the VAX ratio from country 1 to country 2, but they simultaneously raise the VAX ratio from country 1 to country 3 as they contribute to the exports of value added, without any direct export transactions.

Timmer et al. (2015) calculate the aggregate VAX index for a range of countries using four different global input-output databases. While the exact values for each country varies a bit for different sources, the overall country rankings is quite similar. Unfortunately, they do not include the Eora data in their calculations, but we expect similar results also for this source of information as it is constructed using similar official data sources. The VAX ratios are highest for more isolated countries that specialize in exports of raw materials, e.g. Russia and Australia, while it is lowest for smaller countries that are strongly integrated in regional production networks, such as smaller EU countries, e.g. Luxembourg and Slovakia.

The VAX ratio can also be calculated for specific sectors. In that case, the sector-specific VAX ratio will also deviate from unity as its exports will embody domestic value added from other sectors if some inputs are sourced domestically. At the same time, a sector’s VAX ratio will increase to the extent that its output is embedded in exported products of other sectors.

Los, Timmer and de Vries (2016) proposed a very intuitive way to calculate the domestic value added content in exports using the extraction method. The idea is to set the final demand for one country’s output in the rest of the world equal to zero, but leave the entire production structure, both domestically and internationally, unchanged. Foreign sectors will still use inputs from this country in their production structure, but they will no longer have direct final demand for its output. We can solve this modified IO system for the counterfactual vector of GDP values in each country-sector. The difference between the actual GDP of a country and this counterfactual GDP equals the domestic value added contained in a country’s exports.

The domestic value added content of trade can also be calculated on a bilateral basis, but we are only interested in each country’s total domestic value added, summing up across all of its export destinations. In practice, we start from the country-specific IO tables that we discussed earlier and collapse them one step further, combining all export destinations. This leads to the following IO system, that we represent here in simplified form: The _GO_ vector stacks the gross output vector of both countries, first the country under study and below the rest of the world aggregate. The number of rows are twice the number of sectors _S_ in the IO table. The _FDc_ vector similarly stacks the final demand of country _c_ for both types of products: the first _S_ elements is demand for output of country _c_ itself and the next _S_ entries is demand for output produced in the rest of the world. The _FDrow_ vector similarly stacks all final demand from the rest of the world, with again demand for output from country _c_ in the first _S_ rows of the vector. The matrix _A_ is the global IO matrix that has dimensions (2 _S_ ) x (2 _S_ ). Using the input coefficients in matrix _A_ , we can calculate value added once we know the gross output of a country-sector.

As discussed above, we can simply replace the actual final demand from the rest of the world for products from country _c_ , i.e. the first _S_ elements in the _FDrow_ vector, by zero. We then solve for a counterfactual _GO_ vector that will imply lower equilibrium output from all 30