A war on public debt and Paul Krugman has been raging over at FreeAdvice. On the one side are Krugman's defenders, principally me and Gene Callahan, versus his critics, principally Bob Murphy, Nick Rowe and Major_Freedom. The debate has spread over many threads, and even some other blogs, and become so diffuse and shambling that I want to summarize my case for Krugman here.
Krugman argues that internally held debt cannot in any direct way impoverish America as a whole. Internal borrowing rather than taxing imposes no extra burden on any future America in toto, because both are transfers between then living Americans. Internally held debt represents a flow of assets is within a given pool, and so the pool is not directly diminished by the debt. Krugman gives a good analogy: Imagine a "Santorum tax" that just transfers funds between Americans. Leaving an internally held debt is just like a Santorum tax.
I think Krugman's argument is sound, convincing, and correct. But Bob Murphy and Nick Rowe insist, reasonably enough, that the claim be tested against some models to see if they can disprove it. Bob presents his model, and claimed counter-example, here. The rest of the discussion takes place within the context of this model.
At first blush it looks like Bob has made a point. We do indeed see people who eat fewer apples. But in fact this is not a counter example at all. I'll come back to why but we must first translate Krugman's claim into this model. Krugman talks about future states of America.
The natural and correct interpretation of Krugman here is that a state of the whole country at any moment corresponds to a row in the table, and a period of time corresponds to a contiguous block of rows. (We know this is what he means because he tells us so with the Santorum tax). Krugman's assertion is that at no point in time and for no period of time is a future America impoverished. This is plainly true in the model: each row (point in time) has 200 apples. The period claim follows from the point in time claim. If that's what a future state really is, then Krugman's claim holds in this model.
So the question reduces to: is this the appropriate definition of future state? Bob's example assumes not. Rather than level sections, Bob presents diagonal sections. He includes for example Young Frank, Old Frank, Young George, Old George but not Young Hank or Old Eddy, slicing diagonally through the table. In any of his slices there is always one person from the first level and one from the last level omitted. And this is the problem. At no point in time and for no period of time are the people and assets of a diagonal section co-extensive with the population and assets of the Island. In the real world a slice like this might include all the people whose names end in vowels who were born before 2012 and all those who names do not end in vowels who were born after 1970. That diagonal section never, not for a moment, not for a period, is all and only the population of the country. A diagonal section is not a state of the country. Bob's diagonal sections may be interesting -- I will return to this point -- but they do not correspond to a future state of the country. Since they do not refer to what Krugman is talking about -- future states -- they cannot be counterexamples to Krugman's claim.
So Bob's construction is not a counterexample after all. But don't Bob diagonal sections show something? After all he seems to show a loan impoverishing 65 generations. Doesn't that prove something? No, not about the aggregate consequences of debt anyway.
First Bob's example does not show one loan affecting 65 generations. He shows 65 consecutive loans affecting 65 consecutive generations. In each case the whole daisy chain would be ended unless each generation takes from the next while both are alive. Gene Callahan put this well: I can eat my son's desert, and when I am dead he can eat his own son's desert, but that doesn't mean I ate my grandson's desert. I explicate this point in detail in comments on that thread. Borrowing from Young Hank does not burden the future, it burdens Hank.
Do Bob's diagonal sections correspond to anything meaningful? Perhaps they do, but not for the purpose of looking at the aggregate effect of debt or transfers. I illustrate this with an example where imposing a debt on a diagonal section seems to enrich it. This is pretty odd if you want to argue the section corresponds to something meaningful, which is burdened by the infliction of a debt. But a diagonal section is really just an incomplete set of accounts. There is no mystery why you can make an incomplete set of accounts seem unbalanced in odd ways.
So Krugman is right, in detail, and Rowe and Murphy have merely exhibited a combinatorial artifact, which they misinterpret.