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Who Pays and When? An Assessment of Generational Accounting November 1995

In terms of present value, imposing the zero-sum constraint is the same as requiring that the debt be retired at some time (or that interest be paid from taxes rather than further borrowing). The zero-sum constraint requires that an increase in debt be matched in present value by an increase in future net taxes. But the increase in debt is simply the present value of its interest and repayment (if it is ever repaid). Therefore, paying the higher net taxes in the future is equivalent in present value to either retiring the debt or paying the interest forever.

In traditional analysis, the zero-sum constraint is necessary if the interest rate on debt is greater than the growth rate of output. To illustrate, suppose that there is an initial debt and that the "primary deficit" (the deficit excluding interest payments) is zero. With a primary deficit of zero, current net taxes would exactly pay for current purchases. But the ratio of debt to output would rise; the debt would grow at the rate of interest, and output would grow at a lower rate. Furthermore, a vicious cycle would start because the higher debt would require higher interest payments, which would make the debt grow even more in relation to output, which would raise the interest rate, and so on.

Keeping debt from growing in relation to output would require a primary surplus equal to the interest on the debt. A primary deficit of that amount would require a permanent increase in net taxes equal to interest on the debt. Being equal, they would have the same present value, which is simply the value of the debt. That condition is just the zero-sum constraint--the higher net taxes needed to maintain stability are equivalent in present value to retiring the debt.



Why Does the Zero-Sum Constraint Matter?

In principle, some conditions might enable government to keep the ratio of debt to output stable when "rolling over" the debt; that is, government could forever issue new debt to pay interest on old instead of raising net taxes (or cutting purchases) to pay interest. In that case, each generation would inherit debt from previous generations, add to it, and pass it to following generations. In present value, the debt would never be retired.

Traditionally, economists have thought that two conditions would make persistent rollover feasible. First, the rate of interest on debt must be lower than the rate of growth of output. Second, the primary deficit must not be too large as a share of output. To illustrate, suppose the interest rate is less than the growth rate, and the primary deficit is zero. Then the ratio of debt to output will fall because debt grows at the rate of interest, whereas output grows at a higher rate. If the primary deficit was greater than zero, it would also add to debt. Consequently, the ratio of debt to output could remain stable--neither rise nor fall--if the primary deficit was greater than zero, as long as it was not too much greater. (Of course, the debt would still displace capital that the public would otherwise own.)

More recently, some economists have considered models in which rollover is feasible even if the interest rate is greater than the growth rate. That possibility arises when public debt gives people a chance to pool risk in a way that private markets cannot.⁽¹⁾ Holding public debt is less risky than holding private assets. If private markets cannot satisfy the demand for less risky assets, public debt provides a link for pooling risk between current and future generations.

One observation suggests that this could be the case. Compared with bonds, equity shares seem to earn far too high a rate of return to justify the difference on the basis of their relative risk.⁽²⁾ (Alternatively, the price of equities is too low in relation to that of bonds to explain easily the difference on the basis of risk.) Thus, there could be an unfilled demand for less risky assets that private markets cannot satisfy, although other factors might also explain the observation.

Clearly, whether or not the zero-sum constraint is necessary matters a great deal. If it is, current generations will have to contribute more or future generations will have to pay a huge bill. But if the zero-sum constraint is not necessary and the primary deficit is not too big, all future generations could pay net taxes at the same lifetime rate as current newborns and roll over the debt. Neither current nor future generations would ever have to make a sacrifice.



Can We Roll Over Debt?

Although it might succeed, trying to roll over the debt would be a gamble. So imposing the zero-sum constraint is like buying generational insurance.⁽³⁾ Debt incurred now irrevocably commits the government to make payments (as interest or repayment of debt). If rollover turned out not to be feasible, the government could make the payments when they came due only by reducing spending or raising net taxes. Reducing debt (and implicit obligations) now reduces the risk that this choice will be forced on society later.

A number of considerations suggest that a rollover policy would be risky. First, the interest rate has been above the growth rate since about 1980, and the Congressional Budget Office projects that it will remain so for the foreseeable future. Of course, those forecasts are highly uncertain, and the interest rate may fall below the growth rate. But history suggests that such a result cannot be relied upon.⁽⁴⁾

Second, the interest rate could rise above the growth rate in many periods even if it remained below the growth rate on average. Given a very long time horizon, it becomes virtually certain that the interest rate will exceed the growth rate for a long enough time to bankrupt the government if it flouts the zero-sum constraint by running primary deficits.

Third, it is not clear whether public debt fills an unmet demand for less risky assets and makes rollover feasible. The general conditions under which it is feasible are not known; there are only specific theoretical examples of economies for which it is feasible, and their relevance to the U.S. economy is not clear.

In any case, rollover is not feasible under prevailing policy; the primary deficit would grow too large in relation to output to allow rollover even if the rate of interest remained below the rate of growth. Moreover, the rate of interest is not necessarily the cost of transferring resources between periods, even if it is the relevant rate for stability of the debt. If risk makes the cost of transferring resources between periods greater than the rate of growth, rollover may be undesirable even if it is feasible.

1. ¹Olivier Blanchard and Philippe Weil, "Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games Under Uncertainty," Working Paper No. 3992 (Cambridge, Mass.: National Bureau of Economic Research, February 1992).
2. ²Rajnish Mehra and Edward Prescott, "The Equity Premium: A Puzzle," Journal of Monetary Economics, vol. 15, no. 2 (March 1985), pp. 145-162.
3. ³This analogy appears in Laurence Ball, Douglas W. Elmendorf, and N. Gregory Mankiw, "The Deficit Gamble," Working Paper No. 5015 (Cambridge, Mass.: National Bureau of Economic Research, February 1995).
4. ⁴Ibid.

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