Surreal fantasies of self-damping debt

I do strange things in my sleep.  I must.  I mean, I’m not sure what dreams really are, but I have the feeling that they should be filled with emotional jabber, with things the mind enjoys or fears or would like to do over but with superpowers.  Dreams should be sexy or scary or strange and slightly surreal.  I woke up this morning with a brain filled with algebra and graphs about how different people see the relationship between deficit and debt.  Well, ok, that could be scary.  But it’s definitely not sexy, and doesn’t involve any superpowers.  I really need some dream upgrades.  I’ll have to look into that.

I’m usually a little reluctant to post a lot of algebra in this blog.  But last summer, while sailing up the Potomac approaching the Wilson Bridge on our way back to the Washington Sailing Marina, my friend Jeff told me he thought that would be ok.  He thought algebra would be acceptable.  And this bit of algebra ends up with a picture that I think is interesting---if you really trust me, you can skip past the algebra and get to the pictures, but I’m leaving the algebra to show how I got there.  So, here it is.  

Everyone is interested in debt as a share of GDP, and how that changes over time.  The algebra of that is something like this---start with plain nominal debt, not as a share of anything:

I’m using---or at least approaching---the symbols used in the IMF’s chapter on debt overhang last fall (see page 104), but I end up with a slightly different version because I’m looking forward and they were looking back.  That means I’m asking what this year’s deficit will do to next year’s debt, rather than asking what last year’s deficit did to this year’s debt.   I mention that chapter because it keeps coming back to pester me.  The authors found only 26 episodes since 1875 in the entire IMF membership where debt to GDP rose above 100%, and none where it rose above 300%.  Only one, Israel in 1977,  was above 250%.  Why is that?  Why were there no instances of debts of, say, 500%, or 1000%?  Is 300% some kind of limit, beyond which nations simply dissolve or crash something?  Maybe.  But few of the countries in the study actually did crash.  A few had high inflation rates in the 15 years after they reached a debt of 100%, but some also had deflation.  It’s hard to know what those extreme episodes mean, though, because they were usually during or just after major wars.  

In any case, the B in the equation above is debt, i is the rate of interest paid on the debt, and the D is deficit.  The subscripts denote time periods---probably years.  (I know that the interest rate and the growth rate also change over time, and probably the time subscript should be applied to them also, but for this part of the algebra I only need the subscripts I used so why clutter everything up?  This is informal algebra, comfortable algebra, algebra en famille.)  The equation says that next year’s debt will be this year’s debt plus interest, plus whatever the primary (non-interest) deficit adds to or subtracts from the debt.  

I’m using capital letters so far, instead of the lower case used in the IMF chapter, because in this version the symbols are just talking about the raw numbers, nominal debt for example, rather than debt as a share of GDP.  But we want debt as a share of GDP.  So we need another equation:

Where Y, of course, is GDP.   I want to look just at the numbers, at nominal Y, so  is nominal growth rate.  To get to something like the IMF version, we would add that 

Where is inflation and g is real growth rate.  But I don’t need that decomposition to get where I’m going, so I’ll stick with the nominal rate.  

So the ratio of debt to GDP next year will be---just substituting in from the equations above---

 

Where the lower case letters are ratios of GDP, and the upper case letters are nominal.  

What we want to know, really, is whether debt as a share of GDP is rising or falling.  That is, algebraically stated, we want to know whether       is positive (debt/GDP is growing) or negative (falling).  I’ll call that difference     just because I like using Greek letters.  It looks sophisticated.

Since         ,  the sign in that last version depends completely on the sign of the phrase inside the last square brackets.  Whether the debt as a share of GDP is growing, stable, or shrinking is determined by whether 

 

(I’m using the braces there to indicate options---growing, stable or shrinking if greater than, equal to or less than.)

But the strange thing, the thing that crossed my eyes a little as I woke up this morning, was stating this condition a different way.  Let’s just look at the case where debt as a share of GDP is shrinking, so I don’t have to write that monster in braces all the time.  So shrinking debt/GDP implies that

Or

Or, assuming that debt is positive,

And this is where the weirdness comes in.  If this inequality holds, b, the debt to GDP ratio, is declining.  In this form it looks as though the bigger b is, the more likely it is to decline.  I mean for any given   , the ratio    gets smaller in absolute value as  gets bigger.  That would make the inequality above easier to achieve---right?  So at high levels of debt to GDP, decreasing that ratio would become easier, according to this.  But can that be true?  Is debt somehow self-damping?  That’s absolutely not what we keep hearing in the political world.  We keep hearing that debt will become so huge that it will be “unsustainable”, that it will accelerate out of control, that compounded interest will make it explode.  But if nominal growth and interest rate were fixed, and we limited the primary-deficit-to-GDP ratio d at some fixed positive value, then the weird result above would imply that it is true, and that instead of running away, debt as a share of GDP would have a tendency to slow down and reverse itself, or at least slow to a stop, as it gets bigger.  And if it were true, maybe that would explain why nations never have debt to GDP ratios in the thousands of percent range.  

That would be a great relief, wouldn’t it?  If debt were self-slowing, we could all stop worrying about it.

But of course it isn’t quite that easy.  growth rate and interest rate are not fixed.  In fact, they are a function of the deficit d, among many other things.   Figuring out what the function  might look like is complicated.  I didn’t wake up with the algebra for that in my head and I don’t want to spend a lot of time trying to get at it.  If anyone knows what that should look like, let me know.  At a wild dream-state guess though---and for the moment it isn’t any more than that---we could postulate that nominal growth and interest as a function of d have shapes that looks something like this: 

Here’s the dreamy excuse I dreamed up for these dreamy shapes, kind of nodding to a lot of different people’s beliefs about the impact that deficits might have.

The nominal growth to the left of the vertical dashed line is mostly real growth, and to the right it’s mostly inflation.  Interest rates are low until we get out to the right, and then they rise because of inflation, and because the high deficits are soaking up a lot of the available money.  While interest rates are near zero the growth curve is rising, because multipliers of the deficit are relatively large there, so higher deficits result in higher growth; near the inflection point it’s flatter because multipliers are smaller (because the central bank counteracts any fiscal stimulus to avoid inflation).  Out to the right it’s big again because the deficits are so big the Fed has lost control, and inflation is pushing nominal growth.  

I’m not wedded to these shapes, they’re just the shapes I woke up seeing.  They might be wrong.   Still, it's not crazy to say that fiscal multipliers will be bigger when the economy is weak and we are far from full employment and smaller when we are close to full employment, either because it's hard to push the economy very far past that or because the central bank will push in the other direction to avoid inflation.  And it's not crazy to say that interest rates will be low when the economy is weak, and rise as the economy gets stronger.  So the critical part of the shape of these curves is at least not crazy: the slope of the difference between growth and interest rates will decline, or at least not rise, as deficits as a share of GDP increase.

If the shapes in the first graph are right then that difference, is the gap between the blue and red lines in the first picture, looks something like this

I haven’t put a vertical axis on these graphs because it’s not clear where it would go.  It depends on what the economy is doing.  If we are in a deep recession, the vertical axis will be farther to the left, farther toward the flat low interest rate area; if we are in a boom it will be farther to the right.  But the interesting thing happens when we put that axis in---let’s suppose we are in a weak economy, so the axis is farther to the left.  Then we can complete the graph that was giving me a headache when I woke up like this:

The solid green line is the ratio of deficit to debt when the debt is just a bit over 100% of GDP. (It would be a 45 degree line if b, which is debt/GDP, were exactly 1.)  If the deficit/GDP ratio is less than B and greater than A in this picture, then debt as a fraction of GDP is declining.  Above B, of course, the size of the deficit just overwhelms any increase in GDP that may result, and we have a pretty icky outcome: growing debt and rising inflation.  Below A, though, the economy is so weak that we are pushed into a slowly growing or even declining GDP, and the ratio begins to rise again: if the deficit is too low in this weak-economy situation, then we also have an icky outcome, with weak or negative real growth and also rising debt as a fraction of GDP.  That would not be true in a stronger economy; as the economy improves, the axis shifts to the right (and so does the green line, since it has to go through the origin).  

But the curious thing is the dotted green line.  This is a d/b line with higher b.  And notice that the gap between A’ and B’ is bigger than the gap between A and B---in this vision, a wider range of deficits will reduce the debt to GDP ratio if that ratio is already high.

So maybe there is something in the idea that high debts are---well, not self-capping, but at least they push against an increasing resistance as they get larger.

Does any of this make any sense at all?  Or is this all just as surreal as dreams are supposed to be?  If it makes sense, then maybe debt as a fraction of GDP does naturally slow down as we get up past a couple hundred percent---and there are several examples, such as Japan right now, where debts in that range have not created catastrophe.  I'm not suggesting that debt really doesn't matter, or that we should ignore it; it does make a lot of things harder to do, and it is a nuisance.  But maybe we also shouldn't panic about the specter of a runaway, exploding debt that seems, in this dream anyway, to be unlikely.

Of course it's just a simple model that came out of dream.  It may disappear after enough coffee.   And even if this does turn out to fantastic enough, surreal enough to be a proper dream, I still prefer dreams where I get to have superpowers.

Oh, and if you didn’t like the algebra, we can blame Jeff.

On debt and pie holes

One of the headlines on the front page of the Washington Post yesterday turned out to be an irritating brain-worm.  I just glanced past it at the time, scanned the attached article by Edwin Cody.  And I don’t want to criticize Cody himself; the text of the piece did have some interesting data---nothing that could surprise anyone who is following Europe with any interest at all, but nothing very wrong either.  I know Cody didn’t write his own headline.  

But the headline was this: “In impatient Europe, some see more debt as answer”.  And that line has festered.  A little.  It has festered a little.  I woke up this morning thinking about it. 

I don’t want to get all caustic or anything.  I mean I don’t want to say something to the headline writer like: “if you don’t know the difference between deficit and debt, then shut your &^*% piehole about economic issues”.  Still, I would like to remind the headline writer that there is a difference between debt and deficits, and that there is no economist that I am aware of anywhere on the political spectrum who thinks that “more debt” is good, or that debt on its own will solve anything.  A few of the more ardent of the MMT community might follow Abba Lerner’s original formulation that government debt doesn’t hurt, that debt is harmless in an economy with fiat money where (they might claim) the government can always cover the interest on the debt and also achieve its policy goals with respect to employment and inflation.   And many on the left, and even increasingly through much of the right side of the political economic landscape, would say that the long run risk imposed by massive and continuing unemployment may be larger than the risk imposed by short run deficits, since long unemployment causes skills to atrophe and creates the habit and expectation of unemployment among the young.  But no one, no one, claims that a large government debt by itself actually helps.  

The people in Europe have no desire for more debt.  They don’t even have a desire for more deficits, although I believe that they would accept deficits if that’s the only way to stimulate the economy.  It’s not, at least not in Europe: there’s still scope for monetary expansion there, and certainly scope for a modest increase in inflation in Germany as an alternative to grinding deflation in Spain.  

What I think the headline writer meant to say was that in Europe many people are very sensibly tired of the stubborn advocates of austerity and recurring dips into recession.  I don’t think they care whether the stimulus is fiscal or monetary or exports to mars.  They just want someone to recognize that economic stimulus is necessary, and that it should come soon.  

Here are some graphs from this source.  

Unemployment since 2008 in the United States:

A big surge in 2008-2009, followed by a slow but steady decline.  It’s still just under 8%, and long term unemployment is dangerously high; the clear cause of initial unemployment and decline of output was lack of demand, not distribution of skills.  But the longer the unemployment rate stays high, the more this becomes structural, rather than cyclical.  It gradually becomes a permanent change in our ability to produce.

Now here’s the unemployment rate since 2008 in the Euro area:

A big surge in 2008-2009---and pretty much no decline.  In fact, the recent trend is dramatically up.

Now here’s the unemployment rate in Spain:

Notice the scale, on either side of the graph.  In the United States unemployment is just under 8%, and we’re pretty anxious about that.  In Europe in general, it’s over 12%.  In Spain it’s over 27%, and among the young its over 55%.

No one wants debt.  In the long run, debt may indeed be a burden.  It may, although there really is no evidence that it's decisive at anything close to the levels we see in Europe.  But the continuing austerian terror of debt is causing a certain burden, both short run and long.  For the economies of the GIPSIs (Greece, Italy, Portugal, Spain, Ireland) it’s creating a structural change that will last for decades.  For the young in those countries it is causing a catastrophe, a burden from which they will not recover within the span of their lives.
 

Eliminate the Corporate Income Tax

It’s been a few weeks since I posted here, for a variety of personal reasons.  It’s hard to get back into harness again after a pause.  I thought about writing about the potential long run economic benefits of crowding out private investment, but that’s complicated and I’m tired.  I thought about writing about the worldwide Excel Depression, but that’s been covered exhaustively by others, and I have nothing exceptional to say about it.  I thought about writing about the chained-CPI controversy, and I probably will soon in an effort to get my fellow progressives to mellow out about it a bit.  But I’m taking the easy way out: I’m transferring a discussion on corporate income taxes from email to here.
 

A few days ago my brother in law Craig sent the text of an opinion piece in the New York Times by James Livingston to me and my nephew Dan, wondering what we thought of it as economists.  Livingston’s point is that since corporations have now, by Supreme Court edict, been promoted from having some of the legal rights of human beings to having all of them, to being almost embedded in living flesh, then they should pay the personal income tax rates too.  He points out that the share of federal revenues paid by corporations has fallen from about a third in the nineteen-fifties to about 9 percent now, and so that seems like a good place to look for new revenues that we clearly need to reduce our deficits in the future.
 

But, economically speaking, I’m uncomfortable with all of this.  My response to Craig’s question (why shouldn’t corporate incomes be taxed like personal incomes, since the Supreme Court and Mitt Romney say they are people) was this: 
 

“Well, because corporations are not people.  They are legal fictions created by the states.  That's why I didn't support Citizens United, and that's why I don't think corporations should pay any income tax at all.  (That doesn't mean they should pay no taxes---they should be the collectors of Pigovian taxes for us, because there isn't any more efficient way to collect them.  And they should also be the recipients of Pigovian subsidies...)”
 

To which he responded that he thought Pigovians were characters in Angry Birds.  And he very reasonably questioned the ability of the state to calculate a correct level of Pigovian taxes.  

I was too brief in my response to him, so let me be a bit more complete.  Corporations should pay taxes that internalize the full cost of creating the products they sell.  Pigovian taxes account for externalities.  For example, a carbon tax helps increase incentives to find less carbon-intensive processes and products.  But corporations should also pay user fees or excise taxes for the public goods they directly use up as inputs to their business efforts (such as gas taxes to pay for maintenance of the roads they use to deliver goods to market).  And I’m sure that’s not a complete list of taxes they should pay.  But they shouldn’t pay income taxes because strictly speaking, as non-persons, they don’t have personal income.  Their revenues pay their workers or buy equipment or inputs, and their profits belong to their shareholders and creditors. 
 

My primary objection to corporate income or profits taxes in general is that they are just a pass-through.  Real people, not legally constructed fictional people, pay all taxes in the end.  It might feel as though raising revenues through taxes on corporate profits would reduce the need to tax personal income, but it doesn’t.  It just changes the way those taxes are collected. The corporation's customers, or workers, or owners will pay corporate taxes in higher prices, lower wages, or reduced dividends, or in some other way.   And by applying income taxes at the corporate level we are allowing the corporate managers to decide who will pay them.  Corporate managers are unlikely to distribute the tax burden in any very equitable way, or in any progressive way.  They’re more likely to try to shield their owners, and collect the tax from someone else.
 

I appreciated Craig’s point about the limits to information available to any central authority; in a perfect Hayekian world prices would supply all the communication required for local actors to act in globally optimal ways.  Consumers don't need to know the details of how the product is made, or what resources are used in producing it.  They (and only they) know how much they will benefit from purchasing a product.  If the product’s price reflects the cost to strangers in distant places of creating and transporting it, then the consumer’s choice about how much of the product to purchase at the market price achieves a cost/benefit optimization that no central authority could possibly have enough information to solve analytically.  And producers also know how much to produce; producers of rolled steel don’t have to know the details of every household’s personal consumption choices to know how much they can profitably produce at the price the market will pay.  
 

But the Pigovian criticism is that there are some situation, such as, for example, pollution leading to global warming, where prices don't fully provide that information, because producers are not required to pay for costs (or can’t capture benefits) external to their own direct transactions. Just because it's difficult for a central authority to gather information to estimate that external cost doesn't mean it shouldn't try, because the long run cost of ignoring global warming could be catastrophic.  And public fees or excise taxes can be used to make companies reflect the cost of providing public goods that truly are inputs to the creation and delivery of their products.  
 

So I don’t mean that corporations should not pay taxes.  They should pay taxes to make prices provide better information about the costs of productions, and those may be substantial.  These taxes should not be applied to raise revenue, exactly, although we can certainly use the revenue they produce.  They are applied to make sure that the price system functions well, and provides both consumers and producers with the real and complete information they need to make globally optimal private decisions about what and how much to consume, and what and how much to produce.

But corporate income taxes don’t improve local decisions; they just increase the cost of doing business, and reduce the incentive to produce, without providing either corporations or customers with any improvement in their ability to make good choices.  
 

I didn't make this idea up.  I've forgotten where I first ran across it long ago, but I found it convincing then, and I still do.  It’s a bit lonely, though.  I don’t see a lot of calls for the elimination of corporate income taxes in the econoblogosphere.  Even the conservative blogs seem to call for the reduction of corporate income taxes, not their elimination.   But until someone explains where the flaw is in the argument above, I still say, as a progressive: eliminate the corporate income tax.  We should demand that our elected representatives decide which real flesh-and-blood people should ultimately pay for the cost of providing government investments, services, and protections, rather than ceding that power to corporations animated by the profit motive.  And we should be wary of actions that reduce the incentive to produce, to create, and to hire without providing any corresponding good economic effect, particularly when the result may be a distribution of the tax burden that is likely to be less progressive, and will certainly be no smaller.