Despite widespread claims, China is still far from a capitalist economy. There is still a considerable amount of command-and-control, and the state-owned enterprises still comprise a large and heavily subsidized sector of the economy. One aspect of a command economy with a (still) poor finance and insurance sector is that it can enforce some sharing mechanism to alleviate the consequences of local business cycle shocks or offer some redistribution across geographical regions. Such mechanisms are also in place in Western economies, mostly implicitly (for example, a national unemployment insurance) and when it is explicit, it leads to tensions as some always pay and some always receive (examples: Canada, Bolivia). Anyway, back to China.
Julan Du, Qing He and Oliver Rui find that the state-imposed fiscal channel of redistribution during the business cycle has a relatively minor impact: it dampens business cycle fluctuations by only 9%. A much larger impact comes from movements in labor, which is actually surprising as the state actively impedes such movement with an internal passport system and undocumented workers face major hurdles for public services. Still an in all, there is very little inter-provincial smoothing going on. I would have expected the central government to do a much better job in this case.