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{{Short description|Economic assessment of a country's debt}}
[[File:Gdp to debt ratio.svg|thumb|450px|lang=en|Heatmap of the development of debt-to-GDP ratio for some European countries, in percent of GDP from 1995 to 2017.]]
 
In [[economics]], the '''debt-to-GDP ratio''' is the [[ratio]] between a country's [[government debt]] (measured in units of currency) and its [[gross domestic product]] (GDP) (measured in units of currency per year). A low debt-to-GDP ratio indicates that an economy that produces and sells goods and services sufficient to pay back debts without incurring further debt.<ref>{{CitationCite Neededweb|datelast=AugustKenton|first=Will|title=What 2018the Debt-to-GDP Ratio Tells Us|url=https://www.investopedia.com/terms/d/debtgdpratio.asp|access-date=2020-09-22|website=Investopedia|language=en|archive-date=2020-09-22|archive-url=https://web.archive.org/web/20200922091913/https://www.investopedia.com/terms/d/debtgdpratio.asp|url-status=live}}.</ref> Geopolitical and economic considerations – including [[interest rates]], [[war]], [[recession]]s, and other variables – influence the borrowing practices of a nation and the choice to incur further [[debt]].<ref name=StLouisFed>{{cite web|url=http://www.stlouisfed.org/publications/cb/articles/?id=874|title=Budget Deficits and Interest Rates: What is the Link?|publisher=Federal Bank of St. Louis}}</ref> It should not be confused with a '''deficit|access-todate=2013-GDP ratio''', which, for countries running budget deficits, measures a country's annual net fiscal loss in a given year ([[Government budget balance10-09|total expenditures minus total revenue]], or the net change in debt per annum) as a percentage share of that country's GDP; for countries running budget surpluses, a ''surplusarchive-todate=2014-GDP ratio'' measures a country's annual net fiscal ''gain'' as a share of that country's GDP02-01|archive-url=https://web. archive.org/web/20140201193646/http://www.stlouisfed.org/publications/cb/articles/?id=874|url-status=dead}}</ref>
 
It should not be confused with a '''deficit-to-GDP ratio''', which, for countries running budget deficits, measures a country's annual net fiscal loss in a given year ([[Government budget balance|total expenditures minus total revenue]], or the net change in debt per annum) as a percentage share of that country's GDP; for countries running budget surpluses, a ''surplus-to-GDP ratio'' measures a country's annual net fiscal ''gain'' as a share of that country's GDP.
== Global Statistics ==
At the end of the 4th quarter of 2019, [[United States public debt]]-to-GDP ratio was at 106.7%.<ref name=freddata>[https://fred.stlouisfed.org/series/GFDEGDQ188S Federal Debt: Total Public Debt as Percent of Gross Domestic Product] Federal Bank of St. Louis.</ref>
The level of public debt in Japan was 246.1% of GDP, in China 16.7% and in India 61.8%, in 2017 according to the IMF,<ref>International Monetary Fund: [https://www.imf.org/external/pubs/ft/weo/2019/02/weodata/weoselgr.aspx All countries Government finance>''General government gross debt''(Percent of GDP)]</ref> while the public debt-to-GDP ratio at the end of the 2nd quarter of 2016 was at 70.1% of GDP in Germany, 89.1% in the United Kingdom, 98.2% in France and 135.5% in Italy, according to [[Eurostat]].<ref>[[Eurostat]] - News release: [http://ec.europa.eu/eurostat/documents/2995521/7709577/2-24102016-AP-EN.pdf/bb6c47ac-d5ed-400c-b536-fbd9b0464907 Government debt fell to 91.2% of GDP in euro area] 24 October 2016.</ref>
 
Two-thirds of US public debt is owned by US citizens, banks, corporations, and the [[Federal Reserve Bank]];<ref name=USforeigncreditors>
{{cite news
|url=https://www.nytimes.com/imagepages/2011/07/19/business/2110719_yuan_graphic.html?ref=business
|work=[[The New York Times]]
|date=19 July 2011
|title=America's Foreign Creditors
}}</ref> approximately one-third of US public debt is held by foreign countries – particularly China and Japan. Conversely, less than 5% of Italian and Japanese public debt is held by foreign countries.
 
Particularly in [[macroeconomics]], various debt-to-GDP ratios can be calculated. The most commonly used ratio is the [[government debt]] divided by the gross domestic product (GDP), which reflects the government's finances, while another common ratio is the total debt to GDP, which reflects the finances of the nation as a whole.
 
The debt-to-GDP ratio is technically not a [[dimensionless quantity]], but a unit of [[time]], being equal to the amount of years over which the accumulated economic product equals the debt.
== Units ==
The debt-to-GDP ratio is generally expressed as a percentage, but properly has units of years, as below.
 
By [[dimensional analysis]] these quantities are the ratio of a stock (with dimensions of currency) by a flow (with dimensions of currency/time), so<ref group="note">Currency/(Currency/Time) = Time</ref> they have dimensions of time. With currency units of US dollars (or any other currency) and time units of years (GDP per annum), this yields the ratio as having units of years, which can be interpreted as "the number of years to pay off debt, if all of GDP is devoted to debt repayment".
 
This interpretation must be tempered by the understanding that GDP cannot be entirely devoted to debt repayment — some must be spent on survival, at the minimum, and in general only 5–10% will be devoted to debt repayment, even during episodes such as the [[Great Depression]], which have been interpreted as [[debt-deflation]] — and thus actual "years to repay" is debt-to-GDP divided by "fraction of GDP devoted to repayment", which will generally be 10 times as long or more than simple debt-to-GDP{{Citation Needed|date=August 2018}}.
 
== Changes ==
The change in debt-to-GDP is approximately "net change in debt as percentage of GDP";{{Dubious|date=August 2018}}; for government debt, this is [[Government budget deficit|deficit]] or ([[Economic surplus|surplus]]) as percentage of GDP.{{Dubious|date=August 2018}}.
 
This is only approximate as GDP changes from year to year, but generally, year-on-year GDP changes are small (say, 3%),{{Citation Neededneeded|date=August 2018}}, and thus this is approximately correct.{{Dubious|date=August 2018}}.
 
However, in the presence of significant [[inflation]], or particularly [[hyperinflation]], GDP may increase rapidly in nominal terms; if debt is nominal, then its ratio to GDP will decrease rapidly. A period of [[deflation]] would have the opposite effect.{{Citation Neededneeded|date=August 2018}}.
 
A government's debt-to-GDP ratio can be analysed by looking at how it changes or, in other words, how the debt is evolving over time:
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<math display="block">\frac{B_t}{Y_t} - \frac{B_{t-1}}{Y_{t-1}}=(r-g)\left(\frac{B_{t-1}}{Y_{t-1}}\right)+\left(\frac{G_t-T_t}{Y_t}\right)</math>{{Clarify |reason=Variables not defined|date=August 2018}}
 
The left hand side of the equation demonstrates the dynamics of the government's debt. <math display="inline">\frac{B_t}{Y_t}</math> is the debt-to-GDP at the end of the period {{var|t}}, and <math display="inline">\frac{B_{t-1}}{Y_{t-1}}</math> is the debt-to-GDP ratio at the end of the previous period ({{var|t-}}&minus;1). Hence, the left side of the equation shows the ''change'' in the debt-to-GDP ratio. The right hand side of the equation shows the causes of the government's debt.{{Dubious|date=August 2018}}. <math display="inline">(r-g)(\frac{B_{t-1}}{Y_{t-1}})</math> is the interest payments on the stock of debt as a ratio of GDP so far,{{Citation Neededneeded|date=August 2018}}, and <math display="inline">\frac{G_t-T_t}{Y_t}</math> shows the primary deficit-to-GDP ratio.
 
If the government has the ability to [[Money creation|print money]], and therefore [[Monetizing debt|monetize]] the outstanding debt, the budget constraint becomes:
 
<math display="block">\left(\frac{B_t}{Y_t} - \frac{B_{t-1}}{Y_{t-1}}\right)+\left(\frac{M_t}{Y_t}-\frac{M_{t-1}}{Y_{t-1}}\right) =(r-g)\left(\frac{B_{t-1}}{Y_{t-1}}\right)+\left(\frac{G_t-T_t}{Y_t}\right)</math>{{Citation Neededneeded|date=August 2018}}
 
The term <math display="inline">\frac{M_t}{Y_t}-\frac{M_{t-1}}{Y_{t-1}}</math> is the change in money balances (i.e. money growth). By printing money the government is able to increase nominal money balances to pay off the debt (consequently acting in the debt way that debt financing does, in order to balance the government's expenditures).{{Clarify|date=August 2018}}. However, the effect that an increase in nominal money balances has on [[Seigniorage|seignorage]] is ambiguous, as while it increases the amount of money within the economy, the real value of each unit of money decreases due to inflationary effects. This inflationary effect from money printing is called an [[inflation tax]].<ref>{{Citationcite book|url=https://books.google.com/books?id=HSVakrh8TToC&q=seigniorage+macroeconomics&pg=PA246 |title=An Encyclopedia of Macroeconomics|first1=Brian |last1=Snowdon|first2=Howard R. |last2=Vane Needed|date=August11 April 2018 |publisher=Edward Elgar |isbn=9781840643879 |page=274 |access-date=11 April 2018 |via=Google Books}}.</ref>
 
== Applications ==
Debt-to-GDP measures the [[financial leverage]] of an economy.{{Citation Neededneeded|date=August 2018}}.
 
One of the [[Euro convergence criteria]] was that government debt-to-GDP should be below 60%.<ref>{{CitationCite web Needed|date=August2020-07-10 2018|title=Convergence criteria |url=https://www.ecb.europa.eu/ecb/orga/escb/html/convergence-criteria.en.html |access-date=2022-11-26 |website=European Central Bank |language=en}}.</ref>
 
The World Bank and the IMF hold that “a"a country can be said to achieve external debt sustainability if it can meet its current and future external debt service obligations in full, without recourse to debt rescheduling or the accumulation of arrears and without compromising growth".{{Citation Neededneeded|date=August 2018}} According to these two institutions, external debt sustainability can be obtained by a country “by"by bringing the net present value (NPV) of external public debt down to about 150 percent of a country’scountry's exports or 250 percent of a country’scountry's revenues".<ref>{{Cite web|url=https://www.imf.org/external/np/hipc/2001/lt/042001.pdf|title=The Challenge of Maintaining Long-Term External Debt Sustainability|website=[[World Bank]] and [[International Monetary Fund]]|url-status=live|archive-url=https://web.archive.org/web/20080408192556/http://www.internationalmonetaryfund.com/external/np/hipc/2001/lt/042001.pdf]|archive-date=2008-04-08}}</ref> High external debt is believed to have harmful effects on an economy.<ref>{{cite journal |last=Bivens, |first=L. Josh (|date=December 14, 2004). [|url=http://www.epinet.org/Issuebriefs/203/ib203.pdf |title=Debt and the dollar] {{webarchive |archive-url=https://web.archive.org/web/20041217041437/http://www.epinet.org/Issuebriefs/203/ib203.pdf |archive-date=December 17, 2004 }}|journal=EPI ''Issue Brief |publisher=Economic Policy Institute''. Retrieved on|number=203 |access-date=July 8, 2007. |at=p. 2, "US external debt obligations."}}</ref> The United Nations [[Sustainable Development Goal 17]], an integral part of the [[Sustainable Development Goals|2030 Agenda]] has a target to address the external debt of highly indebted poor countries to reduce debt distress.<ref>{{Cite web|title=Goal 17 {{!}} Department of Economic and Social Affairs|url=https://sdgs.un.org/goals/goal17|access-date=2020-09-26|website=sdgs.un.org|archive-date=2020-09-22|archive-url=https://web.archive.org/web/20200922124356/https://sdgs.un.org/goals/goal17|url-status=live}}</ref>
 
In 2013 [[Thomas Herndon|Herndon]], Ash, and [[Robert Pollin|Pollin]] reviewed an influential, widely cited research paper entitled, "[[Growth in a Time of Debt]]",<ref name=reuters18April2013>{{cite news|title=How a student took on eminent economists on debt issue - and won|date=18 April 2013|first=Edward| last=Krudy|url=https://www.reuters.com/article/2013us-global-economy-debt-herndon-idUSBRE93H0CV20130418|work=Reuters|access-date=5 July 2021|archive-date=26 January 2021|archive-url=https:/04/18web.archive.org/web/20210126125058/https://www.reuters.com/article/us-global-economy-debt-herndon-idUSBRE93H0CV20130418|workurl-status=Reuterslive}}</ref> by two Harvard economists [[Carmen Reinhart]] and [[Kenneth Rogoff]]. Herndon, Ash and Pollin argued that "coding errors, selective exclusion of available data, and unconventional weighting of summary statistics lead to serious errors that inaccurately represent the relationship between public debt and GDP growth among 20 advanced economies in the post-war period.".<ref name=Herndonpublicd15april2013>{{cite journal|journal=PERI Working Paper Series|issue=322|url=http://www.peri.umass.edu/fileadmin/pdf/working_papers/working_papers_301-350/WP322.pdf |title=Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff |first1=Thomas |last1=Herndon |first2=Michael |last2=Ash |first3=Robert |last3=Pollin |date=15 April 2013 |publisher=[[Political Economy Research Institute]], [[University of Massachusetts Amherst]] |accessdateaccess-date=18 April 2013 |url-status=dead |archiveurlarchive-url=https://web.archive.org/web/20130418125357/http://www.peri.umass.edu/fileadmin/pdf/working_papers/working_papers_301-350/WP322.pdf |archivedatearchive-date=18 April 2013}}</ref><ref name=blogmarketwatch2013>{{cite web |url=http://blogs.marketwatch.com/thetell/2013/04/16/the-spreadsheet-error-in-reinhart-and-rogoffs-famous-paper-on-debt-sustainability/ |title=The spreadsheet error in Reinhart and Rogoff's famous paper on debt sustainability |first=Steve |last=Goldstein |website=[[MarketWatch]] |date=April 16, 2013 |access-date=April 18, 2013 |archive-date=November 29, 2014 |archive-url=https://web.archive.org/web/20141129014051/http://blogs.marketwatch.com/thetell/2013/04/16/the-spreadsheet-error-in-reinhart-and-rogoffs-famous-paper-on-debt-sustainability/ |url-status=dead }}</ref> Correcting these basic computational errors undermined the central claim of the book that too much debt causes recession.<ref name="Alexander01">{{cite news | first = Ruth | last = Alexander | title = Reinhart, Rogoff... and Herndon: The student who caught out the profs | date = 19 April 2013 | url = https://www.bbc.co.uk/news/magazine-22223190 | work = [[BBC News]] | access-date = 20 April 2013 | archive-date = 20 April 2013 | archive-url = https://web.archive.org/web/20130420051732/http://www.bbc.co.uk/news/magazine-22223190 | url-status = live }}</ref><ref>{{cite web |url=http://www.cepr.net/index.php/blogs/beat-the-press/how-much-unemployment-was-caused-by-reinhart-and-rogoffs-arithmetic-mistake |title=How Much Unemployment Was Caused by Reinhart and Rogoff's Arithmetic Mistake? |publisher=[[Center for Economic and Policy Research]] |date=April 16, 2013 |access-date=April 18, 2013 |archive-date=April 19, 2013 |archive-url=https://web.archive.org/web/20130419112713/http://www.cepr.net/index.php/blogs/beat-the-press/how-much-unemployment-was-caused-by-reinhart-and-rogoffs-arithmetic-mistake |url-status=live }}</ref> Rogoff and Reinhardt claimed that their fundamental conclusions were accurate, despite the errors.<ref name=FT16April2013>{{cite news|url=http://blogs.ft.com/money-supply/2013/04/16/reinhart-rogoff-initial-response|date=16 April 2013|title=Reinhart-Rogoff Initial Response|first=Robin|last=Harding|newspaper=Financial Times|access-date=25 April 2013|archive-date=21 April 2013|archive-url=https://web.archive.org/web/20130421135430/http://blogs.ft.com/money-supply/2013/04/16/reinhart-rogoff-initial-response/|url-status=live}}</ref><ref>{{cite news|url=https://www.theguardian.com/business/economics-blog/2013/apr/17/rogoff-reinhart-defend-debt-study|title=Rogoff and Reinhart defend their numbers|first=Phillip|last=Inman|date=April 17, 2013|work=[[The Guardian]]|access-date=April 18, 2013|archive-date=October 18, 2013|archive-url=https://web.archive.org/web/20131018040909/http://www.theguardian.com/business/economics-blog/2013/apr/17/rogoff-reinhart-defend-debt-study|url-status=live}}</ref>
{{cite web |url=http://blogs.marketwatch.com/thetell/2013/04/16/the-spreadsheet-error-in-reinhart-and-rogoffs-famous-paper-on-debt-sustainability/ |title=The spreadsheet error in Reinhart and Rogoff’s famous paper on debt sustainability |first=Steve |last=Goldstein |website=[[MarketWatch]] |date=April 16, 2013 |accessdate=April 18, 2013}}</ref> Correcting these basic computational errors undermined the central claim of the book that too much debt causes recession.<ref name="Alexander01">{{cite news | first = Ruth | last = Alexander | title = Reinhart, Rogoff... and Herndon: The student who caught out the profs | date = 19 April 2013 | url = https://www.bbc.co.uk/news/magazine-22223190 | work = [[BBC News]] | accessdate = 20 April 2013}}</ref><ref>{{cite web |url=http://www.cepr.net/index.php/blogs/beat-the-press/how-much-unemployment-was-caused-by-reinhart-and-rogoffs-arithmetic-mistake |title=How Much Unemployment Was Caused by Reinhart and Rogoff's Arithmetic Mistake? |publisher=[[Center for Economic and Policy Research]] |date=April 16, 2013 |accessdate=April 18, 2013}}</ref> Rogoff and Reinhardt claimed that their fundamental conclusions were accurate, despite the errors.<ref name=FT16April2013>{{cite news|url=http://blogs.ft.com/money-supply/2013/04/16/reinhart-rogoff-initial-response|date=16 April 2013|title=Reinhart-Rogoff Initial Response|first=Robin|last=Harding|newspaper=Financial Times}}</ref><ref>{{cite news|url=https://www.theguardian.com/business/economics-blog/2013/apr/17/rogoff-reinhart-defend-debt-study|title=Rogoff and Reinhart defend their numbers|first=Phillip|last=Inman|date=April 17, 2013|work=[[The Guardian]]|accessdate=April 18, 2013}}</ref>
 
There is a difference between external debt denominated in domestic currency, and external debt denominated in foreign currency. A nation can service external debt denominated in domestic currency by tax revenues, but to service foreign currency debt it has to convert tax revenues in the [[foreign exchange market]] to foreign currency, which puts downward pressure on the value of its currency.
 
== Global Statisticsstatistics ==
{{See also|National debt of Japan}}
[[File:Debt to GDP.webp|thumb|300px|Debt to GDP for the [[United States]]
{{legend|#FFD932|[[List of states and territories of the United States|State]] and [[Local government in the United States|local]] debt to GDP}}
{{legend|#EE220C|[[Federal government of the United States|Federal]] debt to GDP}}
]]
[[File:European debt to GDP ratios.webp|thumb|300px|European debt to GDP ratios
{{legend-line|#001489 solid 3px|[[Greece]] }}
{{legend-line|#CD212A solid 3px|[[Italy]] }}
{{legend-line|#F1BF00 solid 3px|[[Spain]] }}
{{legend-line|#046A38 solid 3px|[[Portugal]] }}
{{legend-line|#970E53 solid 3px|[[France]] }}
{{legend-line|#FF8200 solid 3px|[[Ireland]] }}
{{legend-line|#000000 solid 3px|[[Germany]] }}
{{see also|European debt crisis}}
]]
At the end of the 4th1st quarter of 20192021, the [[United States public debt]]-to-GDP ratio was at 106127.75%.<ref name=freddata>[https://fred.stlouisfed.org/series/GFDEGDQ188S Federal Debt: Total Public Debt as Percent of Gross Domestic Product] {{Webarchive|url=https://web.archive.org/web/20170220171902/https://fred.stlouisfed.org/series/GFDEGDQ188S |date=2017-02-20 }} Federal Bank of St. Louis.</ref>
According to the IMF World Economic Outlook Database (April 2021),<ref>International Monetary Fund: [https://www.imf.org/en/Publications/WEO/weo-database/2021/April World Economic Outlook Database''General government gross debt''(Percent of GDP)] {{Webarchive|url=https://web.archive.org/web/20210407050829/https://www.imf.org/en/Publications/WEO/weo-database/2021/April |date=2021-04-07 }}</ref> the level of Gross Government debt-to-GDP ratio in Canada was 116.3%, in China 66.8%, in India 89.6%, in Germany 70.3%, in France 115.2% and in the United States 132.8%.
 
Two-thirds of US public debt is owned by US citizens, banks, corporations, and the [[Federal Reserve Bank]];<ref name=USforeigncreditors>
{{cite news
|url=https://www.nytimes.com/imagepages/2011/07/19/business/2110719_yuan_graphic.html?ref=business
|work=[[The New York Times]]
|date=19 July 2011
|title=America's Foreign Creditors
}}</ref> approximately one-third of US public debt is held by foreign countries – particularly China and Japan. ConverselyIn comparison, less than 5% of Italian and Japanese public debt is held by foreign countries.
 
==See also==
* [[CreditEconomic bubble]]
* [[Debt levels and flows]]
* [[Debt ratio]], for companies
* [[Debt-to-income ratio]], for households
* [[Leverage (finance)]]
* [[List of countries by public debt]]
* [[List of countries by external debt]]
* [[List of countriessovereign states by tax revenue as percentage ofto GDP ratio]]
 
==Notes==
{{Reflist|group=note}}
 
==References==
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{{Reflist}}
 
[[Category:GovernmentDebt-to-GDP debtratio]]
[[Category:Financial ratios]]