User:Nick Gardner/Public debt/Tutorials

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Implications of the debt trap identity

The identity

According to the debt trap identity, the annual increase in public debt as a percentage of GDP is given by:

Δd = f + d(r - g)

where d is public debt as a percentage of GDP and f is the primary budget deficit (shown with a negative negative sign if a surplus) as a percentage of GDP,

(for proof of the identity, see the addendum subpage[1])

Sustainability

A necessary but not sufficient condition for long-term sustainability is that Δd does not consistently exceed zero - since otherwise the interest due would eventually amount to a greater percentage of GDP than could conceivably be financed from taxation. Subject to two qualifications, this implies that
-   if the interest rate is greater than the growth rate, sustainability requires a budget surplus ratio equal to at least d(r-g) and
-   if the growth rate exceeds the interest rate, it requires that the budget deficit ratio does not consistently exceed d(g-r).
The first qualification is that monetised deficits do not add to public debt, and the second is that financial returns from public expenditure reduce public debt. By assumption, the interest rate and the growth rate are unaffected, but in practice they may be affected by public expenditure with positive or negative consequences for sustainability. The implications of those qualifications are discussed further in the main article.

International comparisons

( % of GDP )

	Japan	Italy	France	Germany	United States	United Kingdom	China	Australia
2007	195	107	65	65	62	44	20	9
2014 est	222	118	79	77	100	76	19	4

(Source: IMF [2])