The Debt Capacity of a Government

In a deterministic overlapping-generations economy with production and physical capital, the market value of debt is not necessarily equal to the present discounted value of future budget surpluses: it can be positive without any budget surpluses being in the offing, because debt incorporates a rational bubble. Yet the dynamics of debt remain a function of the dynamics of the primary budget deficit. The true fiscal cost of excessive government debt issuance cannot be assessed just from the current rate of interest or any current macroeconomic variable. Rather, it should be assessed in a dynamic context reflecting anticipated deficits and population growth going forward. As a way to study their joint behavior, we specify the variation of a structural deficit in the form of an underfunded social-security scheme. We define debt capacity as the level of debt that can be just sustained without a change of policy all the way to an unstable steady state. When it starts below the capacity, the debt converges to a stable steady state, in which the bubble is sustained. Above capacity the bubble unravels and the deficit cannot be financed. In several realistic scenarios occurring in economies, we calculate the needed policy response, which is the true "fiscal cost" of exceeding debt capacity.