Consider two possible worlds:
World A: Us old people bequeath our government bonds to the next generation (as a freebie).
World B: Us old people sell our government bonds to the next generation (they pay us for the bonds).
See the difference?
In world A the next generation inherits the tax liabilities inherent in the bonds, and really does inherit the bonds too. It gets given a liability, and gets given the corresponding asset too.
In world B the next generation inherits the tax liabilities inherent in the bonds, but does not inherit the bonds. It gets given a liability, and does not get given the corresponding asset. It pays for the corresponding asset.
World A is the world of Barro-Ricardian Equivalence, where government debt has no intergenerational distributional implications.
World B is the world of Buchanan and Overlapping Generations models, where government debt does have intergenerational distributional implications.
World A is not Paul Krugman's world. Paul is not a fan of Barro-Ricardian Equivalence. So why does Paul suddenly switch to talking like someone who believes in Barro-Ricardian Equivalence when he says:
"Antonio Fatas, commenting on recent work on deleveraging or the lack thereof, emphasizes one of my favorite points: one of my favorite points: no, debt does not mean that we’re stealing from future generations.
….
Debt has distributional implications, and it may have macroeconomic effects because of those distributional issues. But again, all this is within the current generation; it’s not about the present versus the future."
and:
"And the problems with public debt are also mainly about possible instability rather than “borrowing from our children”. The rhetoric of fiscal debates has been, for the most part, nonsense."
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.
Dammit! I thought I had this whole point about debt burden on future generations sorted out back in the great debt blog war of 2011/12.
Or, ignore me. Listen to Simon Wren-Lewis get it right.
Ours the task eternal.
(Antonio Fatas, by the way, is correct in saying that if the government issues debt to buy real assets, and if future generations inherit (as a freebie) those real assets as well as the tax liabilities inherent in the debt, it can all cancel out.)
Worthwhile Canadian Initiative 
“It gets given a liability, and does not get given the corresponding asset.”
But it also inherits the money used to purchase the bonds in the first place.
Britonomist: “But it also inherits the money used to purchase the bonds in the first place.”
As a freebie? Or does it have to work to earn (pay for) that money? Big difference.
Nick, does it matter in aggregate? I don’t think parents make their kids work for their inheritance, or the owner of a company make their successor do more work than he otherwise would. Any work is used by the capital owners/’rentiers’ of the new generation by purchasing labour with the inherited money, but in aggregate it’s already passed on to the next generation.
Britonomist: yes it does matter in aggregate. Suppose the government sells bonds to finance transfer payments to the current generation. It gives the current generation bonds. And suppose the grandkids (yet unborn) will pay higher taxes to pay off those bonds. Does this cause the current generation to increase their bequests to their kids by an equal amount?
World A: the current generation gives the bonds to its kids, who give the bonds to the grandkids, who hand them back to the government in lieu of taxes. Nobody’s consumption is affected.
World B: the current generation sells the bonds to its kids, so the kids consume less when young and the current generation consume more when old. Ditto when the kids sell the bonds to the grandkids.
OH CHRIST! I don’t want to have to explain this whole damn thing all over again!! Go read my old posts linked to above.
But if you are asking: does it matter if the kids inherit $100 in bonds or $100 in money? No of course it doesn’t matter.
I’m not saying I disagree with you, I’m just trying to make sense of your model. I actually find it easier to understand a model when it’s formulated mathematically than when it’s verbalized.
There is another way to look at this public debt issue:
We begin by assuming that government bonds are held by the private sector.
The bonds held by the private sector have ALL been bought with money earned someone working for government or selling a product to government.
Government, when it borrowed the money from the private sector had a choice: Government could have borrowed directly from the Federal Reserve (United States). It did not do that; it borrowed from the private sector.
Now turn to the question of this post: inter-generational effects.
When children inherent bonds, they inherent the monetary value of the labor and products earned by their parents. It is worthless (in the sense that it will not cause productive or consumptive activity) unless it is converted a liquid form such as money. How might that be done?
Government has two ways to retire bonds:
1. Tax and repay the bonds.
2. Do not renew the bonds.
For option 2, government would replace private borrowing with borrowing from the central bank. This sounds a lot like QE.
The two methods correspond with your World B and World A. My option 1. would equate with your World B. Taxes equate to a forced sale of the bonds to the working generation.
My Option 2 equates to your World A although the generational timing seems weak. The government is giving back the money earned in past times. The private economy will have additional money to spend in amount equal to the privately held debt retired.
All assets that are not consumed must be transferred between generations and they can be inherited or sold, but the value of those assets is not independent of whether they are inherited or sold. The more assets that are sold, the lower the price they will command so much of this will still fall on the generation selling. Debt and destruction can transfer between generations, of which war is the leading cause, just as our creations and discoveries transfer forward, but we shouldn’t get carried away just because we can put a number on it when there are so many others more important that we can’t.
Good Grief. People…
Krugman isn’t claiming that it’s impossible for the government to transfer wealth from one generation to another.
His point is that the conventional “Eek! Debt!” view is nonsense. The nonsense is the view that if US federal debt is $18 trillion, that means our children are going to have to consume $18 trillion less than they would if our federal debt were $0. I used to worry about that when I was in college. “How will I ever pay off all this government debt my parents racked up?” Now I realize how silly that worry was, because even if the government taxed all the children and paid back the bond holders, whomever held the $18T in bonds at that point can increase their consumption by $18 trillion. Government debt might result in redistribution of future consumption, and with overlapping generations, that redistribution might apply across generations, but government debt does not reduce future consumption in aggregate. Government debt does not make future real output disappear. It does not make our children collectively poorer. It does not make us poorer in the future. That’s all Krugman’s trying to say.
Everyone reading and commenting on this blog is smart enough to understand all of that. Why are we not smart enough to realize that Krugman is pointing out something obvious? Why do we take the most extreme “straw-man” interpretation of Krugman and then burn it?
-Ken
Kenneth Duda
Menlo Park, CA
The big weakness in the overlapping generations model is thus. The funding of pensions certainly involves oldies robbing youngsters (i.e. “overlapping”). That’s obvious with pay as you go pensions: today’s taxpayers fund today’s oldies. As to pensions funded by government bonds, that’s little different: today’s taxpayers buy bonds and in their retirement, sell them to youngsters.
But suppose the optimum amount of government debt is more than is needed to fund pensions. E.g. suppose all pensions were pay as you go and that over and above that, everyone held a stock of government bonds. In that case, oldies would simply leave their bonds to their children in their wills.
Conclusion. The “oldies robbing youngsters” phenomenon, i.e. the overlapping generations phenomenon occurs as part and parcel of any pension scheme. Plus, assuming everyone has the pension arrangements they want, there is no scope for any more of that overlapping generations stuff.
Do you think this is only about public debt? What’s your analysis of debt between individuals in an OLG world? I have my own thoughts on this, but I’m interested in yours.
Nick: “Paul [Krugman] is not a fan of Barro-Ricardian Equivalence.”
What makes you say that? I don’t think Krugman is a Barro fan in a general way, but what makes you think he’s a Pigou follower, on this particular issue?
Also, what Kenneth Duda said.
Agree with Duda.
But without the sanctimony – because Krugman writes sloppily:
“The additional debt represents a claim by one set of Americans on another set of Americans — and we’re talking about people here now, not future generations… but again, all this is within the current generation; it’s not about the present versus the future.”
When he says “current generation”, he’s referring to the existing total population of multiple co-existing generations currently at different stages of life. And when he says “one set of Americans”, he’s talking about one of those co-existing generations. And when he says “future generations”, he’s talking about co-existing generations in aggregate at a future point in time. Very sloppy.
Your explanation is clear Nick. I doubt Krugman would disagree with it.
(I’m not familiar with the academic literature on “overlapping generations” – other than what I’ve picked up in previous discussions here – but I suspect population theory as part of actuarial mathematics is a more elegant treatment of this subject in terms of the demographic piece.)
Britonomist: read my old posts linked under “Time travel is possible” and “back”. Or Simon Wren Lewis link.
Ken: ” The nonsense is the view that if US federal debt is $18 trillion, that means our children are going to have to consume $18 trillion less than they would if our federal debt were $0.”
That view is not nonsense.
I too used to believe it was nonsense. I was taught the official “we owe it to ourselves” view as an undergraduate. Then in 1982, having read Barro, and Buchanan, and spending a lot of time with examples figuring it out, I realised it was not nonsense. Bob Murphy is another person who thought that view was nonsense, then changed his view 180 in 2012. Or read Simon Wren-Lewis, who is as new-orthodox as they come, and is very far from a wild-eyed idiot.
That view is not nonsense, though there are cases where it is false, like in Samuelson 1958, where r < g, so it is possible for the government to run a sustainable Ponzi scheme so future generations never need to pay higher taxes to service the debt, which can be rolled over with interest forever.
Nick E: good question. That one came up in the 2011/12 debt war.
If my kids are liable for my private debts (which used to be the case in the olden days, I think), then private debt is the same as public debt. We all borrow and consume, die with negative net wealth, sticking our kids with the liability. And they in turn might pass some of it on to the grandkids. The generation that gets told “pay up now or else!” is the one that gets screwed.
But that can’t happen nowadays. My kids aren’t liable for my debts, unless I bequeath them assets of greater value than those debts.
Nick, you haven’t addressed Ken’s point.
Whether or not r < g, future generations may have to pay higher taxes to service the debt, but those receiving the payments will be alive and receiving the debt service at the same time as those future generations.
Do you believe the amount of debt service paid at time t does not equal the amount of debt service received at time t?
Everyone: if you use the ” < ” symbol, be sure to leave a space either side of it. Otherwise Typepad has a funny turn, and your comment won’t come out right. (I edited foosion’s comment to fix it.)
foosion: of course the debt service payments paid at time t equal the debt service payments received at time t. I can do accounting too.
The kids who own the bonds pay taxes to themselves to service the bonds. But if the kids also paid their parents to buy the bonds, they paid twice for those debt service payments. If they inherit the bonds from their parents as a freebie, they only pay once. BIG DIFFERENCE.
This whole thing is very embarrassing for me, as an economist. We laugh at the ignorant peasants who think that debt is a burden on future generations, who can’t do the simple accounting. But the ignorant peasants are basically right (though there are exceptions). It is (most) economists who can’t do the inter-generational accounting.
Krugman is right, I think.
OLG is about transfer of real assets from old to young, but this could be because the young borrow to buy the assets (like a house) or because the young save to buy the assets (like a retirement account or buying slices of land each month). In one model, the young are in debt to the old. In the second model. no one is in debt at all. Both models are OLG.
OLG transfers, or Barro-style bequeaths, have absolutely nothing to do with borrowing or lending, which is what Krugman is talking about.
Borrowing and lending describe the liability side of the real asset — how is the asset financed. OLG/Barro is about who owns the real asset.
You can have a change in financing without a change in ownership, or vice versa.
Krugman is describing aggregate increases/decreases in debt — how assets are financed. This has no implications in the aggregate economy because we owe the money to ourselves. It does have implications for things like financial stability and demand.
Kevin: Paul thinks that increasing the deficit by cutting taxes increases AD (unless there’s monetary offset). Which would not be true under Barro-Ricardian Equivalence.
Nick,
But Ricardian equivalence requires the interest rate to be less than the growth rate. If the market clearing rate is below zero, for example, but can’t get there, then Ricardian Equivalence fails to hold. Then an increase in government debt does increase the interest rate, and we can increase it up until the market clearing rate hits zero — e.g. eat up all the free lunches by increasing debt until there are no more free lunches and we are back to the Ricardian Equivalence situation.
rjs: “But Ricardian equivalence requires the interest rate to be less than the growth rate.”
No. Ricardian Equivalence assumes the interest rate is greater than the growth rate.
(Maybe you meant to say “greater than”?)
Nick, it was a rhetorical question.
You still haven’t directly addressed Ken’s point.
The kids who own the bonds pay taxes to themselves to service the bonds. But if the kids also paid their parents to buy the bonds, they paid twice for those debt service payments. If they inherit the bonds from their parents as a freebie, they only pay once. BIG DIFFERENCE.
There is no fundamental difference between buying a bond from a 20 year old and buying a bond from a 70 year old.
No one is denying that wealth can be transferred. The question is whether debt is the generational evil it’s portrayed as being.
The two sides of this seem to be talking past each other.
Nick: “Paul thinks that increasing the deficit by cutting taxes increases AD (unless there’s monetary offset).”
To the extent that he accepts the case for tax cuts as stimulus (and I agree that he does up to a point), it’s partly because he thinks liquidity constraints are important. That borks Ricardian Equivalence, but not in the way you have in mind. Here’s an example, from his blog (August 5, 2010):
Krugman is quite happy to use models which exhibit Ricardian Equivalence. Of course that doesn’t mean he thinks it’s true, but clearly it’s not a simplification that offends him in the way that RBC models do. Relatedly, he’s willing to accept that the Pigou Effect may exist but thinks it’s too weak to be worth bothering with. So I don’t think there’s much inconsistency in his thinking about debt, contrary to what your comments imply.
foosion: This is what Ken says:
“[1]…but government debt does not reduce future consumption in aggregate. Government debt does not make future real output disappear. [2] It does not make our children collectively poorer.”
1 is true (except in an open economy, or with distorting taxes, or where it crowds out real investment). Aggregate consumption in any year is the same.
2 Is false. The lifetime consumption of some future generation(s) will be smaller (unless r < g so Ponzi schemes are sustainable and the debt can be rolled over with interest forever). Moreover, the lifetime Utility of some future generation(s) will be smaller still (unless r < g).
Recalling now the discussion several years ago here, it seemed to me that it all hinged on the interpretation of the effect of a primary surplus today.
There is no net effect on yesterday’s total population of running a deficit yesterday – in the sense that those who borrowed consumed and those who lent abstained.
There is no net effect on today’s total population of running a primary surplus today – in the sense that those who cash in their bonds consume and those who pay tax abstain.
There is a net effect between the yesterday’s borrowers and today’s taxed. Those who borrowed yesterday consume and those who are taxed today abstain. I thought that was Nick’s main point, at least in earlier discussions.
But there is no net effect between yesterday’s total population and today’s total population. Aggregate consumption is the same in each case. That’s consistent with Krugman’s point I think.
Brian [I mean Kevin, sorry]: Barro-Ricardian Equivalence assumes that the representative agent will save the whole of a bond-financed tax cut, because he understands the future tax liabilities inherent in the public debt, and increases his bequests to his kids by the full amount (in Future Value terms) of the bond-financed tax cut.
And if half the agents are liquidity constrained, that will not happen.
JKH: yep, there are two ways to do the accounting. We can do the accounts for each year; and we can do the accounts for each cohort. “The future” means something quite different in each case, and Paul Krugman (like many of us economists, and like me myself once) conflates the two.
Plus, in an r > g world, and where the debt/GDP ratio stays the same over time (we tax to pay the interest on the debt, but not to reduce the debt/GDP ratio) each person’s lifetime utility will be lower even if their total lifetime consumption is the same. (The Present Value of their lifetime consumption is less, because they consume one apple less when young and one apple more when old, but the discounted value of the extra one apple when old is less than the value of the one apple less when young).
Nick, I agree with what you say to Brian. But (in case I am Brian), I’ll add that I don’t think it invalidates anything I said.
Kevin: sorry! I always get names and faces muddled. There’s a name for what people like me have got, but we can never remember what it is.
But I never get muddled about anything else!
Right, I meant Ricardian Equivalence requires r > g. Then you get the result that an increase in Government debt leaves r unchanged. But it’s not like r and g are cosomological constants — attributes of the world and not of the current size of savings stocks — The choice is not “do we live in a Ponzi world” or “Do we live in an honest world”, the question is by how much can we increase the debt so that all the free lunches are eaten.
Right now, the U.S. can borrow for 10 years at 1.96%. In that case, it seems really, really silly to imagine that there is any possibility of Ricardian Equivalence holding.
Nick,
I think your answer to me is that it is not the same for private debt, and I’d agree with you that it doesn’t work the same way. Nevertheless, I think private debt is not without intergenerational consequences as a result of its potential impact on asset values. Where credit availability is a limiting factor, I can imagine a scenario where a relaxation in the credit constraint led to an increase in asset values increasing the spending power of older generations. A later tightening of the credit constraint might then reverse the effect to the cost of later generations.
rjs: well, it’s not quite that simple (though it still might be right), because we need to know whether r will be < g when the debt comes due. (If we issued NGDP perpetuities, things would be very different.)
But Paul Krugman makes no mention of r < g. If he came right out and said “r < g. So we can and should run a sustainable Ponzi scheme” the howls of outrage would be even greater, and the Piketty fans would join in the fun, but he would be getting the economics right.
Nick E: “I think your answer to me is that it is not the same for private debt, and I’d agree with you that it doesn’t work the same way.”
Yes. We agree. If we could make net negative bequests to our kids (they were liable for our debts when we die), then private and public debt would be (roughly) the same. Only the government can enforce negative bequests on future generations.
I tend to agree with the rest of your comment. There may be (and generally will be) indirect effects.
I almost feel like copying and pasting my ok comments from your previous debt wars post. Bond holders could for the most part be bequeathing their bonds and the world could still be non Ricardian if all the non bond holding dynasties are credit constrained.
Thinking in terms of models where everyone is identical and therefore ‘worlds’ themselves as Ricardian or non Ricardian is problematic in my view.
I meant to type ‘old’ rather than ‘ok’ in my comment above but I think in this case the typo is in fact ok!
“[1]…but government debt does not reduce future consumption in aggregate. Government debt does not make future real output disappear. [2] It does not make our children collectively poorer.”
1 is true (except in an open economy, or with distorting taxes, or where it crowds out real investment). Aggregate consumption in any year is the same.
2 Is false. The lifetime consumption of some future generation(s) will be smaller (unless r < g so Ponzi schemes are sustainable and the debt can be rolled over with interest forever). Moreover, the lifetime Utility of some future generation(s) will be smaller still (unless r < g).
Now I’m confused. If aggregate consumption in any year is the same, how can lifetime consumption be smaller? For lifetime consumption to be smaller, consumption in some year must be smaller.
What am I missing?
I think we have a conflation of micro-economic and macro-economic arguments here. First the micro-economic argument:
A single child-parent combination may include ownership of a government bond earned by the parent. Ownership of the bond will pass to the child at death with no macro-economic effect. Yes, the child may choose to not renew the loan to government which would create a macro-economic event for government but the parent had the same option.
Notice that this micro-economic example presupposes an uneven distribution of wealth. Not all inheritances include government bonds. The unbalanced distribution of wealth has been aggravated by the existence of government bonds.
Now look at the macro-economic situation. Within any one time period, the population of young and old is roughly the same (allowing that trends occur). It follows that micro-economic flows (such as the previous example) will be invisible in the data from any one time period.
Continuing the macro-economic example, what will be visible over multiple time periods is that debt has increased (or decreased). Debt is always held by wealthy people and owed by less wealthy people. The observation that debt is increasing over several time periods indicates that the gap between wealthy and poor is increasing.
Following this analysis, I think that the observation “Debt does have intergenerational distributional implications” is correct but not in the way that Nick relates. Debt is not taking apples out of the mouths of our children. Debt is changing who has apples to distribute.
Nick, thanks for the response. You and Simon Wren-Lewis are awesome, and right. You right:
Nick,
I’m not sure what you mean by “when the debt comes due”. When you sell a 10 year note for 1.9%, you know exactly what the terms are. Point being you should keep selling those up until r=g, at which point there are no more free lunches. That is very different from a ponzi scheme.
In fact we can say that r < g is prima facia evidence that we are not deficit spending enough, and the market is begging us to spend more.
Now, I have an idea for a fiscal taylor rule, that everyone can agree on:
Let r be the current yield on 10 year notes, and g the expected growth rate over the next 10 years.
When r < g sell some 10 year notes (run primary deficits)
When r > g buy back some 10 year notes (run primary surpluses)
Completely ignore things like Debt/GDP.
No one could attack this policy using Ricardian Equivalence. And it is fiscal policy NGDP targeting. Should be popular with the right and left.
Ken: thanks!
“So Krugman is trying to kill off a really silly idea, and you are pointing out that there’s a much smaller effect that sounds a little bit like $18T of debt is cheating our collective children.”
Except it’s not smaller. In present value terms, it’s exactly the same size. In lifetime utility terms, it’s actually slightly bigger (if r > g, and we have a standard lifetime utility function where people like to smooth their consumption, because debt causes consumption to become unsmooth, where we consume more when old than when young).
If Krugman is trying to slay the fallacy that increasing debt will create a negative demand shock in the future due to reasons other than distributional, they that doesn’t seem worth slaying. It definitely doesn’t seem worthy of Krugman’s rhetoric, although if one complained every time that happened one would have no time for anything else.
Kenneth Duda – if P’s cohort gets 18 trillion more real goods then they should have, how much poorer do you think G will be?
rjs: I approximately agree. It’s not quite that simple though. But I want to go skating on the canal, and my brain is full anyway.
foosion: it’s weird, isn’t it? I could only get my head around it myself with a numerical example. Bob Murphy had to do the same, and spent hours on a spreadsheet.
Here’s my example from my old post linked above:
“My argument does not involve time travel. It doesn’t require we can take apples grown 100 years from now, put them in a time-machine, send them back in time, and eat them today. But it is as if we could.
My argument is obvious. At least, it’s obvious to anyone who has thought about overlapping generations models. And it’s equally obvious to the unsophisticated uneducated rube who has never thought about overlapping generations models.
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.)
Yes, the national debt is a burden on future generations.”
primed: that world will be half Ricardian. The debt imposes a burden on the kids of the credit-constrained, but not on the kids of those who make offsetting bequests. A $100 debt is a $50 burden on future generations.
Gone skating.
If you start off with an OLG model where each living cohort gets 50% of available resources , and then in a given time period a transfer is done from the young to the old then:
– the old cohort have done better than all cohorts under the previous 50/50 distribution
– it is impossible to get back to the 50/50 distribution without making at least one future cohort worse off
– by endlessly repeating the initial transfer between generations it is possible to ensure that future generations all have equal and maximum resources allocated to them. It will not be equal between time periods, and this may or not be a good thing depending upon their consumption function. The old who benefited from the initial transfer come out ahead, and in theory the piper never has to be paid.
It is possible that other old generations can pull off the same trick. It can be repeated in theory until all resources are being transferred from the young to the old. Successive older generations can consume more than under the 50/50 system.
Sooner or later the young may grow tired of this – they refuse to comply withe the transfers when young. To get back to the 50/50 distribution one (or more) cohorts need to consume less than 50% over their lifetime.
So we have some generations that consume more than 50% of what is produced during their lifetimes and some later generations than consume less than 50%. Have these resources been transfer back in time ? Obviously not in a physical sense and (in my opinion) not in an accounting sense either. In both senses we know exactly where the lost/gained resources are coming from – other people living at the same time !
You can construct narratives about the allocations in a given time period using taxes, transfers, bonds, interest payment , defaults etc as the tools but that doesn’t change the fact that the cohorts alive in a given time period get to choose the distribution in that time period, and this is what decides which cohorts win and which lose. They can’t change the past, they can only factor that in to decision they make about the present.
The government transfers apples from the young to the old for a number of years, then stops doing so. The first year old get a benefit they didn’t pay for and the last year young have to pay and don’t get a benefit.
This doesn’t seem a general problem with debt, it seems a problem with the design of this transfer arrangement.
I think Nick’s apple example shows pretty well how government debt can be a problem in a OLG model. However, does it not hinge on the fact that the government simply transfers the surplus apples between cohort A but issues bonds with a positive interest? In that case, government contribution to g is 0 but r > 0. Imagine instead that the government had used the surplus apples (produced but unconsumed by cohort A) to plant apple trees. Then, g > 0 which will justify r > 0. The bonds will be backed up by a larger production of apples which will mean a higher living standard for future generations. IMHO, $18T is just a number; what are the real assets (investments) that back up that number will determine whether future generation will be better or worse off.
Regarding r < g, nobody thinks it would be a free lunch for China to swap its hoard of U.S. treasury bonds for the S&P 500. Maybe a good idea, depending on the circumstances, but not a free lunch, because one is riskier than the other. Issuing treasury bonds isn’t a free lunch either.
MF: I agree (I think).
foosion: “This doesn’t seem a general problem with debt, it seems a problem with the design of this transfer arrangement.”
If r > g, then this transfer arrangement (current cohort better off, some future cohort(s) worse off) is inevitable. Otherwise the debt grows faster than GDP, as you rollover principal + interest, and the debt grows faster than GDP, until eventually you hit the point where you must increase taxes and make some cohort worse off, or else default and make the previous cohort worse off.
Odie: if the government borrows to finance productive investment, where the returns on that investment are enough to pay the debt eventually, then sure, it’s no burden on future generations.