The JGB Paradox

Are the rising yields in JGBs a sign of an incipient expected real economic recovery? Are they a sign of the market being ahead of Abenomics? And what about the paradox, that on the one hand the massive bond-buying BoJ is seeing bond prices fall instead of rise, should they be concerned about the impact this has on their debt servicing costs?

On the one hand, the rational-investor-Kyle-Bass approach makes a bit of sense. If the BoJ is trying to drive up inflation to 2% (and erode the value of JGBs), this would imply the success (somewhat) of Abenomics and the selling of JGBs to buy foreign bonds/equities.

But this is similar to Richard Koo's balance sheet approach to doomsday. It's the same end but different means really. Once inflationary expectations pick up, the BoJ will essentially lose control of any ability to control a rise in yields. And then you can let your imagination run...loss of faith...beginning of the end...(insert apocalypse now scenario here).

It's pretty obvious that there's a time variant issue here. That economic recovery is relatively a more long-term implication than the volatility in interest rates. The reaction of the markets is immediate and often ahead of policy action. But if investors start selling, are they anticipating success or failure? And if long-term rate rises precede signs of real economic recovery, will lenders choke off borrowing and bring the whole experiment to an end?

Abe himself, is not one to discount the worrying impact of short-term volatility and rises in borrowing costs. In parliament, he said that, "sharp increases in long-term interest rates could have a grave impact on the economy and the government's fiscal conditions".

But perhaps Abe should not be overly worried at the moment. After all, the BoJ is the BoJ - a central bank with more in its arsenal.

And this sort of runs contrary to what Nick Rowe says over at Worthwhile Canadian Initiative. He claims that it's not just what you buy, but what you buy it with; and his example is paying for taxi medallions with newly produced bicycles. Thus, an increase in the stock of money in circulation (we have to be careful here!), will have an effect on the demand for bonds (by raising the expected future price level thus reducing the demand).

But the key here (and the paradox too!) is that if you're flooding the monetary base and forcing yields down in the hope that inflation expectations will pick up and spark a real recovery...and this will cause "a rise in investment, fall in savings..." and if you intend for all this to happen and will gladly accept the consequence of rising yields then are you really trying to force yields down in the first place? And if yields rise (we've come full circle here), has your policy succeeded or failed?

Rowe says that the easiest way to think about this (and he's mostly right) is that it's a battle to push bond yields down but a war for economic traction and recovery. Thus, if you win the war, you'll lose the battle and essentially, you'd want to lose that battle.

Because this we do know, that when and if the Japanese economy recovers from its deflationary trap and stagnant growth, nothing much can (and perhaps should) be done about an accompanying shift in the yield equilibrium. In that sense, the more any attempt is made, the higher it might rise. And if there's a real economic recovery (Not just expectations of it)? Then a new equilibrium might be the point at which the BoJ stops restraining yields.

So throw Econ 101 out of the window, which tells us that the more you buy of something, the higher its price goes. The expectations of Japanese and foreign investors could be different. As Noah Smith points out, JGB investors are largely Japanese which most equity flows have been driven by foreign funds. And in this sort of a Keynesian set-up, a rapid interest rate rise perhaps could only be explained by a multiple equilibria theory where "Abenomics kicks the economy out of its bad equilibrium very abruptly, and the economy is shocked back to a sustainably higher rate of nominal growth".

Thus, according to Smith, "Japan's only hope is to cause the kind of recovery where interest rates stay very low for a very long time". But he says this with the debt ratio in mind, assuming rationally that sharp rises in borrowing costs would have unwanted consequences on the fiscal position. From Rowe's point of view, this prolonged-low-rate environment will prove impossible by the design of its theory.

Lest we forget though, that instead of rises in nominal rates, the reason for the rise in nominal rates will impact the function of real interest rates. And if things seem to be working and Japan really kicks itself out of its deflationary liquidity trap then real rates will go down irrespective (barring a vigilante attack I suppose) and the real value of existing debt stock will be eroded even though debt-servicing costs rise.

In that sense, Koo is right but he's just a bit wrong too. With balance sheet constraints, budget deficits and NOT monetary policy moves are the solution but this ignores the fact that even in a balance-sheet scenario, there will be creditors who respond to lower real rates.

Once again, the key here is the time boundary. Volatility may not be something to be over-worried about and  neither is the paradox. And therefore, betting on Abenomics to end up as a failure is definitely not the right move to make at the moment. 

Politically Correct or Woefully Ignorant?

Question: I have two questions. The first one is: do you see any risk of deflation in some countries in the euro area?

The second question is, yesterday, the IMF issued another mea culpa with regard to the austerity measures which were imposed on Greece. I wondered if the ECB also had some mea culpa to offer.

Draghi: Well, not really.

First, on deflation: ... we do not see it. In addition, some of these changes I hinted at are actually changes in relative prices, so they are positive. They show that there is real adjustment taking place, which can be seen in the export levels, which have gone up in some of the stressed countries.

On your second point, on the issue of mea culpa, no, I do not think we do; in fact, one good thing, as far as I understand, about this IMF paper is that the ECB is not being criticised. So, that is one thing. There has been a statement by the European Commission this morning which responds to this IMF paper. It makes several points and I do not want to go back over these points. I would not to say something different. Looking at the present situation, Greece has undertaken an extraordinary adjustment process. There is ownership of this adjustment by the government and we have to acknowledge the progress that this country has made. If we think back to a few years ago, it would have been unthinkable. Of course, if this paper by the IMF – which I have not read – decides to offer mea culpa and identifies the reasons for mistakes that have been made and other things, we will certainly have to take them into account in the future. However, often this mea culpa is in fact, as I will call it, a mistake of historical projection, i.e. you tend to judge the past by today’s standards. We cannot forget that four or five years ago, when the discussions about the adjustment in Greece were taking place, the climate was, in general, much worse. There was a fear of contagion there and very high volatility. That is, in a sense, where the fragmentation of the euro area really started. So, it is always very hard to pass ex post judgement on what happened four years ago. Having said that, rather than looking backwards, why do we not look forward and take stock of the extraordinary progress made and the positive path that has been taken?

Question: You talked about dramatism a few minutes ago and I am afraid I will be a little bit dramatic now because I am from a country that has an unemployment rate of 27%, which is a number of a great depression, a fiscal policy that is contractionary and a monetary policy in Spain and also in other countries that is also contractionary because credit is not available to small and medium-sized companies. Are you telling the Spanish, Portuguese, Irish or even Italian people that the ECB can’t do anything else with inflation actually lower than 2%?

Draghi: Well, I am not sure I get the point, but I think I get it. 

First, the fact that inflation is low is not, by itself, bad; with low inflation, you can buy more stuff. 

Second, we don’t see deflation and that is what we have to fear. We don’t see that yet. 

Third, fiscal consolidation is and remains unavoidable. It should be clear I think to everybody that you cannot have growth with endless debt creation. Sooner or later, you are going to be punished and the whole thing stops and that’s exactly what happened after the financial crisis in many countries. 

Fourth, are there ways to make fiscal consolidation growth-friendly? The answer is yes. Fiscal consolidation in most countries has taken the shape of increasing taxes and there are many reasons for that. Often this was done in an emergency situation or unfortunately because the easiest thing to do is to raise taxes. Now that is not growth-friendly and it is not growth-friendly because it happens in parts of the world where taxes are already very, very high. So what would be a better way? A better way would be the difficult way, namely to reduce unproductive government expenditure and reduce taxes together. But once you have done that – and in a sense I hinted at this before – you also have to ask yourself why these countries were not competitive. Why did they have to rely for growth in the good times, or “fairyland” times, on the protected sectors that were shielded from international competition? And then you ask yourself what should these countries change to become more competitive? And then what adjustments are needed in order to achieve this objective? The encouraging thing is that we see that most countries, if not all of them, are in this process, which of course is very painful, and I don’t think I miss one opportunity to make sure that you all know how aware of this we all are in the ECB.

Because I'm sick of R, R (and R)

I promised myself that although I wouldn't shut my eyes if i came across more RR to-and-fro (should we make that RRR now?), I would at least not ever blog about it again unless it was something seriously worthwhile.

I broke my promise and Michael Heller made me do it. Now to be fair, it's a bit unfair to say that this hasn't been going both ways because it has. The difference is that one side (PK, JBL etc.) has been substantive. They've focused on content, on causation and on concept...

...which (I may have got the chronology wrong)...led to a longg letter from Reinhart to Krugman, a sort of dismissive, lazy and im-tired-of-arguing-with-walls response and then....a severely ungracious piece on Project Syndicate by Michael Heller that reeks of being stuck in a corner and throwing jabs into thin air.

Dean Baker's retort includes a gem or two:

"This is the sort of piece that should really have the general public thinking about defunding economics programs everywhere"

"Anyhow, if Heller can read Krugman's latest column and declare R&R the winner, he must also believe that George Foreman defeated Muhammed Ali back in Rumble in the Jungle back in 1975. Such is the state of the economics profession."

WHY DOESN'T THIS END?!

Moby Ben and the Widowmaker - A Post Script

I'm late on this but it's worth thinking about. Post Bernanke-bashing at the Ira Sohn conference, JBL came out with one of the best pieces I've read in a while. What he essentially does is draw a contrast between two counter-parties with a common 'party' - the fund guys.

Of course, you know the backdrop to the London whale:

a) For while, he was more famous than Moby
b) He still ain't a patch on the real whale i.e: Moby Ben

So while the big funds may have finally sighed in relief as their counterparty could no longer continue (because naturally JP was seeing far too much red ink already), that logic doesn't apply to the Fed. And the way to go about this is to think along a more general line of thought and keep it simple.

If the treasury yield is reflected by the path of expected short term rates, inflationary expectations and the term premium, and the Fed shows no concrete signs of future QE moves then it's not entirely unreasonable to see why its easy to get attracted to the 'widowmaker'.

As JBL states, back in the late 90's toward the end of the Clintonia surpluses, the treasury bond traded between 5% and 7% while after the turn of the century, in a relatively much weaker economy, it hovered around the 4-5% mark. Hence the questions such as why was there a low-yield peak and why/when does it return to the 'fundamental'.

Cue Big Ben, printer of deposits, mass purchaser-in-chief of treasuries thus acting as chief culprit in pushing prices up well beyond 'fundamentals'. But here's where reason takes a short step out the window.

Rather than easing off, the buying persisted and fund managers made a very wrong comparison between the little whale and the big whale. While the little one was severely constrained due to obvious reasons, the big one should have been constrained by goals of financial stability and price stability. And just as the little one was answerable to Ina Drew and eventually Dimon, so should the big one have been....waitaminit...

Moby Ben answers to no one, and any dissent that he faces at the FOMC is not even worth writing home about relative to the broader consensus. While the CDX IG9 had a fundamental (the payouts of the bankruptcies times the probability of occurrence), the little whale could not alter the fundamental through his bets and positions.

And the key here is a healthy economy. Because in a healthy economy, the treasury has a fundamental. In a healthy economy, pricing power is partially determined by workers and the Fed's mandate is keeping inflation in check. Is this a healthy economy? No pricing power. Downward nominal wage rigidity. Unlimited market appetite for zero interest cash. Far from it.

Moreover, the Fed is not a profit-making enterprise. It's balance sheet stands at seeming odds with its goals. Unwinding positions and incurring portfolio losses is something the Fed will gladly take if it returns the economy to a steady and healthy state.

Now sure, it's logical to expect a rise in rates and you'd be well-off if you were a very patient investor. Use a crude Taylor rule (for example, the Mankiw rule) with an indicator of about 9.5 and you'll end up plotting an S-shaped curve picking up somewhere in the latter half of 2014.

And if you're screaming inflation and hyperinflation from every rooftop like a lot of people have over the past few years, then you might do well to read about the dog that never barked.

I don't know why exactly it's called the widowmaker but the real widowmaker is a coronary artery that is fatal if blocked.

The analogy seems dubious but still, shorting the bonds:

1) of a sovereign nation that
2) issues debt in not just a currency it controls
3) but a currency that acts as the global reserve currency
4) in a depressed economy
5) is foolish

Pooling Debt

Paul De Grauwe of the European Institute at LSE has a cry out for an EU fiscal union over at Project Syndicate. The good news is that he tries to be practical about it. As you might recall, De Grauwe sort of popularized the self-fulfilling prophecy theory for the EU - that namely the fundamental flaw of the EU is that its members issue debt in euros and the euro is a currency that they have no control of.

Thus, none of them can provide any sort of guarantee to their bondholders. A little fear in the markets prompts sell-offs that can lead to liquidity crises and drives these sovereigns closer to default. With not much to play with, they implement austerity programs that exacerbate recessions and lead to further banking crises.

De Grauwe used very simple univariate relationships among debt-to-gdp ratios, credit spreads, austerity, and growth to illustrate this concept. What you expect to observe is strong relationships between austerity and spreads (in 2011) - thus higher spreads -> greater austerity. you can consider the causation both ways here too.

Further, he charts the change in spreads to the initial spreads (to look at the impact of the ECB's announcement), the change in debt-to-gdp vs spreads (a negligible fit), and the usual austerity vs growth and austerity vs increases in debt-to-gdp.

But I digress: the voxeu article is here and the CEPS "Governance of a Fragile Eurozone" can be downloaded here.

To get past this fundamental flaw of the EU - that member nations have no control of the currency in which their debts are issued - debts must be pooled. The immediate response to this, of course, is that's not happening. Germany, for one, is highly unlikely to even look down that path.

Still, De Grauwe mentions the obstacles involved. The first obstacle is naturally that of moral hazard. But there are some more obvious ones such as the willingness of 'stronger' countries to accept inevitably higher interest rates on their own debts with the advent of any sort of joint liability.

To overcome these, he offers the following three:

1) The share of pooled debt must be strictly limited to the extent that each member nation remains largely responsible for a significant portion of their own debt (you can see the grey area already!)

2) An internal transfer mechanism between member nations to counter the "one-way-traffic" argument. Essentially, less credit-worthy countries must compensate their polar counterparts.

3) A supervisory authority to monitor members' progress toward sound public finances and the ability to implement consequences on those that don't adhere (remember the Maastricht treaty anyone?)

Just like the rest of us, de Grauwe understands that a fully fledged fiscal union a la the US is wholly unrealistic. The point is, however, to be practical and begin with really small steps. He emphasizes the need for the EU to convince financial markets that it is there to stay - permanently. And for this to happen, a process must start.

But see, that's the problem. If the process was to start, it would have started. The opposition is far too great and powerful and the false sense of contentment with a kick-the-can approach has manifested itself with the polity that makes decisions. There are factions, there are vested interests and then there are the people.

De Grauwe ends with the Alexander Hamilton narrative - that rather than wait for a political integrating process, he took action that spurred the United States to a full-fledged m-f-p union.

The question is, who on earth is Hamilton here? Rehn? Weidmann? Merkel?

Initial Claims vs the SP500

The initial jobless claims as a variable is basically a quicker indicative measure of what's happening in the labor market before you really see the effects. Because it reflects individuals filing official jobless claims (for unemployment benefits etc.), it's sometimes seen as a valuable enough indicator or measure-of-health by analysts. 

Starting from 2008, a simple plot between the S&P 500 index and an inverted claims variable reveals phases of high co-movement. Overall, there's a -.92 correlation and a simple regression line has a fit of roughly 0.85.  The key though, is not the relationship necessarily (right now, for example, the claims aren't low enough to justify the additional buoyancy in the stock market). Or for that matter, since the S&P 500 was/is close to 1620, a claims estimate would be around the 250,000 mark - a far cry from the 324,000 it is now. 

This is what the graph over time looks like:

And the scatterplot looks like this:

The main thing over this time period though (beginning 2008 to present) is the convergence of the two. The gap widens (I rebased them to start as an index and looked at the difference) till it peaks in March 2009 and then a convergence begins till it hits zero in January this year and turns once again:

A simple equities-fundamentals disconnect? A rotational impact? Where to now?

Why this time is not different - revisiting debt and growth for the infinite time

Well, if I don't get this out now, I'm not likely to do it later because I would have read the whole paper and a lot more people would have too. It turns out there is something amiss this morning! - namely this. It's a paper by 3 UMass researchers that sought to duplicate the famous (infamous to me!) Reinhart-Rogoff narrative on what high debt levels do to growth, and among other things- median growth rates for countries with public debt over 90 percent of GDP are roughly one percent lower than otherwise; average (mean) growth rates are several percent lower.

I don't think I've been quite critical enough of these debt-growth studies - but most of the time, there are enough people doing the taking down. This time is not different.

Tim Fernholz at Quartz lays less into the study and more into the blatant disdain political figures showed while repeatedly misusing it. He quotes a passage from Republican senator Tom Coburn's book of debt that describes a scene where, in April 2011, 40 senators met R&R for a briefing - here's what transpired (all emphasis is mine):

“Absolutely,” Rogoff said. “Not acting moves the risk closer,” he explained, because every year of not acting adds another year of debt accumulation. “You have very few levers at this point,” he warned us.

Senator Kent Conrad...explained to his colleagues that when our high debt burden causes our economy to slow by 1 point of GDP, as Reinhart and Rogoff estimate, that doesn’t slow our economy by 1 percent by 25 to 33 percent when we are growing at only 3 to 4 GDP points a year.

Reinhart echoed Conrad’s point and explained that countries rarely pass the 90 percent debt-to-GDP tipping point precisely because it is dangerous to let that much debt accumulate. She said, “If it is not risky to hit the 90 percent threshold, we would expect a higher incidence.”

I present to you -  the "scratch-your-head-till-it-hurts-and-you-find-the-least-smart-comment-game"...STARRING...:

 -  “[I]t is widely acknowledged, based on serious research, that when public debt levels rise about 90% they tend to have a negative economic dynamism, which translates into low growth for many years.” — European Commissioner Olli Rehn.

 -  “Economists who have studied sovereign debt tell us that letting total debt rise above 90 percent of GDP creates a drag on economic growth and intensifies the risk of a debt-fueled economic crisis.” — House Budget Committee Chairman and former Republican vice-presidential candidate Paul Ryan.

 -  “It’s an excellent study, although in some ways what you’ve summarized understates the risks.”— Former US Treasury Secretary Tim Geithner. 

 -  “[W]e would soon get to a situation in which a debt-to-GDP ratio would be 100%. As economists such as Reinhart and Rogoff have argued, that is the level at which the overall stock of debt becomes dangerous for the long-term growth of an economy. They would argue that that is why Japan has had such a bad time for such a long period. If deficits really solved long-term economic growth, Japan would not have been stranded in the situation in which it has been for such a long time.” Lord Lamont of Lerwick, former UK chancellor and sometime adviser to current chancellor George Osborne.

 -  “The debt hurts the economy already. The canonical work of Carmen Reinhart and Kenneth Rogoff and its successors carry a clear message: countries that have gross government debt in excess of 90% of Gross Domestic Product (GDP) are in the debt danger zone. Entering the zone means slower economic growth.”— Doug Holtz-Eakin, Chairman of the American Action Forum.

This is a close one but I've just got to give it to L-cube for those really fancy initials and of course the Japan parallel. Your winner emeritus - Lord Lamont of Ler...

...Anyway, on to more serious critiques, Mike Konczal (Rortybomb/NextNewDeal) summarizes the three issues of the HAP do-over (I would think that this was the post on the econoblogosphere that set off things):

"First, Reinhart and Rogoff selectively exclude years of high debt and average growth. Second, they use a debatable method to weight the countries. Third, there also appears to be a coding error that excludes high-debt and average-growth countries. All three bias in favor of their result, and without them you don't get their controversial result."

There's more detail on these three here if it interests you. But there's something else too!

That would be the average excluding Belgium, which had a robust 2.6% growth in a "time of high debt". Yes, that's the cell not being dragged all the way down - it leads to the average being 2.2 instead of -0.1%. 

But Krugman has some more insight on this. He points to two studies that have acted as a sort of foundation for this harmful austerity drive. The first is the Alesina-Ardagna paper on the expansionary macro-benefits of austerity. The second of course, is the R-R study, and the point he makes (perhaps justifiably!), is that while some could obviously observe the effects of observed correlation and reverse causation, the "crime" so to speak, lies with all the policymakers that actually used it as a public defense of their agenda. Think of this in a David-Li-and-the-Gaussian-Copula way. Should he blamed because rating agencies and investment firms adopted his interpretation?  

Anyway, Krugman uses his own scatterplot but differentiates between countries so as to test the effects of the weighting system. His sample is only 1950-2009 and works for the G-7 only (which in retrospect might not be a bad thing at all). While he concedes that there does seem to be some sort of an association, "most of the apparent relationship is coming from Italy and Japan; Britain didn’t seem to suffer much from its high debt in the 1950s. And it’s quite clear from the history that both Italy and (especially) Japan ran up high debts as a consequence of their growth slowdowns, not the other way around."

But I saved the defence for the last! Here's what Reinhart-Rogoff state in a WSJ piece (in response to the HAP research):

"...On a cursory look, it seems that that Herndon Ash and Pollen also find lower growth when debt is over 90% (they find 0-30 debt/GDP , 4.2% growth; 30-60, 3.1 %; 60-90, 3.2%,; 90-120, 2.4% and over 120, 1.6%). These results are, in fact, of a similar order of magnitude to the detailed country by country results we present in table 1 of the AER paper, and to the median results in Figure 2. And they are similar to estimates in much of the large and growing literature, including our own attached August 2012 Journal of Economic Perspectives paper (joint with Vincent Reinhart) . However, these strong similarities are not what these authors choose to emphasize.

The 2012 JEP paper largely anticipates and addresses any concerns about aggregation (the main bone of contention here), The JEP paper not only provides individual country averages (as we already featured in Table 1 of the 2010 AER paper) but it goes further and provide episode by episode averages. Not surprisingly, the results are broadly similar to our original 2010 AER table 1 averages and to the median results that also figure prominently.. It is hard to see how one can interpret these tables and individual country results as showing that public debt overhang over 90% is clearly benign...

...By the way, we are very careful in all our papers to speak of “association” and not “causality” since of course our 2009 book THIS TIME IS DIFFERENT showed that debt explodes in the immediate aftermath of financial crises. This is why we restrict attention to longer debt overhang periods in the JEP paper, though as noted there are only a very limited number of short ones...

...Lastly, our 2012 JEP paper cites papers from the BIS, IMF and OECD (among others) which virtually all find very similar conclusions to original findings, albeit with slight differences in threshold, and many nuances of alternative interpretation.. These later papers, by the way, use a variety of methodologies for dealing with non-linearity and also for trying to determine causation. Of course much further research is needed as the data we developed and is being used in these studies is new. Nevertheless, the weight of the evidence to date –including this latest comment — seems entirely consistent with our original interpretation of the data in our 2010 AER paper."

=================================

In a way, it's kind of what you expect, perhaps a bit more defensive, a little less calm - I wouldn't know, I'm not too good at gauging reactions. 

What I do know is that any kind of study that seeks to establish an association, tries to imply causation and uses historical data that might be of little use in the world we live in today must be taken with a pinch of salt. 

It can be used to provide perspective and complement or contradict other lines of thought. What it shouldn't do however, is be misused as a tool, and treated as "evidence" just so that politicians and policy makers can advance an agenda. 

================================

P.S: Some further further reading (because it just never stops):

 - Ryan McCarthy has a good encapsulating summary at Counterparties

 - Matt Yglesias at Slate asks what exactly this will really change

 - The folks at Alphaville (Garcia/Cotterill) have a far more specific critique of the study in general and the lack of vetting that went along with it

 - Tyler Cowen, at Marginal Revolution, on a lighter note, has an interesting and fair point-by-point take on future consequences. He asks whether this should change the ratios (quant/narratives) of what he reads.

 - Dean Baker at CEPR emphasizes the implications that this paper led to (it's provocatively  titled "how much unemployment was caused...") along with a follow-up of his own post post-response

 - Noah Smith has his own noahpinion where he chooses to focus instead on the book that sheds light on historical financial crises. He also excuses the "gotcha" excel moment (which I do think is fair, hey it could happen to me!)

 - Owen Zidar has his own take presenting us with two graphs from a collaborative effort on an IMF presentation with Tyson and DeLong.

 - Dylan Matthews at Wonkblog had a detailed "debt/deficits/spending etc" piece just over a week ago. One of the sections is "Countries with debt over 90 percent of GDP enter a danger zone". Worth the read

 - Ryan Avent plays the twitter role

 - The last word should go to Robert Shiller for his Project Syndicate piece almost two years ago with this gem, 

"A paper written last year by Carmen Reinhart and Kenneth Rogoff,...found that when government debt exceeds 90% of GDP....

...One might be misled into thinking that, because 90% sounds awfully close to 100%, awful things start happening to countries that get into such a mess. 

But if one reads their paper carefully, it is clear that Reinhart and Rogoff picked the 90% figure almost arbitrarily. They chose, without explanation, to divide debt-to-GDP ratios into the following categories: under 30%, 30-60%, 60-90%, and over 90%. And it turns out that growth rates decline in all of these categories as the debt-to-GDP ratio increases, only somewhat more in the last category".