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==Proof of the debt trap identity==


<small>
===Projections of Public Debt 2007-2014===
Let D and Y be the levels of public debt and GDP at the beginning of a year; and,<br> let F be the primary, or discretionary budget deficit (the total deficit excluding interest payments) and,<br> let r be the annual rate of interest payable on the public debt;
:( % of GDP )


- then the public debt at the end of the year is&nbsp; D<sub>1</sub>&nbsp;=&nbsp;D&nbsp;+&nbsp;F&nbsp;+Dr; the GDP at the end of the year is &nbsp; Y<sub>1</sub>&nbsp;=&nbsp;Y(1&nbsp;+&nbsp;g); <br>and the ratio of public debt to GDP has risen from &nbsp;D/Y&nbsp;to&nbsp; (D&nbsp;+&nbsp;F&nbsp;+&nbsp;Dr)/{Y(1&nbsp;+&nbsp;g);
:::{|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"| Average <ref> average of advanced G20 countries</ref>
|-
|2007
|align="center"|195
|align="center"|107
|align="center"|65
|align="center"|65
|align="center"|62
|align="center"|44
|align="center"|79
|-
|2009
|align="center"|217
|align="center"|117
|align="center"|77
|align="center"|80
|align="center"|89
|align="center"|69
|align="center"|101
|-
|2010
|align="center"|226
|align="center"|123
|align="center"|84
|align="center"|87
|align="center"|100
|align="center"|82
|align="center"|110
|-
|2014
|align="center"|239
|align="center"|132
|align="center"|95
|align="center"|91
|align="center"|112
|align="center"|100
|align="center"|120
|}


- thus the increase in the ratio of public debt to GDP in the course of a year is:
:::::<references/>


::(D/Y)&nbsp;=&nbsp;(D&nbsp;+&nbsp;F&nbsp;+&nbsp;Dr)/{Y(1&nbsp;+&nbsp;g)}&nbsp;-&nbsp;D/Y
::(Source: ''The State of Public Finances: A Cross-Country Fiscal Monitor'',  IMF Staff Position Note SPN/09/, 21July 30 2009, [http://www.imf.org/external/pubs/ft/spn/2009/spn0921.pdf])
Let&nbsp;1/{Y(1;+&nbsp;g)}&nbsp;=&nbsp;A
&nbsp<br>
- then:<br>
:::Δ(D/Y)&nbsp;=&nbsp;A(D&nbsp;+&nbsp;F&nbsp;+&nbsp;Dr)&nbsp;-&nbsp;D/Y
::::=&nbsp;&nbsp;A(&nbsp;D&nbsp;+&nbsp;F&nbsp;+&nbsp;Dr&nbsp;&nbsp;-&nbsp;D/AY)
::::=&nbsp;&nbsp;A(&nbsp;D&nbsp;+&nbsp;F&nbsp;+&nbsp;Dr&nbsp;-&nbsp;D&nbsp;-&nbsp;Dg)
substituting for A:
:::Δ(D/Y)&nbsp;=&nbsp;{F&nbsp;+&nbsp;D(r&nbsp;-&nbsp;g)}/{Y(1&nbsp;+&nbsp;g)}
or, approximately:-
:::Δ(D/Y)&nbsp;=&nbsp;{F&nbsp;+&nbsp;D(r&nbsp;-&nbsp;g)}/Y
Let &nbsp;f&nbsp;=&nbsp;F/Y&nbsp;,and&nbsp;d&nbsp;=&nbsp;D/Y<br>


- then&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Δ(D/Y)%&nbsp;&nbsp;=&nbsp;&nbsp;f&nbsp;+&nbsp;d(r&nbsp;-&nbsp;g)
==Management of the national debt==
Responsibility for the management of the national debt rest in the United States with the Bureau of the Public Debt  <ref>[http://www.publicdebt.treas.gov/US  US Bureau of the Public Debt website]</ref>, and in the United Kingdom with the Debt Management Office <ref>[http://www.dmo.gov.uk/ UK Debt Management Office website]</ref>,  which are executive agencies of their respective Treasuries.


where f is the primary budget deficit as a percentage of GDP, and d is the initial public debt as a percentage of GDP
==Deficit-limiting rules==
The maintenance of investor confidence is a matter of mutual concern among governments  because  crises that can lead to [[sovereign default]]s can be contagious, in much the same way that bank [[Run (banking)|runs]] can generate banking panics. That consideration has prompted currency unions such as the European Monetary Union to set up deficit-limiting rules and monitoring systems.


</small>
===The EU's Stability and Growth Pact===
The Stability and Growth Pact<ref>[http://ec.europa.eu/economy_finance/sg_pact_fiscal_policy/index_en.htm?cs_mid=570 ''Stability and Growth Pact'', European Commission 2009]</ref> that was introduced as part of the Maastricht Treaty in 1992,  set arbitrary limits upon member countries'  budget deficits and levels of national debt at 3 per cent and 60 per cent of gdp respectively. Following multiple breaches of those limits, the pact has since been renegotiated to introduce the flexibility necessary to take account of changing economic conditions. Revisions introduced in 2005 relaxed the pact's enforcement procedures by introducing "medium-term budgetary objectives" that are differentiated across countries and  can be revised when a major structural reform is implemented;  and by providing for abrogation of the procedures during periods of low or negative economic growth <ref>[http://ec.europa.eu/economy_finance/emu10/emu10report_en.pdf "Fiscal Governance". para 10.2 of ''EMU@10 Successes and Challenges After 10 Years of Economic and Monetary Union'', European Commission, 2008]</ref>.
 
 
===The UK's Code for Fiscal Stability===
In November 1997 the British government  announced<ref>[http://archive.treasury.gov.uk/pub/html/docs/fpp/code/main.html ''A Code for Fiscal Stability'', H M Treasury November 1997]</ref> its adoption of two rules of fiscal conduct:<br>
:-  a "golden rule":that over the economic cycle, the government would  only borrow to invest and not for public consumption, and <br>
:- a "sustainable investment rule": that over the economic cycle, the government would ensure the level of public debt as a proportion of national income is held at a stable and prudent level (subsequently interpreted as 40 per cent of gdp);<br>
and an analysis <ref>[http://www.hm-treasury.gov.uk/d/pbr08_endofyear_403.pdf ''Meeting the Fiscal Rules Over the Past Cycle'', (1997-98 to 2006-07) - Chapter 2 of End of Year Fiscal Report HM Treasury, November 2008]</ref> published by the Treasury in 2008 concluded that:<br>
:- the average surplus on the current budget over the previous economic cycle was positive, thus meeting the golden rule; and,<br>
:-  public sector net debt  remained below the 40 per cent of GDP limit of the sustainable investment rule over the cycle.<br>
But in November 2008 the government announced <ref>[http://www.hm-treasury.gov.uk/prebud_pbr08_repindex.htm ''Pre-budget Report'', HM Treasury November 2008]</ref> the replacement of those rules by a "temporary operating rule" under which it would  set policies to improve the cyclically adjusted current budget each year, once the economy emerges from the downturn, so that it would reach balance with debt falling as a proportion of GDP once the global shocks had worked their way through the economy in full.
 
==References==
<references/>

Latest revision as of 23:55, 4 June 2010

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This addendum is a continuation of the article Public debt.

Projections of Public Debt 2007-2014

( % of GDP )
   Japan       Italy       France      Germany    United States United Kingdom Average [1]
2007 195 107 65 65 62 44 79
2009 217 117 77 80 89 69 101
2010 226 123 84 87 100 82 110
2014 239 132 95 91 112 100 120
  1. average of advanced G20 countries
  2. (Source: The State of Public Finances: A Cross-Country Fiscal Monitor, IMF Staff Position Note SPN/09/, 21July 30 2009, [1])

    Management of the national debt

    Responsibility for the management of the national debt rest in the United States with the Bureau of the Public Debt [1], and in the United Kingdom with the Debt Management Office [2], which are executive agencies of their respective Treasuries.

    Deficit-limiting rules

    The maintenance of investor confidence is a matter of mutual concern among governments because crises that can lead to sovereign defaults can be contagious, in much the same way that bank runs can generate banking panics. That consideration has prompted currency unions such as the European Monetary Union to set up deficit-limiting rules and monitoring systems.

    The EU's Stability and Growth Pact

    The Stability and Growth Pact[3] that was introduced as part of the Maastricht Treaty in 1992, set arbitrary limits upon member countries' budget deficits and levels of national debt at 3 per cent and 60 per cent of gdp respectively. Following multiple breaches of those limits, the pact has since been renegotiated to introduce the flexibility necessary to take account of changing economic conditions. Revisions introduced in 2005 relaxed the pact's enforcement procedures by introducing "medium-term budgetary objectives" that are differentiated across countries and can be revised when a major structural reform is implemented; and by providing for abrogation of the procedures during periods of low or negative economic growth [4].


    The UK's Code for Fiscal Stability

    In November 1997 the British government announced[5] its adoption of two rules of fiscal conduct:

    - a "golden rule":that over the economic cycle, the government would only borrow to invest and not for public consumption, and
    - a "sustainable investment rule": that over the economic cycle, the government would ensure the level of public debt as a proportion of national income is held at a stable and prudent level (subsequently interpreted as 40 per cent of gdp);

    and an analysis [6] published by the Treasury in 2008 concluded that:

    - the average surplus on the current budget over the previous economic cycle was positive, thus meeting the golden rule; and,
    - public sector net debt remained below the 40 per cent of GDP limit of the sustainable investment rule over the cycle.

    But in November 2008 the government announced [7] the replacement of those rules by a "temporary operating rule" under which it would set policies to improve the cyclically adjusted current budget each year, once the economy emerges from the downturn, so that it would reach balance with debt falling as a proportion of GDP once the global shocks had worked their way through the economy in full.

    References