"The sooner we come to grips with this excessive level of assets on the balance sheet of the Federal Reserve-that everybody agrees is excessive-the better," he said in a " Squawk Box " interview. "There is a general presumption that we can wait indefinitely and make judgments on when we're going to move. I'm not sure the market will allow us to do that."
But if the Fed moves too quickly in reining in its accommodative policies, he added, it could shock the market, which is already dealing with a very large element of uncertainty.
Greenspan said he's not sure the markets will allow an easy exit. "Gradual is adequate, but we've got to get moving."
(Read More: Markets May Have Gone Too Far on Taper Talk: Plosser )
"The most important positive force in the economy at the moment is the fact that equity premiums are so high, which means the downside on stock prices is quite limited," he said. "If we can get stock prices to rise, which they will if this thing stabilizes, then you get a lot of asset-growth effect on the economy."
"I think the issue is not only a question of when we taper down, but when do we turn," he explained, meaning actually decreasing the Fed's balance sheet, which stood at $3.357 trillion on June 5, compared with $3.342 trillion on May 29.
"The markets may not give us all the leeway we might like to do that," he observed, pointing out that tapering is still increasing the Fed's balance sheet.
As far as the Fed's near-zero interest rate policy, he said it's helped stock prices, but the markets need to be prepared for a faster-than-expected rise in rates.
"Bond prices have got to fall. Long-term rates have got to rise. The problem, which is going to confront us, is we haven't a clue as to how rapidly that's going to happen. And we must be prepared for a much more rapid rise than is now contemplated in the general economic outlook."
(Read More: No Swoon: Job Creation Continues, Rate Up to 7.6% )
"We're still well below the [rate] level we normally ought to be at this stage," he said. "The consequence of that is that when the bond market begins to move we may not be able to control it as well as we'd like to. And that has a lot of ramifications with respect to all sorts of markets."
"I don't say that's a high probability," he qualified, "but I think we're underestimating the probability that that could happen. And not being aware of the fact that there's got to be some 'Plan B' of what one is going to do and I'm certain my former colleagues have been talking about this at great length."
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