So, I was out there shovelling snow, thinking about writing a post on the burden of the debt on future generations. And about how macroeconomists' beliefs on this question had silently shifted about 30 years ago, and about how we as a profession have engaged in a sort of "memory falsification" (like Timur Kuran's concept of "preference falsification"), because we didn't want to admit that we now believe something we used to believe only unsophisticated economically illiterate rubes believed.
And I then I thought "Nah, what's the point of rehashing old ground?. Nobody nowadays believes that old "we owe it to ourselves" stuff that we used to believe."
And then I came inside and read Paul Krugman's blog post. Now I absolutely have to write the post I had decided not to write.
"That’s not to say that high debt can’t cause problems — it certainly can. But these are problems of distribution and incentives, not the burden of debt as is commonly understood. And as Dean says, talking about leaving a burden to our children is especially nonsensical; what we are leaving behind is promises that some of our children will pay money to other children, which is a very different kettle of fish."
Sorry, but that's just plain wrong. The economically illiterate rube who thinks that the national debt is a burden on our children or grandchildren is basically right. It's the exact opposite of "especially nonsensical". Unless you believe in Ricardian Equivalence.
[Update: Paul Krugman has a second post.
"And you don’t have to be a right-winger to acknowledge that yes, very high marginal tax rates act as a disincentive to productive activity. So real GDP may well fall significantly.
This is what I mean when I say that the burden of debt is about incentives, not about having to deliver resources to other people.
……
The general point is that the analogy with a family that owes too much is all wrong. Unfortunately, this dumb analogy dominates our national discourse."
And I'm saying that it's not (just) about incentives, and it is about having to deliver resources to other people, and that the analogy with the family is not dumb and not all wrong (even though, like all analogies, it doesn't work perfectly).]
In the olden days we all used to believe NB. At least, all educated sophisticated people believed NB. Only uneducated unsophisticated people believed B. But we all smugly knew that "the man in the street" was wrong. In fact, a quick test for whether someone was educated and sophisticated was whether he believed B or NB. Maybe a few of us educated sophisticated people might have believed B, or didn't really understand why NB was so obviously correct, but we kept our beliefs secret, because we didn't want other people to think we were uneducated or unsophisticated rubes.
I can still remember an economics seminar at Carleton, sometime in the 1980's. The visiting speaker was an older guy, an old-school Keynesian from one of the top US universities (I have forgotten his name). Halfway through the seminar, he said "I assume that the audience here is economically literate, and that nobody here believes B?" He paused and glared around the room. The blood went to my face (a grad student told me afterwards my face was red). I raised by hand, and said that I believed B.
James Buchanan was not a sophisticated macroeconomic theorist. He didn't do macro. He did political economy/public choice. He had zero authority in macro theory. James Buchanan argued for B. But he was just a farmboy, like me. (Yes, I do have a slight chip on my shoulder; why do you ask?)
Then, all of a sudden, it seemed like all the educated sophisticated people switched to believing B. It was a very quiet revolution. There were no visible signs of argument at all. One day we all (I mean all we educated sophisticated people) believed NB; and the next day we all believed B. And we all stopped our smug condescension about the poor ignorant "person on the street" who believed B. In fact, we never mentioned the fact that we all used to believe NB. We wiped our old beliefs from our memories, like Soviet photographs. It was just too embarrassing to talk about.
There's a danger to this sort of memory wiping, and silent shifts in belief. Some people never got the memo, and still believe the old NB like we all (all educated sophisticated people) did once. Plus, it says something about our beliefs in general if we all just believe what it is fashionable to believe. (And we do, very often, which is why many of our beliefs, especially educated sophisticated beliefs, really suck).
Paul Krugman is a much better economist than me. But he never got this memo. It's time to re-open this old box of suppressed memories.
Let me make some simplifying assumptions so we can get to the heart of the distinction between B and NB. (Yes of course these assumptions are false and unrealistic, but by excluding areas where we agree we can focus on the area where we disagree.)
Assume: closed economy; no investment or real capital of any kind; lump-sum non-distorting taxes with zero collection costs; positive real interest rate and zero real growth; exogenous full-employment level of output; apples are the only output good; apples cannot be stored; identical agents; overlapping generations; no funny stuff.
Suppose the government makes a transfer of 100 apples to the current cohort, financed by borrowing. Does that create a burden on future generations? Yes or no? B or NB?
I say Yes. I say B. It does create a burden on future generations. The only case where it does not create a burden on future generations is where Ricardian Equivalence holds. According to Ricardian Equivalence, the person in the street realises it will create a burden on future generations, and so saves the whole of the transfer payment, including interest, passes it on as a bequest to his children, who pass it on to their children, precisely because he wants to offset that burden on future generations.
The person on the street, in his unsophisticated uneducated ignorance, is basically right. The debt is a burden on his kids, or grandkids. Only if he anticipates that burden, and decides to offset it by increasing his bequests, a la Barro-Ricardo, does he eliminate that burden
No. 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.
Can that burden on future generations be offset in some cases? Yes.
Ricardian Equivalence means that inviduals decide to offset the burden by each cohort giving rather than selling their bonds to their kids in the next cohort. So if you believe in Ricardian equivalence, you can consistently argue that the national debt is not a burden. But it's only not a burden because individuals see it is a burden and take offsetting action. That ignorant uneducated person in the street is still right.
And if the debt is used to finance investment in the kids' education then the burden is offset.
And if the interest rate is permanently less than the growth rate then the "No Ponzi" condition does not hold, and the debt can be rolled over with interest forever without taxing future generations, so cohort A eats more apples and no subsequent cohort eats fewer apples (there is never a cohort like cohort C, they are all like B).
I can relax all the other simplifying assumptions, and show that the basic message is still roughly the same. But not today.
Worthwhile Canadian Initiative 
JKH: “C must judge the risk of taxation in light of the return available from the apple discount on the bonds it has the option of buying.”
But an individual member of C will be taxed whether or not he chooses to buy the bonds.
I am so pissed. This post has one link, from jamesoswald http://azmytheconomics.wordpress.com/
The econoblogosphere establishment is just ignoring my post.
Ian. Yep. “Now you could say that the government can increase the tax on those that recieve the extra amount but this is basically renegging on the comittment you made to pay a certain percentage when you initially issued the bond.”
And, if people expect the government to impose a (say) 10% tax on bondholdings, this just means the interest rate would have to be 10% higher.
Nick,
“But an individual member of C will be taxed whether or not he chooses to buy the bonds.”
True, but the tax itself is not the main issue.
The fact that buying bonds is C’s choice means that consuming apples or not consuming them is also C’s choice. And that is the crux of the burden issue as you have defined it.
Taxation is a risk that C must assess in making the decision on whether or not to buy the bonds. That risk will be reflected in the market price of the bonds. If C judges the risk high enough, there may be no price at which C is willing to buy the bonds. And that means C still has the apples.
As far as the tax itself is concerned, the assumption is that the tax is levied entirely on generation C. There are two possibilities. Either C has bought the bonds prior to the tax; or C has inherited the bonds prior to the tax. C pays the tax in either case. And in either case, the tax and the bond redemption are an intra-generational wash. The only difference is that if C has refused to buy the bonds, thereby forcibly inheriting them, C has also retained and eaten the apples it would have otherwise paid for the bonds, at whatever discounted price.
JKH: “Taxation is a risk that C must assess in making the decision on whether or not to buy the bonds.”
No, you are still not getting it. An individual member of C will be taxed anyway, regardless of whether or not he buys the bonds.
“Taxation is a risk that C must assess in making the decision on whether or not to buy the bonds. That risk will be reflected in the market price of the bonds. If C judges the risk high enough, there may be no price at which C is willing to buy the bonds. And that means C still has the apples.”
This just assumes that the government is allowed to legitimately break any contract, explicit or implicit, at any time. I dont think you solve this problem simply by assuming away the rule of law. Yes, if the government can renege on any liability it has at any time then there is no “debt problem”. Of course this creates a whole host of other problems that we can see when we look at the many banana republics that choose to follow this path.
Also, what Nick said
Ian: Breakable bonds or T-Bill rates that are lower than expected NGDP growth. In the absence of convex utility functions you need to choose one or the other. But you can’t have both.
“No, you are still not getting it. An individual member of C will be taxed anyway, regardless of whether or not he buys the bonds.”
Nobody knows the timing or even the occurrence of the tax in question until the government actually makes the decision to tax. Therefore, taxation is a risk for every cohort that buys or inherits the bonds of the previous cohort. It is a risk until the event of the tax actually occurs. C faces that risk and must make a judgement about its probability – before C actually knows about it. And you didn’t read my comment if you think I don’t know that C will be taxed anyway, whether or not he buys the bonds.
Ian,
Nothing in my comment about the government breaking a contract.
You have convinced me that, although the issue is complicated, it is true at least as a first cut that the debt is a burden even in the case with unemployment (assuming that Ricardian Equivalence fails because people don’t fully take into account future taxes, or because they lack a bequest motive, not because they are liquidity constrained, which is an even more complicated case). But you really have to address the unemployment issue (which is ignored in the main text of this post) explicitly. If you assume full employment, the argument is not convincing: it seems like a model that misses an essential feature of the world we’re trying to describe, and one would be inclined (as I was in my original comment) to attribute the result to this assumption.
According to Bohn, “exponential debt growth is consistent with (9)(=Transversality Condition) if the growth rate is strictly less than r(=real interest rate).”
So, C doesn’t have to pay off all the debt. If A, B, C, …, each pay back 1 to the government in form of tax on interest income, the debt can be rolled over forever and yet Transversality Condition holds.
JKH: sorry. Between marking exams, and the blogosphere not picking up on this post, I’m not as relaxed as I should be.
Andy: I’m really pleased you are basically on board. Yes, I think I need to work through a simple case with unemployment too.
But I’m still sort of puzzled/surprised though. I thought everyone had basically rejected the “it’s not a burden on future generations because we owe it to ourselves” view. I though everyone was more or less familiar with OLG models. And there’s PK, saying something totally wrong, and nobody’s calling him on it.
How come?? What the hell is wrong with macro? This is a zombie idea, that I thought was long-dead?
“Nobody knows the timing or even the occurrence of the tax in question until the government actually makes the decision to tax. Therefore, taxation is a risk for every cohort that buys or inherits the bonds of the previous cohort. It is a risk until the event of the tax actually occurs. C faces that risk and must make a judgement about its probability – before C actually knows about it. And you didn’t read my comment if you think I don’t know that C will be taxed anyway, whether or not he buys the bonds.”
While this may not be explicitly stated within a bond contract I am pretty sure most bond holders go into purchasing a bond contract with the implicit assumption that the government is not going to simply tax their gains away at a later time, else why would they buy the bond in the first place? When people expect that their gains will not be taken back it is within the power of the government to implement a suprise tax on the gains of bond holders. Once investors realign their expectations with the reality that government bond contracts are worthless the government is going to have a hard time selling its bonds. I guess we could call this an implicit default even though the government has not explicitly broken any of its bond contracts.
No American buys a T-bill because some American somewhere will eventually benefit from it. Americans buy T-bills because they expect to make a profit and that means that the Americans that benefit from the borrowed money are expected to pay it back to those that purchased the T-bill.
“But I’m still sort of puzzled/surprised though. I thought everyone had basically rejected the “it’s not a burden on future generations because we owe it to ourselves” view. I though everyone was more or less familiar with OLG models. And there’s PK, saying something totally wrong, and nobody’s calling him on it.”
I am having 4th year macro flashbacks, even though I tried so hard to forget that stuff 🙂
I suspect that what PK has in mind is a dynastic household/infintely lived agent model.
Nick is right here, with OLG and a real interest rate above the growth rate, something that will generally be true, then eventually someone is gonna lose. It didn’t have to be cohort C, Nick was just giving an example, but some cohort will lose.
Ian, Adam: thanks.
Adam: “I suspect that what PK has in mind is a dynastic household/infintely lived agent model.”
Maybe yes. But the only way the kids aren’t harmed is if Ricardian Equivalence holds in that dynastic model. And PK is not a fan of Ricardian equivalence.
Old-school Keynesians (not NKs) want to have it both ways. They seem to invoke RE when they say the debt is not a burden, but they reject RE when they want to say that tax cuts increase spending.
JKH:”If C judges the risk high enough, there may be no price at which C is willing to buy the bonds. And that means C still has the apples.
As far as the tax itself is concerned, the assumption is that the tax is levied entirely on generation C. There are two possibilities. Either C has bought the bonds prior to the tax; or C has inherited the bonds prior to the tax. C pays the tax in either case. And in either case, the tax and the bond redemption are an intra-generational wash.”
No, in Nick’s example cohort C absolutely is burdened whether they buy the bonds or not. In no case do they inherit the bonds. One way or the other C, when young, transfers 121 apples to old B. C never gets any apples back when they get old.
Nick chose to say that young cohort C buys the bonds for 121 apples from old cohort B, then the government taxes them and retires the debt. The net effect is that C, when young, transfers 121 apples to B and then when C is old they get no transfer back.
If C declines to buy the bonds from B they certainly don’t inherit them, the bonds would still belong to the old cohort B. The government then taxes 121 apples from C and gives them to B to retire the debt.
One way or the other the government is going to make sure that young C transfers 121 apples to old B. Then, since the bonds are now retired C will not receive any transfer from young D when they themselves are old.
Either way C loses, whether they buy the bonds or not doesn’t matter.
With the interest rate below the growth rate…? I mean, is it generally the case that the real interest rate is at least the growth rate?
If the initial apples are borrowed from Cohort A and distributed among Cohort A, all bond sales among the public are intra-generational, the only inter-generational bond transfer is through inheritance, and the last cohort that pays the tax is also the cohort that owns the bonds at that time, is the debt still a burden?
I thought I had my head wrapped around it yesterday but today (after trying to understand JKH), I think this may be another required assumption for the debt to be a burden (bond sales have to inter-generational).
If this is indeed the case, I guess it’s an empirical matter to check to what extent the young generation inherits rather than buys bonds.
Primed, the model works like this:
Period 1: Cohort A is young, there is another cohort who are old but play no role. A gives 100 apples to the government to buy the bonds, they get the 100 apples back in a transfer payment. Net effect, the bonds were created and given to young A.
Period 2: A is now old, B is young. B gives A 110 apples, B gets bonds in return.
Period 3: B is now old, C is young. C gives B 121 apples, C gets the bonds. Then C pays 121 in taxes and gets the same 121 back to redeem the bonds. Net effect, young C has given old B 121 apples but now C has no bonds.
Period 4: C is old, D is young. C has no way of getting anything from D. C and D consume what apples they produce.
A won, they got 110 extra apples when old, these apples were produced by young B.
B is gave up 110 apples when young but got back 121 when old. They are neither worse nor better off.
C gave up 121 apples when young and got nothing in return. C lost.
Nick@12:14PM:”the only way the kids aren’t harmed is if Ricardian Equivalence holds in that dynastic model.”
Not necessarily. Small tax on interest income, which is generally imposed in practice, seems to be enough. See my previous comment@11:29AM.
(I forgot to mention in it, but the real interest rate in the Bohn’s paper is adjusted for economic growth; therfore, that Transversality Condition holds even if the nominal interest rate is greater than the nominal economic growth rate.)
The second-post PK model has an interest rate equal to the nominal growth rate, in that all the additional borrowing induces exactly an identical increase in nominal GDP.
@Adam – I think I understand Nick’s model (though I am very slow). What I am saying is that in an ALTERNATE OLG model, where B, C, D, etc. inherit rather than buys the bonds, there is no debt burden.
Empirically, we can test whether bond sales are, on average, inter-generational. My guess is that indeed, bond sales will be inter-generational on average implying that there is a debt burden. If, on the other hand we find empirically that bond sales are not inter-generational on average, and bonds are mostly inherited, there will not be a burden.
I still hear NB all the time from the intelectual middle-class who is many of Krugman readers. The first Krugman citation is typical middle-brow economics.
Btw, I started disagreeing with the relevance of your argument at “Assume: closed economy”. It’s an intelectually interesting case, but no application to the real world.
@Adam P: “…a real interest rate above the growth rate, something that will generally be true…”
You use the future tense, so maybe you have a basis for making that prediction, although I would assume you’re not referring the temporal future but using the tense in a “probabilistic” sense — i.e. “It would be true in most reasonable models.” As a matter of historical experience (using the present perfect), for the US at least (and I suspect for most large countries that borrow in their own currency and have vaguely reasonable macro policies), it generally has not been true. I assert this as per Darby, 1994 (PDF). Based on casual observation, I would imagine that subsequent experience has strengthened Darby’s finding. (Actually, in the linked paper, Darby cites Ibbotson and Sinquefield, 1982, for the empirical result, but I seem to recall another version in which he presented his own evidence. In any case the point should be fairly obvious from a brief look at the historical data.)
I don’t give Krugman a pass on this point, because it’s really a different issue. (Krugman appears to assume that the debt will be a burden on someone and argues that the burden is offset if you aggregate across each generation. The r < g argument implies that the debt is not a burden on anyone.) Nonetheless it is relevant to the practical question of whether the debt is a burden on future generations.
The most you can argue is debt could possibly be a burden but would also have to admit it may also be a blessing, such as times like these, and most of the time it is neither. Governments normally operate in the non Ponzi regime but at the edge. I expect we will have just as much debt as the Fed determines we should have. It is possible to over promise but it usually doesn’t happen intentionally because such promises are so transparently laughable.
Primed, if succesive generations are linked so that they inherit the assets of the preceding generation then that would not be OLG as it’s generally understood.
You’re describing a dynastic household model.
Surprised myself at the lack of MMT-type responses. JKH, please help me out here if I’ve missed the point or have improperly represented these ideas.
Nick, I’ve been pulling me hair out since you made this post because I don’t understand why your model is analogous to real world govt debt that markets perceive as default-free, which is a world that also involves govt-backed currency, a banking system, and modern capital markets. In that world, investors in govt debt don’t face the same tradeoff Cohort B, for example, must make, and it theoretically doesn’t reach a point where the debt becomes too large to be rolled over (though, on other grounds, this theoretically could become undesirable at some point given inflation etc). Rather, money can always be created out of thin air and borrowed at an interest rate the Fed sets, and it can be used to purchase govt debt, ultimately at an interest rate the market necessarily bids down to near the rate of interest they’re borrowing at, if they view the debt to be default free. And they will view it that way, whether you take MMT’s perspective, Warren Buffett’s, Glenn Hadden’s, or if the Fed has to actually threaten or actually engage in purchases of debt in the secondary market at a named interest rate.
You left a comment on Wray’s blog a while back, at the time in support of Krugman, although I think your point is similar to the one you are making here (correct me if I am wrong). Fullwiler responded to you, but you never commented back. I think his points are relevant here.
Nick Rowe wrote: “[Wray] misunderstands Paul Krugman. If the public doesn’t want to hold bonds, what does it want to buy or hold instead?”
Scott Fullwiler wrote: “This goes to both Mark and Randy’s points. Let’s look at the real world for a change. First, there are these things called primary dealers, who can borrow at the repo rate and fix their costs for any maturity in forwards and buy any Tsy issue that goes above the borrowing costs. And the repo rate–created out of thin air with just a previously issued security as collateral–always arbitrages with the overnight target rate. Second, there are these things called hedge funds–like 100s of Warren Moslers–who can (and in the case of Mosler, have and will continue to) borrow at LIBOR and fix this rate at any maturity in swaps or forwards. And LIBOR arbitrages at the overnight target rate, while eurodollars are created out of thin air like any bank loan. Third, if the public doesn’t want to hold bonds, there are these things called banks that offer these things called time deposits, and the public can hold these and earn interest at virtually any maturity. And then the bank can hold a Tsy and earn a spread, or it can hold interest earning reserve balances and earn a spread. These don’t work nearly as well for countries for which there is any significant risk of default (Greece), but that’s another story and perfectly consistent with MMT.”
Nick, in this post, you wrote: “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 that is just not how govt debt works in the real world, and the decision the bond market faces is of a different nature than the apple producers and consumers. They ultimately are not giving anything up like Cohort B, and thus the interest rate on the debt is not determined by the kind of decision the apple people are making. Let’s get the real world buyers and what they do straight: a) bank primary dealers that can simply take govt debt onto its balance sheet in exchange for the creation of a Treasury deposit; b) non-bank primary dealers that can buy govt debt with reserves that the central bank creates out of thin air and trades them for previously issued govt debt; c) investors who can borrow money out of thin air at an interest rate set by the central bank. See Fullwiler’s above comments for a more sophisticated expose. There is no opportunity cost or “persuasion” here other than to not make the trade. The act of issuing govt debt creates a free profit opportunity that drives or essentially arbitrages the rate on govt debt in line with the path of expected short-term rates set by the central bank.
Nick, in this post, you wrote; “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.”
But the above is untenable in a theoretical model of the real world (not the apple world), where money can be created ex nihilo at some interest rate which can be used to buy new IOUs. See above. Or let’s even assume the following: that the govt needs to raise a 100 IOU, but markets cannot get more than 50 in financing together for a debt auction (I am trying to arbitrarily create a scenario where some unsustainable-type auction is reached). Let’s just focus on non-bank PDs which hold 50 IOUs. The Fed can swap 50 IOUs the nonbank PDs hold with reserves, which can be used to purchase a new 50 IOU. The process can then be repeated, giving them another 50 reserves in exchange for that new 50 IOU, with which the PDs buy another 50 IOU. And then bam, you’ve created net new 100 IOUs.
Maybe I changed the goal posts with that last example, but I just don’t get how your world resembles the market for govt debt at all. Demand pull inflation of course is still the issue when the economy has reached full capacity, but that’s another issue, and the relevant one IMO.
Hopefully I didn’t make a fool of myself here. I really just don’t get it.
Nick, believe a recent post of mine was sent to the spam receptacle.
@Adam P: I am mostly in agreement. It should be easy to check whether the OLG or Dynastic model is more applicable in this case by looking at the market for government bonds. Are sales typically inter-generational? (My guess is yes).
In Krugman’s piece, he mentioned the children of Bill Gates – presumably he was assuming that when it comes to inter-generational transfers of government bonds, inheritance dominates sales.
Also, as a side note, I can’t see why we cannot construct an OLG model with inheritance: http://cowles.econ.yale.edu/P/cp/p10a/p1049.pdf (A Stochastic Overlapping Generations Economy with Inheritance)
It isn’t in the rules of the game, but what if the taxes weren’t just a straight-up transfer? Say they were used, at least partially, to increase productivity (maybe their is a taboo against anyone but the gov’t growing trees from seeds, so some of the apples are collected to grow more trees).
A very enjoyable post. It makes me look forward to being back in the University of Cambridge Library with a collection of multiple editions of textbooks and looking at the changes over time.
On the assumptions: I want to analyse the long-run. The very long run. The VERY long run. The VERY VERY long-run.
Economic growth, amongst other things, requires resources. There are a lot of resources in the world and there are a few more in the rest of the universe, but there’s not an infinite amount of materials. Eventually, the real growth rate of the human economy will fall to 0% PA and then contract. We can regard this as an imperialistic invasion of economics by cosmology.
Since the real interest rate on bonds can’t fall below zero without inflation, eventually there are generations for whom the rate of interest is above the rate of growth. Government debt is only not an intergenerational burden in a universe with infinite resources where we use all the resources; we don’t live in such a universe; ergo, as far as we are concerned government debt is always an intergenerational burden*.
* A morbid scenario that is nearly an exception is a sudden total extinction prior to the inheritance of the debt by the next generation. Though, even then, that means that the generation who hold the debt at that point in time have not fully got their “due” and so they have inherited a burden from THEIR parents’ generation.
Primed, yep I agree. We could have many variations on the theme that were somewhere in between the two canonical specifications.
I just got on this because JKH was talking about inheritance and seemed to be doing it the context of Nick’s model (I could have missed where he introduced an alternative specification).
wh10: found it in spam, and retrieved it. Sorry.
wh10: this is a very short response: you are assuming unemployed resources. My model assumes full employment. See my discussion with Andy above about the case where there’s unemployed resources.
Patrick: if the government uses to proceeds from the bonds to invest for future generations (like the education example in my post) then that creates a benefit to future generations that offsets the future burden of the debt.
primed: “Also, as a side note, I can’t see why we cannot construct an OLG model with inheritance: …”
You can. That’s what Barro did. But in that case (at least normally) you get Ricardian Equivalence.
luispedro: “Btw, I started disagreeing with the relevance of your argument at “Assume: closed economy”. It’s an intelectually interesting case, but no application to the real world.”
Geeez. I assumed apples are the only good. But they aren’t. Therefore my model has no application to the real world. It’s a MODEL. Do you know why I assumed closed economy?
Thanks, Adam P. Now I think I have my head finally wrapped around it.
Nick, please let me know if this is a satisfactory summary.
Debt is a burden on future generations IF:
1. The debt does not lead to an increase in long run output that counteracts the burden.
2. There is a last cohort (if real interest is greater than growth rate there has to eventually be a last cohort although there could be a last cohort for other reasons too).
3. Government bonds are transferred across generations mostly through sales rather than inheritance.
Nick – thanks. I will say then, the title of the article seems to me to be misleading, regardless of where Krugman went wrong, given the 1) interest rate assumption and 2) employment assumption.
Wait, but Nick, even in my model, assuming fully employed resources, the tax on Cohort C never has to come. There is no such thing as unsustainability in terms of purchasing new IOUs. Rather, inflation might become an issue. But then, isn’t this a distributional issue – how the new money is spread across the economy?
primed: “Are sales typically inter-generational?”
Good luck with that. US treasury volume is well over $100 Tn/year or about 10X the outstanding amount. So bonds turn over on average several hundred times per generation. And transactions are in the names of the executing brokers. And the vast majority of bonds are held by investment funds and other institutional investors.
W Peden: “Since the real interest rate on bonds can’t fall below zero without inflation, eventually there are generations for whom the rate of interest is above the rate of growth.”
So I guess we’ll need some inflation, right? And in the distant future that you are contemplating why would you still assume the existence of physical currency enforcing the ZLB? (Liquidity traps are soooooooooo easy to fix. Just abolish paper money and set rates negative.)
Nick: “You can (construct an OLG model with inheritance). That’s what Barro did. But in that case (at least normally) you get Ricardian Equivalence.”
Isn’t Ricardian Equivalence violated for many reasons other bequests as well? For instance, what if government bond owners (and subsequent bequesters) are like Bill Gates and are not credit constrained while other tax paying individuals are credit constrained?
primed: “Nick, please let me know if this is a satisfactory summary.”
Basically yes, as far as I can see.
“Isn’t Ricardian Equivalence violated for many reasons other bequests as well?”
OK, true. The burden in those cases is more complex.
wh10: “Wait, but Nick, even in my model, assuming fully employed resources, the tax on Cohort C never has to come.”
If the nominal debt is inflated away, by a surprise inflation, it’s just like default, or an inflation tax. Cohort C still bears the burden, because it buys bonds that turn out to be worth nothing.
Nick/Ian,
Let me try this one more time. I don’t think I’m getting through here, because the responses indicate a reaction to something quite different than what I’m trying to say.
In your post, cohort B sells the bond to cohort C in exchange for 121 apples.
This happens when B is old and when C is young.
So at that point cohort C has 121 apples less than it started with.
And sometime later the government taxes cohort C 121 apples and redeems the bond in exchange for 121 apples. That part is a wash.
So the end result is that cohort C, the one that has the bad luck to be the one that is taxed, is the one that ends up being short the apples that cohort A started out being long on. The amounts, 100 and 121, are equivalent on a present value basis.
But the reason that Cohort C ended up short is that it CHOSE to buy the bonds in the first place. That was my point. There is no getting around this. It is a choice.
It could have been cohort C’s choice not to buy the bonds. In that case, it would have kept and eaten the 121 apples. It would have ended up with the same amount of apples and in that way hedged the upfront risk that it might be the one to be taxed.
If you regress this process, each cohort is in a position whereby it can SHIFT the risk that it will be the one that is taxed back to the preceding cohort – by not buying the bonds. C can shift the risk to B. And B can shift the risk to A.
And again, the tax risk in question here is the risk that a given cohort will be the one that ends up being taxed due to the bad debt mathematics and the government’s decision to tax that problem away.
So in that sense, any given cohort can hedge this tax risk by not buying bonds from the previous cohort. If it doesn’t buy the bonds, it keeps and eats the apples. If it does buy the bonds, and doesn’t keep and eat the apples, the risk is that it won’t be able to sell the bonds to a subsequent cohort – because the risk is that it may be taxed, in which case the bonds can’t be sold to the next cohort, because the government has called them in. Cohort C is that cohort in the example. It faced the risk up front, and the risk materialized. It was sucked into buying bonds, but unable to get out of them for more apples at the end. But if cohort C had perceived this kind of tax risk more accurately BEFORE THE RISK EVENT HAPPENED, it may have thought twice about selling its apples for bonds up front, or at least may put a lower bid on the bonds that reflects such risk. Note though that a non-zero bond price will always be an imperfect hedge, because any drop in cohort C’s apple level will become a net drop if it is the one that ends up being taxed. It can no longer get any apples for its bonds from the subsequent cohort, because the bonds no longer exist. And finally, note that even cohort B could have hedged its risk by not buying the bonds, in which case cohort A would NOT have ended up net long apples. It was the fact that cohort B initially decided to accept the risk that it might be the one to be taxed that caused it to make the decision to buy the bonds in the first place – the decision that led to cohort A being the only cohort that could possibly end up net long apples.
Nick, behind all this, your model seems quite reasonable. I think the math looks quite reasonable. I’m just trying to make a point of logic here that is also reasonable, because I don’t see anything wrong with it as a point of logic. And BTW, the point of logic has a certain ponzi feel to it.
AND I HAVEN’T EVEN GOTTEN INTO ANY MMT YET!
JKH, this statement is flat out false in the model: “But the reason that Cohort C ended up short is that it CHOSE to buy the bonds in the first place. That was my point. There is no getting around this. It is a choice.
It could have been cohort C’s choice not to buy the bonds. In that case, it would have kept and eaten the 121 apples. ”
If C chooses not to buy the bonds then B still owns them and the government owes B 121 apples. The government obtains the apples by taxing C. The government then gives the 121 apples to B to pay off the debt.
In no case can C keep and eat these 121 apples in the period when they’re young.
“But the reason that Cohort C ended up short is that it CHOSE to buy the bonds in the first place. That was my point. There is no getting around this. It is a choice.”
If I choose to park my million dollar Ferrari in a bad neighbourhood and it gets stolen I did technically chose to bear the increased risk but that still does not mean that when it gets stolen the thief is justified in his actions. The perpetrator is the government that cant handle its finances not the people trying to save but are prevented from doing so.
“If you regress this process, each cohort is in a position whereby it can SHIFT the risk that it will be the one that is taxed back to the preceding cohort – by not buying the bonds. C can shift the risk to B. And B can shift the risk to A.”
Choosing between being taxed and foregoing any savings at all is not a free choice. The threat the government poses eliminates a third option, saving money without the risk of it being taxed. Its like you are trying to argue that its all a choice while neglecting that the government has conveniently removed one of the most important choices, namely the free choice afforded to every cohort before it. Eliminating this choice reduces Cohort C’s utility and therefore is still a cost they must bear.
JKH: I think I am following your reasoning.
Consider this:
1. Suppose there were exactly one person in each cohort. Then everything you say is (unless I missed something) absolutely correct. In fact, in this case, it is inconceivable that B would have bought the bonds from A, because B would know that C wouldn’t buy the bonds from B, etc. By refusing to buy the bonds from A, future generations force A to pay for his own transfer.
2. Suppose there were one hundred people in each cohort. Then what you say is incorrect.
(That is what I was talking about when I made the distinction between what is individually rational and what is collectively rational. When there’s only 1 person per cohort, collective and individual rationality of a cohort are the same thing.)
Nick,
I don’t think that’s true. The bonds are created when A is young, if in the next period when A is old B refuses to roll the debt then the government would tax young B to pay the 110 apples to old A.
Either that or the government defaults on the bonds.
Nick, I struggle to make sense of your response because it doesn’t seem consistent with your model; maybe it’s over my head though. In your model, cohort C, or some future cohort, doesn’t have the option of buying new debt because it becomes too much. That’s the constraint in your model. In mine, that constraint doesn’t exist. I am also confused because if your model is always at full employment, then the govt spending is necessarily causing inflation in every generation.
In any case, in the real world, if some future generation (cohort C) has to buy IOUs that cause inflation, that means there is a rise in prices. How the net new nominal wealth resulting from the issuance of the govt IOU is spread across the economy is what ultimately affects how peoples’ wealth relative to the size of the economy changes. If it’s spread evenly throughout cohort C, then nothing changes for each individual member of Cohort C on a relative basis.
Maybe this isn’t how your apples model works, but as I said, I don’t understand how your model bares resemblance to the real world, which is the model guiding my thoughts.
Seems to me that once the bonds are created, provided the government doesn’t default then A is gonna receive a transfer. The only question is which cohort pays.
Sorry, Adam P.; the statement is flat out true.
In Nick’s model, the point of the government’s decision to tax is given and fixed, because the math that leads to the concern is a given and fixed. According to the timing in Nick’s model, this taxation occurs during the lifetime of cohort C, post cohort B.
So assume cohort C refuses to buy the bonds.
That means it must inherit them, because that’s the only other option, given that the point of taxation is fixed, and is during the lifetime of cohort C. The bonds exist, C must own them, and must have inherited them because it didn’t buy them.
So C keeps the 121 apples it didn’t use to buy the bonds. It eats the 121 apples, and the tax/bond redemption during C’s lifetime is a wash.
JKH, the point of taxation is not post cohort B. B is alive and old, C is young when the taxation occurs.
If C didn’t buy the bonds then B still owns them.
The way the model works, the only way it makes sense, is if cohorts buy bonds when young, sell them when old.