No, I don't think it is. But I think "Is Japan already dead?" is a much better question to ask than "Will the increased interest rates from economic recovery kill Japan?"
This is just a supplement to three posts: by me; by Noah Smith; and by Paul Krugman. (This also harks back to Livio's post and my earlier post). I think I've finally figured out a way to articulate something I couldn't explain very well before.
If Japan pays nominal interest rate i on government debt, and if Japan's Nominal GDP is growing at rate n, then Japan needs to run a primary surplus as a percentage of NGDP equal to (i-n)x(Debt/NGDP) in order to keep the Debt/NGDP ratio constant over time, and therefore sustainable.
If you prefer, we could re-write that formula by subtracting the inflation rate from both i and n to get (r-g)x(Debt/NGDP), where r is the real interest rate and g is the real growth rate of GDP. It's the same thing.
Economic recovery means that n will increase. Partly through higher inflation and partly through higher real growth, though we don't know the exact mix. Theory and observation tell us that economic recovery means that i will increase too.
If economic recovery causes i to increase more than n, so that (i-n) increases, that makes it harder for Japan to service the debt. But if n increases more than i, (i-n) decreases, that makes it easier to service the debt.
Or we could say that if economic recovery causes r to increase more than g, so that (r-g)
increases, that makes it harder for Japan to service the debt. But if g
increases more than r, (r-g) decreases, that makes it easier to service
the debt.
Paul Krugman thinks that looser monetary policy (by raising expected inflation) will cause r to fall. In which case it is clear that economic recovery caused by looser monetary policy must make it easier to service the debt.
I disagree with Paul a bit. I think that if looser monetary policy causes g to rise, that in turn will cause r to rise. (Very briefly, I think the IS curve may slope up, because higher expected future income reduces current saving and increases current investment.) So I think that both r and g will rise, and it is an open question which one rises more, and whether this makes debt service easier or harder.
Let's assume the worst-case scenario. Let's assume that I am right and Paul is wrong, so r increases. And let's also assume that r increases more than g, so (r-g) increases. (Or (i-n) increases, if you prefer.) So economic recovery, by assumption, makes it harder for Japan to service the debt.
Let us also assume that Japan is like an OverLapping Genererations model, where Ricardian Equivalence is false, and where the equilibrium level of (r-g) is an increasing function of the debt/NGDP ratio.
These worst case assumptions mean that there must exist some maximum Debt/NGDP ratio, call it Rmax, such that if the actual debt/NGDP ratio exceeds Rmax, then it would be impossible for Japan to service its debt if economic recovery causes interest rates to rise. Japan would either have to default, or create a big enough unanticipated rise in the price level to inflate away the old debt and bring the debt/NGDP ratio back down below Rmax.
Let us further assume that Japan's current debt/NGDP ratio exceeds Rmax.
In other words, I have deliberately set up a case in which Richard Koo would be right (maybe for the wrong reasons, but let that pass). I have deliberately made worst-case assumptions so that the higher interest rates caused by loosening monetary policy creating economic recovery would cause Japan to default on its debt, either literally or via very high inflation.
Does this mean that "Japan cannot afford recovery"?
No. It means that Japan is already dead. It just doesn't know it yet.
Sure, the Bank of Japan could abandon Abenomics, tighten monetary policy, reduce the inflation target, squash all hopes of recovery, and bring nominal interest rates back down again. But if the past is any guide to the future, this means the debt/NGDP ratio will keep on growing. Because Japan will be scared to tighten fiscal policy in a recession when the Bank of Japan won't offset that tightening by loosening monetary policy. Which means that recovery, when it does finally come, will cause an even bigger default, because the debt/NGDP ratio will be even bigger.
And recovery will come eventually, one way or another. If not by happenstance, then because there is a limit to the debt/NGDP ratio that the young generation in an OLG economy will be willing to buy from the old.
If Japan is already past the point of no return, then recovery will mean default. But delaying recovery will simply mean an even bigger default.
Now I'm going to cry over spilt milk, and ask: why oh why didn't they do Abenomics earlier, before the debt/NGDP ratio had grown so big? What was all this talk about "balance sheet recessions", where monetary policy was impotent to increase Aggregate Demand, so fiscal policy had to be used to prevent AD from falling? And how did we suddenly switch from "monetary policy is impotent" to "monetary policy is very dangerous because it will increase AD which will only cause inflation and higher interest rates which will cause default because loose fiscal policy has made the debt/GDP ratio so big"?
Worthwhile Canadian Initiative 
A: As the current price of wheat rises, relative to the expected future price of wheat (i.e. as the real interest rate rises) people will reduce their demand for current wheat. So too (presumably) should the government reduce its expenditure on current wheat. For example, it should maybe reduce the amount of wheat it pays to the soldiers, and to the poor. But if you wanted to reduce the real rate of interest all the way back down to zero, the government would need to reduce its own expenditure on wheat by a large enough amount so that private consumption of wheat returns to normal. That would mean that (absent storage of wheat from one harvest to the next) the soldiers and the poor (or whoever) would have to cut their consumption by the full amount of the harvest losses. (And in a good year, the soldiers and the poor would eat all of the extra harvest.) Because the only way you can keep real interest rates at 0% is if private consumption stays exactly the same from one year to the next (assuming bad harvests are the only shock).
If you want fiscal policy to adjust to keep the real rate of interest at zero, it can (usually) be done. (I say usually, because it might mean making G negative in some years). But it doesn’t seem very sensible to have a fiscal policy in which soldiers and the poor starve in lean years and are stuffed in good years, with everyone else eating the same amount of wheat in good and lean years.
Nick Rowe:
You’re talking about a real supply side shock. Somebody has to go without. That’s the simple reality of the situation.
If you choose to do nothing, inflation will set in, you’d lose price stability of the currency, and the limited wheat would simply go to the wealthiest. If the soldiers are not the wealthiest, they’d go out – just as in your fiscal example.
If you choose to use monetary policy, those willing to save will lose out today – but be granted a far greater portion of next year’s harvest. Depending on the extent of the price shock, you may not be able to maintain price stability – many countries have seen high inflation despite offering 17%+ interest rates to anyone willing to just save instead.
If you choose to use fiscal policy your options are endless. You could cut the solider’s pay, as you suggest. You could increase taxes on any sector of the community. Wealthy consuming so much wheat so that there’s not enough to go around? Increase taxes on that sector. You could, if you decided, even subsidise savings – for monetary policy is just a subset of the options available to you. Again though, you’ll have difficulty maintaining price stability through a large shock by merely giving everyone more money, as monetary policy would do.
A: We agree that in this supply shock case, we have 3 options:
1. Change fiscal policy in a way we might not want to do (because the soldiers and poor would starve)
2. Allow inflation to fluctuate so that real interest rates rise above zero
3. Allow nominal interest rates to rise above zero so that inflation can stay constant.
I prefer options 3.
Now let me change the example away from a supply shock.
The important ingredient in my bad harvest example is that people expect next year’s consumption will be higher than this year’s consumption. That’s what drives real interest rates up above 0%. Lets simply assume that real economic productivity growth causes the wheat harvest to rise by (say) 2% every year. You get the same results. Only now the real interest rate will be above 0% every year, if consumption is rising at 2% per year. And if we wanted to push real interest rates down to 0%, fiscal policy would have to do something very strange. We would have to tell the people that the soldiers and the poor would be eating all of the increased wheat production in future years, so that private consumption of wheat would stay constant over time. So government would be taking a larger and larger fraction of total wheat output every year, as the country got richer, while private consumption would stay the same every year.
That doesn’t sound like a very sensible fiscal policy.
Yes, fiscal policy has lots of options. There are a lot of different things you might want to do with fiscal policy. But if you constrain fiscal policy, by telling it that fiscal policy must make sure that real interest rates are 0% each and every year, you won’t be able to do some of those things, and you will probably end up with a very silly fiscal policy. So maybe you could let monetary policy handle the job of getting aggregate demand right, and let fiscal policy free to do those other things well.
You’re saying some simply bizarre things. Why do the poor/soldiers have to starve? Why can’t you simply increase taxes on the rich, reducing their consumption? Why do the poor and soldiers have to eat all excess production in the future? Why can’t you simply lower taxes in those times of high wheat yields?
I don’t know why you see the expenditure side as having to make up the entirety of the deficit. Soldiers don’t have to lose all the food in bad times and absorb it all in boom times – you can just as easily alter taxes, sharing the burden however you want according to your political goals.
Monetary policy is just a tiny tiny tiny subset of the options available, and a blunt weak tool at that. It often can’t restrain inflation. It feeds money straight to the boom sectors, an inherently inflationary practice (one reason we aim for 2% inflation) whilst leaving many towns and cities across the continent shrinking. There just really isn’t much to recommend it by.
Also, you seem to be making out that the government has to force interest rates down. It’s actually quite the opposite. It’s not a matter of “allowing nominal interest rates to rise above zero” – what you’re referring to is the central bank restraining liquidity such that they do. It’s a deliberate action by the central bank to subsidise savings, it’s not a simple case of “allowing” interest rates to move.