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"?