Suppose you claim that it is impossible for a debt to create a burden on future generations unless: it causes a reduction in investment that reduces future output; the higher future taxes cause disincentive effects that reduce future output; it is owed to foreigners so we have to pay part of our future output to foreigners and have less future output for ourselves.
Suppose I then come up with one counter-example, with no investment, no disincentives, and no foreigners. Where the debt can't reduce future output, because I'm holding future output constant. But where the debt does make some future generation worse off.
Doesn't that prove that your claim is wrong?
You don't start complaining that my counter-example is "unrealistic", because I'm assuming output is constant, or making some other assumption you don't think is realistic. It's a counter-example.
Here's my (old) counterexample:
Assume: closed economy; no investment or real capital of any kind;
lump-sum non-distorting taxes with zero collection costs; positive real
interest rate and zero real growth; exogenous full-employment level of
output; apples are the only output good; apples cannot be stored;
identical agents; overlapping generations; no funny stuff.
Suppose the government makes a transfer of 100 apples to the current
cohort, financed by borrowing. Does that create a burden on future
generations?
The government borrows 100 apples from each of cohort A, then gives
each person in cohort A a transfer payment of 100 apples. It is exactly
as if the government had simply given each person in cohort A an IOU for
100 apples. That IOU is a bond.
So far there is no change in cohort A's consumption of apples.
Cohort A then sells the bonds to the younger members of cohort B. So
each person in cohort A gets an extra 110 apples (assume 10% interest
per generation), which he eats. Cohort A then dies.
Cohort A is better off. Each member of cohort A eats an extra 110
apples. In present value terms, those extra 110 apples are worth 100
apples at the time the transfer payment is made.
Cohort B eats 110 fewer apples when young, but 121 extra apples when
old, and they sell their bonds to cohort C. Although cohort B eats 11
more apples in their lifetimes, the present value of their total
consumption of apples is the same. The rate of interest must be high
enough to persuade them to eat fewer apples when young and more apples
when old, otherwise they wouldn't have bought the bonds from cohort A.
So cohort B is not worse off.
But (given my assumption) the debt is rising faster than GDP. The
government knows this is unsustainable. It cannot rollover the debt
forever, because eventually the next cohort will be unable to buy the
bonds from the older cohort. So the government decides to pay off the
debt by imposing a tax of 121 apples on each young person in cohort C,
which it uses to buy back the bonds from cohort C.
Each member of cohort C eats 121 fewer apples.
Cohort A eats more apples, and cohort C eats fewer apples. It is
exactly as if apples travelled back in time, out of the mouths of cohort
C into the mouths of cohort A. (With interest subtracted as they travel
back in time through the time machine.)
P.S. For those of you who missed last year's argument, here is Bob Murphy's excellent (and very funny) review. HT Daniel Kuehn.
Worthwhile Canadian Initiative 
JKH: Assume the intertemporal government budget constraint holds (that means Ponzi is not possible).
Then Outstanding debt = PV of primary surpluses
Yeah – it all depends on whether or not taxes need to be paid. I thought we settled all of this. So Baker’s idea is no more zombie than Nick’s – it depends on the assumptions.
So you guys should argue about whether taxes eventually need to be paid. That’s the interesting part!
wh10: “So you guys should argue about whether taxes eventually need to be paid. That’s the interesting part!”
Agreed. It’s also the very hard part. Because we don’t know for sure if r will be less than or greater than g in the future. And I can’t get my head around it. The best I could do is this post.
I don’t agree with JKH that the crux of Nick’s argument is the future tax to pay off the bonds, and that you get a sound argument if that future tax exists. The future tax itself just transfers money from people in that future generation to other people in the same generation.
What Nick’s argument depends on are the claims that (i) bonds are transmitted from older generations to younger generations by the members of younger generations transferring things of value to the older generations in exchange for the bonds, and (ii) the value that is transferred to the older generations from the younger generations remains entirely with the older generations to which it is transferred. As a result, Nick is positing a permanent net flow of value from young to old. Nobody loses so long as r < g, and each generation receives more in transfer from its posterity than it transferred to its ancestors, and the process continues indefinitely. But if there is a last generation, then that last generation gets stuck with the loss from its own transfer of value to buy the last issue of bonds.
But if you sufficiently relax either (i) or (ii) above, you don’t get the problem.
I don’t really see what Nick’s argument has to do with debt and bonds. The bonds are a red herring. Suppose instead we just have a permanent tax on all working people below a certain age which is used to support the lives of all retirees above a certain age. The tax is a continuing drain of value from young to old, and the young who lose value recover it when they are are themselves old. But if there is a last generation, they don’t recover anything and are stuck with the loss. The bonds just add an extra inessential wrinkle to this scheme: we imagine instead a process in which the old first borrow value from each other in exchange for bonds promising future return of the value plus interest, and then they tax the younger generation the full sum of that borrowed value plus extra and give them the bonds in return. Same result. It’s not the debt that is the burden. It’s the tax. Similarly in Nick’s cases it’s not the bond issuance that is the burden; it is the ongoing decision by the young to buy the bonds from the old that causes the problem.
And so if the sum total of a society’s public debt were contracted solely to boost the consumption of the older members of society, and if the real value to boost this consumption were always taken from the younger members of society, then the Rowe mechanism would be operative. But neither if things is uniformly true in the real world. Public borrowing is used to finance a variety of public goods and services, many of which directly or indirectly benefit the younger members of society. And in many cases the older members of society borrow from each other to do this, and the interest is paid in “real time” so to speak via an intra-generational transfer among the older members of society. And bonds that are transmitted to the young are often gifted to them, not sold.
The real problem with public borrowing, when it is a problem, is that it represents an ongoing transfer from the less affluent to the more affluent. The affluent lend the less affluent something off value and are paid back with interest, and as a result the rich get richer.
“I don’t agree with JKH that the crux of Nick’s argument is the future tax to pay off the bonds, and that you get a sound argument if that future tax exists. The future tax itself just transfers money from people in that future generation to other people in the same generation.”
You’re assuming that the tax is used for govt spending. If it’s not, non-govt NFA are reduced across the board.
Hang on, Nick.
I think I was right all along, notwithstanding the primary balance detour, etc.
Your argument depends on the fact that some future generation doesn’t have bonds to sell to the next generation.
The reason they don’t have bonds is that bonds have been repaid with taxes.
If existing bonds have been repaid, they have been destroyed by taxes.
If existing bonds have been repaid in the current accounting period that means there’s been a primary surplus in the accounting period. Taxes have been sufficient – not only to pay interest on current bonds (preventing an addition to the deficit and debt) but to pay down existing debt and bonds.
In any event, bonds have been destroyed by taxes.
And it is the destruction of bonds that prevents them from being sold to the next generation.
And therefore the current generation incurs a burden relative to prior generations who could sell their bonds to the next generation.
Forget the PV stuff on the budget constraint. Think future accrual accounting – which is what I described above.
Wh10 has the right idea with “NFA” reduction. That means taxes destroy debt.
And:
“So you guys should argue about whether taxes eventually need to be paid. That’s the interesting part! … agreed.”
That’s what I said basically.
wh10, sure, but I’m trying to meet Nick’s argument on its own ground. Isn’t his counterexample about cases in which the public pays off its bonds in the final generation by taxing itself?
Dan, in step 1, the govt taxes the nongovt sector, which lowers NFA in the nongovt sector by that much. Step 2, the govt uses their account marked up by the amount of taxes to repay the bonds – this is just a swap of that tax money for bonds, with no counteracting increase in NFA. NFA has been net lowered by the amount of the tax.
But I guess my comment that you must have been assuming the govt spends the tax money didn’t make much sense either. That’s not necessarily a redistribution, but it is a net increase in non govt NFA.
Wh10, I don’t think I follow you. That’s what I said: If the government pays off its bonds by taxing the repayment amount and then spending it on repayment, then the result is only an intra-generational transfer, not a net gain or loss among that generation. On Nick’s picture, the reason the imagined final generation loses out is because they have paid the departed older generation for the bonds before the final repayment occurs.
But I’m trying to stick within Nick’s framework which depends on thinking in terms of real value – things like apples – and not monetary operations. My argument is that even if we do that, his bad-case scenario packs in a few important assumptions that need not, and in many real world cases do not, correspond to reality.
If we bring in the fact that in the real world what is being taxed, borrowed and repayed is not apples, but money, and that money is being created and destroyed in the process of carrying out all these operations, then we bring in a bunch of additional factors about level changes, government employment of resources without corresponding taxes and borrowing, etc. that Nick seems to want to leave out of the picture.
then we bring in a bunch of additional factors about level changes, government employment of resources without corresponding taxes and borrowing, etc.
should be
then we bring in a bunch of additional factors about price level changes, government employment of resources without corresponding taxes and borrowing, etc.
“Wh10, I don’t think I follow you. That’s what I said: If the government pays off its bonds by taxing the repayment amount and then spending it on repayment, then the result is only an intra-generational transfer, not a net gain or loss among that generation.”
No, it is a net loss – NFA is net lowered. My example is pretty clear. If the govt needs to pay down $100 in bonds, and it taxes $100, and then swaps $100 cash for $100 bonds, NFA is lower by $100. It’s not just swapping the $100 around from the within the generation.
Now I agree I am talking in nominal terms there, not real, but the portion of your writing that I quoted seems to be discussing matters in nominal terms as well.
You say apples can not be stored.
So you can eat only apples that are growing on the trees NOW.
Who produced the extra 110 apples that cohort A ate?
What happened to the 121 apples that cohort C didn’t eat ?
JKH said: “Actual debt is destroyed if the tax covers more than the interest, which was my assumption.”
This is a problem with gov’t debt. There are lots of times when the gov’t debt is not set up to pay back both interest and principal so there is no rollover risk (the gov’t debt/bond is paid off). I believe almost all private debt is set up so that interest and principal payments are made.
OK, I see what you are saying wh10. It does make a difference between whether we are talking real or nominal here.
That’s absolutely correct in a zero growth society. If you allowed for growth, for example, improved apple breeding, tree planting and more effective picking and packing, the system would be sustainable with each cohort eating more apples than the previous.
It’s like physics. Near absolute zero, liquids can flow without friction, but don’t rely on this in your own home or industrial plant.
What is the burden?
Let us assume Nick’s basic setup: An island economy with no economic growth, no population growth, and no money, where everyone eats apples. Once a generation, the gov’t sells bonds to the younger generation for apples and uses the proceeds to retire the bonds of the older generation. The interest on the bonds is r per generation.
One year a crisis develops. The older generation bought the bonds for X apples, but the younger generation cannot afford to pay X + rX apples to them. As the date for the new bond auction approaches, it dawns on members of the younger generation that they cannot afford to buy enough bonds to pay off the older generation. They talk among each other, and finally the prime minister calls a caucus of the younger generation to discuss the problem.
After the caucus the prime minister announces to the older generation, “We are sorry, but we cannot afford to pay you what we owe. The bond auction would fail. We have to default on your bonds. What we can afford is to pay you Y apples instead of X + rX. That is still more than the X apples you paid to your parents’ generation. That’s the best we can do. Take it or leave it.”
The older generation caucuses with the former prime minister. After some grumbling they decide to accept what they can get.
The gov’t sells 0% interest bonds to the younger generation for Y apples and pays them to the older generation. The younger generation then throws a week long celebration to commemorate the agreement and entertains the older generation.
One generation later the gov’t sells 0% interest bonds to pay Y apples to the older generation. It also declares Sustainability Week as a national festival.
Soon after the original sale of the 0% interest bonds, a reporter interviews the prime minister. Here is a portion of that interview:
Reporter: Several members of the older generation are complaining about the deal. They bought their bonds in good faith and feel that receiving only Y apples places an unfair burden upon them.
Prime Minister: That is their greed speaking. Any burden is in their minds, and is self inflicted.
Reporter: Their greed?
Prime Minister: Yes. When they bought their bonds they were both greedy and irrational. One of the human cognitive skills is the ability to imagine yourself in another’s place and to understand their thoughts, feelings, and behavior from their standpoint. That is called empathy. If they had put themselves in our place, they would have realized that we could not afford to pay X + r*X apples. They would have foreseen the eventual default if they asked for so much. They failed to do so because their greed was greater than their empathy. Their emotions overcame their rationality.
Reporter: But they were following tradition.
Prime Minster: Yes. The tradition contained a fatal flaw that was not obvious to our ancestors, who somehow believed that it could go on forever. But it was unsustainable. With our 0% bonds we have implemented a sustainable tradition. It is curious, in a way, that our ancestors, who at some point consumed the same number of apples in old age as in their youth, set in motion events that culminated in our current system, in which we consume more apples when old than when young, something that we much prefer. They were greedy and irrational, but changed our world for the better.
Oh my … Please not this again. Guys, it is CRYSTAL CLEAR that Nick is as right as it is ever possible to be right. Please don’t do this. I already had to battle my cognitive dissonance once, when Nick showed me by this example how wrong my thinking is – and now I am starting to lose my faith that there are some fairly smart people doing macro. I beg you – stop putting up these silly counter arguments, or at least use Google search on this page. The only thing you all achieved so far (DeLong and Krugman included) is that I am starting to feel that there is no hope to push forward those slightly more complicated measures like nominal income targeting.
Nick: Sorry for my totally unproductive rant, but this is all so incredibly frustrating. I feel for you …
JV: I feel a bit the same way. But then I remember how long it took me to get my own head around this stuff.
J.V. Dubois, you can still get “burdens” with “income targeting.” What happens if inflation outpaces growth? The old consume more than the young.
(BTW, I think your counterexample is valid, but calling it unrealistic is a valid argument.)
What’s missing? We have a debt crisis. What do we do?
1. Try to inflate away the “burden” and/or give the bondholders a haircut.
2. Resign ourselves to cyclical burdens. (Perhaps trying to “correct” them is either too hard or will do more harm than good.)
Can we all agree that :
1) No AD policy is distribution-neutral. (Except, perhaps, helicopter drops).
2) All distributively non-neutral policies are burdens on some cohorts, relative to some baseline.
3) To the extent that cohorts defined by age/birth can be assumed to share tax regimes, variations in tax rates are burdens on some ‘generations’ and transfers on others. This is true for any variation in tax rates.
But why to talk about overlapping generations when one means equi-fiscal cohort. Heterogeneity of lifetimes means that ‘all people born today’ is not necessarily a better Borgesian category for fiscal outcomes than ‘all people alive today’. It could be. But that’s not obvious.
Sorry, I should have said – ‘why to talk about overlapping generations’ when one means ‘overlapping equi-income fiscal cohorts’.
So let’s flesh out the apples analogy a bit. Now, since apples are the only product in the economy, let’s assume that taxes are collected in apples.
Scenario 1, no government borrowing.
Generation 1 – Let’s say the economy produces 1000 apples, the government collects 200 apples through taxation, and distributes 200 apples to citizens.
Generation 2 – The economy again produces 1000 apples. The government again collects 200 apples through taxation, and distributes 200 apples to citizens.
Scenario 2, government borrowing.
Generation 1 – Let’s say the economy produces 1000 apples, the government collects 200 apples through taxation, borrows another 100 apples at a 10% coupon FROM PRODUCERS WITHIN THE COUNTRY, and distributes 300 apples to citizens.
Generation 2 – The government wants to pay off its debt. The economy again produces 1000 apples. The government raises taxes to 310 apples, distributes 200 apples to the broad population, and repays its debt of 110 apples to the producers it borrowed the original apples from.
Where does the impoverishment occur? The population still produces and eats 1000 apples in either scenario. Who within the population changes, but that’s all; it’s redistribution.
Now of course, if you borrow the apples from a foreign country, it is a different story.
Andy: see today’s post.
Andy: I take the same view as you, i.e. consider the distribution of consumption in a horizontal sense, and there of course you only have a re-distribution of the production at any point of time among everybody then living.
I believe that this is actually the question we are facing, so this view makes the most sense to me.
Nick is taking a longitudinal view, integrating up the lifetime consumption of any cohort of people of the same age.
His point is then trivial: If there is a change in the horizontal re-distribution mechanism during the lifetime of any one cohort, this can end with them having overall a smaller lifetime consumption than other cohorts. I.e. if they forgo consumption in their youth, to support the old people then living (horizontal redistribution), and if the horizontal re-distribution scheme is then ended when they themselves expect to receive benefits, but before these actually arrive, of course they will be able to consume less over their lifetime than other cohorts, who either did not pay in or did receive their benefits.
Sure, if Congress cancels Social Security today, everybody who has paid in and has not yet received his full benefits gets shafted.
However, this is always a decision that the people living at that time make, about a distribution of consumption and resources at that time.
It is not a forgone conclusion following from the existence of the debt.
Overall, I don’t find this view very useful, since it does not really tell us anything about how to solve the horizontal distribution problem, which in my view is the real problem.
Shining Raven said: “Sure, if Congress cancels Social Security today, everybody who has paid in and has not yet received his full benefits gets shafted.”
While the people who received benefits at the beginning without paying anything in received the benefits. Right?
Is Medicare the same way?