The NYT has a confusing analysis of the China's economy in which it tells readers that the country suffers from a labor shortage because employers in certain sectors (nursing homes and restaurants) can't afford to pay workers enough to pull them away from other sectors. This is not evidence of a labor shortage, this is the way capitalist economies work.
As an economy grows and goes through sectoral shifts there will always be businesses and sometimes whole sectors that collapse because they are no longer competitive. For example, in the United States millions of farms went out of business because they could not afford to pay workers as much money as they could earn in manufacturing. This did not mean that the United States had a labor shortage, it simply meant that many farms had become uncompetitive.
Similarly, if China has restaurants or nursing homes that can't afford to pay the prevailing wage then it means that they are not competitive. If there is real demand for these services in China, then they should be able to raise their prices enough to pay higher wages. (There may be demand for nursing home care which is not being met because people cannot afford to pay for it, but this is a problem of income distribution, not evidence of a labor shortage.)