Root Issue for USA Budget Impasse

What happens when the national debt matches or exceeds the GDP? --Yahoo!answers question from "Gardenfoot"

The interest rate we pay on the debt usually is equal to or a little more that the growth rate of the GDP, That means that we must tax enough to not only pay for current government services but also the interest on the debt, or it will grow as a faction of GDP until we will not be able to pay the interest so we will default. It can be managed, the debt was 110% of GDP at the end of WWII and after the wars with Napoleon England had a debt of about 200% of GDP. Our problem today it that we did not get our debt because of extraordinary events that required spending that will end, but because we did not want to pay for government services that people still want, so it is difficult to either cut them or increase taxes to pay for them
--Yahoo answer from "Meg" –and she’s right!

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From Oxford University in 2007:

• When the interest rate on government debt exceeds the growth rate of GDP, the debt-to-GDP ratio will increase without bounds.

• The dynamics of debt accumulation can only be stopped if the primary budget deficit (as a percentage of GDP) turns into a surplus.

• Alternatively, it can be stopped by seigniorage [itself the difference between the value of money and the cost to produce and distribute it, [ie, hardening the currency]

-- Chapter 10, Fiscal Policies in Monetary Unions, Oxford University Press powerpoint presentation in 2007, slide 7 – see

http://www.uwlax.edu/faculty/brooks/mcts/slides/chapter10_7ed.ppt
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Debt to GDP Ratio [from Wikipedia]
In economics, the debt-to-GDP ratio is one of the indicators of the health of an economy. It is the amount of national debt of a country as a percentage of its gross domestic product (GDP). A low debt-to-GDP ratio indicates an economy that produces a large number of goods and services and probably profits that are high enough to pay back debts. Governments aim for low debt-to-GDP ratios and can stand up to the risks involved by increasing debt as their economies have a higher GDP and profit margin. 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 ear was 85% of GDP. Almost a third of US public debt of USD 16 trillion is held by foreign countries, particularly China and Japan. 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.

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 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.

Changes
The change in debt-to-GDP is approximately "net increase or (decrease) in debt as percentage of GDP"; for government debt, this is deficit or (surplus) as percentage of 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.

Applications
Debt-to-GDP measures the financial leverage of an economy; some economists, such as Steve Keen, advocate using it as the key measure of a credit bubble (both its level and its change – particularly of private debt and total debt), and high levels of government debt (public debt) are widely decried as fiscal irresponsibility.

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.

Economists Reinhart and Rogoff Warn
of Risks of High Debt-to-GDP Ratio
This Time is Different: Eight Centuries of Financial Folly (2009) was published just after the financial crisis of 2007-2008. In This Time is Different they studied the striking similarities of the recurring booms and busts that have characterized financial history.
Herndon, Ash and Pollin reviewed an influential, widely cited research paper entitled, "Growth in a time of debt," by two eminent Harvard economists, Carmen Reinhart and Kenneth Rogoff. Herndon 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.

http://en.wikipedia.org/wiki/Debt-to-GDP_ratio
Afterword by the Blog Author
The Wikipedia link above has many references.

There are two particularly insightful books that correctly predicted this situation:

The Coming Generational Storm: What You Need to Know about America's Economic Future by Laurence J. Kotlikoff and Scott Burns
Comeback America: Turning the Country Around and Restoring Fiscal Responsibility by David M. Walker
These two books emphasize the need to reduce "entitlements," a mandatory element in reducing the debt-to-GDP ratio back to a level consistent with stable government and economic growth.
The argument from the left, that taxes can always be raised to support the "entitlements," in unworkable when public debt exceeds gross domestic product. In Washington, D.C., it is the Democrats who are refusing to bargain and who are risking "default" because of an iron-hard faith in the necessity of redistributing income. Redistribution will only be capped or reduced if the government’s borrowing power has been capped and not raised.