Only the big matter?

It seems that only the US, China, the EU (especially Germany, France and Britain) matter to the world economy. Maybe some OPEC countries could influence the world economy by affecting the oil price, but as currently they could not meet any agreement in the meeting, their influence will be much weakened. The three economies I just mentioned are the three largest economies. People always say that globalisation makes our economies more interacted; it is partially true as it is only true if the economy is significantly large. Japan is another large economy. It does have some influence on the other economies, especially the Asian economies. However, in terms of the global economy, it becomes much less insignificant. As we can see that the Japanese economy has been in a bad shape for decades, the world economy is going on a different path. The Brazilian economy is in recession, but it seems that there is no influence on the world economy. It is not because only the biggest economies matter, it is because when we are talking about the world economy, we only take the largest economies into account and leave out the rest of the world. Although these three economies could represent a large part of the true economy, it is still worth to take all economies into account with different weights which depends on their population sizes.