In economists' terms that potential can rise only as a result of an increase in capital, labour or greater productivity in using them.
The International Monetary Fund reckons 2 percent is possible provided Japan tackles all three with deregulation, tax and labour market reforms, bringing more women and elderly into the workforce and easing curbs on immigration.
"If everything that we are suggesting is introduced as a package then medium term potential growth could increase from around 1 percent to 2 percent," said Giovanni Ganelli, senior economist with the IMF Asia-Pacific office in Tokyo.
That is a big if.
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Sceptics say demographic headwinds are so strong -- the 18-24 age group is a third smaller than two decades ago -- that nothing short of a miraculous burst of innovation will do, given significant immigration remains a political and social taboo.
But while Abe has been telling audiences from London's City to Wall Street that "Japan is back", at home many plans aimed at lifting the economy's metabolism have been watered down, delayed or shelved.
The hard yards
Asked what the Abe administration has done so far to benefit Japan in the long-run, most economists point to decisions to join talks on the U.S.-led Trans Pacific Partnership (TPP) free trade pact and to raise sales tax next April.
The TPP is expected to open some new markets for Japan but also bring more competition at home while the tax hike marks a first serious step to address the sorry state of public finances, a major source of uncertainty.
The Bank of Japan's monetary stimulus can also help boost long-term growth if it succeeds in defeating deflation, economists say.
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"The inflationary environment makes it easier for companies to invest, hire and produce," said Masahiro Kawai, head of the Asian Development Bank Institute in Tokyo.
Some economists also mention the government's efforts to shorten waiting lists at day-care centres to allow more women to return to the workforce, though many say much more is needed, including further changes in the tax code and corporate culture.
But the list of disappointments is far longer.
Nomura Securities economists estimate the government's growth strategy will add just over 0.3 percent to annual output by 2020 -- not exactly the comeback Team Abe has been promising.
Scant progress in tackling labour market rigidities and a deep divide between well protected regular workers and a growing army of temporary and part-time staff tops the disappointment list.
Japan's labour productivity, at less than two-thirds of U.S. levels, offers ample room for improvement but companies must first feel more comfortable to hire and train staff.
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"Corporations are afraid to go into new areas in Japan because once they hire people it is almost impossible to fire them," says Tomo Kinoshita, chief Japan economist at Nomura Securities.
Yet a proposal to test labour liberalisation in special economic zones got struck out from the final plan.
Decisions on two other items high on corporate wish lists have been pushed back: a cut in corporate tax, now one of the highest in the OECD, and social security reform.
"If anything there's re-regulation happening now," says Takuji Okubo, chief economist at Japan Macro Advisors. He says he learned it first-hand this year when he applied for a subsidy for start-ups as founder of his research boutique.
"The growth strategy is just a way to let the bureaucrats tell businesses how to spend the money."