NEW YORK (CNN/Money) – Individual accounts might serve as a "lockbox" for Social Security while boosting national savings, according to Federal Reserve Chairman Alan Greenspan.

"We need, in effect, to make the phantom 'lockboxes' around the trust fund real," Greenspan said in testimony Tuesday before the Senate's Special Committee On Aging.

As the system is now, the surplus that has been paid into Social Security over the past 20 years has been treated as part of the general budget and has already been spent by the U.S. Treasury.

If the accounts, as proposed by President Bush are created, workers would be allowed to divert up to a third of the payroll taxes they and their employers pay into Social Security and invest the money instead. That money would belong to them and be unavailable for the government to spend.

"The major attraction of personal or private accounts is that they can be constructed to be truly segregated from the unified budget," Greenspan said in his testimony.

In that case, he added, "the Congress is much more likely to view the transfer of funds (to these accounts) as raising the deficit and would then react by taking measures to lower it."

Here's why: the payroll taxes paid for Social Security are treated as part of the total budget. So if that revenue is reduced because workers are transferring some of their payroll taxes to individual accounts, the government's debts would appear larger relative to its income.

For example, in 2004, if Social Security'surplus had not been spent by the Treasury, the budget deficit would have been $150 billion higher than was reported.

The combination of money being set aside for a worker's retirement and the government reducing its deficit would boost national savings.

And that's good for the economy and, in turn, retirees, Greenspan asserts. In previous testimony before the House and Senate, he argued that increased national savings can provide capital for investment. Greater capital investment boosts productivity, which in turn creates the goods and services needed when one retires.

Greenspan reiterated that his support for accounts was qualified. His recommendation is to start small since there is no way to know how the market will react to an increased deficit. And he only supports them if, in fact, they do lead to measures that reduce the government deficit.

Critics of President Bush's plan argue that the creation of individual accounts further exacerbates the system's shortfall over the near term – two Democratic senators during Tuesday's hearing estimated the creation of such accounts could cost up to $5 trillion over 20 years.

(For more on Greenspan's testimony Tuesday and why he says cuts in Social Security benefits will be needed, click here.)