So, will China’s problems cause a global crisis? The good news is that the numbers, as I read them, don’t seem big enough. The bad news is that I could be wrong, because global contagion often seems to end up being worse than hard numbers say it should. And the worse news is that if China does deliver a bad shock to the rest of the world, we are remarkably unready to deal with the consequences.

For those just starting to pay attention: It has been obvious for a while that China’s economy is in big trouble. How big is hard to say, because nobody believes official Chinese statistics.

The basic problem is that China’s economic model, which involves very high saving and very low consumption, was only sustainable as long as the country could grow extremely fast, justifying high investment. This in turn was possible when China had vast reserves of underemployed rural labor. But that’s no longer true, and China now faces the tricky task of transitioning to much lower growth without stumbling into recession.

A reasonable strategy would have been to buy time with credit expansion and infrastructure spending while reforming the economy in ways that put more purchasing power into families’ hands. Unfortunately, China pursued only the first half of that strategy, buying time and then squandering it. The result has been rapidly rising debt, much of it owed to poorly regulated “shadow banks,” and a threat of financial meltdown.

So the Chinese situation looks fairly grim — and new numbers have reinforced fears of a hard landing, leading not just to a plunge in Chinese stocks but to sharp declines in stock prices worldwide.

O.K., so far so bad. And some smart people think that the global implications are really scary; George Soros is comparing it to 2008.

As I suggested above, however, I have a hard time making the numbers for that kind of catastrophe work. Yes, China is a big economy, accounting in particular for about a quarter of world manufacturing, so what happens there has implications for all of us. And China buys more than $2 trillion worth of goods and services from the rest of the world each year. But it’s a big world, with a total gross domestic product excluding China of more than $60 trillion. Even a drastic fall in Chinese imports would be only a modest hit to world spending.

What about financial linkages? One reason America’s subprime crisis turned global in 2008 was that foreigners in general, and European banks in particular, turned out to be badly exposed to losses on U.S. securities. But China has capital controls — that is, it isn’t very open to foreign investors — so there’s very little direct spillover from plunging stocks or even domestic debt defaults.

All of this says that while China itself is in big trouble, the consequences for the rest of us should be manageable. But I have to admit that I’m not as relaxed about this as the above analysis says I should be. If you like, I lack the courage of my complacency. Why?

Part of the answer is that business cycles across nations often seem to be more synchronized than they “should” be. For example, Europe and the United States export to each other only a small fraction of what they produce, yet they often have recessions and recoveries at the same time. Financial linkages may be part of the story, but one also suspects that there is psychological contagion: Good or bad news in one major economy affects animal spirits in others.

So I worry that China may export its woes in ways back-of-the-envelope calculations miss, that the Middle Kingdom’s troubles will one way or another have the effect of depressing investment spending in America and Europe as well as in other emerging markets. And if my worries come true, we are woefully unready to deal with the shock.

After all, who would respond to a China shock, and how? Monetary policy would probably be of little help. With interest rates still close to zero and inflation still below target, the Fed would have limited ability to fight an economic downdraft in any case, and it has probably reduced its effectiveness further by signaling its eagerness to raise rates at the first excuse. Meanwhile, the European Central Bank is already pushing to the limits of its political mandate in its own so far unsuccessful effort to raise inflation.

And while fiscal policy — essentially, spending more to offset the effects of China spending less — would surely work, how many people believe that Republicans would be receptive to a new Obama stimulus plan, or that German politicians would look kindly on a proposal for bigger deficits in Europe?

Now, my best guess is still that things won’t be that bad — nasty in China, but just a bit of turbulence elsewhere. And I really, really hope that guess is right, because we don’t seem to have a plan B anywhere in sight.