and consistent with a Leontief relationship between imported and domestic inputs. Structural estimates of the production function for these firms yield disaggregated production elasticities that are similarly low. Our results suggest that global supply chains are sufficiently rigid to play an important role in the cross-country transmission of shocks.