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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.

From the original post: "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." (my emphasis)

when C is young B is alive and old.

Ian,

Ferrari: my point has nothing to do with government morality as the cause of the problem. It’s about risk management, given the problem.

Regression: it’s not above avoiding the incidence of taxation; there’s no way to avoid the incidence of taxation – whether viewed as a risk or as an outcome. The risk management exercise consists of recognizing the risk of taxation and assessing the corresponding risk of not being able to sell bonds for apples as a result of that risk. That’s what makes the last man standing net short on apples.

Paul Krugman is now responding to his commenters, arguing that it's not a debt to foreigners, but he is still not responding to this post.

http://krugman.blogs.nytimes.com/2011/12/29/the-burden-of-debt-again-again/

The tax is imposed on cohort C.

Cohort B is a dead parrot when the tax is imposed.

Right Nick?

(Otherwise, you'd have no reason not to impose the tax on B as well, and you didn't.)

"Ferrari: my point has nothing to do with government morality as the cause of the problem. It’s about risk management, given the problem."

Yes, and as the government increases the risk that it will be required to tax a cohort the expected value of those cohorts bonds decreases. For example, As government takes on more debt, Cohort B's bonds are riskier and have a lower EV than cohort A, Cohort C less than Cohort B, etc. We may not know exactly when the tax will occur but the ever increasing threat of it will decrease the value of the bonds over time.

In reality, the bonds would be discounted to provide a 0 yield and people would still buy them because what else is there.

Nick,

“Suppose there were exactly *one* person in each cohort. Then everything you say is (unless I missed something) absolutely correct.”

Good.

“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.”

No. It’s not inconceivable. It’s risk management. Nobody knows the future. B has to make a judgement about the risk of taxation during the life of B. If that risk is less than 100 per cent probability, B may buy the bonds. If the probability of taxation during the life of B is less than 100 per cent, then the probability of being able to sell the bonds to cohort C will be non-zero. The bonds will be risk adjusted in price to reflect these probabilities. And when the price is adjusted for the risk, the yield will adjust a well - higher – compensating any cohort that choose to buy the bonds for the risk that it takes on in doing so.

JKH, it's a *net* transfer from young C to old B to redeem the bonds. The government could be collecting taxes from both young and old and providing services to both young and old. Paying off the bonds still means, in total, taking extra net taxes from young C and giving the apples to old B to retire the debt.

Or, it could just be that income taxes are only levied on the young. This would make some sense actually since presumably people produce more apples when they're young than when they're old. They'd want to buy the bonds to smooth out their consumption over the two periods of their life. So it could just be that only the high income young pay any tax.

"Yes, and as the government increases the risk that it will be required to tax a cohort the expected value of those cohorts bonds decreases. For example, As government takes on more debt, Cohort B's bonds are riskier and have a lower EV than cohort A, Cohort C less than Cohort B, etc. We may not know exactly when the tax will occur but the ever increasing threat of it will decrease the value of the bonds over time."

Agreed. In this case, the bond risk is complicated because they are real apple bonds. The bonds are still worth 100 apples on 100 apples for purposes of redeeming them for taxes. But they're not worth 100 apples in the market for bonds, essentially because the threat of the same tax means they'll no longer be available for sale in exchange for apples.

(For those MMT'ers who may be tuned in to this episode of WWCI, this aspect bears an eerie resemblance to Mosler's plan for Greek "Mosler bonds", which would redeemable at par as currency for tax payments.)

JKH: Nick's right. In a two agent model, C can negotiate the old man (B) down to next to nothing for his bond (since C can afford to wait), but where there are many agents an efficient yield (lets assume a policy rate somewhere around expected NGDP growth) will be paid for the bonds. Otherwise rates will rise and the CB will buy the bonds. And C will get stuffed. How, in your model, does the market price of bonds get impacted by the probability of the payment of a tax? The bonds are worth what they are worth by virtue of an arbitrage relationship vs the policy rate.

Nick,

"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.)"

I recognize the connection to your earlier point. I'll have to work this one through in more detail, but I know right now that I disagree.

BTW, regarding the "Mosler bond" reference, I argued with him at very great length on his blog that what he was proposing was essentially a Ponzi scheme (argued politely, that is). The same dynamic appears here in terms of the reliance on an inter-generational dependence of each generation to sell its bonds to the next in order to end up net flat in apple consumption, given that the first starts out net long, but that somebody must end up holding the bag in the event of taxation.

"In reality, the bonds would be discounted to provide a 0 yield and people would still buy them because what else is there."

"And when the price is adjusted for the risk, the yield will adjust a well - higher – compensating any cohort that choose to buy the bonds for the risk that it takes on in doing so."

But as people percieve that the risk will most definately occur before they cash out their bonds they will simply not purchase the bonds no matter how much you promise them in interest because they know you are just going to take it all back.

Like I said earlier, you can do this a couple times by taking a hit on the financial reputation of the government but eventually you end up in banana republic territory where the government has a difficult time taking on any future debt. This removes the benefits of fiscal policy to future generations that previous generations benefitted from.

K,

I don't believe in binding liquidity traps now as a result of the ZLB, let alone with no physical currency, so I certainly don't assume a ZLB problem at the end of expansionary civilisation!

An inflationary burden that is necessary to lower interest rates on government debts (without raising taxation) is still a burden. The "interest rates below the growth rate" seemed interesting precisely because no extra inflation would be necessary.

K,

I think the most reasonable interpretation is that all bonds are one period maturity and when Nick says an old cohort "sells" the bonds to the young cohort then he really means that the government rolls the debt.

Otherwise, as you say the young C can negotiate old B down since B doesn't value future consumption at all (they'll be dead) so any price above zero that they can get is worth it.

The problem with long term bonds is that B should anticipate that they'll be in a lousy bargaining position and so not pay much for the bonds and thus A never gets a transfer.

I think the interpretation here should be that A gets issued one period bonds, when A "sells" them to B this is intermediated by the government. The government sells 110 apples worth of new one period bonds to young B and uses the proceeds to pay its debt of 110 apples to old A who's bonds are maturing.

If B refuses to buy the newly issued bonds then they get taxed 110 apples so the government can pay its debt to A (assuming no default).

I think that's the most sensible interpretation and makes Nick's point the in the starkest way. Once the bonds are created, if the government won't default then some future generation has been burdened.

I don't understand why we have to talk about this fictitious apple world that operates nothing like a banking system with a sovereign govt denominated currency. Why can't we talk about a simplified worlds with bonds, bank loans, primary dealers, and investors? Is that too finance-y? Too complex?

Perhaps the model that Dean Baker and Krugman envision is like this:

The government borrows real goods in period 1 from a few rich dynasties (Gates, Buffet, Walton, etc.) and gives them bonds in exchange (as an aside, it is assumed that the government either trasnfers those real goods or burns them such that total long run output does not increase). These dynasties are not credit constrained and they bequeath the bonds from generation to generation. The rest of the economy is comprised of credit constrained dynasties/overlapping generations. Ricardian equivalence does not hold because a tax cut will lead to higher transitory spending by the credit constrained households.

Eventually at some point, government debt is cleared either through additional taxes (a redistribution from tax payers to the rich dynasties) or through default (a redistribution from the rich dynasties to everyone else). This looks like a dynastic model whithout Ricardian equivalence where the burden of debt is primarily redistributive.

@K - I think we don't need to actually track individual government bond sales to check if they are typically intergenerational. If we assume that government bonds are a fairly fixed proportion of wealth across agents, then all we need to see is how much wealth today has been created by the current generation as opposed to inherited from the previous generation.

As Gates and Buffet are first generation billionaires, I think, empirically, an OLG model as described by Nick is a better fit than the dynastic model above but I am sure this could be tested better.

wh10,

Making things any more complex than they need to be in this exercise is to be avoided. There's a time and a place for detailed institutional descriptions; abstract modelling about the fundamental causal effects of intergenerational debt is neither the time nor the place. Hence the simplifying assumptions.

Adam: I basically fully agree with you (and Nick). There wasn't much more to say after you said:

"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."

Basically if we assume that each cohort overlaps with the next for half of their consumption/production then *one* cohort can decide to increase their share of total consumption by 50% and every cohort after that can give up 50% to the previous cohort and take 50% from the next. It's impossible to take more production than that since you can't pull it back from the future. But as long as a generation has sufficient political power it can pull off the trick. But only one generation can get the benefit, and eventually as W Peden says, given the finite size (or at least very low growth rate) of the universe, the gig will come to end and someone's going to pay.

*Unless* rates, as Andy points out, continue to run below NGDP growth in the long run. In which case we are getting a free lunch thanks to the risk averse preferences of our descendants who choose to share a tiny fraction of their immense wealth with us by collecting infinitesimally less interest than the rate of growth produced by their immense futuristic economies.

W. Peden, but my problem is that I have no reason to trust this model accurately reflects the fundamental causal effects of intergenerational debt as they exist in the real world. And the real world contains a credit system with a central bank, which doesn't exist in this model.

Nick made a comment to me a while back that he'll only trust the MMTers once they demonstrate to him comprehension of some economic concepts he views to be very important (and correct). I have the same problem here. I struggle to trust Nick's thinking until he demonstrates an understanding of the economics behind various the credit system and real-world financial constructs.

You act as if I am talking about icing on the cake that doesn't matter for the main takeaway. I am not. I'm talking about the cake.

primed: Maybe, just maybe. Except, there's a long history of economists saying that it is *impossible* to impose a burden of the debt on future generations, except via lower investment, debt to foreigners, distorting taxes (all of which i have ruled out by assumption). I'm not sure where this "no burden" theory came from. Abba Lerner, possibly? But it was orthodoxy until somewhere around 1980. And Paul Krugman is, most plausibly, just reflecting that old orthodoxy.

wh10: when some economists say something is theoretically impossible, and you want to show that it is possible, you set up the simplest possible model in which that something can happen. Even my model is not simple enough, because we are still arguing about it.

The absolutely last thing we want to do is bring "primary dealers" and stuff like that into the model. They add nothing, and merely obfuscate the picture.

What Nick said.

Put another way: the weather is part of any complete explanation of shifts in economic growth. For instance, some winters are very harsh and cause considerable temporary fluctations in national output. Each country has its own weather policy; even within a country, some areas will deal with the weather better than others. One could make a career out of talking about the institutions, the weather and their relation to changes in output.

Would such a description be relevant to working out the causal relations between fiscal policy and real growth? No. Adding detail SOLELY for the sake of representational is not the point of modelling here. What is interesting is causally relevant details, in particular the logic of an intergenerational sale of government bonds.

Nick,

But why should anyone believe your model is at all representative of how govt debt works in the real world? You never engage, for example, Fullwiler's response that I posted above (and thus, why I never know if you really understand this stuff). Instead, you retreat to your simplified models when faced with what you view to be 'obfuscations' and then proclaim you have it right because it works in your model. Then someone else responds that your model does not properly correspond to the real world, and we're back to square 1.

Fine, throw out 'primary dealers.' How about introducing a central bank and a credit system reflective of how they work in the real world? These are INEXTRICABLY attached to govt debt.

Peden, you and Nick don't get it. You're merely asserting things like a credit system is not important. That's all you're doing. It's absurd.

K,

To be pedantic (it is almost my name!) I wasn't saying that the universe is finite in SIZE, but rather finite in resources (by which I mean usable resources). The universe (or the billions of light-years of it that we can observe) is mostly made up of dark matter and dark energy which have no real use beyond creating employment for physicists who can't do anything else. Paraphrasing Lord Salisbury's comment on the western Sahara, "It's what you might call very marginal cosmos."

Of course, the primary modern constraint on avoiding passing on debt burdens is not the universe as a whole, but the level of modern growth that is commensurate with not destroying civilisation with global warming or radioactivity, which are also burdens on the next generation (i.e. my generation).

W Peden: "An inflationary burden that is necessary to lower interest rates on government debts (without raising taxation) is still a burden."

I don't get this. We are not talking about surprise inflation. We are just talking about higher *equilibrium* inflation in order to accommodate lower real rates at the ZLB. It's not lowering anybody's debt which, in real terms, will continue to compound at the real rate *at equilibrium*.

I didn't say you believed in liquidity traps (my comment about liquidity traps was an aside). But presumably you believe that people wont hold negative nominal rate debt. And the reason for this is the existence of physical currency with zero nominal yield. So if we abolish hand-to-hand currency then we can set negative rates (and then liquidity traps, for those who believe in them, go away).

Krugman still has a good point, though. Lets say generation A, in its old age, decides to throw itself a monster bash and retire in Barbados at the expense of generation B, and they decide to arrange for the government to pay for this through our democratic process. It's not very fair to B, but that's our system and those are the breaks. But have they burdened future generations who are not party to this deal? That really depends on how well B negotiates with C. If C doesn't agree, then B will pay for it, since "C doesn't agree" means "C has the political power to decide who is going to pay". Maybe C will say "sorry, you blew it, Pops. You no longer get social security/medicare. And there's a special new 'pensioner's tax'" So in the end, I agree with Krugman (and in spirit, though perhaps not in technical detail, with JKH). A and B will make whatever arrangements their relative negotiating positions permit and since they were both alive to be party to the transfer, then it's ostensibly a fair deal. From there on, each generation can negotiate (via the tax and transfer system) with the next.

Let me be clear. It's not that I am proclaiming your model is not representative enough in that it doesn't have all the details. I am saying it's not representative enough in that it doesn't properly capture the bare minimum "causally relevant details" that allows us to understand fiscal policy.

And then all Peden does is assert I am wrong. And then I say Peden is wrong. Back and forth.

It would make me happiest student if you would engage the other side on its own terms, instead of retreating to your models that the other side views as a non-starter.

wh10,

"You're merely asserting things like a credit system is not important. That's all you're doing. It's absurd."

Of course a credit system is important, for SOME issues. Is it relevant to modelling intergenerational debt burdens? The assumption is surely "no", since additional assumptions (i.e. an economy at below full-employment) have to be added to make it relevant.

"why should anyone believe your model is at all representative of how govt debt works in the real world?"

There are many different reasons to model. One is to pursue empirical adequacy e.g. you make a long-run growth rate model and test it against the data. Another is to isolate causal connections. In both cases, representational accuracy is important ONLY insofar as it aids the actual goal of the model. That's why you get population models in biology that assume an infinite number of rabbits.

wh10: in this *particular* case, where all I need to do is show how something is possible, because I am trying to disprove someone who says it is always impossible, all I need to do is find *one* case where it is possible.

More generally though, here's how model-building works:

1. The first person lays out a simple model to demonstrate something.

2. If a second disagrees with that model, he can't just say "assumption X is unrealistic". The onus is on the second person to explain why assumption X matters, and why you would get different results if you changed assumption X to assumption Y. Because *any* model, no matter how detailed, is always false in millions of ways. The only true model of the world is the world itself.

But this is wandering off-topic.

Even though i am not keeping up with comments, I just wanted to say I am really pleased to see a number of good commenters here basically on board. Now, how can I attract the attention of the rest of the world, and PK in particular?

One thing I now think I was wrong about: I thought that basically (almost) all macroeconomists understood that the debt is a burden (subject to the exceptions we have already discussed). I didn't think this would be (as) controversial.

"2. If a second disagrees with that model, he can't just say "assumption X is unrealistic". The onus is on the second person to explain why assumption X matters, and why you would get different results if you changed assumption X to assumption Y. Because *any* model, no matter how detailed, is always false in millions of ways. The only true model of the world is the world itself."

I did. I had a huge post above. And it's just ignored. If you can always borrow at x% and earn y%, then you will always do that if y% is anything above x%. And you need a credit system for that. And that's what happens in govt debt. So you need a credit system to understand intergenerational debt.

And that's guaranteed earnings mind you.

More specifically: "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."

Any takers? Or is it back to apples?

"The assumption is surely "no", since additional assumptions (i.e. an economy at below full-employment) have to be added to make it relevant."

That's just entirely false. We're not talking about credit created for private sector activities. I went over this with Nick several weeks ago. See above.

One has to assume the reason government implemented this represents a common need that does not go away simply because they botched the design and no one was smart enough to figure it out. Anyone trying to buy future apples in the present would face the same problem but not buying is not a solution. Yes, people will buy things even if they expect to lose money if that is the best they can do. Apples perish.

I know of no program that started by paying out benefits first and collecting premiums later so this seems remarkably irrelevant. The bigger question is if this benefited A, what did A do with it? In Apple world there isn't much that can be done, perhaps some starving has been avoided, perhaps some heirs are left better off, and perhaps that assurance is enough. The program is modified to accord to reality as best we can anticipate. Facing reality may represent a burden, but not facing it a calamity. You can pretend facing it is some betrayal as it is a burden, but it is only a burden because of your unrealistic expectations.

wh10,

I'll leave the economics (not my field) to Nick Rowe, since my methodological point has been made. I hope it's clear WHY this causal modelling is taking place and WHY saying "that's not a representational model" is missing the point.

Nick Rowe,

"One thing I now think I was wrong about: I thought that basically (almost) all macroeconomists understood that the debt is a burden (subject to the exceptions we have already discussed). I didn't think this would be (as) controversial."

I think that this thread is probably extremely unrepresentative of macroeconomists as a whole. A post like this is naturally going to be more interesting to precisely those people who disagree with that proposition. It's just like a post saying (amongst other things) ABC isn't believed by most economists will attract the Austrians. It doesn't mean that most economists are Austrians or even take ABC seriously.

wh10: and why will all that show it is impossible for the debt to imposes a burden on future generations? Otherwise, yes, it's back to apples.

Lord: "I know of no program that started by paying out benefits first and collecting premiums later so this seems remarkably irrelevant."

??? Whenever the government runs a deficit it is doing just that. Unless all the deficit is used to finance investment for the future generations, which offsets the burden of the debt.

W Peden: you could be right. Sample selection bias is omnipresent in who comments.

Nick and Wh10,

Let me take a stab at attempting to assess wh10’s MMT related concerns in the context of Nick’s model.

Nick, I interpret your government finance model as non-fiat, because it is an apple finance model. The government borrows apples in the first instance. So I assume reasonably I think that you have no apple issuing central bank in this model. If you did, it would be an apple fiat model, and the government could deficit spend in apples, while issuing bonds to drain apple reserves etc., as per MMT. But I assume your model doesn’t extend to the fantasy of an apple creating central bank. Instead, the government is forced to borrow apples when it wants to spend them. Its apple bond financing is constrained by the requirement that the apples already exist to borrow. The government doesn’t have the option of creating them through fiat. So, because this is a non-fiat model, MMT has no direct relevance to the model.

In the apple system, A buys apple bonds and the government makes a transfer payment of apples back to A. A then sells its bonds for apples prior to death. A ends up being a net consumer of apples. And the cohort that is finally taxed, C, ends up being a net producer of apples. The fact that A net consumes while C net producers is interpreted as a burden on C, the future generation.

In the fiat system, A buys dollar bonds and the government makes a transfer payment of dollars back to A. A then sells its bonds for dollars prior to death. A ends up being a net consumer, using the dollars to consume, apples for example. And the cohort that is finally taxed, C, ends up being a net producer of whatever it sells (apples for example) to the preceding cohort in exchange for the dollars they were paid when they sold their bonds to C. The fact that A net receives dollars and net consumes apples, while C net disburses dollars and net produces apples, is interpreted as a burden on C, the future generation.

Those two paragraphs look pretty similar. But I think the MMT response to the second scenario would be something like the following:

MMT maintains that there is no financial constraint on the ability of government to deficit spend in dollars, whether it issues bonds or just leaves the money spent as is. The government always has the operational option of crediting reserves for bond maturities, for example. The only legitimate constraint is real, not financial. Real capacity pressures may lead to inflation pressures, which the government may want to respond to with tighter fiscal policy, for example.

The point is that the financing sequence that led to a government decision to impose an apple tax in Nick’s model is not relevant in the fiat model. The government following MMT policy would never impose a tax merely because of a particular financing sequence. For example, if apples were the only commodity, the government wouldn’t impose a tax at all unless apple producing capacity was binding to point of introducing apple inflation.

In Nick’s apple model, the issue is solvency in apples. In the fiat model, the issue is never solvency in dollars; it’s inflation. (That was the point of the MMT debate with Krugman.)

All that said, Nick assumes a state of full employment. So I guess that means that what becomes an apple solvency issue in Nick’s model becomes a dollar inflation issue in the fiat model, with identical timing. Given that timing, the same decision to tax should result. So the two approaches seem reconcilable.

That’s my initial impression, anyway.

JKH: I think that's fairly accurate.

You can, if you like, assume there's a central bank that always adjusts monetary policy, however defined, to keep the economy at full employment. If that requires setting an interest rate above the growth rate of GDP, which is what I have explicitly assumed, then eventually the government will have to increase taxes, or else create a surprise inflation which "taxes" away some of the value of the bonds held by the grandkids (cohort C). In either case the grandkids pay the burden.

JKH,

One wee quibble: at several points you switch between "fiat model" and "a government following MMT policy". I assume that we're supposed to regard these as equivalent, because that's how I've generally found neo-chartalists to use the terms, but I could be wrong. I was actually under the impression that an MMT government wouldn't finance its operations through bonds in the first place.

I don't think that anyone denies that the government can finance its debts through "printing money". For the purposes of intergenerational burdens, I think that one can regard such inflationary policy as the equivalent of a sales tax on all purchases (though in practice it will be like a series of sales taxes, with the rates depending on the amount of spare capacity in particular markets). Different theories of price determination will differ from that assessment, though, and we'd really be straying off-topic if we got into them...

As it is, I agree that neo-chartalists have anything controversial to say here: debts, under certain assumptions, create certain burdens on future generations that may met through taxation or inflation. I think that, given there are finite resources in reality, those assumptions are always met i.e. the interest rate on debts always ends up exceeding the real rate of growth such that a generation has a burden.

No, only deficits larger than the long run growth rate or larger than that over the cycle and only that without investment value. Certainly wars are a huge generational transfer. Sure hope they appreciated it.

A key assumption in this model is that the interest rate on money is above GDP growth.

Clearly that does not have to be the case. Risk-free assets have a lower interest rate than risky assets. There's nothing strange about an economy where investment returns are above GDP growth, but the return on money is below GDP growth.

K: "Krugman still has a good point, though. Lets say generation A, in its old age, decides to throw itself a monster bash and retire in Barbados at the expense of generation B, and they decide to arrange for the government to pay for this through our democratic process. It's not very fair to B, but that's our system and those are the breaks. But have they burdened future generations who are not party to this deal? That really depends on how well B negotiates with C. If C doesn't agree, then B will pay for it, since "C doesn't agree" means "C has the political power to decide who is going to pay". Maybe C will say "sorry, you blew it, Pops. You no longer get social security/medicare. And there's a special new 'pensioner's tax'" So in the end, I agree with Krugman (and in spirit, though perhaps not in technical detail, with JKH). A and B will make whatever arrangements their relative negotiating positions permit and since they were both alive to be party to the transfer, then it's ostensibly a fair deal. From there on, each generation can negotiate (via the tax and transfer system) with the next."

Doesn't that concede the point that Nick is making? Sure, the exact identity of the generation who bears the burden may be a function of bargaining between the generations, but that concedes that it will be borne by someone other than A (unless ricardian equivalence holds).

As for whether such an outcome is fair, surely the fact that the original decision was made through the democratic process doesn't inherently make the decision fair (after all, by that logic, tax cuts for millionaires are fair, since they were made through the democratic process - surely that's a hard proposition to swallow. Democracy may be a better system than all the others, but it isn't neccesarily fair).

More to the point, because we're having a discussion of government borrowing, both the A's and the B's are agreeing that the cost will be borne by a future generation, otherwise the B's could just "give" (through their taxes) some of their apples to the As. Implicitly, in this model, the A's are saying "give us apples" and the B's are saying "sure, but only if we can try to punt the cost of those apples to the next generation". The B's might fail in so doing (though,in practice, given the electoral advantages of the old in most democracies - they're richer, better connected, they vote, and they get to brainwash the generation after them into believing that social programs that benefit them are a core institution of their society - I'd bet on the "old" generations to kick the can to the young until the government goes under,i.e., the Europe scenario), but there's something decidely unsavoury about that kind of "deal".

The real problem is that, in the absence of some sort of ethical rationale for the proposed redistribution to the As (equality, perhaps, if the A's are expected to be poorer than the Cs - which is surely why people accept the provision of CPP/social security to the first generation of seniors, who paid far less than they took out, as being fair), it's hard to see the fairness in a decision make by one cohort (call them the ABs) to benefit that cohort (or a subset thereof) at the expense of future cohorts (the CDs, DEs) who had no say in the original decision.

"And one of us is totally wrong: either me or PK. It's not like I'm disagreeing with some no-name blogger."

This is nowhere near as mysterious as you are insinuating. To continue in the vein of your "P and NP" terminology*, you and Krugman are both making valid arguments, but yours is false. It profits you nothing to obey the rules of logic but apply them to false premises. Compare and contrast:

1. You assume full employment whereas Krugman assumes substantial slack.
Observation: we are a long, long way from full employment.

2. You assume a Ponzi condition whereas Krugman does not.
Observation: anemic though US growth may be, it still exceeds the nominal rate of interest on government borrowing.

3. You assume that younger generations buy bonds issued by older ones, whereas Krugman does not.
Observation: in fact, older generations are creditors and younger ones debtors.

There is nothing wrong with your argument except that it does not connect with reality at any point. Why would you expect Krugman to come along and rebut you? There is nothing to rebut.

* As you may have guessed, I did not care for this: it did nothing to clarify your argument, and could easily be confused with the subtle, beautiful, and useful ideas of that worthwhile Canadian**, Stephen Cook.

** Though like you, Cook is Canadian by choice, not by birth. All the more dear to us then.

Phil:
1. As discussed with Andy upthread, my argument still holds if we assumed unemployment.

2. Paul Krugman assumes that the current deficit implies future tax increases. That's all I need for my argument. The No Ponzi condition is only needed to make sure there's an increase in future tax increases. Since PK assumes a future tax increase, I don't need it in my argument with him.

3. If the younger generation do not buy the bonds from the older generation, then what exactly do the older generation do with them? Either they give them to the young for free, in which case we are into Ricardian equivalence; or else they take them to the grave with them, for company?

4. The use of P and NP for a proposition and its negation goes back a long way. You do not care for my use of them? Too bad.

Nick Rowe: "in this *particular* case, where all I need to do is show how something is possible, because I am trying to disprove someone who says it is always impossible, all I need to do is find *one* case where it is possible."

Sorry, Nick, you are making a stronger claim than that: Not "Debt may be a burden," but "Debt is too a burden."

Nick Rowe: "More generally though, here's how model-building works:

"1. The first person lays out a simple model to demonstrate something.

"2. If a second disagrees with that model, he can't just say "assumption X is unrealistic". The onus is on the second person to explain why assumption X matters, and why you would get different results if you changed assumption X to assumption Y. Because *any* model, no matter how detailed, is always false in millions of ways. The only true model of the world is the world itself."

You left out an important step, the one where the model builder justifies his assumptions. After all, the model builder has the burden of proof. :)

Now, there are cases where the justification comes afterwards. In such cases the justification is empirical. :) The model acts like what is being modeled in significant ways, within certain bounds of error.

In this case you have modeled the debt burden without money and with gov't policy that guarantees default, and you have also made assumptions about who buys bonds and when, as well as assumptions about parent child relationships, all without justification. Perhaps some empirical justification may be had in gov't defaults. Who got stiffed? :)

Nick"if the generation that benefitted from the deficit is already dead, it's too late to make the choice to tax them. They have consumed the deficit, and you can't get them to pay higher taxes from the grave."

If they are dead, they cant be a burden on the future generation (given domestic financed debt). You are not going to put apples on their graves. If they are dead, the next generation has inherited the bonds and the bonds will stipulate a transfer within that generation.

erik: "If they are dead, they cant be a burden on the future generation (given domestic financed debt)."

Yes they can, as my example showed. They have already eaten 110 of cohort B's apples. Which is OK by cohort B, as long as B can eat 121 of cohort C's apples in return...

I'm sure Krugman understands this. But:

1) This would only mean that the younger generation as a whole loses a portion of the amount borrowed, not the whole thing as is popularly assumed -- and Krugman wants to point out a big reason why this popular assumption is untrue.

2) If the money borrowed is used so that the young cohort can get a much better education, much better childhood nutrition, much more advancement in science and medicine, a world not decimated by global warming, etc., then the younger generation makes out far better on net.

Nick: "Yes they can, as my example showed. They have already eaten 110 of cohort B's apples. Which is OK by cohort B, as long as B can eat 121 of cohort C's apples in return..."

The only way they can take anything from cohort B is if they are alive at the same time.
If they are alive at the same time, and output is Y, they have a choice about how to distribute that output, no matter what some paper is saying (through e.g. taxes, which you can implement since they are alive and not dead).

When cohort A is dead, they can no longer be a burden on B.
When cohort B is dead they can no longer be a burden on C.
If A and B and C is alive at the same time, the distribution of the resourses is primarely a normative issue, and the distribution between generations will mainly be politicaly determined (through e.g. taxes on the working B´s and welfare to the young C´s and old A´s).

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