4. Quantifying Vertical Trade among the B&R Economies Formally, the first type of linkages is referred to as backward linkages. It is the amount of foreign valueadded in gross exports plus the double counted items from foreign sources.<sup>6</sup> The second type of linkages are denominated forward linkages. They are the amount of domestic value-added in intermediate goods that is used to generate exports to third countries.<sup>7</sup> Forward linkages are defined by the final use of the exports and categorized in that form. For example, there is a difference between exports that are going to be consumed in the partner country, exports that are going to be re-processed and shipped to third countries and exports that are going to be shipped back to the original exporter.

The two types of measures are crucial to understand how GVCs effectively redistribute a share of the export revenues to all participating countries. Therefore, we investigate the two types of linkages in depth considering the partners along the B&R and the non-B&R Economies.

We use the state of the art methodology developed by Wang et al. (2013) which decomposes bilateral gross exports in four major terms (Figure 20): domestic value-added absorbed abroad, foreign value-added, domestic value-added that returns home and purely double counted exports. Exploiting the algorithm of Quast and Kummritz (2016) the four terms can be combined to form statistics at the country level which explain vertical specialization from the importing side and from the exporting side. We discuss the findings for the aggregate economy in the next two sections.

# BOX 2: DECOMPOSING VALUE-ADDED IN DIFFERENT COMPONENTS

**We use the methodology pioneered by Johnson and Noguera (2012) and extended by Koopman et al. (2014) and Wang et al. (2013).** The methodology decomposes production on each country according to where it is finally consumed. The goal is to trace production stages and all possible intermediate steps. Through input-output linkages, exports are deflated by the amount of imported inputs, removing the double counting of trade statistics.  The composition relies in complex matrix algebra manipulation, the exact steps are described in Wang et al. (2013). We obtained the indicators with the help of the computational method developed by Quast and Kummritz (2016).

**The decomposition of Wang et al. (2014), which is the state of the art methodology, decomposes bilateral sectoral exports by destination country in 16 terms.** The 16 terms can be formalized in four major groups. Formally, for each exporting country s, exporting industry j and importing country m. Notice that all variables can be indexed by j, m and s. For the sake of simplicity, we omit the subscripts. Gross exports are divided in four major terms.

Exports= VAX+ RDV+ FVA+ PDC VAX is the domestic value-added in exports absorbed abroad. RDV is the domestic value-added first exported, then processed in third countries and then returned to the home country. FVA is the foreign value-added embedded in the exports of country s and industry i. PDC are pure double counted items.

**From these four major components, we further decompose at the bilateral level to get additional indicators of GVC integration between the partners.**

The domestic value-added absorbed abroad can be decomposed in three terms. First, the domestic value-added in exports of intermediate goods that is going to be absorbed by the direct partner, DVA_int. Second, the domestic value-added in final goods exports to the direct partner, DVA_int. Third the domestic value-added in intermediate goods that is going to be re-exported to third countries and finally be absorbed abroad.

RDV is the domestic value-added that returns home. Therefore, it can be decomposed in domestic value-added that returns home via final goods or via intermediate goods’ imports.

> 6 Double counted items occur because some goods cross borders several times and are therefore counted twice in trade statistics while they were only produced once. Input-output tables allow to estimate the percentage of this type of intermediate goods that cross a border several times. Notice that double counting in gross exports is large when GVC trade is prevalent.

> 7 Among backward linkages we might also separate between intermediate goods that are re-exported to third countries and intermediate goods that return to the home market for further processing.

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