Now everybody sing along:

"One of these central banks is not like the others,
One of these central banks just doesn't belong,
Can you tell which central bank is not like the others
By the time I finish my song?"

It's the People's Bank of China -- as Big Bird would have told you, if you'd just asked nicely -- that stands out among the three big central banks that currently have the power to move the global economy.

It's not because the People's Bank faces a significantly smaller challenge than that confronting the Federal Reserve or the European Central Bank. Reviving the growth rate of China's economy while rebalancing the country's economy without letting inflation loose is a bigger problem than the Fed faces, and it's not all that much simpler than figuring out how to fix the euro.

And it's not because the People's Bank is structurally superior to the Fed or the ECB. I think that along a continuum of power in its home economy, it falls somewhere between the Federal Reserve and the European Central Bank.

No, the big difference is that alone among the big three central banks, the People's Bank can count on fiscal policy from the government to do some of the heavy economic lifting. While the Fed looks at a hamstrung national government that will be lucky to avoid sending the U.S. economy over a fiscal cliff come 2013, and while the European Central Bank can't count on anything stronger than words about the need for economic growth from national governments, the People's Bank has the luxury of holding its fire while national and local governments put billions to work to increase growth.

I'm not saying that those government actions in China aren't without long-term dangers. I am saying that the Chinese economy isn't dependent on its central bank in the same way that the U.S. economy and the eurozone economy are currently dependent on theirs.

And investors should factor the way that the People's Bank is not like the others into their decisions on when to put money into the currently very-depressed Chinese stock market.

The China slowdown

Right now, slowing growth in the Chinese economy is enough to send shock waves through the Hong Kong and Shanghai markets, through the stock markets of emerging economies dependent on selling commodities to China, and through the global economy -- whenever it manages to stop worrying about the Greek/Spanish/Italian debt crises.

How slow? Chinese gross domestic product grew at an annual rate of 7.6% in the second quarter. That was the slowest pace in three years. In recent days, that has led economists to cut their forecasts for third-quarter and full-year growth. ING, for example, projects that China's GDP growth will fall to a 7.1% annual rate in the third quarter; Bank of America is looking for 7.4% growth in that quarter. That would bring full-year growth to just 7.5%, according to ING and UBS. That would be the lowest growth rate in 22 years.

That slowdown in growth and those projections for a further slowdown sure haven't been good for Chinese stocks. For the past year (through Sept. 7), the Shanghai Composite Index is down 14.8%, and for 2012 to date the index has dropped 3.3%. That's even worse than it seems when you compare it with other indexes; the U.S. Standard & Poor's 500Index ($INX), for example, is up 24.6% for one year and 14.3% for 2012 to date.

In the longer term, you have to go back to March 2009 to match the Sept. 7, 2012, close of 2,128 on the Shanghai index. (And that Sept. 7 close is an improvement from the August low of 2,038.)

The Shanghai Composite Index does look cheap, trading recently at a trailing 12-month price-to-earnings ratio of just 11.47. (In comparison, the trailing 12-month PE ratio on the S&P 500 was 16.66 on Sept. 7. That's up from 14.34 a year ago. The consensus analyst forecast puts the forward PE at 13.36.)

But even at a PE ratio of 11.47, Shanghai stocks are cheap only if earnings over the next 12 months are going to be higher than they were over the past 12 months. And there's where doubts come roaring in. Recent data suggest that China hasn't finished slowing. According to data from the National Bureau of Statistics, released Sept. 8, production in August grew at an annual rate of just 8.9%, the slowest growth since May 2009. Investment in fixed assets, a key driver of China's economy, grew by just 20.2% in the first eight months of 2012. That was below the 20.4% growth projected by economists. China's customs service announced Monday that imports in August slid by 2.6% from the same period last year. Exports climbed by 2.7%. That was below economists' projections.