The constraint on public debt when r < g but g < m

BIS Working Papers  |  No 939  | 
19 May 2021



Governments in advanced economies are enjoying extraordinary times. In spite of unprecedented public debt levels and consistent if not large, fiscal deficits, yields on public debt are at historical lows. In many countries, yields have even been negative for some years, sparing them the explosion in public debt-to-GDP ratio that could happen with higher yields. But why is this so, and what does this imply for governments going forward?


The paper starts with two observations: the interest rate on US government debt (r) has been below the growth rate of output (g), while the marginal product of capital (m) is above the growth rate of output (g). Based on these observations, the paper addresses three questions. First, what drives the wedges between the yield on government debt r, the growth rate of the economy g, and the marginal return to capital m? Second, given these wedges, is there a level, beyond which public debt becomes unsustainable? Last, how do monetary and fiscal policy affect the government's budget constraint, through their impact on the different wedges?


The paper builds a model where agents have opportunities for investment but face risks as well as financial constraints. By contrast, holding public debt carries no risks. This framework then delivers three predictions. First, the wedge m–r typically increases with public spending. Second, however, the amount of public debt agents are willing to hold decreases with the amount of public spending. Third, there is a maximum level of public spending beyond which the wedge m-r is not sustainable.

In addition, the paper notes that expected inflation does not affect fiscal space, while inflation volatility lowers the safety of public debt and therefore tightens the government budget constraint. Alternatively, financial repression can also create fiscal space, but this comes at the cost of resource misallocation and thereby lower growth. Redistributive policies in turn, to the extent they reduce growth, would rather reduce fiscal space.

To wrap up, there is still a meaningful constraint on how much the government can spend, when r<g<m. Yet, policies can loosen or tighten this constraint through their effect on these three different variables.


With real interest rates below the growth rate of the economy, but the marginal product of capital above it, the public debt can be lower than the present value of primary surpluses because of a bubble premia on the debt. The government can run a deficit forever. In a model that endogenizes the bubble premium as arising from the safety and liquidity of public debt, more government spending requires a larger bubble premium, but because people want to hold less debt, there is an upper limit on spending. Inflation reduces the fiscal space, financial repression increases it, and redistribution of wealth or income taxation have an unconventional effect on fiscal capacity through the bubble premium.

JEL classification: D52, E62, G10, H63
Keywords: debt limits, debt sustainability, incomplete markets, misallocation