Remember Friday, August 7?

That day the stock market tacked 114 points, a huge gain for a market that was looking tired, onto the Dow Jones Industrial Average on news that jobless rolls, rather than swelling by 328,000 as economists had expected showed an increase of just 247,000. That was a huge improvement on the 467,000 jobs lost in June.

The conclusion was that the economy had entered recovery. The headline in the New York Times on the news was representative: “Job Losses Slow, Signaling Momentum for a Recovery.”

And, so with recovery from the Great Recession just around the corner, stocks rallied. Even though it was a Friday, when, normally stocks sell off after a good week. And even though the stock market was looking over-extended and everyone had started to inch toward the exits in preparation for a correction.

Investors—and financial writers—had time to peak into those numbers over the weekend. And by Monday they’d concluded that the top-line results weren’t nearly as conclusive evidence of a recovery as they’d thought.

That’s why the Dow Industrials, which had closed at 9370 on Friday dropped as low as 9290 on Monday and why the Standard & Poor’s 500 dropped as lo9w as 1001.

How seriously should we take those second thoughts? Pretty seriously think. They don’t negate the whole “the economy is recovering” story line, but they do suggest that what’s behind this story is still more wishful thinking than hard evidence.

Begin with the question of where the improvement—the difference of 81,000 between the expected 328,000 in job losses and the reported 247,000– came from. Some came from hiring by federal and local governments as a result of the Obama stimulus package. Those two classes of employer added 7,000 jobs in the month. The consensus forecast had predicted that this sector would net out to job losses.

A bigger chunk came from the auto industry. In normal year, the auto industry lays off workers in July as they shut factories to retool for new models in the fall. But this year, by the time we got to July most of the big layoffs were over. They had taken place in May and June. The auto industry still cut jobs in July—about 8,000—but because of seasonal adjustments to the data (to take account of the normal layoff pattern), the auto industry wound up being credited with adding 28,000 jobs.

Let’s go from the raw numbers to the unemployment rate. A lot of the cheering on Friday was caused by the drop in the unemployment rate to 9.4% from 9.5%. The cheering, to be fair, wasn’t Hip-hip-hooray unemployment is just 9.4%—everyone agrees that 9.4% unemployment is horrendous—but for the decline in the rate. A move from 9.5% to 9.4% was a step in the right direction after months where every move was a move from bad to worse.

Unfortunately, the decline in the unemployment rate was a result of discouraged workers leaving the workforce. In the month 422,000 people who had been looking for work stopped. They had become so discouraged that they couldn’t even be bothered to tell government survey takers that they were looking for work.

If all these people get figured back into the statistics, the unemployment rate in July edged up to 9.7% from 9.5% in June.

The Bureau of Labor Statistics collects a broader unemployment number than the one that’s reported by most of the press. It includes the above people who are so discouraged that they’ve stopped looking for work and also people who are currently working part time but who say they want to work full time but can’t find a full-time job.

By that measure the unemployment rate isn’t 9.5% or even 9.7% but 16.3%.

The number of people who are unemployed, however you define that, isn’t the only important number. The duration of unemployment is also critical. (There’s a good discussion of why being unemployed for six months or more is a really bad thing for people’s ability to eventually get a job on the Freakonomics blog at http://freakonomics.blogs.nytimes.com/2009/08/07/more-on-the-stimulus/ )

And here the numbers continue to look downright ugly. The average duration of unemployment is now up to 25 weeks (that’s roughly 6 months, a key tipping point) and about a third of the unemployed has not been out of work by more than 27weeks. That’s the highest level recorded since the end of World War II.

The long-term unemployed take the longest to be rehired in a recovery. That there are so many workers in this category is one more reason to think this will be a very slow recovery.

Whenever it arrives.

The further we get away from the headlines of Friday, the more these second thoughts are likely to be a drag on investors’ animal spirits.

For the stock market to continue to rally over the rest of August, it will have to find a way to drag these second thoughts uphill with it.