We introduce a quantifiable model of international production of a complex good that consists of multiple parts. Production of any pair of parts in the same country exhibits pair-specific cost complementarity, and consequently, decisions on production locations are interrelated, which generates rich patterns of clustering. We use input- output and other industry-level data from the United States to estimate the model for US production and find that these complementarity costs are highly heterogeneous across industries and, on average, account for 1.86% of total production costs. Gains from trade associated with the decrease in these costs, which we interpret as non-tariff trade liberalization, are 50% larger than in the case of a decrease in tariffs. Finally, using our model, we construct an index of international integration, that, unlike standard measures, accounts not only for the total costs of parts produced abroad but also what parts are produced and how similar these parts are to one another. We find that this index is a better predictor of the welfare consequences of trade liberalization than conventional measures of offshoring.