Miles Kimball and Yichuan Wang find that high government debt doesn’t cause low GDP growth, and Kimball says he finds that surprising, as does Matt Yglesias. But as I suggested in a post last month, I’m not really surprised by this at all.

Governments tax or borrow. The former is withdrawing money from the economy in exchange for nothing (or perhaps a promise not to sanction the taxed) while the latter withdraws money from the economy in exchange for a piece of paper. That’s debt! Evil, evil, debt! Oh, no!

Wait, let’s start over.

The goverment decides it wants to do something it isn’t already doing, and therefore needs to command a higher share of total social production going forward than it has been. Developed-world governments don’t directly commandeer social resources, they claim through the proxy of money, by spending it. Assuming an economy at full capacity (whatever that means), if the government commandeers resources by spending money without removing any money from the economy then you’d have inflation, unless the central bank raises interest rates substantially, which would likely have undesireable negative effects. So the government attempts to roughly balance the resources claims it makes using money by withdrawing an equivalent amount of money from society. Sometimes it does this through taxes, which has some desireable properties (no future obligations on the state, can be used Pigovianly) and some undesirable ones (unintended consequences, involuntary, discourages desireable activity). Borrowing also has some desireable properties (voluntary, compensates those who part with their money) and some undesireable properties (obligates the state).

Therefore, there are two key intertwined questions to be asked about this new government activity, which remember is centrally about taking some resources deployed previously to some private purpose and redirecting them to some other, presumably public purpose – is the new activity more valuable than the activity(s) it is supplanting, and how is it being financed? They are intertwined because the latter question informs the former.

Let’s say we all agree that this new government project – let’s say it’s a SUPERTRAIN, for fun – is widely considered to be of higher value than the marginal private activity it supplants regardless of how it is funded. The government could raise taxes to fund it, but unless it is taxing something undesireable (like carbon or booze or Kardashians) this would have the drawback of incurring some "deadweight loss," not to mention other unintended consequences. It could also borrow the money, which would have two consequences. Firstly, it would supplant something different – rather than raising the cost of work or carbon emissions, it would be more likely to supplant a capital investment of some kind somewhere in the economy. Secondly, it would obligate the government.

And to what would it obligate the government? Key to understanding this is that governments, unlike Lannisters, never pay their debts. They cleverly disguise this fact by paying their debts in full and on time. Huh? From the perspective of a borrower, you get your interest payments, and then your principal in full. But from the perspective of a government, you don’t pay the principal back out of tax revenue, you pay it by rolling over the debt and issuing new debt in the amount of the principal. This works because of NGDP growth (both the RGDP growth and inflationary components). In fact, we’re still likely rolling over all the debt we incurred from WWII, which back then was 110% of NGDP but today is less than 2% of NGDP.

So really what the government does when it issues a bond is issue itself a negative perpetuity. And the key to understanding the value of a perpetuity is knowing the interest rate, since the PV = C/r. Therefore, the obligation on the government is much more dependent on the interest rate path than on the nominal coupon value.

But that interest rate path isn’t just some made-up thing – it’s fundamentally related to NGDP growth. Don’t believe me? Here’s the fed funds rate divided by the NGDP growth rate:

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So when recessions happen, the ratio spikes (and whether it spikes up or down is very interesting), but otherwise it’s very steady; if you exclude just the 12 of 223 periods where the absolute value of the ratio is greater than 3, you get an average of 0.8 and a standard deviation of 0.6.

So what does that mean? As interest rates grow, so does the obligation on the government – but it also implies that the government’s ability to meet that obligation is growing in tandem. Which suggests that, while governments cannot borrow limitlessly, the pain point at which government indebtedness begins to inflict structural economic harm is vastly higher than previous assumptions.

Japan, for example, is often cited as an example of government debt creating a huge drag/time bomb/giant vengeful lizard that is harming Japan’s economy. But since 1990, Japan’s debt/GDP ratio increased from 67% to 211% and GDP-per-capita…grew! Significantly! Not awesomely, not enough to catch-up with the US (in fact, it fell behind), but grow it did. Certainly more than you might think it would if the 90% monster were real and starting smashing major cities or something.

Many people have begun to worry whether the seemingly-inevitable Japanese debt crisis is nearing as yield have crept up. But yields have crept up because NGDP-growth-expectations have crept up. As long as they increase in tandem, contra Noah Smith, Japan should always be able to pay its debts.

And I’d be willing to put money/my reputation on this point. While Noah Smith is 100% right that bets != beliefs, I am nonetheless willing to agree in principle to any reasonably-valued bet that neither Japan nor the United States will default over any arbitrary time period. Any takers?