The United States is out of its recession but recovery will be slow, unemployment remains a problem and declining stock prices are a cause for concern, says former Fed Chairman Alan Greenspan.

The unemployment rate dropped to 9.7 percent in January from 10 percent in December although jobless rates are not going to come down significantly any time soon, Greenspan tells "Meet the Press."

Jobs are created when there is new business in the economy, Greenspan says.

To get people hiring again, the government will need to aid small businesses, Greenspan says, but in any event, it's going to take a while for companies to really hire and the economy to recover because recent economic growth came partly from companies restocking inventories and not from new business ventures.

“It's going to be a slow, trudging thing, but I do think we're going to be moving forward,” Greenspan says of the economy.

“The issue here is basically innovation. Innovation by definition is not forecastable, so we don't know where the jobs are coming from.”

While the United States may be out of the worst recession since the 1930s, confidence in the country's economic direction is questionable if stock prices are any indication, sliding six percent since January.

Further declines should be a cause for concern, says Greenspan.

“It's important to remember that equity values, stock prices, are not just paper profits,” Greenspan says.

“They actually have a profoundly important impact on economic activity. And if stock prices start continuing down, I would get very concerned.”

On a positive note, home prices are likely bottoming out, Greenspan says, but cautions the U.S. cannot keep borrowing money forever.

The U.S. deficit is expected to expand to $1.56 trillion in 2011, which means the world's biggest borrower cannot remain the world's biggest power for much longer.

“History tells us that great powers, when they've gotten into very significant fiscal problems, have ceased to be great powers,” says Greenspan.

To narrow the deficit, Greenspan says, Americans will have to dig deep in their pockets and pay up.

“I have no doubts that we have to raise taxes in order to close this huge deficit,” says Greenspan.

President Barack Obama's budget for the fiscal year to Sept. 30, 2011, predicts a $1.56 trillion deficit in 2010, equal to 10.6 percent of the U.S. gross domestic product.

The Obama administration has pledged to cut the deficit going forward by slashing programs such as returning a man to the moon and instead channel spending to create jobs.

Analysts, however, remain cool to the president's spending policies.

“I don't think there is anything out there that is job creating and I don't have much confidence that some of the spending cuts will actually happen,” Peter Boockvar, an equity strategist at Miller Tabak in New York, tells Reuters.