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In economics, the debt-to-GDP ratio is the ratio between a nation's national debt and its gross domestic product (GDP). It is often expressed as a percentage of the nation's GDP. A low debt-to-GDP ratio indicates an economy that produces and sells goods and services sufficient to pay back debts without incurring further debt. Governments aim for low debt-to-GDP ratios, but geopolitical and economic considerations - including interest rates, war, recessions, and other variables - influence the borrowing practices of a nation and the choice to incur further debt. In 2011 United States public debt-to-GDP ratio was about 100%.  The level of public debt in Japan in 2011 was 204% of GDP. The level of public debt in Germany in the same year was 85% of GDP.  Almost a third of US public debt of USD $16 trillion is held by foreign countries, particularly China and Japan; the other 2/3rds are owned by US citizens, banks, corporations, and the Federal Reserve Bank.  Conversely, less than 5% of 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 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[note 1] 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.
This is only approximate as GDP changes from year to year, but generally year-on-year GDP changes are small (say, 3%), and thus this is approximately correct.
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.
Debt-to-GDP measures the financial leverage of an economy.
One of the Euro convergence criteria was that government debt-to-GDP be below 60%.
The World Bank and the IMF hold that “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.” According to these two institutions, external debt sustainability can be obtained by a country “by bringing the net present value (NPV) of external public debt down to about 150 percent of a country’s exports or 250 percent of a country’s revenues.”  High external debt is believed to have harmful effects on an economy.
In 2013 Herndon, Ash, and Pollin reviewed an influential, widely cited research paper entitled, "Growth in a time of debt",  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." Their research had significant basic computation errors that, when corrected, undermined the central claim of the book that too much debt causes recession. Rogoff and Reinhardt claimed that their fundamental conclusions were accurate, despite the errors. 
There is a difference between external debt nominated in domestic currency, and external debt nominated in foreign currency. A nation can service external debt nominated in domestic currency by tax revenues, but to service foreign currency debt it has to convert tax revenues in foreign exchange market to foreign currency, which puts downward pressure on the value of its currency. So all of the money used to service foreign currency debt has to come from a country's balance of payments transfers.
- Credit bubble
- Debt levels and flows
- Leverage (finance)
- List of countries by public debt
- List of countries by external debt
- List of countries by tax revenue as percentage of GDP
- Currency/(Currency/Time) = Time
|Wikimedia Commons has media related to Debt-to-GDP ratio.|
- "Budget Deficits and Interest Rates: What is the Link?". Federal Bank of St. Louis.
- Cecchetti, Fabrizio; Zampolli, M S (PDF). The future of public debt: prospects and implications (Report). BIS Working Papers. Bank of International Settlements. http://www.bis.org/publ/work300.pdf.
- "America's Foreign Creditors". New York Times. 19 July 2011.
- Bivens, L. Josh (December 14, 2004). Debt and the dollar Economic Policy Institute. Retrieved on July 8, 2007. p. 2, "US external debt obligations."
- Krudy, Edward (18 April 2013). "How a student took on eminent economists on debt issue - and won". Reuters.
- Herndon, Thomas; Ash, Michael; Pollin, Robert (15 April 2013). Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff (PDF). Political Economy Research Institute, University of Massachusetts Amherst. Retrieved 18 April 2013.
- Goldstein, Steve (April 16, 2013). "The spreadsheet error in Reinhart and Rogoff’s famous paper on debt sustainability". MarketWatch. Retrieved April 18, 2013.
- Alexander, Ruth (19 April 2013). "Reinhart, Rogoff... and Herndon: The student who caught out the profs". BBC News. Retrieved 20 April 2013.
- "How Much Unemployment Was Caused by Reinhart and Rogoff's Arithmetic Mistake?". Center for Economic and Policy Research. April 16, 2013. Retrieved April 18, 2013.
- Harding, Robin (16 April 2013). "Reinhart-Rogoff Initial Response". Financial Times.
- Inman, Phillip (April 17, 2013). "Rogoff and Reinhart defend their numbers". The Guardian. Retrieved April 18, 2013.