Debt does have intergenerational distributional implications

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.)

Comments

[Britonomist]

"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.

[Nick Rowe]

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.

[Britonomist]

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.

[Nick Rowe]

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.

[Nick Rowe]

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.

[Britonomist]

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.

[Roger Sparks]

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.

[Lord]

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.

[Kenneth Duda]

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

[Ralph Musgrave]

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.

[Nick Edmonds]

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.

[Kevin Donoghue]

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.

[JKH]

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.)

[Nick Rowe]

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 Rowe]

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.

[foosion]

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?

[Nick Rowe]

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.)

[Nick Rowe]

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.

[rjs]

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.
* * *

[Nick Rowe]

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.

[rjs]

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.

[Nick Rowe]

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"?)

[foosion]

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.

[Kevin Donoghue]

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):

So if we give money to people likely to be liquidity-constrained, they are likely to spend it. That’s why aid to the unemployed is an effective stimulus; it also suggests that tax cuts for lower-income workers will be relatively effective at raising demand. But the affluent, who typically have lots of assets and good access to borrowing, are much less likely to be in that situation. So tax cuts for the lower 60 or 80 percent of the population are an OK, not great but OK, form of stimulus; tax cuts for the top 2 percent, not at all.

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.

[Nick Rowe]

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).

[JKH]

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.

[Nick Rowe]

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.

[Nick Rowe]

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).

[Kevin Donoghue]

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.

[Nick Rowe]

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!

[rjs]

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 Edmonds]

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.

[Nick Rowe]

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 Rowe]

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.

[primedprimate]

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.

[primedprimate]

I meant to type 'old' rather than 'ok' in my comment above but I think in this case the typo is in fact ok!

[foosion]

"[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?

[Roger Sparks]

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.

[Kenneth Duda]

Nick, thanks for the response. You and Simon Wren-Lewis are awesome, and right. You right:

> 2 Is false. The lifetime consumption of some future
> generation(s) will be smaller (unless r < g ...)

Let's assume r=g so we are neither outgrowing our debt nor is it outgrowing us. The disagreement is not there.

We all agree that the government can redistribute consumption among living people.

We all agree it's possible that in every period, the government redistributes some consumption from child to parent, so that some initial parent P gets more, and then some arbitrarily long chain of children C1, C2, C3, ... get their "fair share", and then some grandchild G gets less (than they would have under neutral policy).

Hah! Parents robbing from descendants! So you are right!

Except this effect is not what the "Eek! Debt!" people imagine, and has nothing to do with the fallacy Krugman is trying to slay. "Eek! Debt!" people imagine $18T of foregone consumption across all living persons at the time the debt is paid off. In your model, even in that year where G gets less consumption (because G's great great ... great grandparents had received extra), some people, namely G's children, get more than they would have had government policy continued to pass the redistribution down the chain of descendants. So total consumption even in that year where G is getting screwed is unaffected by the debt. Krugman and I and foosion and everyone else are also right about the thing we're actually trying to say.

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. You are right about the effect you are pointing out. It's unhelpful to Krugman's debate, because your effect is a different thing. You and Krugman are trying to slay different fallacies. He's trying to slay one believed by millions of economically illiterate people who aren't even trying to figure out the actual truth. You're trying to slay a fallacy that is a point of confusion among a small set of people who are paying attention and trying, but not quite getting it. Which I appreciate. Thank you for this awesome blog.

-Ken

Kenneth Duda
Menlo Park, CA

[rjs]

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.

[rjs]

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.

[Nick Rowe]

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).

[Kyle Johansen]

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?

[Nick Rowe]

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."

[Nick Rowe]

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.

[Market Fiscalist]

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.

[foosion]

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.

[Odie]

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.

[Max]

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.

[Nick Rowe]

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.

[ignormaus]

NR: 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.

Likely a stupid point, but let's consider the following-period; I have something like this in mind
O D
Y O
- Y

where in the first period we have old, young, and not yet born, and in the following period a new young generation is born, the young become the old, and the old from the previous period die - and thus have to transfer all their assets, including any money they received for their bonds in the previous period (or other assets bought with that money) to others. So beyond the fact that they / the government may choose to distribute those assets differently amongst the newly old and young than if they had given away their bonds, I don't see how it represents theft from future generations.

[Nick Rowe]

ignormaus: "- and thus have to transfer all their assets,..."

"transfer" can mean "give away as a freebie", or it can mean "sell, and consume the proceeds". That's what makes the difference.

If it means "sell", then the old get to consume extra apples that had been produced by the young, but the young expect to get compensated with extra apples to consume when they are old and sell the assets to the next generation.

[Roger Sparks]

Bonds are property. Being property, they require maintenance. It is the maintenance of bonds that can become problematic for future generations.

Bond maintenance includes maintaining bond records, plans for bond placement or payoff, plans for payment of interest, and plans for protection of the rights of bond owners. All of these maintenance requirements become an obligation of future generations.

Consider the inter-generational aspects of bond transfers. Bonds as property are no different than other property such as stocks, land, or machines. The transfer of each example is a simple title transfer. In itself, title transfer has no macro-economic consequences. It is the maintenance of bonds that has potential for problematic impact on future generations.

Assume that when a government issues debt, it issues a bond and receives money. The money is immediately spent and dispersed widely in the economy. The money immediately becomes difficult to recover for return to the bond purchaser. The difficulty grows with repeated borrowing and spending event. The need for bond maintenance increases with each bond sale.

Nick says (I am paraphrasing) that debt DOES cause problems for future generations. I certainly agree. The maintenance of a debt becomes a problem that grows as the amount of debt grows.

[JF]

Nick Rowe - I loved this one above from 7:46 "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."

Look now, current period, it is the reverse (a wealth transfer to the first generation) if taxes are foregone on those who get the bonds. If taxes match the outlays needed to faithfully execute the public's laws - then there are no borrowing in the first period, no problem in the second.

Economists just need to state plainly and clearly in all these discussions, in my opinion: here is what they should say, 'the first thing to understand is that govt budgets should be balanced if economies are OK (but not necessarily when they are not OK)'. I am not trying to debate what OK means, of course; that is up to others to say.

I think that is all we "ignorant peasants" are asking. Though admittedly I did ask Prof Krugman to come out and plainly say he is against redistribution wealth-transfers upward as one of thing self-govt does as a public finance scheme. I suppose I'd like it if all economists would say that too.

[Scott Sumner]

Nick, You convinced me a few years ago. I feel the same in having to constantly push back on the "helicopter drops are sure to work" claim. Sisyphus and I both give you our sympathy.

[Nick Rowe]

Roger: it's the taxes that are needed (or may be needed) to service the debt that are the cost on future generations, yes.

JF: yep, but the devil is in the details, because there are some cases where it's good to run a deficit, even if the economy is doing OK. Like if it's to finance (good) investments, or if r < g and will stay < g.

Thanks Scott. Most economists who read my posts on the debt burden seem to get the point, though it sometimes takes a bit of convincing, and they disagree on details (which is fine). But I'm not sure if my message is getting out there, to Paul Krugman, and maybe others.

Funny thing is, I don't actually care a lot about this topic, as a policy question. In Canada, for example, I don't know if the deficit is too big or too small. You can make a good case either way. But dammit, I do want economists to at least get the economics right! When good economists like Paul Krugman keep getting it totally wrong, it's embarrassing!

[JKH]

Nick,

The intergenerational buy/bequeath distinction seems a bit oblique to the point you want to make. I think there’s another way to get to the same conclusion. In doing so, I would avoid the bequeathal scenario. I don’t think it’s necessary to make your point about the real potential for intergenerational distribution effects.

It seems intuitive to me to treat intergenerational bond transfers by purchase as standard, in the context of treating the rollover of government debt as standard (i.e. no primary surpluses).

A primary surplus with debt retirement would be interpreted as “exceptional” in this context (but still appropriate to consider). And it is this surplus effect that reveals the potential for an intergenerational burden.

I come to the same conclusion, with the analysis transformed a bit. In particular, the explanation of the final stage would be different. You say:

“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."

I would extend your description one more iteration:

Suppose young C pay the tax that pays off the bonds. But notwithstanding that tax, young C experience no net effect on their consumption at that point. They would not have consumed in either case – with or without the tax – it was only a question of whether their money went to buy bonds or to pay tax. It is only when they reach the point where they become old C, co-existing with young D, that their burden becomes evident. Old C have no bonds to sell to young D, so old C forgo consumption. That is what is different than the previous cases.

But even then, there is still no reason to assume that aggregate consumption for the combined cohorts of old C and young D changes from what it would have been without the earlier tax. Only the distribution changes. Without the tax, old C would have consumed. With the tax, and without the bonds, they consume less, with young D consuming that difference as an addition to their consumption without the tax.

Thus, the tax burden does not bite as a constraint on consumption until young C ages to old C – and even then it is not an aggregate burden.

Again, I think it is this aggregate constant (other things equal) that Krugman was probably thinking about when he referenced future generations – effectively meaning multiple generations in the future – where the aggregate consumption is unchanged.

But the intergenerational distribution across different cohorts changes as per your model.

Anyway, I think all of that is consistent with the message of your post, which is about the intergenerational distribution implications of debt. One must just explain that to mean the implications for different cohorts as they co-exist at the same time, where one original generation is seen to be adversely affected. It does not pertain to cohorts collectively viewed at the same time, where there is no adverse effect on consumption in aggregate.

[Frank Restly]

Nick,

Maybe splitting hairs but:

"...but the devil is in the details, because there are some cases where it's good to run a deficit, even if the economy is doing OK. Like if it's to finance (good) investments, or if r < g and will stay < g."

Even if r < g, a government can still run into trouble if the annual change in debt outpaces the difference in the interest rate and the economic growth rate.
r = 3%
g = 5%
Annual debt growth = 5%

Annual interest payments will grow at about 8% per year (3% interest + 5% debt growth) while tax revenue will grow at 5% annual in line with economic growth. Sure the government can try Ponzi finance (make a portion of interest payments from new bond issuance) but I have to wonder how stable that would be. Why wouldn't 'r' explode to infinity as government in essence extends maturity to an infinite time horizon?

Would r stay at 3% if a person was forced by the government to hold it's bonds for a time longer than they were planning? Suppose I buy a ten year bond and ten year bond rates are 3%. I believe that there is a 50% chance that my ten year bond will become a 30 year bond (because the government will force me to roll it over). Would I accept 3% on the bond or demand a higher rate of return?

[Gene Callahan]

Yes, Nick, this was sorted out in 2012: you were shown to be wrong on this point. People don't sell their bonds to future generations: they sell them to whomever will buy them, which might well be people older than them. I created a model in which debt was transferred to *older* people, if you recall.

Government debt and inter-generational transfer are orthogonal issues.

[Jussi]

I think in Nick's model the younger generation doesn't own (at birth) nothing even political power. So they always have to work or be supported by the older generation (bequeaths etc).

The government debt doesn't change this does it? The generation in power can always tilt the game on their favor but even then it can be made without government debt.

[Nick Rowe]

Gene: "Government debt and inter-generational transfer are orthogonal issues."

You can't tax the dead. To prevent an intergenerational transfer, you need to tax only the cohort who benefited from the debt, and pay off the debt completely before they all die. You would need a complete set of age-contingent taxes to get that, so only the class of 55 gets to pay the taxes to service the class of 55 bonds. (And if everyone sells bonds to people older than them, they eventually run out of people to sell them to.)

With debt, the taxes come after the benefits, and some of those who benefited will be dead and won't be pay the taxes, and some of those who pay the taxes won't have been born at the time of the benefits. That's what makes it non-orthogonal.

[Nick Rowe]

Here's a model in which debt is negatively correlated with transfers from young to old:

Assume the risk of death in any year is a *decreasing* function of age. And that the birth rate is less than the death rate, so the population is declining over time. Increase transfers today, financed by debt. The people who are alive in future to pay the taxes will (if the birth rate is low enough) on average have been born earlier than those who benefit from the transfers.

[Nick Rowe]

If debt postpones extra taxes, and if those who pay extra taxes in year t+1 are on average born later than those who pay extra taxes in year t, then debt means a transfer from those born later to those born earlier. Unless you have a population that is aging faster than one year per year (so every year the average age of the population increases by *more than* one year), or age-contingent taxes (where the tax you pay is an increasing function of age, holding income constant), you get my result.

[Kevin Donoghue]

Nick, no problem, I do try to look on the bright side of life.

You may have a point, but I'm not convinced. To convict Krugman of inconsistency, you need to show that his rejection of Ricardian Equivalence logically requires him to reject the proposition: debt is money we owe to ourselves.

You have not shown this. I don't believe you can. I can reject Ricardian Equivalence on the grounds that some households (or even immortal dynasties) won't save a temporary tax cut, without conceding that intergenerational complications are important. There's no inconsistency in that.

I don't think Krugman is blind to the fact that, in OLG models, burdens can be transferred from one generation to another. AFAICT he just doesn't see that point as having much practical relevance. In fact I can't think of a case where he has used an OLG model for any purpose whatever, though I guess he must have done at some time in his career.

[JKH]

Nick,

I’m still recalling where I got to on this several years ago.

Which I think was that whoever bears the marginal tax burden in the event of a primary surplus is de facto the generation to which the burden has been transferred.

If the young hold bonds that they’ve purchased from the old (a not unreasonable assumption), and if the young are taxed with a marginal surplus, then the young are out of luck in terms of net wealth (no bonds) and future consumption when they are old (no bonds to sell).

If for some reason the old are taxed, they bear the burden. It doesn’t really matter whether they are taxed before or after they sell their bonds. And even then, the old can be considered a future generation by those at the start of the bond purchasing chain.

(But, as per Krugman), aggregate consumption for co-existing cohorts is not necessarily affected by the tax alone. For example, if the young are taxed, their consumption pattern when they are young doesn’t necessarily change – they pay the tax instead of paying for bonds. It changes when they are old because they have no bonds, but the then young pick up the slack.)

So two things are key to determining the effect:

a)The occurrence of a primary surplus

b)The identity of those who get taxed at the margin for that surplus

Isn’t it that simple?

Am I missing any of the basics of your point with that?

[Nick Rowe]

Kevin: I'm trying to think of a vaguely sensible model where Ricardian Equivalence is false, and at the same time *all* the bonds are bequeathed to the kids. It's easy to get a half and half model, but a 50%/100% model is hard.

"I don't think Krugman is blind to the fact that, in OLG models, burdens can be transferred from one generation to another. AFAICT he just doesn't see that point as having much practical relevance."

Then why doesn't he say that, instead of just repeating the "we owe it to ourselves" fallacy? It would be so much easier for him to say "sure, but people live a long time, and we will bring the debt/GDP ratio down again soon, and so most of the debt will be paid off by people who are alive today, so the burden on the kids will be small. Plus, we want to borrow to build roads, and the kids will benefit from those roads.".

Just you wait! Any day now, he will be walking along, reading my posts, see a blinding light, and Paul will become Saul!

JKH: it's pretty much that simple. We might want to add the sort of obvious point:

c) those in b will probably be born later, the longer we wait to run that surplus.

[Nick Rowe]

Kevin: plus, he totally missed the point of Antonio Fatas' post, which was explicitly talking about cases where the debt was offset by the government buying assets. This strongly suggests he can't see the difference for future generations between borrowing to buy assets and borrowing to finance transfer payments or tax cuts.

[Kevin Donoghue]

Nick, the "Debt Is Money We Owe To Ourselves" post is accompanied by a picture showing the two huge spikes in UK debt caused by the Napoleonic wars and the two 20th century world wars. Nobody was borrowing to build roads. The money was mostly spent on high explosives. Was Victorian Britain an economy crippled by debt, full of young people cursing the older generation for the debt burdens imposed on them with no assets to match? No, they were singing:

When Wellington thrashed Bonaparte,
As every child can tell,
The House of Peers, throughout the war,
Did nothing in particular,
And did it very well;
Yet Britain set the world ablaze
In good King George's glorious days!

Honestly, debt is not a burden. The effects you are interested in result from changes in debt. And if those effects were empirically significant, the Victorian era would have been a bleak time for Britain, with each generation painfully shrinking the burden it had inherited from the previous one. It wasn't like that.

[J.V. Dubois]

OH NO! NOT THIS AGAIN. I read Krugman's piece and immediately came here to see what you have to say. Then I jumped into comments fully expecting people supporting you. I was a fool and I believed that great blog war of 2012 where the opposition was utterly beaten and disintegrated was not fought for nothing. And to everyone who does not know about it yeat it was a really tough war. There were many people dragged into it, some constructing verbal stories, some constructing models and I think that there was somebody making a computer program for this. Go read Nick's links and then come back.

But it is even worse then that. Some very smart people and longtime readers of this blog and who were part of that war like JKH are armed and ready to fight again. Is this what happened to Krugman? Are we living in some weird version of Groundhog Day? I do not understand.

[JF]

This is a great post. Thanks.

For those who have touched on state and local govt finance (not current period budgeting; related but different), you will clearly know that when you finance the building of an asset that you determine serves the public for quite some time then you should figure some way to smooth out the costs across the generations served - duh, public debt has been used as a financing tool for millenia for these reasons. Also, historically, public debt was used for another common sense reason - if you taxed the large sums needed to finance the building from across the current-period population (trying to reach those use benefit from the new asset, which is not the few wealthy who may never use it) you would throw yourself into a tailspin economically - and that really makes no sense. This last point has a political matter and taxation matter to it, of course.

What is interesting to me now, at least for the US, Europe and Japan where there are huge wealth positions accumulated now, we need less to be concerned about sources of taxation because of the huge accumulation while it is still true that the current-taxing of the general population to build such a sensible new "public-good' asset can produce harm.

Since I consider that much of this huge new wealth accumulation was a windfall of political-rents (like the tax-cut-and borrow from the same group scheme that is the topic of this thread) and including the rent-seeking outcome/fact that productivity gains over the last 30 or so years flowed to the wealthy and not into the general wage population - the public should consider raising taxes on this windfall-wealth instead of so much debt that spreads to the general population and across generations, even for the building of long-lived public good assets. Of course, pragmatism also says you should be borrowing when the rates are so low. Obviously we should do a bit of both.

It is a political question of how to finance (tax and borrow), and even the notion of what one considers a good asset is a political question (as the wealthy often do not want to agree with this notion if it is used to justify taxation of them).

This blog thread is helping inform and to bring more light to the places where the political questions need to be decided. Thanks again for that.

[Kevin Donoghue]

Nick: "I'm trying to think of a vaguely sensible model where Ricardian Equivalence is false, and at the same time *all* the bonds are bequeathed to the kids."

It doesn't seem hard to me. Maybe I'm missing something? Consider a two-period "manna" model with two types of household: thrifty patricians and spendthrift plebs. The government consumes and levies taxes in both periods. The only asset is the government's bonds, which are all held by patricians. (The plebs have a higher rate of time preference.)

Now suppose the government cuts current taxes, leaving its current and future consumption unchanged. The plebs promptly increase current consumption. To keep aggregate consumption unchanged, the patricians must be induced to reduce consumption; it's not enough for them to save the amount of the tax cut, they must save enough to accommodate the plebs' increased consumption. So the real interest rate must change, no? Ricardian Equivalence doesn't hold, but Krugman's "Debt Is Money We Owe To Ourselves" claim makes perfect sense.

[Nick Rowe]

Kevin: 200% of GDP x (say) 4% interest = 8% of GDP to keep the debt constant. If GDP is growing at (say) 3% that falls to 2% of GDP to keep the debt/GDP constant. It's manageable. And if GDP per capita is growing over time, at (say) 1% per year, so about 30% per generation, the kids would still have been much richer than their parents.

Plus, the Victorians (unlike certain countries today) were not likely to "demonstrate" (in the Victorian sense).

Post WW2 inflation did a lot to reduce debt/GDP. Grandma's bonds were partly confiscated, but she didn't understand what was happening.

(I was watching Baldrick's historical walks on TV Ontario last week. He was walking around Cornwall, talking about my ancestors and those like them, who were free traders before it was cool. All because of the tariffs needed to finance the debt from fighting the French.)

[Nick Rowe]

JV: "OH NO! NOT THIS AGAIN."

Just what I thought too! And it was just after Groundhog day.

(But I'm pretty sure that JKH gets it. JKH just has a different way of saying things, but it comes out the same, eventually.)

JF: thanks! Yep, the debt question is a question about smoothing out the costs over cohorts in a sensible manner. Not an easy question to answer, but much better than either extreme simplistic answer.

[Nick Rowe]

Kevin: that's a 50/50 model. 50% of the burden of the debt is born by the plebs' kids, who will be paying higher taxes and consuming less. The interest rate only rises half as much as if all were plebs. (And if the plebs' kids don't pay taxes, it's a redistribution of wealth from the infinitely-lived patrician dynasty to the current generation of plebs, which will raise the natural rate.)

[ignoramus]

Nick, perhaps I wasn't clear. When the old die any non consumed assets are distributed. the important question here is whether they consume any more as a result. The act of selling assets is not sufficient. They have to burn through the money they receive. assuming that they don't do that literally all the money must return to the living. They may however consume more perishable resources than otherwise. But that probably has limits. They can eat better but not necessarily more.

[Roger Sparks]

No one seems to be embracing the 'bonds are property' theory. Inter-generational transfer of debt is much easier to follow if we carefully consider the property aspects of bonds.

No one will deny that gold is property. Now consider the discovery of the American hemisphere which resulted in a vast increase in the supply of gold. At that time, gold was money. It follows that more gold property was accompanied by an increase in the money supply.

The historical record tells us that the period of gold discovery and increase in money supply was accompanied by an increase in economic activity. Jumping to the conclusion, I think that the prospect of traveling to a newly discovered continent seeking money (seeking new property in the form of gold) destabilized the old economic order and incentivized increased economic activity.

Fast forward to fiat money. We can think of the creation of a bond as creation of property. In a stable fiat system, the economic result of the creation of a NEW bond is identical to the discovery of NEW gold.

I emphasize NEW because ONLY NEW, destabilizing, property-increasing-events lead to increased economic activity. The increase realized will persist until the new gold mines are exhausted or in the case of fiat money creation, until the annual increase in money supply is stopped. (Gold mines provide annual employment, an annual fiat deficit funds government economic activity)

The total economy records increasing amounts of gold property while the gold mines are running, and increasing amounts of debt property while the annual deficit is increasing.

I will leave it to the reader to consider the effect on the economy if government decides to reverse the property creating events. What happens when government decides to put gold into a vault and retire debt?

Would this be an inter-generational transfer of wealth or would this be a reorder of economic goals and activity?

[Nick Rowe]

ignoramus ("ginormaus" would be a better name!): Yep. If there's a bond-financed transfer of $100 to the old, then unless the old increase their consumption by $100 before they die, they will leave increased bequests (in some form or other), so the burden on future generations will be less than $100.

[Majromax]

@Nick:

> 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.

One interesting point here is that these two situations -- tax or default -- are equivalent in an old/young model. In the former case, the young pay taxes and don't receive bonds, so their old consumption suffers. In the latter case, the old have their bonds snatched away, so they can't sell them on and their old consumption suffers.

In turn, this raises what I feel is a compelling point: if debt is "owed to ourselves" to the extent its level is relatively unimportant, then why shouldn't the government default by choice?

I feel like the answer here would also suffice as an explanation of why Ricardian equivalence doesn't hold.

[Kevin Donoghue]

Nick: "50% of the burden of the debt is born by the plebs' kids, who will be paying higher taxes and consuming less."

I don't see it that way. Measured by manna consumed, the losers are tomorrow's plebs and today's patricians, while the winners are today's plebs and tomorrows patricians. So it's a +25/-25/-25/+25 model, if I understand your terminology correctly.

The crucial point, though, is that (a) Ricardian Equivalence doesn't hold in this world; but (b) debt can be described as "money we owe to ourselves".

[Philippe]

Nick,

"World B: Us old people sell our government bonds to the next generation (they pay us for the bonds)."

But the next generation decides how much to pay for the bonds. They are not obliged to pay anything for them. If they don't want to buy the bonds, their price falls to zero, and it's the oldies who get nothing for the bonds. So the next generation only buy the bonds if they think it is worth it, and then they can decide later whether to tax themselves to pay off the debt.

There is only a burden on another generation if one generation (which owns the debt) taxes another, which is alive at the same time, to pay off the debt. That is redistribution within the group of people alive at one point in time, not time travel.

[Majromax]

@Kevin Donoghue:

Can you define "we" and "ourselves"?

With the broadest definition of "all of humanity throughout infinite time and space," then all debt is trivially owed to ourselves and this is a null-argument.

With the narrowest definition of "a particular demographic and social cohort alive at this very moment," (say, "old patricians" or "young plebeians") then debt is externally owned and owed, and this is a live argument.

The trick is that all of our arguments are implicitly indifferent to redistribution within "us", but we care a great deal about redistribution between "us" and "not us", suitably defined.

[Nick Rowe]

Majro: I agree. In a world of ricardian Equivalence, default would not change the distribution of wealth across generations. It would only change the distribution of wealth across dynasties, if some held more bonds and paid less taxes than others.

Kevin: I really had to think about that one.

An individual old patrician can, if he chooses, keep his consumption exactly the same, and bequeath all of his transfer payment to his kids. If he chooses to consume less and bequeath more than his transfer payment, then he revealed prefers doing so. And if the old patrician already has assets and was planning to save, the increased rate of interest gives him an additional positive wealth effect.

Philippe: If the next generation collectively refuses to buy the bonds or pay extra taxes to service the debt, then yes you can't impose a burden on future generations. But for each individual, taking his own taxes as exogenous, the rate of interest will in equilibrium be high enough that it is individually rational to buy the bonds. What is true for all is not true for each.

[Kevin Donoghue]

Majromax: Can you define "we" and "ourselves"?

That's the crux of the matter. I take Krugman to mean all of us who are alive at any given time. In the example I've been discussing, a tax cut raises the consumption of today's plebs and reduces that of today's patricians.

On my reading, Krugman isn't trying to make any subtle point, so yes, it's trivial. As Kenneth Duda remarked in his first comment: "the conventional "Eek! Debt!" view is nonsense" -- that's really all he's trying to say. Krugman isn't opposing Nick Rowe's argument; sadly, he's just not interested in it.

Nick: An individual old patrician can, if he chooses, keep his consumption exactly the same, and bequeath all of his transfer payment to his kids.

Yes, which tells us that the real interest rate must change, since the plebs will certainly increase their consumption. Of course an individual pleb can do so too, but I'm assuming he won't. So if revealed preference is what interests you, everyone is better off with the deferral of taxes! WTF?! I think that touches on a point you've made in another context, about seemingly paradoxical implications of optimization; but I don't recall the details. Note however that at a higher interest rate, the PV of the bonds is reduced. If I was teaching this model I think I'd spend a bit of time thinking that aspect through, but I'm not so I won't.

BTW, I wasn't thinking of young & old plebs & patricians; this 2-period model just has thrifty patricians who own bonds, and spendthrift plebs who don't.

[JKH]

Krugman:

"But again, all this is within the current generation; it’s not about the present versus the future."

That tells you right there that he's being ambiguous in the use of the word 'generation'.

He's equating current generation with 'the present'.

Which means the current generation includes presently co-existing old and young cohorts according to him.

Which means it includes more than one generation according to Nick's use of the word.

Which means its just a current (intra-generational) distribution problem according to Krugman.

Which means its an inter-generational distribution problem according to Nick.

Sloppy writing on K-man's part.

In any event, he's never addressed Nick's point - not 2 years ago, not now.

[JKH]

the real point being that *somebody* is going to lose or bear the burden of the debt in the event of a primary surplus - i.e. whoever is taxed for it

[Philippe]

JKH,

people talk about the burden on future generations. Krugman correctly points out that time travel is not possible.

[JKH]

Krugman's role in the interpretation of the term 'time travel' is moot - in the context of his wider trail of terminological ambiguity.

Whoever gets taxed for a primary surplus is paying the price for debt previously incurred - since the normal use of a primary surplus is to pay down debt - and that holds notwithstanding that the proceeds of the tax get transferred to somebody in the present who gets to use it.

[Nick Rowe]

Philippe: My post on how time travel is possible

[Philippe]

JKH,

"Whoever gets taxed for a primary surplus is paying the price for debt previously incurred"

In that case, one group of currently living people is being taxed to pay another group of currently living people. They might even be the same people. Future people are not being taxed to pay past people.

[JKH]

That's right and that's what I just said.

But you're not understanding the point.

Which is that future people are being taxed to pay for the debt incurred by past people.

[JKH]

Here is my version of time travel, in the spirit of how Nick uses the term (although I haven’t checked back to his previous post yet):

Today:

The government makes a bond financed transfer to A.

Tomorrow:

The government taxes B to pay off the bond.

Interpretation:

B is the future generation that has borne the burden of the original debt – because the government has decided to tax finance the retirement of debt and has chosen to tax B for that purpose – and B by construction lives in a later period than A.

Net:

A is up $ today.

B is down $ tomorrow.

That is time travel in terms of benefit and cost.

But that does NOT mean that B has paid A.

It means B has paid bond owner C today.

But that is NOT a net benefit to C.

It is merely an exchange of one asset for another from C’s perspective.

Cross sectional asset exchange is not inconsistent with cost/benefit time travel.

[Philippe]

JKH

"future people are being taxed to pay for the debt incurred by past people"

But the payment is only going to future people, not to past people. The future people paying the tax might even be the same future people who are receiving the payment (or they might not be). However, time travel is impossible so future people can not be taxed to pay past people.

[JKH]

geez

that's just what I said too

you're not getting the point at all

[JKH]

the time travel is in terms of cost and benefit

not in terms of the clearing system for today's payments

[JKH]

the payment clearing system is cross sectional

the cost benefit equation is time travel

[Philippe]

cost/benefit is not that simple though, because the debt might have been used to improve future conditions.

[JKH]

true

its an other things equal type calculation for sure

[Philippe]

the future generation can impose a cost on themselves by taxing themselves to pay off the debt which they have bought from the past generation, but that is a cost that they impose on themselves rather than a cost that is forced on them by people who are now dead.

[JKH]

true

running a primary surplus is a choice

but that choice implies the judgement that the debt has become a burden

[Philippe]

"that choice implies the judgement that the debt has become a burden"

in what sense is it a burden? The future generation voluntarily buys the debt from the past generation, which then dies. The future generation is under no obligation to tax themselves to eliminate the debt, so why is it a burden to them? As I said, they can impose a cost on themselves by taxing themselves to pay it off, but that is their choice - not something which is forced upon them.