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September 13, 2023

Sustainability-linked bonds and public debt dynamics: a detour into sovereign debt maths

As noted in our previous blog, this deep-dive into the weeds of sovereign debt maths builds on the argument for why debt stock shouldn’t be the main focus when looking at sovereign debt sustainability.

A temporary rise in the debt stock doesn’t necessarily imply a deterioration in the debt profile if it is offset by favorable performance in other variables such as budget surpluses, low interest rates, and high GDP growth or inflation.

Debt sustainability depends on flow variables such as the primary budget balance (the difference between fiscal revenues and expenditures, excluding interest payments), the effective interest rate on debt, the prevailing inflation rate, and economic growth. A simplified version of the relationship between these variables is encapsulated in the following equation:

The first term is the primary budget balance, the second term is the growth-interest differential (r-g), or the difference between the nominal interest rate on debt and the nominal GDP (gross domestic product) growth rate.  

Debt write-downs and restructurings, including distressed exchanges such as the recent debt-for-nature swaps, are reflected in the last term — SFA, or ‘stock-flow adjustment’ — along with valuation effects due to currency movements, privatizations, and any other change that is not captured by the other concepts.  

It follows from this equation that a temporary rise in the debt stock doesn’t necessarily imply that a deterioration in the debt profile if it is offset by favorable performance in other variables such as budget surpluses, low interest rates, and high GDP growth or inflation. For instance, new debt that funds growth-enhancing investments can actually serve to lower debt burdens over time if it boosts nominal GDP.  

The role of the r-g differential is especially important in driving debt reduction. In their extensive study of the public debt since the beginning of the 19th century, ‘In Defense of Public Debt’, Barry Eichengreen and authors decompose the evolution of debt stocks over two centuries.  

They show that the contribution of the r-g differential far outweighed both budget surpluses and stock-flow adjustments during periods of significant debt consolidation such as the inter-war 1920s and post-war 1950s-1970s.  

For example, in the three decades after World War II, the average public debt-to-GDP in Advanced Economies fell by 73 percentage points (ppts) from 95% to 22%. Of this change, the g-r differential subtracted 83 ppts off the stock of debt, compared to -23 ppts from primary budget surpluses and +32 ppts from SFA.  

Figure 2. Historical drivers of debt consolidation

Debt-to-GDP (%), advanced economies

Post-World War I (1920s)

Post-World War II (1950s-70s)

A graph of numbers and a number of numbersDescription automatically generated with medium confidence

*SFA = Stock-flow adjustments

A graph of a chartDescription automatically generated with medium confidence

Source: Eichengreen et. al. (2022):  

That specific example mainly reflects a combination of robust reconstruction-driven economic growth coupled with widespread financial repression (i.e., caps imposed on interest rates). The situation facing EMDE sovereigns today is far less benign.  

War in Europe and synchronized monetary policy tightening have piled additional pressure on EMDE budgets that are still reeling from pandemic-induced fiscal overhangs and confronting escalating costs related to climate change, although higher inflation has provided some relief by eroding the real value of public debt and flattering nominal GDP growth (and thereby improving the g-r differential).  

Furthermore, the deadlock over a common framework for treating sovereign debt suggests there are limited prospects for meaningful and comprehensive debt relief in the foreseeable future.  

Issuing SLBs has genuine potential to narrow the prodigious gap in climate and nature financing (link to our ‘more for less’ paper). SLBs can also benefit public financial management and macroeconomic policy making more broadly - requiring high level of inter-ministerial coordination and robust infrastructure. Read more in our blog.

A narrow reading of sovereign risk that focuses excessively on debt stock ignores the multiple pathways through which SLBs can promote debt sustainability.

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