China matters because of its size. Based on GDP, China is the second biggest country after the USA. It is not the second biggest economy because if you added up all the member of the Eurozone, their economies would collectively be larger than China. Any slowdown in China will have knock on effects for the rest of the world economy which is why it is getting so much attention right now.

Commodities, for example is an area where Chinese influence is strong. China accounts for about 50% of industrial commodities such as copper, coal or iron ore. The slowdown will affect countries that mine those commodities, mainly Australia, Canada and Brazil. There will be a knock on effect on countries that produce the heavy industrial machinery used to mine the commodities such as Germany and the USA.

China has been the major producer of mobile phones and Chinese consumers, who are among their largest purchasers, ensured that China was the fastest growing user of smartphones in recent years. Apple and a lot of tech companies who benefitted from that growth will now see some effect from a Chinese slowdown as will exporters of semi-conductors used in the manufacturing process.

Apart from these industries, worries about the effect of a slowdown might be overdone. The reason is China remains a very insular country and not very well connected to the rest of the world. China accounts for less than 1% of US GDP, 3% of German GDP and 6% of Australian GDP. For contagion to occur, interconnection must be strong, as was the case during the global banking crisis which spread to most developed countries very quickly.

Some analysts speculate that a slowdown in China is just the excuse used to justify selling off shares, causing prices to fall. Most developed stock markets are highly valued and there has not been a correction for almost four years. Other worries, such as the recent Fed decision to hold interest rates steady and worries about future corporate earnings might also have been a factor.