## 3 Results
### DfG and Economic Growth
The DfG in most other countries and regions did not change much though, especially in Africa and South America. The major changes in DfG can at least be partially be attributed to the global financial crisis in 2008. Interestingly, by 2018, as shown in Figure 2c, the DfG in India and Vietnam had decreased significantly. This clearly reflected transfer of many production activities to India and Vietnam in recent years. Overall, compared with 2008, the pattern of the spatial variation of DfG for most countries in the world in 2018 did not change significantly. This suggests that the negative impact of the 2008 global financial crisis has been quite long-lasting. Figure 1: The distribution features of the two parts of RCA index (**a,b**) and the Probability Distribution Function (PDF) of RCA index (**c,d**) for Germany and Japan under the HS4 scheme in 2018. Second, let us focus on the regional spatial aggregation phenomena in Figure 2. That is, countries with smaller DfG are mainly concentrated in North America, Western Europe and Eastern Asia, while countries with larger DfG are mainly concentrated in Africa, South America, Western and Southern Asia. It is worth paying attention to the Eastern Asia represented by China, Japan and South Korea. In 1998, the DfG in this region was larger than USA and Germany. By 2008, this gap had shrunk substantially, and by 2018, the level of DfG in this region was already comparable to that in North America and Western Europe. By now, we can conclude that this aggregated region with smaller DfG represented by China, Japan and South Korea has been well formed. It is worth noting that these three regions are not in the same region, but in the same region, the region is not in the same region. Figure 2: Spatial variations of the DfG in 1998, 2008 and 2018 under the HS4 scheme. areas with fairly small DfG are very consistent with the description of \"The world seems to have three interconnected production hubs for the extensive trade in parts and components\" in the \"Global Value Chain Development Report 2017--Measuring and Analyzing the Impact of GVCs on Economic Development\". The pattern of DfG's spatial variation suggests that DfG may be indicative of a country's economic performance. To check this idea, we have examined the relationship between DfG and GDP (current dollars) from 1991 to 2019. The result is shown in Figure 3. We observe that DfG and the logarithm of GDP is strongly negatively correlated. This means that the larger the economic scale of a country, the smaller its DfG. In other words, the larger GDP a country has, the easier for the country to have the distribution of its RCA index to converge to a Gaussian distribution. This observation suggests that the level of specialization and division of labor is connected to the deviations from normality in the distribution of a country's RCA index. Generally, the bigger a market (as characterized by GDP) is, the more its participants can specialize and the deeper the division of labor in the market can be achieved. Finally, let us turn to discuss the dynamic evolution of the DfG for a few more or less arbitrarily chosen countries, including China, India, Australia and Zambia. The results are shown in Figure 4. We observe that China's DfG basically monotonically decreases in most of the time. India has similar behavior, especially after 1999. In contrast, Australia's DfG has largely been increasing most of the time, while the DfG for Zambia has been fluctuating. Considering that DfG is highly negatively correlated with the logarithm of GDP, we have good reason to conclude that DfG characterizes the trade as well as economic structure of a country to some degree. Therefore, we can associate the temporal variation of DfG for a country with the temporal evolution of its trade and economic structure, as a result of its effort in maintaining competitiveness in the world economy. In short, in general, DfG of a country must be expected to vary with time with trends, instead of being stationary.