According to Greenspan a debt of zero is a bad thing:
"The most recent projections, granted their tentativeness, nonetheless make clear that the highly desirable goal of paying off the federal debt is in reach before the end of the decade. This is in marked contrast to the perspective of a year ago when the elimination of the debt did not appear likely until the next decade.
But continuing to run surpluses beyond the point at which we reach zero or near-zero federal debt brings to center stage the critical longer-term fiscal policy issue of whether the federal government should accumulate large quantities of private (more technically nonfederal) assets. At zero debt, the continuing unified budget surpluses currently projected imply a major accumulation of private assets by the federal government. This development should factor materially into the policies you and the Administration choose to pursue.
I believe, as I have noted in the past, that the federal government should eschew private asset accumulation because it would be exceptionally difficult to insulate the government's investment decisions from political pressures. Thus, over time, having the federal government hold significant amounts of private assets would risk sub-optimal performance by our capital markets, diminished economic efficiency, and lower overall standards of living than would be achieved otherwise.
Short of an extraordinarily rapid and highly undesirable short-term dissipation of unified surpluses or a transferring of assets to individual privatized accounts, it appears difficult to avoid at least some accumulation of private assets by the government.
Private asset accumulation may be forced upon us well short of reaching zero debt. Obviously, savings bonds and state and local government series bonds are not readily redeemable before maturity. But the more important issue is the potentially rising cost of retiring marketable Treasury debt. While shorter-term marketable securities could be allowed to run off as they mature, longer-term issues would have to be retired before maturity through debt buybacks. The magnitudes are large: As of January 1, for example, there was in excess of three quarters of a trillion dollars in outstanding nonmarketable securities, such as savings bonds and state and local series issues, and marketable securities (excluding those held by the Federal Reserve) that do not mature and could not be called before 2011. Some holders of long-term Treasury securities may be reluctant to give them up, especially those who highly value the risk-free status of those issues. Inducing such holders, including foreign holders, to willingly offer to sell their securities prior to maturity could require paying premiums that far exceed any realistic value of retiring the debt before maturity. "
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The time has come, in my judgement, to consider a budgetary strategy that is consistent with a preemptive smoothing of the glide path to zero federal debt or, more realistically, to the level of federal debt that is an effective irreducible minimum. Certainly, we should make sure that social security surpluses are large enough to meet our long-term needs and seriously consider explicit mechanisms that will help ensure that outcome. Special care must be taken not to conclude that wraps on fiscal discipline are no longer necessary. At the same time, we must avoid a situation in which we come upon the level of irreducible debt so abruptly that the only alternative to the accumulation of private assets would be a sharp reduction in taxes and/or an increase in expenditures, because these actions might occur at a time when sizable economic stimulus would be inappropriate. In other words, budget policy should strive to limit potential disruptions by making the on-budget surplus economically inconsequential when the debt is effectively paid off.
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So a zero or close to zero debt would lead to an accumulation of private assets by the Feds and that isn't a good thing.