User:Nick Gardner/Public debt/Tutorials: Difference between revisions

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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[http://en.citizendium.org/wiki/National_Debt/Addendum])''
===Sustainability===
A necessary  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. The dept trap,  implies, therefore,  that <br>
-&nbsp; &nbsp;if the interest rate is greater than the growth rate, sustainability requires an average  budget surplus ratio equal to at least d(r-g) and <br>
-&nbsp;&nbsp;&nbsp;if the growth rate exceeds the interest rate, it requires that the budget deficit ratio does not on average exceed d(g-r).
However, the identity embodies the implicit assumptions  that deficits earn no return, and that they do not affect  growth rates or interest rates.
Since many diferent combinations of r, g are possible the debt trap identity does not define a unique relation between the the debt/gdp ratio, d and the minimum value of surplus/gdp (or maximum value of the deficit/gdp) ratio, f that is necessary for sustainability, even under the assumptions that have been implicitly adopted.
Some light can nevertheless be thrown on the issues by inserting some typical values for r and g and by qualifying the implicit assumptions.
Interest rates are usually greater than gdp growth rates, so an average budget surplus will usually be required  for sustainability. <br> If, for example, r were 5% and g were 2% then - on the original assumptions -  a debt of 50% of gdp would require an average surplus of 1.5% of gdp a debt of 100% of gdp would require an average  surplus of 3% of gdp,  and so forth.
The first qualification to those conclusions is that a deficit devoted  exclusively to  investments having  positive net present values in financial terms would, by definition, be self-financing and would therefore not require a surplus for sustainability. Thus the debt trap applies only to that part of the debt that is undertaken for other reasons.
==International comparisons==
:( % of GDP )
:::{|class = "wikitable"
|
|align="center"|&nbsp;&nbsp;&nbsp;Japan&nbsp;&nbsp;&nbsp;
|align="center"|&nbsp;&nbsp;&nbsp;Italy&nbsp;&nbsp;&nbsp;
|align="center"|&nbsp;&nbsp; France&nbsp;&nbsp;
|align="center"|&nbsp;&nbsp; Germany &nbsp;&nbsp;
|align="center"| United States
|align="center"| United Kingdom
|align="center"| &nbsp;&nbsp;China&nbsp;&nbsp;
|align="center"| Australia
|-
|2007
|align="center"|195
|align="center"|107
|align="center"|65
|align="center"|65
|align="center"|62
|align="center"|44
|align="center"|20
|align="center"|9
|-
|2014 est
|align="center"|222
|align="center"|118
|align="center"|79
|align="center"|77
|align="center"|100
|align="center"|76
|align="center"|19
|align="center"|4
|}
::''(Source: IMF [http://www.imf.org/external/np/pp/eng/2009/030609.pdf])''
==References==
<references/>

Latest revision as of 03:28, 22 November 2023


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