Monday, March 8, 2010

It Takes Two to Tango: A Look at the Numerator AND Denominator

This is a guest contribution by Marshall Auerback, Braintruster at the New Deal 2.0

by Marshall Auerback

A new book by Kenneth Rogoff and Carmen Reinhart, "This Time It's Different: Eight Centuries of Financial Follies", has occasioned much comment in the press and blogosphere (see here and here)

The book purports to show that once the gross debt to GDP ratio crosses the threshold of 90%, economic growth slows dramatically.

But that's too simplistic: a ratio is just a number. Debt to GDP is a ratio and the ratio value is a function of both the numerator and denominator. The ratio can rise as a function of either an increase in debt or a decrease in GDP. So to blindly take a number, say, 90% debt to GDP as Rogoff and Reinhart have done in their recent work, is unduly simplistic. It appears that they looked at the ratio, assumed that its rise was due to an increase in debt, and then looked at GDP growth from that period forward assuming that weakness was caused by debt instead of that the rise in the ratio was caused by economic weakness. In other words, they have the causation backwards: Deficits go up as growth slows due to the automatic countercyclical stabilizers.They don't cause the slow down, etc.

After the Second World War, the debt ratio came down rather rapidly—mostly not due to budget surpluses and debt retirement but rather due to rapid growth that raised the denominator of the debt ratio. By contrast, slower economic growth post 1973, accompanied by budget deficits, led to slow growth of the debt ratio until the Clinton boom (that saw growth return nearly to golden age rates) and budget surpluses lowered the ratio.

From 1991 through 2001 the growth of government debt had been falling and since then rising most recently at a faster pace. The raw data comes courtesy of the St. Louis Fed (and attached spreadsheet).

The Ratio of the rates of change of Debt / GDP is rising faster than the change in Debt indicating that both the increase in Debt and the fall in GDP are contributing to a rising Debt / GDP ratio. For policy makers who obsess about a rising Debt / GDP ratio, they fail to understand that austerity measures that cut GDP growth will cause a rise in the Debt to GDP ratio. Basically, it boils down to this simple observation: it is foolish, dangerous, and thoroughly counterproductive to treat fiscal balances in isolation. In particular, setting a fiscal deficit to GDP target equal to expected long run real GDP growth in order to hold public debt/GDP ratios at a completely arbitrary (indeed, literally pulled out of thin air) public debt to GDP ratio without for a moment considering what the means for the feasible range of current account and domestic private sector financial balance is utterly nonsensensical.


It is crucial that investors and policy makers recognize and learn to think coherently about the connectedness of the financial balances before they demand what is being currently called fiscal sustainability. As it turns out, pursuing fiscal sustainability as it is currently defined will in all likelihood just lead many nations to further private sector debt destabilization. To put it bluntly, if the private sector continues to pursue a high net saving/financial surplus position while fiscal retrenchment is attempted, unless some other bloc of nations becomes large net importers (and the BRICs are surely not there yet), nominal GDP will fall in the fiscally "sound" nations, the designated fiscal deficit targets WILL NEVER BE ACHIEVED (there can also be a paradox of public thrift), and private debt distress will simply escalate.


In fact, if austerity measures are based on measures of debt relative to economic growth there is a very real risk of a downward spiral where economic growth declines at a faster pace than government debt and the rising Debt / GDP ratio leads to ever greater austerity measures. At a minimum, focusing only on the debt side of the equation risks increasing the Debt / GDP ratio that is the object of purported concern is likely to lead to policy incoherence and HIGHER levels of debt as GDP plunges. The solution is to recognize that the increase in the ratio is in some fair measure the result of declining economic growth and that only by increasing economic growth will the ratio be brought down. This may cause an initial rise in the ratio because of debt financing of fiscal stimulus but if positive economic growth is achieved the problem should be temporary. The alternative is to risk a debt deflationary spiral that will be much more difficult (and costly) to reverse.

10 comments:

  1. "This may cause an initial rise in the ratio because of debt financing of fiscal stimulus but IF positive economic growth is achieved the problem SHOULD be temporary."

    Marshall - apologies - don't mean to chase you all over the net, but I do read Rebecca frequently. I'm still digesting your points above and on Credit Writedowns in the Rogoff post, and I've put the 2 words in capitals in the quote above that trouble me, and I <span>am</span> troubled by these qualifications of IF and SHOULD. I 'd still venture to say that if growth (better than anaemic) does NOT occur, the debt problem could be permanent and potentially terminal in the longer run.

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  2. It seems that both the numerator & denominator are specious.  Total debt is the sum of: federal, state, & local governments, international, & private debt (households, business, financial, trust funds, etc). 

    Total debt is serviced by volume of current gross savings, international investment, & debt monetization.  It is not serviced by nominal GDP.

    <span><span>Deficits create a demand for loan-funds.  The larger the deficit, the higher the interest rates, or the less interest rates will fall.   High interest rates reduce taxable income & increase the volume of taxes necessary to service debts.   Higher interest rates and higher taxes erode to tax base & increase future debts.</span></span>
    <span><span></span></span>
    <span><span>Higher inflation rates create higher inflation expectations.  Higher expectations will be reflected in the loan-funds markets long before inflation can reduce the burden of debt.</span></span>
    <span><span></span></span>
    <span><span>The burden of debt is also determined by how the debt is spent...</span></span>

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  3. Yes it is a combination of two numbers. Debt and GDP. However, has anyone looked at the composition of the GDP? For example, if the number is primarily an increase due to government then that can't be too good. Or, as an outlier, If the Exxon Valdese oil spill generates local activity cleaning up the beaches of Alaska and BC, and the activity is included as a positive input to GDP then that too can't be good. It depends on the quality of the GDP. So also, the quality of the Debt is a factor. Debt for debt's sake can't be good, but if the debt went to productive enterprise and contributed to infrastructure that enhanced the business prospects for the future then the quality of that debt is certainly worth consideration. The summary of this argument is that the number generated from dividing debt by GDP deserves a wide range of consideration before hard rules of thumb are applied.

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  4. This numerator/denominator stuff... it's sixth-grade math. Above post is the first time I've seen it properly treated in an economics discussion.

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  5. Hi gang, I'm back.

    Doing a little study of debt and all, wanted to capture FLOW5's thoughts on debt service. CTRL-C'd the comments & pasted 'em into a Notepad textfile. Turns out I then saw the following hidden info:

    [This user is an administrator] Windemup
    [This user is an administrator] flow5
    [This user is an administrator] gaius marius
    [This user is an administrator] Stevie b.

    Turns out every comment but mine is by an administrator. Or maybe by the SAME administrator, idunno. So I thought I'd say what I think: I think FLOW5 or me, one of us, does not know what DEBT SERVICE is.

    1. I think "debt service" is the money spent for interest and principal on debts.

    2. FLOW5 says: "Total debt is serviced by volume of current gross savings, international investment, & debt monetization.  It is not serviced by nominal GDP."

    3. I'm not writing just to be a dick. I'm preparing a post on debt and I'm looking for good information on debt service.

    4. CURRENT gross saving, I assume, is NEW ADDITIONS to saving. But if I save a dollar, that does nothing to reduce my debt. So, saving is not debt service.

    5. International investment, I assume, is investment; and it is said that investment is always equal to saving. But (as noted in item 4) saving is not debt service.

    6. Debt monetization, I assume, is when the Federal Reserve buys Treasury Bills.... That puts more money into the economy, and it supports the creation of debt, but it is not debt service.

    7. I agree that debt is not serviced by GDP. But GDP is output, and output is equal to income (at least, according to the same people who say saving equals investment).

    8. So I'm thinking, maybe the money that services debt is the money people call "income."

    Okay, FLOW5, so how is debt serviced?

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  6. Hi Stevie,

    I am catching up on comments. There is, of course, a risk - and that's why the current policy response is so critical. If given two possible scenarios: (1) run larger deficits and risk bond markets pricing in lack of confidence and inflation via rates but with replacement aggregate demand (note that th effect of interest rates in this situtaion is completely ambiguous) and at least the possibility of income growth generation, or (2) raising taxes knowing full well how the private sector will act under these circumstances (Japan), I'd certainly take the former.

    By the way, you'll have to track down Marshall in various places - he's everywhere!

    Rebecca

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  7. Hi windmeup,

    You bring up a very good point: <span>The summary of this argument is that the number generated from dividing debt by GDP deserves a wide range of consideration before hard rules of thumb are applied.</span>

    The government does not have the best track record of allocating resources! There is another possibility: tax cuts.

    Rebecca

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  8. Hi flow5,

    this is the crowding-out argument. I am not sure even if that holds in this currenct economic scenario. I would surmise that some sort of case for supply could be made, but even if rates rise, the effect on investment would be ambiguous at best.

    Please see comments to Stevie b. below.

    Rebecca

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  9. <span>"CURRENT gross saving, I assume, is NEW ADDITIONS to saving. But if I save a dollar, that does nothing to reduce my debt. So, saving is not debt service."</span>
    I am slightly confused by this. If one starts with zero debt then saving is done so only at the cost of current consumption, adding more consumption later in life. If one starts with positive debt on balance, saving still comes at the cost of current consumption but the future consumption is now one unit greater (or less negative since you are running a positive amount of debt) - i.e.debt is lower. That's how it looks to me in the aggregate. Clearly, this analysis abstracts from the idea of income generation.

    "<span>International investment, I assume, is investment; and it is said that investment is always equal to saving. But (as noted in item 4) saving is not debt service.  "</span> 
     
    That is NOT true with open borders - the difference between saving and investment is called the current account.  
     
    By the way, I am the only administrator. :)

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  10. hmmm...Authurian: i couldnt duplicate your experiement but: im an administrator on three google blogs, but not here: you might try the same on this comment & see if i come up as admin...

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