The old debt puzzle is back

Occasionally I try to use philosophy to clarify debates in economics, particularly in the abstract, highly conceptual realm of macroeconomics. I often find that both sides are talking past each other because of some conceptual ambiguity. Philosophical intervention, in a very traditional sense, seems very much called for — and that’s a rare thing.

Usually both sides end up yelling at me that I don’t know what I’m talking about. They tell me that the issue doesn’t hang on a conceptual ambiguity. Rather it hangs on the other side being wrong. When I try to explain, I end up talking past both sides. My attempt to clarify and pacify creates more confusion and often more aggro.

Luckily, I’m not an empiricist, and I have a great feeling this time will be different. Anyway, the debate this time is between Nick Rowe, who is always open-minded, and Paul Krugman, who is rarely open-minded but would never engage with me in any case.

So. Paul Krugman did a tweet:

He means the national debt. What sparked the outburst was this:

RipCurlDog committed a logical solecism, according to Krugman. It is impossible to ‘borrow from our children’s future’ in this way.

The reasoning is now pretty familiar to readers of economics blogs. Future generations will consume whatever they produce, with some transfers of course occurring among those alive. They can’t, however, send real resources back in time to us. Thus, no matter how much the national debt grows today, future generations will not be any poorer for it in real terms. Nor will we be any richer at their expense. Without inventing time-travel, we can’t steal from the future to pay for the present, except in the sense that we can consume non-renewable resources. But that’s a separate issue from the national debt. Debt is not a burden on future generations.

Nick Rowe pushes back against Krugman. He’s written a few blogs that explain beautifully, using Overlapping Generations Models, how debt can be used to transfer real resources from future to present generations. Here is the shortest and sweetest, which I quote in full:

Suppose you wanted to take milk away from people on the east coast, and give it to people on the west coast. But you don’t have any way of transporting the milk quickly enough to stop it spoiling before it gets from one coast to the other.

Here’s how you do it:

You take milk away from people on the east coast. You move it a few kilometres west, then swap it for fresh milk from the people living a few kilometres inland from the east coast. Then move that second batch of milk a few kilometres west, and repeat. And keep on repeating until you get to the west coast.

Suppose you wanted to take milk away from people who won’t be born until 100 years in the future, and give it to people alive today. But you don’t have a time-machine.

Here’s how you do it:

You borrow milk from people who are young and give it to the people you want to give it to. You wait a few years, then borrow some more milk from people who are young, and use it to repay the milk you borrowed from the people who were young but are now old. And keep on repeating until you get to the people who were born 100 years after you started. You don’t borrow milk from them; you just take it.

So now we see that debt can be used to transfer real resources from later to earlier generations — in a sense. It isn’t necessarily so; whether or not it occurs in real life depends on interest- and growth-rates, and so on. But the point is that it’s possible. Rowe writes: ‘Even in: a closed economy; with no investment of any kind; and purely lump-sum non-distorting taxes, we can take apples out of the mouths of yet unborn future generations, and eat them ourselves. Time travel is possible.’

The last sentence is false, of course, and I say this not to nitpick but because it’s getting very hard to keep all the concepts straight here, and figures of speech are not helping. We can see this when we look back at what Krugman says. He doesn’t dispute Rowe’s point. He concedes that:

It’s quite possible that debt can raise the consumption of one generation and reduce the consumption of the next generation during the period when members of both generations are still alive. Suppose that after the 2016 election President Santorum tries to buy senior support by giving every American over 65 a gift of newly printed government bonds; then the over-65 generation will be made richer, and everyone under 65 will be made poorer (duh).

But that’s not what people mean when they speak about the burden of the debt on future generations; what they mean is that America as a whole will be poorer, just as a family that runs up debt is poorer thereafter.

That seems right. In Rowe’s model, there are always two generations alive during each period. During each period while the ‘milk-transfer scheme’ is being run, the younger generation is made richer while the older is made poorer. But ‘America as a whole’ — that is, all the living people of both generations alive in that period — is never any poorer on the whole. There are transfers in the period, but the consumption within a period is always the same. So is Rowe wrong?

No. Run his model again. At 100 years, the younger generation have their milk taken and given to the old. Now let the old die off in the next period. The younger generation — let us call them the Milksnatched — become the older generation. Suppose that every period 100 units of milk are produced by the younger generation. At the start of the milk-transfer scheme, the government borrows 50 units from the young and gives it to the old. When the young become old, they get repaid with 50 units borrowed from the new young. Thus every generation consumes 100 units over its whole lifetime. Until we get to the Milksnatched. They lose 50 units when they are young, and they aren’t given another 50 when they are old. They consume only 50 units of milk over their whole life.

So is Krugman wrong? No! It remains true that any pair of generations alive during a period consumes a total of 100 units of milk during that period. When the old Milksnatched consume zero, their spoiled, avocado-toast-gobbling children consume the whole 100 they produce. ‘America as a whole’ is never poorer in terms of consumption during a period. How could it be, if milk production never goes down in any period? It would require actual time-travel to reduce consumption in a period in order to increase it in an earlier period.

The question is thus whether we’re identifying ‘America’ synchronically or diachronically. If we’re thinking about what’s consumed in any period, it’s true that the borrowing operation doesn’t bring that down. This, I think, is Krugman’s point.

But if we take the total lifetime consumption of all the people alive during a given period, that can be brought down by a borrowing operation. This, I think, is Rowe’s point. His model shows a borrowing operation that has the result that two pairs of generations alive in a period — the Milksnatched and their parents, and then the Milksnatched and their children — consume less than they would have without the borrowing operation. Without it, every generation would consume 100 units while young and zero while old. Thus of any two pairs alive, their total lifetime consumption would be 200. But with the borrowing operation in place, the Milksnatched consume 50 while young and 0 while old. Thus they plus their parents have a total lifetime consumption of 150, as do they plus their children.

Where did the missing 50 units go? Well, in the very first period of the milk-transfer scheme, the older generation got 50 extra units of milk. In their youth, since there was no transfer scheme, they presumably consumed the 100 they produced. Thus they got 150 over their lifetime. 50 units of lifetime milk consumption were, indeed, ‘transferred’ to them, over time, from the Milksnatched.

And yet Krugman’s point still stands if we take ‘America’ synchronically and look only at what is consumed within a given period. That never changes. So is it possible that all the people alive in some period consume less than they would have if some borrowing operation hadn’t happened? No if you mean ‘consume less in that period’: in any given period the total consumption is 100 units. But yes if you mean ‘consume less over their lifetimes’.

Logically speaking, there’s something like a scope ambiguity here. It is the case that, because of the borrowing, everyone alive in some period consumes less than would otherwise have been the case. It isn’t the case that, in some period, everyone alive consumes less than would otherwise have been the case.

Scope ambiguities are notoriously tricky and fooled almost all the great philosophers at least once. It’s no wonder that Rowe and Krugman can’t see eye to eye on this.