Debt-to-GDP ratio

Statistics

Main article: List of countries by government debt

]] According to the IMF World Economic Outlook Database (April 2021), 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%.

]] At the end of the 1st quarter of 2021, the United States public debt-to-GDP ratio was 127.5%. Two-thirds of US public debt is owned by US citizens, banks, corporations, and the Federal Reserve Bank;

Applications

Debt-to-GDP measures the financial leverage of an economy.

One of the Euro convergence criteria was that government debt-to-GDP should be below 60%.

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. The United Nations Sustainable Development Goal 17, an integral part of the 2030 Agenda has a target to address the external debt of highly indebted poor countries to reduce debt distress.

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". Correcting these basic computational errors 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 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.

Changes

The change of debt-to-GDP ratio can be represented as:

\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) , where\frac{B_t}{Y_t} is the debt-to-GDP at the end of the period t, and \frac{B_{t-1}}{Y_{t-1}} is the debt-to-GDP ratio at the end of the previous period (t−1). The left side of the equation shows the change in the debt-to-GDP ratio. The right hand side of the equation separates the effect of real interest rate r and economic growth g on previous debt-to-GDP, and the new debt or government budget balance-to-GDP ratio\frac{G_t-T_t}{Y_t}.

If the government has the ability of money creation, and therefore monetizing debt the change in debt-to-GDP ratio becomes:

\left(\frac{B_t}{Y_t} - \frac{B_{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)-\left(\frac{M_t}{Y_t}-\frac{M_{t-1}}{Y_{t-1}}\right)

The term \frac{M_t}{Y_t}-\frac{M_{t-1}}{Y_{t-1}} is the change in money supply-to-GDP ratio. The effect that an increase in nominal money balances has on seigniorage 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.

References

References

1. Kenton, Will. "What the Debt-to-GDP Ratio Tells Us".
2. "Budget Deficits and Interest Rates: What is the Link?". Federal Bank of St. Louis.
3. Jonathan D. Ostry, Atish R. Ghosh and Raphael A. Espinoza, "When Should Public Debt Be Reduced?", IMF Staff Discussion Note 15/10 (2015), pp. 4–6, [https://doi.org/10.5089/9781498379205.006 doi:10.5089/9781498379205.006].
4. 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. link. (2021-04-07)
5. [https://fred.stlouisfed.org/series/GFDEGDQ188S Federal Debt: Total Public Debt as Percent of Gross Domestic Product] {{Webarchive. link. (2017-02-20 Federal Bank of St. Louis.)
6. (2020-07-10). "Convergence criteria".
7. "The Challenge of Maintaining Long-Term External Debt Sustainability".
8. Bivens, L. Josh. (December 14, 2004). "Debt and the dollar". Economic Policy Institute.
9. "Goal 17 {{!}} Department of Economic and Social Affairs".
10. Krudy, Edward. (18 April 2013). "How a student took on eminent economists on debt issue - and won". Reuters.
11. (15 April 2013). "Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff". [[Political Economy Research Institute]], [[University of Massachusetts Amherst]].
12. Goldstein, Steve. (April 16, 2013). "The spreadsheet error in Reinhart and Rogoff's famous paper on debt sustainability".
13. Alexander, Ruth. (19 April 2013). "Reinhart, Rogoff... and Herndon: The student who caught out the profs". [[BBC News]].
14. (April 16, 2013). "How Much Unemployment Was Caused by Reinhart and Rogoff's Arithmetic Mistake?". [[Center for Economic and Policy Research]].
15. Harding, Robin. (16 April 2013). "Reinhart-Rogoff Initial Response". Financial Times.
16. Inman, Phillip. (April 17, 2013). "Rogoff and Reinhart defend their numbers". [[The Guardian]].
17. (11 April 2018). "An Encyclopedia of Macroeconomics". Edward Elgar.