14

- **GVC** _sr_ = **GVC** _PureForwsr_ + **GVC** _PureBacksr_ + **GVC** _TwoSidedsr_

- **GVC**<sup>_X_</sup> _s_<sup>=</sup><sup>**GVC**</sup><sup>_PureForw_</sup> _s_<sup>_X_+</sup><sup>**GVC**</sup><sup>_PureBack_</sup> _s_<sup>_X_+</sup><sup>**GVC**</sup><sup>_TwoSidedX_</sup> _s_

- The overall indicators of GVC-related trade and GVC-related output, and their forward, backward and two-sided components can be computed by summation at any level of country-sector aggregation.

- At the aggregate world level, i.e. summing across exporters _s_ , importers _r_ and sectors _n_ , the ‘GVC pure backward-related trade’ is equal to the ‘GVC pure forward-related _G G_

- trade’, i.e. �<sup>=</sup> �<sup>Thesameprop-</sup> _s,r_ = _s_<sup>**u**</sup><sup>_N_</sup><sup>**GVC**</sup><sup>_PureBacksr_</sup> _s,r_ = _s_<sup>**u**</sup><sup>_N_</sup><sup>**GVC**</sup><sup>_PureForwsr_.</sup> _G G_

- erty holds for GVC-related output, i.e. � _s_<sup>=</sup> � _s_<sup>.</sup> _s_<sup>**GVC**</sup><sup>_PureForwX_</sup> _s_<sup>**GVC**</sup><sup>_PureBackX_</sup>

# **3.3.2 Regional GVC trade**

The GVC-related trade measures presented above can also be computed so to distinguish between intra-regional and extra-regional value chain participation. The same holds for its sub-components, i.e. pure forward, pure backward and two-sided participation presented in equations (2), (3) and (4).

More specifically, given a country _s_ , member of a region _K_ , for each exporting sector _n_ , intra-regional value-chain participation is defined as the sum of : _i_ ) domestic value-added of sector _n_ re-exported by a regional member (pure forward); _ii_ ) import content of inputs sourced directly from a regional member _t ∈ K_ and exported by sector _n_ to final markets (pure backward); _iii_ ) import content of inputs sourced directly from a regional member _t ∈ K_ and exported by sector _n_ to partners that re-export them (two-sided).<sup>13</sup> Extra-regional valuechain participation is then computed as the difference between the total GVC participation and the intra-regional one. In Section S2.2.2 of the supplementary online appendix we provide a detailed derivation of these terms.

# **3.3.3 Measures of Domestic and Traditional Trade Output**

The framework developed to single out GVC-related output allows also to compute the share of output that never crosses a border, i.e. purely domestic, as the sum of the domestic inputs� � and value-added that are not exported at all, **Dom**<sup>_X_</sup> _s_<sup>=</sup><sup>**V**</sup><sup>_s_</sup><sup>**L**</sup><sup>_ss_</sup><sup>**A**</sup><sup>_ss_</sup> **L** _ss_ **Y** _ss_ + **V** _s_ **L** _ss_ **Y** _ss_ , as well as output related to traditional trade, i.e. crossing only one border before being absorbed by final demand, **Trad**<sup>_X_</sup> _s_<sup>=</sup><sup>**X**</sup><sup>_s−_</sup><sup>**Dom**</sup><sup>_X_</sup> _s_<sup>_−_</sup><sup>**GVC**</sup><sup>_X_</sup> _s_<sup>.Inthisway,wehaveobtainedafull</sup> decomposition of the output produced by a country, i.e. **X** _s_ = **Trad**<sup>_X_</sup> _s_<sup>+</sup><sup>**Dom**</sup><sup>_X_</sup> _s_<sup>+</sup><sup>**GVC**</sup><sup>_X_</sup> _s_<sup>.</sup>

# **3.3.4 Forwardness Index**

Finally, to fully assess the extent and nature of involvement in GVCs, it’s possible to compute a relative measure of participation that we will label as “Forwardness Index”. This index ranges from _−_ 1 to +1, and takes a value equal to _zero_ at the global level. It is calculated by first subtracting the measure of “Pure Backward Participation” from that of “Pure Forward

> 13See Section S2 in the supplementary online appendix for detailed formulas.