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Debt Dynamics

We looked at a paper Hoshi & ItoNote that argues Japan’s budget deficits are not sustainable, indeed that without adjustment bond issues will exceed total domestic financial assets in the mid- to late-2010s. Since bonds ARE a domestic asset, something will have to give. Their focus isn’t on what that means, but in effect the economy is situated between [perhaps temporarily] disabling pain and disaster.

What of the US? That follows an overview of their framework, which is standard.

The core item (using lower case to indicate per GDP, eg bonds B/y = b) is their equation (1), though here I use gamma γ as more natural for GDP growth.


We can then add the surplus (deficit) term (g-t). Again, that is in per GDP terms.

Now they define sustainability relative to private domestic financial assets “a”. A starting point though is to ask what level g-t [g=expenditures, t=taxes as shares of GDP] needs to be to stabilize b at a constant level. If

What seem reasonable levels for “r” and “γ” in the US context? What is “b”?

What is “net debt”? Does it matter? [Hoshi & Ito think not: if the Bank of Japan buys JGBs (J govt bonds) then they pay for that in “money” that the govt then uses to pay its bills, and that money constitutes a domestic financial asset. They show that on its current trajectory the amount of Japanese government bonds will exceed the amount of domestic financial assets in the mid-2010s.]

Finally, Japan is not a federal system; local, prefectural and national are more-or-less one big pot of debt. How about the US?

Now it would be many hours of work (3-4 hours, once data are in hand?) to do a simplified simulation for the US along the lines of what they have done. We can however do crude back-of-the-envelope calculations. When I did that for Japan many years ago I got more-or-less the same answer, but at that point debt levels were much lower so the fiscal adjustment required was smaller. So I think we’ll learn a lot from doing simple calculations for the US.

Part 1: My first attempt to calculate r-γ, done in class, used nominal GDP and nominal interest rates. However, periodic inflation-fighting monetary policy meant that “r” varied by large amounts, and did not produce any useable information. However, if we compare real GDP growth with real interest rates (the latter drawing upon TIPS to get inflation-adjusted long-term rates), we do get fairly consistent results: r-γ ≈ -0.5. That lowers the burden of our debt, but because deficits are far higher than 0.5% of GDP our fiscal situation is nevertheless unsustainable. But that leads to a second question: is it really reasonable to think that interest rates consistently lie below growth rates? After all, that means that buying a “GDP portfolio” beats buying bonds.

Part 2: Order of magnitude Federal debt is approximately 100% of GDP. Hence (conveniently for the arithmetic) b ≈ 1. With r-g ≈ -0.5 we can run a deficit of 0.5% of GDP forever. Unfortunately, our current deficit is about 3% of GDP. Now that’s a vast improvement over the -10% of GDP level at the trough of the Great Recession. Subsequently employment growth and profit growth and a drop in unemployment-related expenditures led to a 7% of GDP improvement. We can’t expect further gains, that is, there’s little upside potential. If we average across any future “downs” then we should view a likely average across time as at best -3.5% of GDP. So Congress needs to “enhance net revenue” by 3% of GDP. Unfortunately the current Republic Party talks about balancing budgets but in practice cuts taxes and not expenditures.

In sum, our current Federal fiscal stance is not sustainable.

Addenda: US-heavy portfolio strategies are great for the sustainability issue, bad for the US dollar. And is it good for management to be able to reap bonuses from achieving high stock prices without actually having to generate higher profits?

Note: Hoshi, Takeo, and Takatoshi Ito. 2014. “Defying Gravity: Can Japanese Sovereign Debt Continue to Increase without a Crisis?” Economic Policy 29(77): 5–44.


  1. dawejko dawejko

    I don’t think holding g or t constant is feasible. Since 2003 Federal tax revenue has more than doubled..but our deficit is still increasing at a faster rate than our tax revenue is. Tax revenue is supposedly around 19% of GDP in America, which is actually low. As unrealistic as it sounds, we could increase taxes on middle-class households while simultaneously making massive spending cuts and easily reach a surplus. I don’t know if that’s what Congress wants though…

    • Tax revenue has not doubled as a share of GDP. You need to consistently deflate everything that way – you (correctly) do so in the rest of your comment. For tax revenue you also need to make sure you don’t have one end point lying in a recession, another in a boom. Expenditure is less affected by changes in GDP.

      We know very much what the party in control of the House does not want to do, which is raise taxes. There aren’t many “conservative” Republicans left in the House when it comes to fiscal prudence. The Senate is slightly better, but every Republican there is looking over their shoulder at radicals who might challenge them in the next primary.

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