Shirakawa calculates that a 10 percent-or-so fall in the yen's value adds only 1 percent to export volumes over two quarters, half of the effect it had in the period before the global financial crisis.
That is because of the "hollowing out" of Japanese manufacturing as firms shift production and procurement overseas. Years of yen strength contributed to that shift, but the currency's retreat failed to reverse the trend as the desire to move closer to faster growing markets, tariffs, lower taxes and labor costs all played a role.
A Cabinet Office survey of manufacturers showed the share of overseas production of Japanese companies rose to 17.7 percent last year from just over 13 percent a decade ago and is seen reaching 21.3 percent in five years.
Another survey by the trade ministry showed that overseas investment as a share of manufacturers' capital spending has also been climbing, reaching a record 21.5 percent in fiscal 2011/2012 compared with 15.9 percent two years earlier.
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"Steps are needed such as corporate tax cuts and promotion of free trade pacts in order to encourage firms to locate their bases at home," Miyagawa said.
"Without such efforts, the economy will go into a steady decline," he said. Japan has started negotiating trade pacts with the European Union and Pacific Rim nations led by the United States, but it continues to debate the merits of cutting corporate taxes that are among the highest in the developed world.
Finance Ministry data shows that while the yen's decline has driven up the yen value of exports, boosting exporters' earnings, it has failed to shore up export volumes which peaked in 2007 and have been in a steady decline since 2010.
That reflects both the declining share of products "Made in Japan" in companies' overseas sales and their reluctance to risk trade tensions by using the yen's weakness to boost market share by cutting overseas prices, analysts say.
While export prices calculated in yen rose 14.3 percent in the year to July, when measured in contract currencies they only declined by 1.5 percent, Bank of Japan data showed this month.
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Japanese carmakers are a case in point. Most, including Toyota Motor and Honda Motor, have reported a decline in export volumes so far this year, partly because they continue to shift production abroad.
For example, Honda moved the production of its popular CR-V SUV a year ago from its Sayama plant near Tokyo to its North American factory.
Japanese carmakers have also avoided cutting prices for their exports in major overseas markets, partly because of sensitivities in the United States and elsewhere about Japan using the yen's weakening to gain a competitive edge.
Economists say as long as Japanese exporters choose to cash in extra profits rather than aggressively pursuing bigger market share abroad, thus boosting business investments at home and wages, the weak yen will have little effect on economic growth.
"The key for the effects of a weak yen is whether export prices will be reduced and thereby export competitiveness will rise," Masahiko Hashimoto, an economist at Daiwa Institute of Research, said in a research note.
"As long as export volume does not rise markedly, there's no need to boost domestic production, so it won't have much ripple effect on the economy."