The most China can realistically do for the struggling global economy is to ensure its own growth holds up, and that won't be nearly enough to lift the world.
Visions of China putting its $3.2 trillion (2.07 trillion pounds) in reserves to work by launching another government spending spree or buying up European bonds ignore the political and economic reality that China, like any other country, puts its own needs first.
Right now, China's economy doesn't need more stimulus and its leaders are wary of making bad bets on European debt, which means if conditions worsen in the United States or Europe, China would respond only if and when trouble shows up at home.
But even if you sweep aside domestic considerations and imagine Beijing announced $600 billion in government spending, like it did after the Lehman Brothers collapse in 2008, there is little chance it could deliver the same economic boost.
What ended the post-Lehman panic was a globally synchronised, massive infusion of government spending and interest rate cuts. The United States and Europe cannot deliver significant doses of either right now, and China alone can't compensate.
"China to the rescue? Mission impossible," said Jun Ma, Deutsche Bank's chief economist for China, based in Hong Kong.
To offset the impact of a 3 percent drop in U.S. and European growth, China would need to increase its own growth by 18 percent, he said.
WHAT CHINA MAY DO
The image of China riding to the world's rescue after Lehman misses a critical point: China's response made sense for China. That it also came at an opportune time for the rest of the world was a bonus.
Back then, China, the United States and Europe were on the same page. Lower interest rates and higher government spending were the logical policy choices in every major economy as confidence evaporated and global trade collapsed.
Not so today.
China's stimulus package carried some unpleasant side effects that are still causing trouble in the economy today. The two biggest issues -- high inflation and heavy local government debts -- argue strongly against Beijing going for a bold new spending plan now.
China's Communist Party prizes stability. Runaway inflation can trigger social unrest. Tales of squandered public money can spark outrage too.
But if conditions worsen abroad and China's own economy shows signs of slowing more sharply than expected, there is some room to ease. The grand total would probably be well shy of the $586 billion post-Lehman package.
Beijing already expects growth to slow next year, and in fact would welcome a modest cool-down to ease inflation. A government official acknowledged earlier this month that 2012 growth may dip below 9 percent for the first time in a decade.
Anything below 8 percent would certainly set off alarm bells. Many economists consider that the minimum needed to generate enough jobs for a rapidly urbanising population.
Barclays economists recently cut their 2012 growth forecast to 8.4 percent, joining a long list of economists predicting growth will sink close to that critical line.
If that threshold were threatened, China's most likely approach would be to direct spending to areas Beijing has already identified as underdeveloped or in need.
The investment list would probably include building more housing for low-income families, developing agriculture, or perhaps cutting taxes for small- and medium-sized businesses.
For the rest of the world, such measures might mean a bit more demand for building materials and perhaps a slight uptick in consumer spending that benefits multinational companies.
But if the United States or Europe slips into even a mild recession, the lost output would quickly dwarf any incremental Chinese growth.
In 2009, the worst phase of the global recession, U.S. gross domestic product fell 3.5 percent.
Let's say it drops a relatively modest 1 percent in a new downturn. That would work out to about $133 billion, or roughly 23 cents out of every dollar China spent in its last stimulus.
As for buying more European debt or perhaps increasing IMF funding, there is some scope for Beijing to help. But that will involve overcoming strong opposition from some important officials -- not to mention incurring taxpayers' ire should the investments go sour.
"Europe should absolutely not put too high expectations on China," Wei Jianguo, a former Chinese vice commerce minister who now heads a top government think tank, told Reuters in an interview on Thursday.
WHAT ELSE CHINA COULD DO
Ironically, stepping up stimulus spending would take China in the opposite direction from what the Group of 20 has recommended to try to even out imbalances between surplus and deficit countries.
China is often accused of over-investing and doing too little to spur domestic demand. Investment now amounts to almost half China's GDP, higher than even 2008, when Beijing ramped up spending to host the Olympics.
One of the most valuable contributions China could make to rebalance the global economy and lift growth is to let the tightly managed yuan currency rise more rapidly. It appeared ready to do so in August, when the central bank set a series of record-high trading midpoints.
But it pulled back a bit in September. If anything, some investors are now betting that the currency will weaken in the next year, although that also looks unlikely.
A stronger yuan would give the rest of the world a competitive advantage in trade and boost Chinese consumers' spending power. But Beijing is worried that it would hurt its own exporters, who are vital for job creation.
China could also lower interest rates. The People's Bank of China has raised interest rates five times since October, and could conceivably unwind some or all of those moves.
However, Beijing seems reluctant to make that move. Premier Wen Jiabao has insisted that fighting inflation remains the top policy priority. That suggests the most likely central bank course is a pause, not a cut.
WHAT CHINA WON'T DO
As long as price pressures are high, China will play conservatively no matter what the rest of the world might want it to do.
Just as the U.S. Federal Reserve dismissed criticism of its $600 billion bond-buying programme by pointing out that a stronger U.S. economy was good for the world, Beijing can argue that a stable China is in everyone's best interest.
Annual inflation was running at 6.2 percent as of August, well above Beijing's target of 4 percent. Five interest rate hikes and nine increases in bank reserve requirements in the past year have not been enough to cool prices.
Too much money finds its way into the economy through non-bank lending. Indeed, some economists warn that China's shadow banking system looks ominously similar to that of the United States before the last financial crisis -- enormous, murky, and loosely regulated.
Flooding the economy with more money through a huge stimulus package would only make matters worse.
Big questions remain over how the last pot of money was spent. Beijing encouraged banks to lend freely to government projects such as railways, airports and roads. Some of the loans have soured, and local government defaults now pose one of the biggest threats to China's growth.
Local governments liabilities amount to nearly 27 percent of China's total annual output, and some economists think as much as a quarter of that total could end up in default.
If Beijing has to bail out those local governments, its pockets suddenly won't look so deep, and the rest of the world's problems would have to wait.
"China's role this time around will be different," said Yi Xianrong, an economist at the Chinese Academy of Social Sciences. "China is suffering a big hangover from what it previously did, which has created huge risks in the Chinese economy. The role that China can play is minimal."
(Reporting by Emily Kaiser in Singapore; Additional reporting by Alan Wheatley in London and Kevin Yao in Beijing)