BOSTON — Is it safe to exhale?

It felt like it this week, as the U.S. unemployment rate edged down to 9.4 percent in July — its first decline in 15 months.

Employers cut jobs in July at the slowest rate in almost a year (though that’s little consolation to the 247,000 Americans who were pink-slipped last month).

Both of these figures were pleasant surprises. Most economists thought America’s unemployment rate would go up again, and that employers would slash 320,000 jobs.

So, to use the technical term: phew.

But jobs aren’t the only source of relief lately.

Last week we learned the world’s largest economy shrank at a pace of only 1 percent between April and June. That’s good news. If you can bear to remember, it contracted 6.4 percent in the previous quarter — a sickening rate and its worst showing in 27 years.

The U.S. housing market is also showing signs of life. Last week the closely watched Standard & Poors/Case-Shiller index marked the first rise in home prices in three years, suggesting, perhaps, the worst may be over for this battered engine of the economy. Corporate profits are getting better, too: U.S. banks are back to making gobs of money and even AIG — last year’s corporate villain — this week announced its first profit in two years. Toss in rising auto sales thanks to the government’s wildly popular "Cash for Clunkers" program, (refueled by an additional $2 billion from Congress this week), plus an ebullient mood on Wall Street and it’s almost starting to feel like the good old days.

There are even quiet, hopeful murmurs that the U.S. recession may have, in fact, already ended.

""We saw it happen two weeks ago — it’s over," economist Dennis Gartman said in an interview with Fortune Investor Daily, pointing to improvements in two data points: weekly jobless claims, and a ratio from the Conference Board that divides coincident economic indicators (in English: real time data like industrial production and personal income) by lagging ones, such as unemployment.

Hope, too, has been a renewed theme out of the Obama administration in recent days.

‘‘There are signs the recession is easing,’’ U.S. Treasury Secretary Timothy Geithner said on ABC television last weekend.

"The great, great likelihood is that we’ll see growth going forward in the second half of the year," White House economic adviser Larry Summers opined to NBC television.

Even that former-economic-god-turned-Mr. Magoo character Alan Greenspan said on ABC that the crisis was "not quite" over. "But we’re getting there," he added.

So what does all this emerging, if tempered, optimism mean?

No one, of course, really knows yet. This crisis has defied most predictions. And there are still plenty of nasty things that could derail these early shoots of recovery — a surge in oil prices, a collapse of the dollar, a large-scale terrorist attack (my nervous colleague Michael Moran harbors six additional worries).

But these hopeful signs are important. That’s because the key ingredient to any economic recovery is still — and always will be — confidence. Confidence by consumers to spend again (Americans buying stuff, after all, makes up 70 percent of all economic activity in the U.S. economy). Confidence by companies to hire people again. Confidence by banks to lend individuals and businesses capital. Confidence by entrepreneurs to start new firms. Confidence by investors to take risks on innovative new technologies. Confidence by foreigners to lend Washington the staggering amount of money it needs to finance economic stimulus, health care and everything else the government spends and is planning to spend.

A sudden lack of this necessary economic swagger is one of the factors that made this global economic crisis so deep, and so painful, to so many. And its return — however tentative — is just what the doctor (in economics) ordered.

So, yes, exhale. Then shout out the good news while you can.

The U.S. economy, and the rest of the world, desperately needs it.