four anonymous referees and many seminar participants for useful conversations and comments. We thank Zina Saijid for excellent research assistance.

We develop a dynamic trade model with spatially distinct labor markets facing varying exposure to international trade. The model captures the role of labor mobility frictions, goods mobility frictions, geographic factors, and input‐output linkages in determining equilibrium allocations. We show how to solve the equilibrium of the model and take the model to the data without assuming that the economy is at a steady state and without estimating productivities, migration frictions, or trade costs, which can be difficult to identify. We calibrate the model to 22 sectors, 38 countries, and 50 U.S. states. We study how the rise in China's trade for the period 2000 to 2007 impacted U.S. households across more than a thousand U.S. labor markets distinguished by sector and state. We find that the China trade shock resulted in a reduction of about 0.55 million U.S. manufacturing jobs, about 16% of the observed decline in manufacturing employment from 2000 to 2007. The U.S. gains in the aggregate, but due to trade and migration frictions, the welfare and employment effects vary across U.S. labor markets. Estimated transition costs to the new long‐run equilibrium are also heterogeneous and reflect the importance of accounting for labor dynamics.

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A firm's productivity depends on how production is organized given the level of demand for its product. To capture this mechanism, we develop a theory of an economy where firms with heterogeneous demands use labor and knowledge to produce. Entrepreneurs decide the number of layers of management and the knowledge and span of control of each agent. As a result, in the theory, heterogeneity in demand leads to heterogeneity in productivity and other firms' outcomes. We use the theory to analyze the impact of international trade on organization and calibrate the model to the U.S. economy. Our results indicate that, as a result of a bilateral trade liberalization, firms that export will increase the number of layers of management and will decentralize decisions. The new organization of the average exporter results in higher productivity, although the responses of productivity are heterogeneous across these firms. In contrast, non-exporters reduce their number of layers, decentralization, and, on average, their productivity. The marginal exporter increases its productivity by about 1% and its revenue productivity by about 1.8%. AbstractA …rm's productivity depends on how production is organized given the level of demand for its product. To capture this mechanism, we develop a theory of an economy where …rms with heterogeneous demands use labor and knowledge to produce. Entrepreneurs decide the number of layers of management and the knowledge and span of control of each agent. As a result, in the theory, heterogeneity in demand leads to heterogeneity in productivity and other …rms' outcomes. We use the theory to analyze the impact of international trade on organization and calibrate the model to the U.S. economy. Our results indicate that, as a result of a bilateral trade liberalization, …rms that export will increase the number of layers of management and will decentralize decisions. The new organization of the average exporter results in higher productivity, although the responses of productivity are heterogeneous across these …rms. In contrast, non-exporters reduce their number of layers, decentralization, and, on average, their productivity. The marginal exporter increases its productivity by about 1% and its revenue productivity by about 1.8%.