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 dept 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 so 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).

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])