Wednesday, May 25, 2011

Debt dynamics for dummies

Krugman again does a great job showing that the risks of explosive debt are way overblown.  As he says:
"So even with substantial deficits, the pace of long-term budget worsening is very slow."
It is not difficult to understand debt dynamics.  The ratio of debt to income (GDP) is a measure of the capacity to repay debt.  If the economy grows faster than debt, the debt-to-GDP ratio falls.  GDP grows with demand expansion, and debt grows at the pace of the interest on the debt.  In other words, if the economy grows faster than the rate of interest, then the debt-to-GDP ratio will fall even if the government runs deficits.

The graph below shows the growth rate and the real rate of interest on government bonds for the US since 1990.  As it can be seen, since 2003, with the exception of the Great Recession, the rate of interest has been below the rate of growth.

The debt-to-GDP ratio has only increased (see graph below), because the crisis has caused significant deficits to accumulate.  Note that in the 1990s, a combination of lower interest rates, higher growth and fiscal surpluses had stabilized debt, which starting growing in the Reagan years.

Finally, note the growing deficits in the figure below have reversed with a very mild recovery in 2010. Interest will remain low. What is needed is a stronger recovery to get growth going and that would increase revenue (allow for reduced spending on several things like unemployment insurance) and eventually lead to a lower debt-to-GDP ratio.

The way out of the fiscal problems is growing!  Even dummies should get this right.


  1. Matias,

    I do not agree that the debt/gdp for the United States will stabilize as a result of growth... likely the opposite.

    I have heard other Post Keynesians say this as well, and I believe it is incorrect and not properly qualified.

    An increase in domestic demand also brings in a widening of the trade deficit and the whole current account.

    Lets take some standardly assumed numbers. The price elasticity of imports and that of exports is nearly 1 and the income elasticity of imports is 1.7 and that of exports is 1.4.

    So if the rest of the world does not grow that fast, the United States' growth will deteriorate the trade imbalance if this growth is higher than Thirlwall's expression.

    Its possible that slow devaluation of the dollar takes care of some of the growing imbalance but wealth effect brings in some complication as the devaluation leads to holding gains of assets of US citizens/sectors held abroad - so they feel richer (defined by wealth) and consume more.

    Its not so straightforward!

  2. I should add to the comment that I understand the sectoral balances approach and that the deficit in current balance of payments will lead to a higher budget deficit than otherwise because of the Godleyan sectoral balances identity

    NAFA = PSBR + BP

  3. Hi Ramanan:
    It is true that growth will lead to an expansion of the current account deficit, that shrank as a result of the crisis. Still if GDP growth is faster than debt growth, debt-to-GDP ratios will fall. The external situation is a different problem. In the case of the US, because external debt is equivalent to domestic (since all debt is dollar denominated), it is not clear that the current account poses any serious constraint to growth.

  4. Matias,

    In the present circumstances, it is difficult for GDP to grow faster than debt. Thats my point.

    The external situation is not really a different problem because the "three financial balances" are related by an identity.

    Till recently NAFA (or Net Lending in the new terminology) was in the negative territory but has moved backed to a positive and will likely remain positive for a long time. A deterioration of the current account will lead to increase in public debt because of a higher fiscal deficit. This increase in public debt will be faster than the growth rate unless the net exports situation improves.

  5. Yeah, it is difficult, not impossible and the point is that the only way to reduce debt-to-GDP is by growing, and hence by having further fiscal stimulus. Having worked as research assistant to Wynne Godley at the Levy back in the 1990s, I should now something about the identity you confuse. Growth will lead to a deterioration of the current account, but that is NOT a problem. Even with growing debt the economy would grow faster than debt, and additionally revenues would increase, reducing the deficit. That is exactly how debt-to-GDP ratios in general fall. Happened in the UK over the 19th century, after debt-to-GDP reached more than 270% and in the US after WWII when it was around 120%.

  6. By the way, the condition for debt-to-GDP to fall is that the rate of interest (r) is smaller than the rate of growth (g). Unless you think that interest rates are going up, there is no reason for the debt-to-GDP to grow. So debt-to-GDP will grow in the short run, but provided g>r it will eventually fall. The classic paper on the subject was written by Evsey Domar. Still worth reading.

    1. What is the title of the paper? i would like to read it. thank you

    2. The burden of government debt and the national income

  7. Matias,

    Don't think I am confusing.

    Will check Domar but its not even true that r needs to be less than g as per G&L JPKE2007.

    I suspect Domar's analysis is a closed economy case.

    If you check Godley-Cripps Macroeconomics 1983 last chapter, you will see what I am trying to say.

    Imagine the current account deteriorating 1% every year. Can r < g guarantee the public debt will sustain ? I don't think so.

    I am not sure how critical the US imbalance was in the period you mention.

  8. Sorry ... should have said trade imbalance in the last line

  9. First of all, for the US the foreign debt is in domestic currency, so it is always as if you are in a closed economy. Second, you are confusing flows with stocks. The stock of debt will diminish if the flow of income grows faster than the stock of debt. Again a fiscal deficit will do two things, increase the public debt, and lead to economic growth (if you believe that multipliers are positive). Further, it will lead to a current account deficit and foreign debt (that's a different story, but irrelevant since the US does NOT have an external constraint). The current account has no effect on the public debt that results from the fiscal deficit. Note that this is true for all countries, For other countries the sustainability of the current account depends on the growth of exports (and that is why this countries that have an external constraint) sometimes cannot do what the US can always (unless it decides not to do it for political reasons) spend itself out of the crisis. Hope this solves your confusion.

  10. Matias,

    I am not confusing stocks and flows either !!

    I am travelling a bit ... will reply in a few days.

    Again, I am not confused ;-)

  11. No worries. You can always write to my e-mail.

  12. Back with some time hence some comments.

    I have stocks and flows and how they feed into one another completely ingrained in my head.

    The public debt dynamics is roughly

    Closing stock of debt = Opening stock of debt + Fiscal deficit + Revaluations

    Similarly, for the external debt,

    Opening stock of Net IIP = Opening Stock of Net IIP + CAB + Revaluations

    I stress the revaluations because it is somewhat important in the analysis and has been the case with the United States in the 2000s.

    I completely understand that in a closed economy, a fiscal expansion for an economy in recession will bring the public debt into a sustainable trajectory once the economy comes out of the recession as tax revenues grow.

    On the other hand, my comments have been to point out that this does not work out so easily in the case of an open economy.

    This is because if the private sector wants to have a low positive NAFA/GDP, because of the sectoral balances, a widening of the current account deficit also leads to an increased deficit. Deficit is a flow and adds to the stock of outstanding debt and its not clear that DEBT/GDP converges or stabilizes or is sustainable. In fact it is not. On the other hand, if NAFA is negative, it keeps the fiscal deficit low and hence the public debt/gdp doesn't start blowing. But this implies that the private sector is incurring liabilities or is selling assets to finance its deficit and that itself is an unsustainable path.

    If a nation is growing faster than what its trade performance allows it to, either the public debt/gdp is growing or the private sector debt is growing – both unsustainable.

    The fact that the US foreign debt is in US dollars is advantageous but not due to the reasons usually cited, IMO. The real reason is that a depreciation of the dollar prevents capital losses on the liabilities and assets held abroad increase in value due to revaluations. The fact that the Federal Reserve is the issuer of dollars and not some foreign central bank is secondary. Money is not only endogenous, it is also convertible.

    At any rate, even if its “not a problem”, it doesn’t mean that the US public debt will stabilize at some ratio or be range bound.
    The US is under a massive balance of payments constraint in my opinion.

    The closed economy analogy doesn’t work in the case of the open economy. This can easily be seen by assuming a few things about import/export elasticities, assuming a small positive NAFA and some growth paths for the United States and the rest of the world. If growth of exports are like what they have been till now and if the US wants to grow with an even bigger fiscal expansion, the current account will deteriorate and since it is related to the PSBR, the latter too. The PSBR (or deficit) adds to the stock of public debt and a current account which keeps deteriorating will lead to a higher and higher fiscal deficit and hence rapidly growing public debt (i.e., growing faster than the gdp).

    I can see such things in simple spreadsheets as well.

  13. "The US is under a massive balance of payments constraint in my opinion." That is absolutely incorrect. Say that a developing country, oil importer, devalues its currency because of a current account deficit. Oil is priced in dollars, and part of the public debt too. All of a sudden imports are more expensive, and oil being essential, the only way to deal is to reduce the level of activity. Also, the space for fiscal expansion shrinks, since government spending on debt service soars. The US is like a closed economy. In what way would the US be unable to import oil if they devalue their currency? Also, it does not preclude fiscal expansion, because there is no effect on the value of the debt. If debt grows in the US is not a problem. Besides if the economy grows, and interest rates are kept low, public debt as a share of GDP would fall, wouldn't it?


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