Hamada, 76, professor emeritus of economics at Yale University, also called for revising the BOJ Law that guarantees the central bank's independence, to make it more accountable for achieving its policy objectives.
"Generally speaking, the BOJ is making an effort. But there is hardly any change to its pace of 'too little, too late'," said Hamada, who was appointed a special adviser to Abe's cabinet.
"It is necessary to amend the BOJ law," he told Reuters in a telephone interview on Thursday.
The views of Hamada, who had been privately advising Abe before he was sworn in as Japan's prime minister on Wednesday, are likely to have a significant impact on the new government's policies.
"The BOJ should not only buy long-term bonds but purchase a wider type of assets such as commercial paper, real estate investment trusts (REITs) and shares, which will help to have an impact on the economy," said Hamada, who taught BOJ Governor Masaaki Shirakawa when he was a student at Japan's prestigious Tokyo University.
"I think buying foreign currency-denominated assets can also be a part of an effective monetary policy."
Hamada said it was desirable for the BOJ to set an inflation target of 2 to 3 percent to revive the economy and to help keep sharp yen rises in check.
While Japan should not target a specific exchange rate when guiding monetary policy, the level of the yen could be one way of measuring the extent of policy loosening, he said.
"The yen's weakening to close to 95 or 100 yen (per dollar) would be evidence of the effectiveness of monetary policy. The BOJ should ease monetary policy until inflation occurs, and the yen and prices are reacting appropriately," he said.
Abe, whose Liberal Democratic Party won a landslide victory in a lower house election on December 16, has called on the BOJ to set a 2 percent inflation target, double the bank's current goal, and to ease policy "without limits" to beat deflation. He has also threatened to revise the BOJ Law if his demands are not met, turning up the heat on the central bank.
The yen fell to a two-year low against the dollar and Tokyo stocks hit a 21-month high on Thursday, on expectations that Abe's government will pursue aggressive fiscal and monetary stimulus.
The BOJ already eased monetary policy last week via an increase in asset purchases, offering its third stimulus step in four months. It has also signaled that it will set a higher inflation target at its next meeting in January.
But Hamada, who headed the Japanese Cabinet Office's Economic and Social Research Institute, a government think tank, from 2001 to 2003, said the December measures were not enough.
"Everything the BOJ does is behind the curve," he said.
(Additional reporting by Leika Kihara; Editing by Edmund Klamann)
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