Government Ponzi games and the sustainability of public deficits under uncertainty

This paper reconsiders the conditions under which a government may engage in debt roll-over schemes by financing interest payments through the issue of new debt. Output growth rates in excess of interest rates on government debt have traditionally been considered grounds for sustaining such schemes. A government may avoid debt repayment, or even run a primary deficit forever, and yet maintain a bounded debt-to-income ratio. Recent research has pointed at the stronger constraints placed on government behaviour by uncertain output growth. We show that this is not the case when an alternative criterion for solvency is used, namely that the debt-to-income ratio converges almost surely in the long run. In this case, the government is solvent when the asymptotic growth rate of the economy exceeds the asymptotic interest rate on debt, a natural extension of a familiar criterion in a deterministic environment.

Convergence to the long-run outcome may, however, be a slow process. For realistic parameter values, long-run-stable fiscal plans may resemble unsustainable plans over long horizons. This circumstance may explain the observed poor performance of debt ratios as indicators of fiscal sustainability.