# COVID-19's Impact on International Trade
## 3 Results
### World Countries on the PageRank-CheiRank Plane
Excepting these two cases explained by extreme variations of trade volumes, we also observe for some other countries quite large variations from 2018 to 2020; e.g., Brazil gains 5 positions in CheiRank, climbing up to \(K^{*}=9\), whereas its volume of export stays stable around the 24 th position (\(\hat{K}^{*}=24\) in 2018 and 2019, \(\hat{K}^{*}=23\)). A similar gain is observed for Canada (\(K^{*}=16\to 10\)), but with a higher export volume (\(\hat{K}^{*}=12\) in 2018 and 2019, \(\hat{K}^{*}=11\)). India also gained +2 CheiRank positions, which can be attributed to its broad trade connections with Asia, Europe and America and an enhanced export of variety of products--e.g., pharmaceuticals--during the COVID-19 pandemic. Among European countries, we note that the Netherlands, Italy and Spain improved their CheiRank positions from 2018 to 2020. A more synthetic view of the effects of COVID-19 on the rankings can be observed on the PageRank-CheiRank and ImportRank-ExportRank planes displayed in Figure 2.  
Figure 1: Top 20 of countries ranked according to the PageRank, CheiRank, ImportRank and ExportRank algorithms for the years 2018, 2019 and 2020. The countries are represented by their national flag. Globally, the countries are located in the vicinity of the diagonal \(K=K^{*}\) or \(\hat{K}=\hat{K}^{*}\). Indeed, each country tries to keep, at best, a balance between its import and export volumes. Countries located below the diagonal--i.e., those with \(K^{*}<K\) or \(\hat{K}^{*}<\hat{K}\)--are better exporters than importers. Conversely, countries above the diagonal--i.e., those with \(K^{*}>K\) or \(\hat{K}^{*}>\hat{K}\)--have better import than export capabilities. Besides providing a summary of the previously discussed results obtained from the top 20 countries displayed in Figure 1, the \((K,K^{*})\) or the \((\hat{K},\hat{K}^{*})\)-plane directly allow us to observe the effects of COVID-19 on a broader range; here, with \(K,K^{*},\hat{K},\hat{K}^{*}\in\{1,\dots,50\}\). From Figure 2, the changes in rankings that are observed from 2018 to 2020 are highlighted by arrows; the tails (tips) of which show the position of countries in 2018 (2020). Figure 2, bottom right panel, shows that the import and export volumes do not vary a great deal during the COVID-19 crisis, with the exceptions of a few cases, such as Russia and Saudi Arabia, which strongly worsened their relative import-export trade balance, or Vietnam and Ireland, which improved it. The changes are larger in the PageRank-CheiRank plane (Figure 2, bottom left panel), highlighting a large-scale rewiring of the WTN as a response to the COVID-19. In addition, Figure A1 in Appendix A clearly shows that, during the pre-COVID-19 period, here from 2018 to 2019, by contrast with the period 2018-2020 (Figure 2), there are no significant variations of country positions on the PageRank-CheiRank plane and in the ImportRank-ExportRank plane. Figure 2: Distributions of countries on the PageRank \(K\)–CheiRank \(K^{*}\) plane (**left** panels) and on the ImportRank \(\hat{K}\)–ExportRank \(\hat{K}^{*}\) (**right** panels). The distributions are shown for the years 2018 (**top** panels) and 2020 (**bottom** panels). On the bottom panels, each arrow indicates the change between the two years: the arrow tail [head] is located on the point \((K,K^{*})\) for 2018 [2020]. The countries are represented by their corresponding national flag. The Kendall \(\tau\) distances (see definition in Appendix B) between the ranking lists for the different considered years are shown in Figure 3. We clearly see the influence of COVID-19, since for all the rankings, the 2018-2020 distance and the 2019-2020 distance are on average similar but they are two times greater than the pre-COVID-19 2018-2019 distance. For import (export) metrics, we observe that the distances computed between PageRank (CheiRank) lists are, on average, 3.3 (1.8) greater than those computed between ImportRank (ExportRank) lists.