However, unlike the sharp increase in VAX for SOEs, we find no evidence that SOEs’ export-related profits increased the most. In other words, rising SOEs’ value added exports in recent years did not automatically translate into higher SOEs’ profits.

Our paper makes several contributions to the literature. First, it adds to the growing literature on production fragmentation across national borders (e.g., Hummels, Ishii, and Yi, 2001, Johnson and Noguera, 2012a, 2012b; Koopman, Wang, and Wei, 2012; Koopman, Wang, and Wei, 2014). The focus of that literature has been on the relative shares of domestic versus foreign value added in international trade. While establishing these facts and providing accurate measures of trade flows is urgently needed in the increasingly globalized world, the composition and dynamics of the domestic segment of GVC have not been subject to the same level of scrutiny. In particular, understanding how trade liberalization affects intra-national trade between industries and in turn shapes the reallocation of resources and across industries and firms is important for designing development policies. Our paper takes a first step by analyzing intra-national trade between different firm types, focusing on the roles of SOEs and SMEs in China.

Related to the value-added trade literature, our approach extends the IO-table based approach to incorporate the “new new” trade literature that emphasizes firm heterogeneity. In reality, firms differ substantially in their export intensity, import intensity, and position of participation along GVC. Other characteristics such as ownership structure (domestic/foreign, private/public), location, size can also directly affect the way firms respond to trade liberalization and other economic shocks. The usual method that relies on the aggregate IO tables ignores most of the underlying firm heterogeneity. The lack of information on between-firm transactions in the micro data also restricts the construction of IO tables by firm type. Moreover, a widely recognized drawback of using IO tables to measure VAX is the assumption that firms within an industry use the same technology for production. Proportionality assumptions are often made in order to distribute imports into different final uses and different source countries, as information on bilateral trade between suppliers and users is generally not available at the country-industry level.<sup>6</sup> Our paper provides a method to reduce the measurement bias due to heterogeneity in export and import intensities across firm sizes and ownership types.

Our paper also contributes to the literature on the determinants of firm export participation and other indirect export channels. Research in international trade shows that only a small fraction of enterprises,

> 6 These assumptions have been shown to lead to substantial biases in the estimation of countries’ value added, factor content of trade, and our general inference of the impact of trade on countries’ macro-economy (e.g., Puzzello, 2012). For instance, De La Cruz et al. (2011) and Koopman, Wang and Wei (2012) show that by allowing different imported material intensities for processing and non-processing exporters, the estimated foreign value added ratio in aggregate exports from both China and Mexico increases significantly.

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