For a couple of days last week, the Dow Jones industrial average hung above 10,000, a symbolically significant position it hadn’t occupied since Oct. 3, 2008, when the bottom was falling out of the financial markets. At the end of the week, though, investors seemed to tire of propping up the best-known of stock market indexes, and it slid back to 9,996. The question is whether we should be sad or relieved.

The Dow has been climbing for a while and is up roughly 50 percent from the low point the index reached in March. But it should be clearly understood that stock prices, and the Dow in particular, are notoriously bad at predicting the course of the economy’s future performance.

In the long run, of course, stocks rise and fall with the economy. But panic and irrational exuberance are both well-entrenched behaviors among stock investors that greatly exaggerate price swings. And the old saw is roughly right that the stock market has predicted 12 of the past five recessions.

So, while stocks are relatively happy these days because the economy is on the mend, that doesn’t mean that they are sending the correct signal. It may be the case that stocks are in for another fall.

Most analysts predict that the recession — the macroeconomic measurement that shows the economy has been contracting on a broad scale — is over. And since the opposite of contraction is expansion, that should mean good times for all. Except that those same analysts, including smart folks at the Federal Reserve, at the Treasury and in many corporate boardrooms, are also afraid that the rebound will be muted at best. Mostly that’s because there is no job growth now and no prospect for job growth anytime soon.

The truth is, the economy is still hemorrhaging payroll positions at an alarming rate. September saw employers shed 263,000 jobs — equal to more than 3 million losses a year. That’s more lost jobs than disappeared during the duration of every recession since 1945. This is not good.

So how do we reconcile these two closely watched indicators? Over the past half-century, changes in payrolls from time to time correlate with changes in the Dow, though frequently with a lag. At least the two typically move in the same direction. But right now these two gross measures of the economy are very far apart. Stocks are rising rapidly while jobs are merely disappearing at a slower pace.

The surprise is that investors see room for stocks to rise when ordinary Americans remain gloomy about their prospects for work, a condition that’s guaranteed to suppress consumer spending. And if consumers aren’t buying, then companies aren’t selling — and dividend payments to shareholders will be constrained. So, the question recurs: Why are stocks up?

Leading or Lagging?

There are two possible answers to this question. Investors are irrational in their hope for the future. Or they aren’t.

Consider the first. We have only the most tentative signs that manufacturing is picking up. After the “cash for clunkers” ran out, retail sales faltered. And there’s those pesky jobs numbers. The economy has to turn around at some point, and investors may just be trying to be the first through the door — if only so they can be the first to unload in an effort to squeeze out pennies per share in capital gains. It’s also worth remembering that the dollar is cheap overseas these days. Stock purchases abroad increased in the second quarter, and there’s no reason to think that didn’t happen again in the third. So maybe all we’re seeing is a bit of opportunism.

As for the second possible explanation, maybe investors are paying attention and believe correctly that the sun is rising again, if slowly. Next week the government will release its initial estimate of gross domestic product for the third quarter, and odds are that it will show the first expansion in more than a year. That may be all that stock investors are waiting for.