Yesterday, I posted a reply to John Cochrane's Sept 4 post on the national debt. John alerted me to his Sept 6 update, which I somehow missed. Given this update (together with some personal correspondence), let me offer my own update.

John begins with an equation describing the flow of government revenue and expenditure. With a debt/GDP ratio of one, the sustainable (primary) deficit/GDP ratio is given by g - r, where g = growth rate of NGDP and r = nominal interest rate on government debt (I include Federal Reserve liabilities and currency in this measure). John assumed g - r = 1% (so about $200B). In a post I published last year, I assumed g - r = 3% (so about $600B); see here: Is the U.S. Budget Deficit Sustainable?

Two things to take away from these calculations. First, this arithmetic suggests that the U.S. federal government can easily run persistent primary budget deficits in the range of 1-3% of GDP. Not only does the debt not need to be paid off, but it can grow forever. Second, primary budget deficits are presently far in excess of this range. What does this imply?

Let's step back and think about John's equation. The arithmetic of the government "budget constraint" basically says this:

Deficit/GDP = [1 - (1+r)/(1+g)] x Debt/GDP

Note that a sustainable primary deficit is only possible if r < g. If r > g, then a primary surplus is needed to service the interest expense of the debt.

Students of monetary theory may recognize the expression above as a Laffer curve for inflation finance. That is, in the case of currency we have r = 0. Let g represent the growth rate of the supply of currency and assume a constant RGDP (so that g also measures the growth rate of NGDP). Finally, replace debt with currency, so that

Seigniorage revenue = [1 - 1/(1+g)] x Money/GDP

Again, this is just arithmetic. Economic theory comes in through the assumption that the demand for money is decreasing in the rate of inflation, g. If this is true, then an increase in g has two opposing effects: it increases seigniorage revenue by increasing the inflation tax *rate*, but it lowers seigniorage revenue because it decreases the inflation tax *base*. There is a maximum amount of seigniorage revenue the government can collect by printing money. That is, there are limits to inflation finance. (See also my post here.)

Now, I know John is fond of saying that Federal Reserve liabilities and U.S. Treasury securities are essentially the same thing (especially if the former exist mainly as interest-bearing reserve accounts). I happen to agree with this view. But then we can use exactly the same logic to characterize the limits to bond finance, recognizing that U.S. Treasury securities are essentially money. To this end, assume that the Debt/GDP ratio is an increasing function of (r - g). To make things a little simpler, let me continue to assume zero RGDP growth, so that g represents both inflation and NGDP growth. Finally, let me assume that r is a monetary policy choice (just as setting r = 0 for currency is a policy choice).

Next, we need a theory of inflation. In the models I work with, the rate of inflation in a steady state is determined by the growth rate of the nominal debt, g, which I also treat as a policy parameter. So, the magnitude r - g is policy-determined, at least, within some limits. By lowering r and increasing g, the government is making its securities less attractive for people to hold. But this just tells us that the demand for debt is lower than it otherwise might be--it does not tell us how large this demand is in the first place, or how it is likely to evolve over time owing to factors unrelated to r or g (e.g., regulatory demand, foreign demand, etc.).

So, with this apparatus in place, my interpretation of what worries John is the question of what happens if [1] the federal government finds itself near the top of the bond-seigniorage Laffer curve; and [2] a shock occurs that requires a large fiscal stimulus. Barring alternative forms of securing resources (e.g., through direct command/conscription), the government will not have the fiscal capacity to lay claim against the resources it needs. Printing more money/bonds here is not going to help even with zero interest rates. The ensuing inflation would simply put us on the right-hand-side of the Laffer curve -- the government's ability to secure resources would only *diminish*.

Assuming I have captured at least a part of John's concern accurately, let me go on to critique it. To begin, there's nothing wrong with the logic I spelled out (I don't think). But I want to make a couple of points nevertheless.

First, the demand for U.S. government securities (D/Y) seems to be growing very rapidly and for a very long time now. We know, anecdotally, that the UST is used widely as collateral in credit derivatives markets and repo, that foreign countries view it as a safe asset, that investors value its safety, and that recent changes to Dodd-Frank and Basel III have contributed to the regulatory demand for USTs. The global demand for the U.S. dollar is, if anything, growing more rapidly than ever (re: the recent "dollar shortages" that resulted in the Fed opening its central bank swap lines). We don't know where this limit is, but judging by how low U.S. inflation is (together with low UST yields), it seems fair to day that there's still plenty of fiscal capacity. (And I want to stress that this has nothing to do with the ability of a country to pay back its debt -- I'm not sure why John keeps mentioning this while at the same time understanding that this debt is money).

I suspect that John is likely to agree with what I just said. Sure, there may be more room now, but how much more? With bipartisan concern for debt absent in Congress, with no sign of inflation in sight, with interest rates so low, how can we *not* hit this limit at some point?

My own view is that we are bound to hit this limit (though, economists like Simon Wren-Lewis have warned me not to discount the forces of austerity). The question is what happens once we hit that limit? I say we get USD depreciation and some inflation (not hyperinflation). John seems to be worried about hyperinflation after all, which he likens to a debt rollover crisis. I just don't see it. (Of course, if John is simply suggesting that the fiscal authority will continue to run persistently large deficits in the face of high inflation, then I agree with him. While I don't see this happening, who can say for sure?)

Finally, what happens if we're near the debt limit and there's a shock. Well, what type of shock exactly? The type of shock that hit us in 2008 is likely to increase the demand for debt, *expanding* fiscal capacity. So, here too, I'm not sure what form the debt crisis is supposed to take. It would be great to appeal to a model (but please, not one of Greece).