A meaningless answer for a meaningless question

James Hamilton asks Brad Delong:

Finally, let me invite you to answer the questions I posed for Krugman and O’Brien: “Do you maintain that U.S. debt could become an arbitrarily large multiple of GDP with no consequences for yields? If you acknowledge that there is a level of debt at which these effects would start to matter for the United States, what is your estimate of that level, and how did you arrive at it?” We give our answers to these questions in our paper. What’s yours?

I’m going to invite myself into this little debate. This question can be interpreted in many different ways that, I think, is the problem with the fear-mongering behind a particular debt-GDP ratio. What do I mean by this?

The R-R paper infamously notes that after debt exceeds 90% of GDP, yields start rising, because investors no longer have confidence that the country in question can service its debt. Even ignoring the fact that this “limit”, if you will, doesn’t apply to countries that borrow in their own currency, the 90% figure is meaningless.

Presumably, investors worried that countries will have to borrow more to pay interest on its bonds which will lead to a snowball effect of debt accumulation. Therefore, it’s hardly the debt that’s important, but the deficit. So it’s not a particularly worthwhile task to wonder the debt-GDP ratio at which a country “tips over”.

Consider an example. You’re told a country has debt levels at a staggering 500% of national income. You’re also told that its debt has been at this level for the past 500 years, and official estimates predict this ratio well into the next 500 years. The market won’t suddenly demand higher yields, because the country has consistently serviced all its interest in the past, and will do so in the future.

Deficits imply that a country has to borrow to service its interest, debt implies nothing. The 90% figure was likely a correlation with a) the fact that the countries in question couldn’t denominate debt in their own currency and b) they had high deficits.

So yes, I believe debt against GDP can become arbitrarily large so long as a country isn’t running deficits. Of course, on the long journey to huge debt levels, a country does run deficits, and it’s entirely possible that investors deem this to be unsustainable, causing a debt crisis in the interim. You can parse this as a one-time promised deficit of whatever level you choose. Say, if, the US buys all the gold in the world to build statues and create a Cult of Obama. As long as it does it only once, services all its interest, and doesn’t run a deficit next year to do so.

But that’s not the question being asked. The question that’s being asked supposes an arbitrary debt to GDP. Position has no meaning without regard to velocity which, itself, has no meaning without regard to acceleration. I would actually argue that so long as an arbitrarily high nth derivative of debt is negative, the countries fiscal position would be stable. Of course, this is beside the point in reality because the level of confidence with which an investor can know debt is greater than he can know deficits, and so forth. The nth derivative becomes, basically, unknowable, at which point the investor plays it safe.

You might think my answer is meaningless, and to some extent it is. But that’s because it’s answering a meaningless question.


Edit: Note, I don’t actually thing that our long-term debt is irrelevant. In fact, I depart from Krugman in that I think we had better start talking about rising healthcare costs not just in 20 years, but in 50, 100 today. But, unlike others, I won’t wrongly caricature him as someone who doesn’t care about this, but he definitely seems to discount for the future far more (as in have faith that future politicians aren’t clueless).

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