A client sent over an NBER research piece by Berkeley professor Danny Yagan on the role of the r-g gap in public debt dynamics. The client shares my interest in this subject and notes that the paper takes a slightly different approach to the issue than the approach I have highlighted.
The substance of the note is entirely in line with the mechanics of Ponzi Public Finance (no disparagement implied), which are most closely associated with former IMF chief economist – and general macro hotshot — Olivier Blanchard. As Yagan points out, the purpose of the note is not really to break new ground analytically. Rather, it is to reach the general reader by “bridging the gap” between how (conventional) economists treat this issue and how it is mistreated in our increasingly hopeless state media.
I am generally not a fan of dumbing stuff down so the plebs can understand. Or perhaps I should put this more precisely. Economists, especially in policy circles, often confuse legitimate uncertainty around how things work or will work with a “communication” difficulty. The Fed is notorious, for example, for worrying about communication when it is in the midst of being quite wrong. But the paper is meant to be written for a general audience, which I guess means us. So, you may get some value from it. It is indeed an easy read.
The paper departs from what I take to be the standard treatment in two ways, one of which is trivial and the other of which strikes me as a potential source of mischief. The trivial point relates to the gap between r and g. When the interest rate is above the growth rate, whether that gap be measured in nominal or real terms, the ratio of the debt to the GDP will rise by less than the primary deficit as a ratio to GDP, and with consequences that are far more important than simple intuition might initially suggest. Typically, this encourages analysts from the Ponzi school to watch r – g, where both are expressed in real terms and relate to the natural rate and potential growth rate respectively, denoted with asterisks. But Yagan chooses to be slightly more precise on this point, favoring r-g / 1+g, which is what the algebra actually surfaces. If anything, that is an un-simplification. But it is not a big deal either way. Keep in mind that g* would be expressed as 0.02 in this treatment.
The second way this approach deviates from what I take to the standard presentation is that Yagan wants to rearrange the algebra so that he can isolate a line item that might be inserted into conventional debt analysis to highlight in accessible terms the importance of r – g. And what he comes up with is the “nominal growth dividend,” which is the difference between the deficit and change of the debt, both expressed as ratios to the nominal GDP.
This innovation in presentation is seemingly intended mostly to prevent journalists from saying stupid and misleading things, such as the comment from the New York Times, which Yagan highlights on page 3 of his report. Yagan’s insight here is that if we can express the arithmetic of Ponzi Public Finance in a way that allows its main point to enter as a single line item within a CBO report, where all the lines add up, then even journalists will have trouble getting it wrong. Ed note: unless they want to, which they will, going to expert budget analysts Stan Druckenmiller or Jamie Dimon according to which mood strikes.
Yagan’s objective is help journalists avoid saying stupid things

Source: Yagan as linked above, p.3.
But the main problem with this approach is that it leaves a clear impression that higher inflation favors a lower trajectory of the debt / GDP ratio, with the relevant beta there being 1. And that is itself extremely misleading. The US could “fix’ its debt problem with a burst of hyperinflation. But there is no reason to believe that a tolerably small increase in the trend rate of inflation would have any durably relevant “favorable” effect at all. The standard approach highlights this and Yagan’s more user-friendly approach dangerously obscures it. But the substantial point from an analytical perspective is that the basic logical apparatus he applies here is very conventional.
Let me conclude with a very quick editorial comment on the value of dumbing it down. Particularly with the advantage of hindsight, there was a roughly two-decade long period, ending a couple years ago, where having properly internalized the logic of Ponzi Public Finance would have very clearly greenlighted – and made us welcoming of – the huge fiscal expansion that ended up happening. Anybody paying close attention would have been confident that was a good thing. In other words, there was a time when things were indeed clear, although almost universally overlooked by pious analysts who never seemed to be punished for being dead wrong. Some folks call those folks, very serious people.
But recently, r* has risen relative to g* and is near or perhaps even beyond g*. (I would say r* is still slightly less than g*, but it is a near call.) So, we have transitioned from an environment where things were clear to those operating with the best understanding to a point where there is heightened uncertainty and therefore a legitimate case for caution. It seems like a rather odd time, then, to be figuring out ways to dumb it down so that the plebs can understand.
In fairness to Yagan, this is a case of me having my own opinions about “presentation.” To Yagan’s credit he emphasizes in the abstract and discussed in some detail in Section 6, beginning on page 10, the increased need for caution around continued fiscal expansion, by which I mean a large trend primary deficit. My concern here is about presentation, as I am sure the author would appreciate.