The increased exposure of the United States to economic shocks originating from abroad is a common concern of those critical of globalization. An understanding of the cross-country transmission of shocks is of central importance for policymakers seeking to limit excess volatility resulting from international linkages. Firms whose ownership spans multiple countries are one under-appreciated mechanism. These multinationals represent an enormous share of the global economy, but a general scarcity of firm-level data has limited our understanding of how they affect both origin and destination countries. One contribution of this dissertation is to expand the data availability on these firms, using innovative data-linking techniques. The first chapter provides some of the first ever causal evidence on the role of trade and multinational production in the transmission of economic shocks and the cross-country synchronization of business cycles. This chapter leverages the 2011 Japanese earthquake/tsunami as a natural experiment. It finds that those U.S. firms with large exposure to intermediate inputs from Japan -- typically the affiliates of Japanese multinationals -- experience significant output declines after this shock, roughly one-for-one with declines in imported inputs. Structural estimation of the production function reveals substantial complementarities between imported and domestic inputs. These results suggest that global supply chains are more rigid than previously thought. The second chapter incorporates this low production elasticity of imported inputs into an otherwise standard dynamic stochastic general equilibrium model. The low degree of input substitutability, when applied to the share of trade governed by multinational firms, can generate effects in the aggregate. Value-added co-movement increases by 11 percentage points in the baseline model relative to a model where such features are absent. The model confirms that real linkages -- in addition to financial and policy spillovers -- play an important role in business cycle synchronization. The third chapter describes additional characteristics of multinational firms relative to domestic and exporting firms in the U.S. economy. These firms are larger, more productive, more capital intensive, and pay higher wages than other firms. The relative patterns of trade and output offer valuable guidance for the motives for ownership that spans national boundaries.