Japan's aging and shrinking population is causing labor shortages that should be helping workers win higher pay.

But it's not working out that way, in part because of low productivity in the areas of the greatest shortage, according to economists including Hideo Kumano at Dai-ichi Life Research Institute in Tokyo.

Labor intensive sectors like hotels, restaurants and elderly care are suffering from the biggest labor shortage.

The problem is that these same industries — which have fewer opportunities than manufacturing for automation — top the list for lowest productivity per worker.

That crimps their capacity to offer better wages.

In elderly care, the issue is aggravated by government measures to keeps compensation down, said Kumano.

"The labor market is dysfunctional and being distorted," he said.

Average monthly wages in Japan, adjusted for inflation, fell in 2015 for the fourth straight year. In 2016, they are headed for an increase of about 1 percent based on labor ministry data through September. This is well short of what is needed to achieve the central bank's 2 percent target.

Service businesses also have an added problem: a high amount of contracting and part-time employment, which tends to undermine the bargaining power of workers.

"It's not sustainable to simply raise wages without innovation," said Credit Suisse Group economist Hiromichi Shirakawa.