# **1 Introduction**

The nature of international trade changed dramatically in recent decades, as vertically integrated production processes spread across international borders, increasing trade in parts and components along the way.<sup>1</sup> This phenomenon raises a number of important questions for economic policy: How large are the gains from international fragmentation, and how are they distributed across countries? How do changes in trade costs affect trade flows and the distribution of value added across countries? How has China’s entry into the world trading system affected the international fragmentation of production? Answers to these questions require quantitative models that can represent the complexities of international production chains in a tractable form.

Recent evidence has documented substantial variation in supply chain length.<sup>2</sup> Even within chains, firms vary in their contribution to value added.<sup>3</sup> The length of supply chains and the degree to which they are internationalized are difficult to separate from decisions that determine firm scope. The Ford Model T, for example, was produced in a single plant, while the production of modern day automobiles can involve a myriad of heterogeneous suppliers scattered across multiple countries. International fragmentation is limited, ultimately, by the extent of fragmentation at the firm level. Yet the literature lacks a unified treatment that can explain endogenous firm boundaries within chains, formalize endogenous chain lengths, and determine comparative advantage within and across chains.

We offer a framework that accomplishes these goals. In the model, an optimal allocation of tasks determines jointly the scope of sequentially-arranged firms of varying size, the length of chains and the sequence of countries in production.<sup>4</sup> We calibrate the model using key moments from input-output tables on East Asia and the United States.<sup>5</sup> Our focus on East Asia reflects the importance of international fragmentation in that region. Based on our calibration, we are able to quantify the impact on intermediate and final goods trade, fragmentation and welfare, of changes in: 1) international trade costs, 2) productivity in China, 3) transaction costs in China, and 4) a reduction in bilateral trade costs between the US and China.

> 1Baldwin (2012) surveys these developments and provides insights into how they should affect our thinking about the economics of international trade and trade policy.

> 2See Antr`as et al. (2012) and Fally (2012).

> 3See Kraemer et al. (2011), who illustrate the distribution of value added for Apple iPhones and iPads. 4Our framework is perfectly competitive and therefore silent about the distinction between firms and plants. We shall use the term ‘firms’ throughout, but one could reinterpret everything in terms of ‘plants’ without affecting the results.

> 5Such tables have been used to quantify the extent of fragmentation and the allocation of value across countries. Johnson (2014) surveys a series of papers that use such tables to calculate value added trade. Koopman et al. (2010) use Chinese tables to calculate the domestic content of China’s exports. Antras et al. (2012) derive indices of supply chain length from input-output tables.

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