consumption) and ii) the average number of stages embodied in an industry’s production.<sup>9</sup> We also examine more traditional indexes of fragmentation such as gross-output-to-value-added ratios and the share of intermediate goods in trade. We show that, within our framework, we can map each of these indexes to structural parameters and key summary statistics of our model. These mappings are useful when we calibrate the model to data on interregional input-output relationships in East Asia.

A key purpose of this exercise is to offer a model comparison vis-a-vis other papers in the literature. A prominent literature has emphasized that intermediate goods trade magnifies the effect of trade costs on trade. Yi (2010) and Johnson and Moxnes (2013) focus on the response of trade to trade cost shocks, whereas Krugman and Venables (1996), Hillberry and Hummels (2002), Yi (2010) and Johnson and Noguera (2014) link the spatial clustering of activities to trade costs and intermediate goods trade.<sup>10</sup> Clustering also occurs in our model, with sequential activities locating so as to avoid trade costs. Our calibrated model can be used to investigate the response of trade to trade cost shocks, as in Johnson and Moxnes (2013) or Yi (2010).

We also contribute to the recent literature on the welfare implications of trade cost change. Arkolakis, Costinot and Rodriguez-Clare (2012) show that a broad class of models imply the same response of welfare to trade costs, provided that the models are calibrated to generate the same trade response to trade cost change. Costinot and Rodriguez-Clare (2014) and Melitz and Redding (2014) show that welfare effects are magnified when intermediate goods trade is involved. Like other papers in the literature, these presume an explicit input-output relationship that governs supply chain length, in contrast to the endogenous length in our model. The Armington framework used in these papers also precludes movement along the extensive margin (in terms of countries involved in supply chains), while our theory allows this. Our calibrated model implies larger gains than in standard trade models like those described by Arkolakis et al (2012), especially for countries that tend to be downstream, but smaller gains than Costinot and Rodriguez-Clare (2014) or Melitz and Redding (2014).

> 9The first is described as “distance to final demand” in Fally (2012) and “upstreamness” in Antras et al (2012). The second is developed in Fally (2012) and computed using the BEA input-output tables for the US. Using the highly disaggregated US table, Fally (2012) finds that the two indicators are not correlated, and that the indicators do not appear to be especially sensitive to aggregation concerns. Note also that Fally (2012) and Antras et al (2012) compute these indexes using input-output table for a single country. Here we extend these indicators to multi-rational input-output tables.

> 10More recently, Kee and Tang (2013), Bernard et al. (2014) and Antr`as et al. (2014) have used firm-level data to examine both intensive and extensive margins in import decisions. Firm-level data, however, do not allow a full consideration of supply chains over several countries. Multi-country input-output tables are more suitable for exercises like ours.

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