By Ricardo Reis
To quantify the reduction in debt value, one might use a simple rule of thumb: multiply the outstanding debt (101 per cent of GDP) by its weighted-average maturity (5. 4 years at the end of 2012, according to the US Treasury) and by the extra inflation (4 per cent) to get an estimate of a 22 per cent fall in the real value of debt.
Using a simple rule of thumb to estimate the effect of higher inflation on the real value of debt, they venture that US inflation of 6 per cent for four years could reduce the debt-GDP ratio by roughly 20 per cent.
The formula discounts the nominal payments (coupons and principal payments) that the government owes today weighted by the expected (risk neutral) cumulative inflation year by year. Knowing the risk-adjusted probability function for inflation, and the maturity of payments, we can therefore easily calculate the debt burden and then see how higher inflation, through either higher realisations of future inflation or shifts in the distribution for inflation, affect this burden.
If N is as large as 10 years, then 2. 5 per cent more inflation on average over the next 30 years — which previously lowered the real value of debt by 3. 7 per cent — now lowers it by 23 per cent of GDP, almost half of the value of privately-held debt.
However, in our recent work we show that the probability that US inflation lowers the real value of the debt by even as little as 4. 2 per cent of GDP is less than 1 per cent.
While these differences are important — estimates can easily double or halve across different scenarios — the conclusion remains: even for extreme counterfactuals, plausibly higher inflation has only a small impact on the real value of the debt.
This has an immediate consequence for the debt burden that the formula above makes clear: only inflation over the next few years can have any meaningful effect on the real value of the debt burden.
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