* Japan PM has modest immigration aims for skilled workers
* Business lobby seeks to relax rules on foreign household helpers
* Domestic help from Philippines, elsewhere work in shadows
* Plan moving slowly even though could allow more women to work
* Shows difficulty of dealing with wider immigration reform
During the early days of "Abenomics," U.S. businesses were optimistic they could convince Japan's government to make a small change to the nation's tight immigration rules to let more household helpers into the country.
But a year after Prime Minister Shinzo Abe took office, an idea that some thought might be an easy win for immigration reform while meeting a stated aim of Abe's growth strategy has made no apparent progress.
If Abe's government drags its feet on one small step, it suggests scant prospects for any broader measures to let in foreign workers any time soon - which many experts say will be necessary for Japan to sustain its economic growth in the face of a rapidly shrinking workforce.
"Japan needs to let in more foreign workers to solve its population problem," said Hidenori Sakanaka, former head of the Tokyo Immigration Bureau. "Letting in more domestic workers is just a small part of the big picture, but it might make a big difference to the people who employ them."
The proposal has been discussed by three ministries, people familiar with the process say, although Abe has not publicly mentioned the idea. Loosening visa requirements for domestic helpers could allow more Japanese women to return to full-time work, proponents say.
That is one goal in a broader Abe strategy to get Japan on the path of stable economic expansion after almost two decades of debilitating deflation and sluggish growth.
But after Abe won plaudits for pushing aggressive fiscal and monetary expansion after coming to power last December, reaction to his longer-term economic growth plans has been less enthusiastic.
His immigration-reform plans would make it easier for highly skilled immigrants to get work visas and cut the time needed to qualify for permanent residency. This falls short of the comprehensive steps needed to address the country's shrinking birthrate and burgeoning elderly population, experts say.
A quarter of Japan's population is already over 65, and that will increase to almost 40 percent by 2050. Ominously, the number of people aged 18 to 24 has shrunk by nearly a third over the past two decades.
Japan will need 10 million immigrants over the next half century to offset its projected population decline, said Sakanaka, who founded the Japan Immigration Policy Institute think tank after retiring from the bureaucracy.
Officials say changes will take time and might not be as easy as they appear on the surface.
"Before Japan decides to let in more foreign workers for certain jobs, we must first determine whether there are Japanese citizens who could do such jobs," said Yusuke Takeuchi, deputy planning director in the Immigration Bureau at Japan's Ministry of Justice.
The tangle of issues involved in employing foreign workers as housekeepers or nannies helps to illustrate the labyrinthine task Japan would face if it were to try to tackle much broader immigration reform.
There are no clear statistics on the number of foreign household helpers in Japan as many are working informally and those working legally, do so under a broad visa category. But foreign workers themselves say their numbers are shrinking.
"It has gotten much harder since I first came in 1990 on a tourist visa to look for work," said a 69-year-old housekeeper from the Philippines. She has a work visa - but on a passport bearing her dead sister's name.
She said she was forced to leave Japan a few years ago because authorities learnt she was no longer employed by her previous visa sponsor. So she said she was forced to resort to using her late sister's unblemished paperwork to get back into Japan.
Her employer, an American executive, had hoped to hire a Japanese housekeeper.
"I couldn't find anyone who would commit to full-time work and was willing to perform multiple job duties, from childcare to cleaning to marketing," she said.
Abe's plan to get more women working focuses on expanding the number of daycare centres. But Japanese women are finding that daycare centres do not stay open to match the long hours they need to adopt to compete in a male-dominated workplace.
Japanese domestic-help services exist, but many limit the hours and duties of their workers.
Foreign helpers tend to be willing to work for less and are more flexible, but only foreign diplomats and expatriates with an elite visa status can offer legal visa sponsorship and employment.
"The fact that I, as an American national and a foreigner, can sponsor a foreign domestic helper, yet my Japanese peers cannot, is just mind-boggling," said Kathy Matsui, chief Japan strategist at Goldman Sachs.
She estimates that raising women's participation in the labour force to 80 percent, matching men, could lift Japan's gross domestic product by as much as 14 percent.
"The demand is clearly there, the supply exists, but given all of the strict immigration rules here, Japan is not the obvious destination for many of these domestic helpers," Matsui said. "It's as if the government is preventing these supply and demand curves from meeting."
Underlining the point, Japanese and foreign domestic workers comprise less than 0.1 percent of the labour force, the International Labor Organization, a United Nations agency, estimates. That compares with about 0.5 percent in the United States and 7.7 percent in Hong Kong.
The American Chamber of Commerce in Japan urged the government in June to revise its immigration laws to let citizens and permanent residents with household incomes of 7 million yen ($68,200) or more to sponsor household help.
"If you keep the doors open, there are going to be, legitimately, Japanese young families who will be able to employ foreign domestic workers," said Kumi Sato, president and chief executive of public relations firm Cosmo in Tokyo, an author of the U.S. business proposal.
She said some Japanese families already hire foreign workers illegally, so the change would help legitimise some existing arrangements that fall into grey areas.