First of all, there is no federal Chinese government, it is called the Central Government of China. There is no federation any time during China's history - the central government controls everything in every province, the power of any local administration is granted by the Central Government, directly or indirectly.

Secondly, most innovations happen in Beijing, you can count whatever stats you like, such as # of patents filed, high tech start up numbers, VC funds and where they invest their $ etc. You'd be seeing more than half are in Beijing.

To give you a very quick example: Xiaomi, Didi, Mobike and OFO are the 4 unicorns of China's internet industry, all headquartered in Beijing, their R&D are done in Beijing, these four have not gone IPO and the youngest worth $1B.