Because aggregating across people alive at a particular time is not the same as aggregating across time periods in the lifetimes of a particular cohort of people. (See JP Koning on the Borges Problem or Scott Sumner).
[Update: or does Noah get my point? because later on in the comments to his post he says: "Nick Rowe's point is that if the government borrows to consume, then it
can effectively be shortchanging the future generation, whether that
shortchanging is accomplished by reduced investment or by durable
government commitments to future net transfers. This is also a good and valuable point." Dunno.]
[Update 2. OK, Noah does get my point. Sorry Noah. But there is some strange stuff going on in his model. See my discussion with Noah in the comments below.]
Noah Smith is a very smart guy, and a very good economist. And Noah totally misses my point about the burden of the debt on future cohorts. But because Noah is a very smart guy, and a very good economist, he is also beautifully clear in exactly why he misses my point. And I bet lots of other very smart people and very good economists are missing my point for exactly the same reason.
Here's Noah: "Now let's define "burden on future generations". That means that at some time T > 0 (t=0 being today), the potential consumption of the economy will be lower."
NO! That is NOT how we should define "burden on future generations". We should define it as "lower lifetime consumption (or lower lifetime utility) of future cohorts of people".
In comments, Andy Harless (who gets my point) tries to explain this to Noah. Noah responds to Andy:
"You're right that I could use
that alternate definition of "generation". But the result would be the
same, since a negative result for future times implies a negative result
for future generations, since future generations live only during
future times…..Also note that to state my point
more completely, in my response above I should have written "a future
cohort's consumption is just the union of the consumption values for various (i,t>0) pairs.""
NO! It's NOT the same. A future cohort's consumption is NOT just the union of the values for aggregate consumption at various future times when that cohort is alive.
When I was explaining my point about the burden of the debt on future generations, I deliberately chose an example in which aggregate consumption at all future times was constant, and unaffected by the debt. In other words, I deliberately assumed there was no "burden" in the sense in which Noah defines "burden". But I showed that there was nevertheless a burden to a future cohort.
Here is another example in which aggregate consumption is constant at all times and is unaffected by the debt. But the current cohort gains at the expense of ALL future cohorts:
Assume all output is consumed.
Assume people live for 2 periods, produce 100 when young and 100 when
old. Assume one person per cohort (so population is always 2). So
aggregate consumption is 200 at all time periods.
In the baseline scenario each person produces and consumes 100 each period, so lifetime consumption is 200, and aggregate consumption per period is 200.
Now suppose:
In period 0, the young in cohort A consume 100. (Same as baseline)
In
period 1, the old in cohort A consume 200, and the young in cohort B
consume 0. Aggregate C=200. Lifetime consumption of cohort A is 300.
In
period 2, the old in cohort B consume 150, and the young in cohort C
consume 50. Aggregate C=200. Lifetime consumption of cohort B is 150.
In
period 3, the old in cohort C consume 125, and the young in cohort D
consume 75. Aggregate C=200. Lifetime consumption of cohort C is 175.
In
period 4, the old in cohort D consume 112.5, and the young in cohort E
consume 87.5. Aggregate C=200. Lifetime consumption of cohort D is
187.5.
And so on.
The government borrowed 100 and gave it to cohort A to consume, then slowly reduced the debt at the rate of 50% per period.
Every single future cohort has lower lifetime consumption, even though aggregate consumption is always 200 at all time periods. There is a burden on ALL future cohorts (though that burden asymptotically approaches zero as we go into the very distant future).
Here is a second example, where all future cohorts have lower lifetime utility, even though their lifetime consumption stays at 200:
Same as the first example, except the government only borrows 50, and then taxes all future generations to pay the interest on the debt, but leaves the debt unchanged at 50 forever. So all future cohorts consume 50 when young and 150 when old. But they have a utility function U=consumption when young x consumption when old. So their lifetime utility will be 50×150, which is less than 100×100.
Update: And if the rate of interest is positive (above the zero growth rate in this economy) then the government must (eventually) raise taxes to pay at least the interest on the debt, or the debt/GDP ratio will grow without limit until the young cannot afford to buy the bonds.
If Noah doesn't get it after this, then I will despair.
Does this mean that debt always creates a burden on future generations? Emphatically no. It is possible to construct different examples where lifetime utility goes up even if lifetime consumption stays the same (because the rate of interest is always negative). Or where lifetime consumption and utility of all future cohorts goes up even though aggregate consumption is unaffected (because the rate of interest is always less than the growth rate). Or the deficit could finance investment that increases future cohorts' consumption. There may be benefits as well as costs for future generations. But until people get my point, we can't talk about the benefits and costs sensibly.
Worthwhile Canadian Initiative 
Sorry if I’m being obtuse, but what you describe as government borrowing I would call confiscation. It’s not news to me that the government can take from one group of people and give to another. But it’s confusing to call that imposition the burden of debt. It’s more like reparations imposed on the vanquished.
BTW, re your 2nd example: when Krugman writes:
— as I read it, he’s already conceding in advance the point you make there. If a policy favours the old over the young, then it can certainly diminish lifetime utility, if the young have a greater capacity to enjoy consumption (true in my case at least).
Kevin: the government borrows from the young in cohort B, then it taxes the old in cohort B, and all future cohorts, to pay interest on the debt plus retire half the outstanding debt. Taxation is confiscation.
I don’t know whether PK is conceding the point, or simply switching to Ricardian Equivalence (some people inherit the bonds) when it suits him. I really can’t make head or tail of that post of his.
But all I needed to do in this post is to show that Noah is wrong when he says “a future cohort’s consumption is just the union of the consumption values for various (i,t>0) pairs.”
What is really embarrassing for us economists is that it seems to be a lot easier for even some of my heterododox non-economist critics to basically get my point.
JKH, as far as I can see, totally gets it. Dan Kervick, I think, basically gets it, and is haggling over details. Same with rsj. And those guys will come and haggle the details in this post, totally missing the point of this post — which is that lots of really good economists are totally missing the point!
Oh God. I despair.
Nick,
You constructed your “counter-example” post in such a way as to disprove the claim that debt can’t be a burden on future generations unless something reduces future output. I think you succeeded in doing that by demonstrating a case where it holds and where future output isn’t reduced.
This may be a trivial observation (although I don’t think so), but I think you proved something even stronger than that.
It looks to me that your logic holds independently of future output entirely – i.e. it always holds (provided there is eventual taxation, as you assumed in structuring your example).
And once again, the reason that it always holds is because of a decision to tax – for whatever reason.
(But to explain why the decision to tax is critical – one must understand that it’s because of the effect of the tax on the population of bonds outstanding – not because of the effect in transferring money from one bank account to another, as Krugman erroneously thinks is the explanation for why it’s not critical.)
Again, the nature of the burden depends only on the loss of the opportunity to recoup the nominal purchasing power lost by purchasing bonds from the previous generation (or by straightforward lending to it as in your milk example), but being unable to reverse that cost out to the subsequent generation.
So Noah’s following conclusion in comments is wrong I think:
“Paul Krugman’s point is that a high level of existing debt does not mean that society as a whole has to bear a lot of “pain”, since it owes most of that money to itself, thus making it qualitatively different from a household that has borrowed money from outside lenders. This is a good and valid point.
Nick Rowe’s point is that if the government borrows to consume, then it can effectively be shortchanging the future generation, whether that shortchanging is accomplished by reduced investment or by durable government commitments to future net transfers. This is also a good and valuable point.
The points do not really conflict.”
http://noahpinionblog.blogspot.ca/2012/10/debt-and-burden-on-future-generations.html?showComment=1350168123822#c4418592659045964709
Yes, they do conflict at the end of the day. You demonstrated that the future generation can be shortchanged if the government borrows to consume – but as I noted above the reasoning you employed applies in ALL cases, regardless of how government borrowing is used or how effective it is – provided the government makes a decision to tax in the future for any reason at all in order to start paying the interest at least with tax revenue.
And I think this broad applicability if anything is reinforced by the flexibility of possible outcomes demonstrating this, as you illustrated here:
http://noahpinionblog.blogspot.ca/2012/10/debt-and-burden-on-future-generations.html?showComment=1350203921035#c2178303927502662192
And you’ve emphasized that again by including it in your post here.
Yes. Somebody – at least one – owes you a post – and probably numerous others.
And with about 9 months interest I reckon!
Your point is totally valid, yet orthogonal to almost everything that’s been written about it in the blogosphere.
P.S.
Jeez – I hope I haven’t written anything here that causes a retraction of “totally gets it”
🙂
E.g. I don’t think I’ve contradicted this:
“Does this mean that debt always creates a burden on future generations? Emphatically no.”
But I think it is the case that taxes as described do create the conditions for a future burden – always.
P.P.S.
Regarding my comment earlier regarding interest on debt in your examples:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/10/how-time-travel-is-possible.html?cid=6a00d83451688169e2017ee4276629970d#comment-6a00d83451688169e2017ee4276629970d
To recap, if there is a primary surplus, that means the government has enough tax revenue to starting paying the interest cost of the debt in cash, rather than issuing bonds for that amount.
One way this could happen in theory, but still operationally, is the following:
For a given fiscal year, the government funds its total deficit with bonds. At the end of the fiscal year, because it has run a primary surplus, it ends up with surplus cash in its deposit account (e.g. either it’s the treasury account at the central bank or its accounts with the commercial banks.) That cash will then allow it to start buying back bonds it issued to cover the interest cost component of the total deficit.
So that sort of account is consistent with the interpretation of taxing enough to allow the government to start buying back bonds, thereby removing the opportunity of the current generation to sell those bonds to the next generation.
Or, the government could simply apply the cash during the year and not issue bonds for that amount in the first place. That account is consistent with the interpretation of taxing enough such that there is an opportunity cost in terms of the government not having issued bonds sufficient to cover the interest earned by the current generation, thereby precluding the opportunity of the current generation to sell such bonds to the next generation.
JKH: “But I think it is the case that taxes as described do create the conditions for a future burden – always.”
You totally get it up to and including that point.
You are maybe a bit fuzzy on the conditions under which future taxes would or would not have to increase.
P.P.P.S.
Shoot – I STILL don’t have the words right on that (nagging) interest part.
I should just stop.
But maybe like:
“For a given fiscal year, the government funds its interest cost with bonds. At the end of the fiscal year, because it has run a primary surplus, it ends up with surplus cash in its deposit account (e.g. either it’s the treasury account at the central bank or its accounts with the commercial banks.) That cash will then allow it to start buying back bonds it issued to cover the interest cost.
So that sort of account is consistent with the interpretation of taxing enough to allow the government to start buying back bonds, thereby removing the opportunity of the current generation to sell those bonds to the next generation.”
That’s a hypothetical operation. The paragraph after that is more like what actually happens.
Nick,
“You are maybe a bit fuzzy on the conditions under which future taxes would or would not have to increase.”
I’d say I’m not only fuzzy, but oblivious – deliberately.
I leave the conditions that determine the tax decision either way entirely up to the economists. (I might have a few ideas on that, but they aren’t necessary to make my point about your point.)
I’m just saying that your logic holds if a decision to tax has been made – for whatever reason.
“In the baseline scenario each person produces and consumes 100 each period, so lifetime consumption is 200, and aggregate consumption per period is 200.
“Now suppose:
“In period 0, the young in cohort A consume 100. (Same as baseline)
“In period 1, the old in cohort A consume 200, and the young in cohort B consume 0. Aggregate C=200. Lifetime consumption of cohort A is 300.
“In period 2, the old in cohort B consume 150, and the young in cohort C consume 50. Aggregate C=200. Lifetime consumption of cohort B is 150. . . .
“And so on.
“The government borrowed 100 and gave it to cohort A to consume, then slowly reduced the debt at the rate of 50% per period.”
Are these not distributional effects?
Nick
I posted this on one of your other threads as well, but since this is most recent, here goes.
Your point holds for overlapping generations, if ‘generations’ maps equi-outcome fiscal cohorts closely, or better than ‘current taxpayers’. OLG models, including yours, sneak this assumption in. But it’s not at all obvious or intuitive.
Lifetimes are heterogeneous. Births and deaths are continuous. Fiscal timeframes are usually much smaller than lifetimes. What is the net result? I don’t know. Do you?
Are OLG cohorts with their own unintuitive, unspecified assumptions correct Borgesian categories to handle fiscal outcomes?
Okay, Nick, so now you simply say that government can redistribute between various groups of society and, as a result, make one of the groups “richer” and another “poorer”, including redistributing between the old and the young. No one contests that, I think. As I understand Krugman, this is actually the very point that he is making.
What is being contested, though, is the fact that issuance of (financial) debt within and economy PER SE can amount to an intertemporal distribution between the economy as a whole NOW and the economy as a whole at some future stage.
That is simply not true. All financial liabilities and assets in a (closed) economy always net to zero. By definition, so no matter how much debt you issue, the economy as a whole will not get richer or poorer PER SE (interest also accrues to somebody).
Any real effort can always be directed to reasonable things (improving your home or whatever) or stupid things (taking the time to break the windows in your neigbour’s home). Debt (or rather the need to pay it back) is certainly a mechanism that “forces” people to make “an effort”. It all comes down, however, to what people actually do in the REAL world. To make a slightly exaggerated point: If your cohort A starts a nuclear war in period 1, this is for sure going to result in “lower lifetime utility” for all next cohorts. But that has nothing to do specifically with debt, but everything to do with bad decision making. You simply demonstrate that we can screw up the world for our posterity. Which sure we can. But not simply by issuing debt PER SE, but by financing stupid things (and not financing smart things). But this is trivial, in my view.
BTW – what does the younger cohort consume in period 1 in your example?
Min: “Are these not distributional effects?” They are transfers that change the distribution of wealth across cohorts.
Ritwik: you are right. But this is already hard enough to explain. Everybody lives for exactly the same length of time, and every member of a cohort is taxed alike.
It is obvious that debt, both public and private, is a burden because it is a liability which limits freedom. But I have hard time believing that IMF, etc think about the path of future consumption of a particularcohort* of population when they talk about debt burden and fiscal austerity.
Or do they? I am getting completely lost now.
ps. I am a non-economist.
Nick,
I see what you mean about JKH et al. But I really don’t think your despair about the conventionally-trained is warranted. These OLG models can be quite tricky as any student knows. But with a bit of attention to notation and suchlike it’s quite possible to see whether there’s anything of substance being argued. My suspicion is that this is all semantics but I’m not sure. I’m still thinking about it. What more can I do? However I don’t set much store by the fact that non-economists accept your point. Non-economists took the likes of William Greider seriously too, which is what prompted Krugman to write books like The Accidental Theorist and Pop Internationalism. Sometimes common sense works better than buns-and-burgers theory, sometimes it doesn’t.
The key to understanding Krugman is to refrain from reading more into his words than his target audience would. For example: “what people mean when they speak about the burden of the debt on future generations…is that America as a whole will be poorer, just as a family that runs up debt is poorer thereafter.” Here, he clearly does not intend ‘poorer’ to be equated with lower utility. He’s talking about disposable income. In a closed economy the disposable income of a representative household is unaffected by the level of debt. In one respect I think you have refined Krugman’s argument. He writes: “Suppose that after the 2016 election President Santorum tries to buy senior support by giving every American over 65 a gift of newly printed government bonds; then the over-65 generation will be made richer, and everyone under 65 will be made poorer (duh).” Your first example, above, shows how that sort of transaction can form part of a chain which harms a number of generations rather than just one. I don’t think Krugman would dispute that. He would simply refuse to label it “the burden of debt” and AFAIAC he’d be right.
Sergei,
The IMF is mostly concerned with open economies, where the burden of debt mostly comes from (a) the fact that it’s often owed to foreigners and (b) it distorts incentives. All parties to the present dispute are agreed on that, I think. This is really all about the theory of closed economies where (for purposes of the argument) distortions are assumed away.
Nick
I’m saying the reason your model, though obviously correct in its universe, is not breaking much ice is because our intuition of ‘equi-fiscal outcome’ is much more developed than an OLG model, or a Ricardian equivalence model, or a ‘we owe the debt to ourselves model’. And our formal models are foreverprey to Wittgensteinian traps because they refuse to define baselines. (Also because, in economics and the internet, it seems to be a cardinal sin to ever admit that the other person is right.)
This might be another one of those cases where there is so much tacit knowledge that simple models, whether of the Dean Baker kind or the Nick Rowe kind, are actually very unintuitive.
Kevin Donoghue, and why is private debt different whether it is an open or closed economy? For one thing changing all private contracts might be really difficult however changing the terms of the public debt is a much easier task. And it happens all the time. So how come private debt is completely ignored while public debt is given so much attention?
Sergei, those are interesting questions but way off-topic. I agree private debt deserves attention.
Layperson foolishly sticking my head up to ask a question: Is this all because Krugman and Nick have different definitions of wealth, poverty, burden, etc?
Brett: No. It’s because we define “the future” differently. Does it mean “future times”, or “future people”?
Nick,
Here’s the right geographical analogy:
Someone on the east coast steals some milk from someone further west, arguing that the victim can just steal it from someone even further west. Assuming the continent is infinitely big, no problem right?
You want to argue that the first thief places a burden on everyone else. The way I (and also the law) see it, every thief is equally culpable. Having been a victim yourself has no bearing on guilt. So it seems you need a very unconventional view of morality to view the problem in terms of transfers between people not concurrently alive.
There there are a few principal roots of the problem:
1) the political power imbalance that enables the old to steal from the young
2) the inability to identify with distant future victims (thieves often think like this – the victim has insurance right?)
3) the fallacy that humanity can last forever
Moi: “Are these not distributional effects?”
Nick Rowe: “They are transfers that change the distribution of wealth across cohorts.”
I brought that up because, IIRC, in 2011 Dean Baker explicitly stated that gov’t debt could have distributional effects on future generations. Krugman, as I recall, did not state that, and was less precise overall than Baker.
But didn’t Dean mean “distributional effects within future generations”? Dunno.
Well he’s right then. There are no effects that transcend time. Each generation must make a decision to make up its loss by stealing from its kids.
No no no. This is all wrong. Nick, I love ya, man, but no.
Look, your entire point is that the pre-debt distribution of consumption (within periods and across periods) is Pareto efficient and therefore the redistribution that debt implies makes future generations worse off. That’s a fallacy, because it ignores the counterfactual and the benefits the debt generates through funding projects.
More importantly, when people come on the TV and talk about the future debt burden, THEY ARE NOT TALKING ABOUT WELFARE LOSSES FROM REDUCED CONSUMPTION SMOOTHING. That’s the basic point of Noah, Krugman and Baker and when you attack them over this, to me, you come off as small (I’m sorry to be so frank, but it’s true). Noah’s right by his definition, you’re right by yours–Noah’s case is against the more common understanding of debt burden (that it makes us collectively worse off).
BSE: Thanks for being kind (I mean that)!
But I reckon that when people come on TV and talk about the burden they are talking about the extra future taxes (or reduced future spending) that will be needed to service the debt, and the burden that creates. And those future taxes DO make people worse off (perhaps via a loss in future welfare through less consumption smoothing, even though the TV people won’t put it that way).
And the right way to argue against them is to say:
1. Yep. But think of the benefits too!
or
2. Nope, because r will always be less than g, so we can rollover the debt forever and never increase taxes.
Debt is only well defined within a particular economic model. The reason is simply that it’s a contractual relationship and depends for its existence on contract law, the creditor’s realistic ability to draw on the coercive power of government to enforce it and social norms involving debt.
It is possible at any future point for the terms of the debt to be rewritten in bankruptcy, a government to interfere with the terms of the debt or, in many cases, for the debtor to just walk away. We put these under the general headings of systemic and counter-party risk.
When you pose your various hypotheticals, you include in them explicitly or implicitly rules concerning the future treatment of various debt instruments. If you assume such budget constraints are unconditionally binding, you impoverish your model to a point that it models scenarios that can never happen in practice (This is in the face of an average of something like one European sovereign debt default every 3 years).
This doesn’t mean debt can’t be a burden on the future, but rather that the means by which it is a burden require events which most of the current economic models deliberately ignore as unnecessary complications – like credit risk, revulsion and contagion, the role of financial firms in exploiting their superior information, divergence of interest and incentive between fund beneficiaries and fund trustees etc.
In short, Other Peoples’ Money, the fundamental source of profit in the financial system.
You get several different kinds of burdens on future generations (regardless of how you define them).
1) Uncertainty through floating unrealized losses. For instance, the GSE’s took huge losses at the beginning of the recession, but these losses weren’t final. The GSE’s had contractual rights with the originators that would force them to repurchase any loans found to be substandard on audit. They are now suing the banks to recoup FIVE YEARS later. In the meantime, nobody knows what the eventual financial status of the banks will be IIR BOA has another $20 billion of exposure not including any claims for punitive and consequential damages.
Of course handling these matters in the courts is expensive and slow. The lawyers are still working on Lehman and will be for some time.
2) Loss from contagion. Failure of one member of a class of assets increases the risk premium of other members of the same class. The friction from this can be extremely expensive, as it has been for Spain and Italy. The damage to their economies from increased cost of funds has been vastly out of proportion to any actual risk.
3) Revulsion can remove classes of securities from their moneylike status as low information repo collateral. This is an effective tightening of the money supply (of about $4 trillion).
4) Conflict over debt can force debtors and creditors into confrontations that damage both sides (and innocent bystanders) to an extent that vastly exceeds the amount of debt in dispute. The damage that the Greek debt crisis will cause Germany is enormous. For a start, it’s forcing them and their major trading partners into recession.
5) In the US, political divisions fueled by intensive lobbying by interested parties has prevented any timely resolution to the mortgage crisis, while meanwhile a student loan bubble and crisis is becoming inevitable.
6) And we have to include under debt unfunded state and local government pension liabilities.
This is the real future burden, creating a swamp that our children will have to drain. It doesn’t much matter how you categorize it, if you can force future resources to be expended, you create a burden.
Here’s one way of explaining why I don’t think Nick’s story should be described as an illustration of the burden of debt. As he tells it, the consumption of the old in each period follows this sequence: 100, 200, 150, 125,… The consumption of the young follows this sequence: 100, 0, 50, 75,…
Suppose instead that the rip-off is reversed. It is the old who get 100, 0, 50, 75,… while the young get 100, 200, 150, 125,…
“Government debt” is negative. The government is in credit throughout. The lifetime income of the generations follows the sequence 200, 100, 250, 225,…
If Nick’s example is to be called the burden of debt, what do we call this, the bounty of credit? It’s neither. It’s just one group of people being ripped off for the benefit of another; business as usual, some would say. The fact that the government is in the black throughout doesn’t make it any better than the case where government is in the red.
Suppose a certain amount of debt is issued.
Suppose there are two possible future states of the world.
The first, R, where the debt is used wisely, and society is relatively rich.
The second P, where the debt is used unwisely, and society is relatively poor.
Consider future cohorts C (n) and C (n +1).
Suppose these two cohorts include all people living at some future point in time when a tax is imposed to pay down some of the debt (or cover interest on the debt as Nick has emphasized).
Suppose, at that time, C (n) holds all the bonds.
According to Nick’s model, C (n) will incur a debt burden equal to the amount of bonds and/or interest that this cohort will no longer hold in the form of bonds, as a result of the taxed being imposed. That should be clear from the model.
C (n) incurs that burden regardless of whether the world is in state R or state P at that time.
Nick’s model does not compare state R to state P under such conditions.
It compares the case of burden to no burden, implicitly under either intra-R or intra-P state assumptions.
The model is also unaffected by what the distribution of taxation is across C (n) and C (n+1).
If C (n) pays the entire tax or if C (n +1) pays the entire tax or if any combination of taxpayers from the two groups pays the tax – Nick’s model and its conclusions still hold.
Nick’s model concludes nothing about such comparative tax distributions, just as it concludes nothing about comparative future states R and P.
Obviously, the incidence of the tax makes a difference to the final wealth positions of members of C (n) and C (n + 1).
But it doesn’t change the marginal impact of the tax on the holders of the bonds, assumed to be C (n), in terms of the burden as defined.
The only thing that matters is the tax and the fact that C (n) no longer has the bonds that it would have had (and sold to C (n + 1)) without the tax.
That’s what Nick’s model says, IMO.
It shouldn’t be criticized for what it doesn’t purport to say.
And what it does purport to say can’t be proven false, IMO.
Kevin,
Exactly. Or you do it without debt at all. The old just tax the young to fund their retirement. It’s just repeated theft, no more justified just because each generation was victimized by the one before it (see my geographical example above).
Kevin: Neat! The government taxes the old in cohort B, and lends it to the young in cohort C? Then slowly gives away the government credit at 50% per year? Either way, apples are (as if) travelling in time, either forward or backwards.
No, the government taxes the old in period 1 (they got 100 in period 0 when they were young) and gives the 100 to the young in period 1, etc. It’s just your example with the signs reversed. Or did I screw up some numbers? I’ll check.
Sorry, my (somewhat defensive) reaction was to assume the “Neat!” was sarcasm, but maybe that’s not what you meant? Yes, the illusion of travelling apples is created in both your example and mine. But of course there’s only 200 consumed in each period.
Nick,
Yes. But not without consent of each cohort to perpetuate the crime. Any cohort can say no thanks. That’s not my problem. It’s between you and your parents.
Govt debt can affect both the size and the shape of future output and the distribution of that future output.
If the govt borrows some money that would otherwise have gone into private investment and spends it on govt consumption instead then this will (other things being equal) have a real affect of the level and shape of future output.
If the govt makes a commitment at the time the debt is created to how the debt is going to be repaid then it is possible that the fulfillment of that commitment may lead to everyone in a future generation being worse off (or better off if you set up your assumptions differently).
However while effects of the first type (size of future output) are irreversible (goods consumed rather than used for investment cannot br recovered) the effect of govt commitments about debt repayment can be eliminated at the stroke of a pen if the future govt chooses.
For this reason I think that discussion about the effect of govt debt on future output are much more relevant to the real world than discussions of the effect that debt will have on the future distribution of consumption. Ricardian equivalence based on expectations of future govt policy is likely to bring those effects back into the present anyway.
Kevin: My “Neat!” was for real. (I’m not very good at sarcasm, so don’t do it.) But I think we are saying the same thing about who gets taxed etc.
Thank God! I get some serious support!
An important corollary is that when r < g, the government should issue more debt for the sake of efficiency. Not issuing the debt is a form of waste. Or is there some alternative policy you would recommend for situations when r is less than g?
Kevin,
Nick’s model is about the debt and his definition of the debt burden.
It involves the cyclical sale of bonds from old to young.
That produces a cyclical transfer of purchasing power from young to old.
That process becomes impeded when taxation reduces bonds outstanding.
It’s the reduction of bonds outstanding that reduces the amount of purchasing power transferred from the young to the old, compared to the purchasing power the old gave up when they bought the bonds.
That is what constitutes the debt burden in Nick’s definition.
In Nick’s first model, that reduction occurs at some future time due to taxation at that time.
In Nick’s subsequent model, that reduction starts early. It resembles an annuity process whereby periodic taxation erodes the principal value of bonds outstanding steadily over time. The reduction in purchasing power transferred from the young to the old starts early and is progresses in steps over time. As there are progressively fewer bonds outstanding, the young purchase fewer bonds over time and retain more of their income for consumption. The old sell fewer bonds over time, and each successive cohort of the old still incurs a debt burden as defined, because what they are selling is less than what they bought, due to the annuity like nature of the taxation over time.
And as I said in my previous comment, the incidence of taxation is irrelevant to what Nick’s model demonstrates.
So I understand all that I think/hope.
But I don’t understand how your latest inverted sequence develops over time relative to debt and tax patterns, or even what it has to do with debt or the inter-generational transfer of debt or with what Nick has defined as the debt burden.
Haven’t spent much time on it yet though – can you elaborate/help/kick start me on this?
Thanks for saying I basically get it Nick. But I don’t think the point about consumption vs. investment is just a detail, and I think this is an issue Noah addresses too.
It seems to me that all you have shown is that if a society uses public borrowing at every given time to shift consumption from younger cohorts to older cohorts alive at that same time, then you can get long term outcomes like those you have described, with later cohorts suffering a net overall reduction in utility from what they would have enjoyed otherwise.
But if a society uses public borrowing to reduce aggregate consumption and boost aggregate investment, then you can get the opposite result.
I just don’t want people to come away from your posts thinking, “Rowe has proved that public debt burdens posterity.” You haven’t shown that. You have just showed that public debt could be part of public choice regimes that burden posterity. But I want to claim it is equally true that public debt could be part of public choice regimes that benefit posterity. So one policy issue is how to make sure we get the latter rather than the former.
And I think the background context here is that there are a whole host of pundits in the public debate who don’t get the more elementary point that when debt liabilities are transmitted from one generation to a later generation, debt assets are, as a matter of elementary accounting logic, transmitted along with them. They think that the future generation is stuck having to pay back debts, but that somehow the people to whom they are paying them back aren’t part of that generation. You might think that error is too dumb even to be considered, but it’s an error that is widespread and driving much of the public debate. Your counterexample isn’t supporting this man-on-the-street common sense. You are accepting it is wrong and presenting a possible case in which later generations are nevertheless harmed by bad public choices involving public debt. But we can still borrow and not make those policy choices.
primed: ” Or is there some alternative policy you would recommend for situations when r is less than g?”
There possibly is some, but I can’t think of it. (An unfunded government pension plan might be called an “alternative” but it’s really the same thing from the macro POV). If r < g, there’s needs to be a bubble/Ponzi scheme, and the government might as well be the one that runs it (I expect that’s debatable).
What scares me is if we don’t know whether r will be less or greater than g in future.
Dan: “But I don’t think the point about consumption vs. investment is just a detail, and I think this is an issue Noah addresses too.”
Agreed, it’s not a detail (though I have been assuming it away to make my point more clearly). It’s a biggie.
But I think it matters which cohort owns that investment (or if the government owns it). And most of the economists opposing me just look at aggregate investment and ignore the fact that if the current cohort owns it, and sells it to future cohorts, that has no direct benefit on future cohorts. (It might have an indirect effect via higher capital stock leading to higher labour productivity leading to higher wages of the future young.)
It’s exactly the same with debt owed to foreigners. That is no more or less a burden on future cohorts than debt owed to old guys at home.
Nick: You appear to have misunderstood my claim. Check my reply to your comment on my blog for the full explanation.
“NO! It’s NOT the same. A future cohort’s consumption is NOT just the union of the values for aggregate consumption at various future times when that cohort is alive.”
Correct. A future cohort’s consumption is the union of some set of values of INDIVIDUAL consumption at the times when that cohort is alive.
Noah: I thought “i” was “investment”!
I’m sorry if I’m not getting the fact that you are getting my point.
But I still don’t understand your post. Are you saying “If the government wanted to, it could borrow and spend, and then immediately pay off the debt by taxing all the people who are still alive but who weren’t born when it made that decision to borrow and spend, so the debt doesn’t create a burden on the unborn (unless it reduces future output)”?
JKH,
All I wanted to do was argue that the story Nick tells is not one of a debt burden, as simple Sean Citizen understands that term, but rather a simple consequence of the fact that government has power to tax and transfer. In my reworking the direction of the rip-off is reversed. In period 1 the government levies a tax of 100 on old cohort A and lends it to young cohort B to consume, then writes off half the outstanding loan in each period; in period 2 cohort B (now old) pays back 50 in tax, which the government lends to young cohort C to consume, etc. So at all times government is a net lender to the private sector. Angela Merkel would approve!
Dan Kervick: “And I think the background context here is that there are a whole host of pundits in the public debate who don’t get the more elementary point that when debt liabilities are transmitted from one generation to a later generation, debt assets are, as a matter of elementary accounting logic, transmitted along with them. They think that the future generation is stuck having to pay back debts, but that somehow the people to whom they are paying them back aren’t part of that generation.”
Very important point about the context of this discussion.
@ Nick Rowe
I dunno, either. 🙂
Let’s stop pretending that ‘smart’ = someone who can master a bit of mathematical formalism & apply it willy-nilly.
To put it bluntly, idiot savant does not equal ‘smart’.
Greg: in general yes. But Noah is smart.
I would like to make a comment on the following.
“In the baseline scenario each person produces and consumes 100 each period, so lifetime consumption is 200, and aggregate consumption per period is 200.
“Now suppose:
“In period 0, the young in cohort A consume 100. (Same as baseline)
“In period 1, the old in cohort A consume 200, and the young in cohort B consume 0. Aggregate C=200. Lifetime consumption of cohort A is 300.
“In period 2, the old in cohort B consume 150, and the young in cohort C consume 50. Aggregate C=200. Lifetime consumption of cohort B is 150.
“In period 3, the old in cohort C consume 125, and the young in cohort D consume 75. Aggregate C=200. Lifetime consumption of cohort C is 175.
“In period 4, the old in cohort D consume 112.5, and the young in cohort E consume 87.5. Aggregate C=200. Lifetime consumption of cohort D is 187.5.
“And so on.
“The government borrowed 100 and gave it to cohort A to consume, then slowly reduced the debt at the rate of 50% per period.”
What happened at period 2? Why did cohort B give up all of their consumption to cohort A (somehow staying alive)?
After that, why did the gov’t slowly reduce the debt over time?
An obvious answer to the last question is that people would like to even out their consumption, but doing so abruptly would penalize the older generation unnecessarily. (As for never doing so, see Zeno. ;))
What about the first question? If people prefer even consumption, why did they have a massive transfer from young to old? OC, there are any number of possibilities. Perhaps an epidemic afflicted the old without killing them, and cohort B spent 100 to take care of their elders. In any event, they took on the burden.
Then cohort C elected to take part of the burden of cohort B off of their shoulders, cohort D elected to take on part of the burden of cohort C, etc., etc.
Then the story becomes not that the gov’t debt was a burden to cohorts C, D, and so on, but that it was the instrument through which future generations could share the burden of their forebears.
Boundary conditions matter. 🙂
Heh. Thanks for saying I’m smart…
My proof says that given some assumptions (e.g. costless transfers), the consumption possibilities of any cohort not alive at time t=0 are independent of the stock of debt at time t=0.
So in your basic example, at time t=0, the government has transferred consumption from the t=0 young to the t=0 old. At time t=1, consumption is transferred from the t=1 young to the t=1 old through the mechanism of the exchange of government debt. But in this example, the government could implement a tax-and-transfer system at time t=1 that would exactly cancel out the consumption transfer from the t=1 young to the t=1 old. If this were done, the net consumption transfer across all 3 cohorts would be from the t=0 young (who are the t=1 old) to the t=0 old, with the t=1 young experiencing no change in consumption relative to the counterfactual in which the government made no t=0 transfers. So if this happened, the t=0 young (t=1 old) would be screwed. However, this generation is not a “future” generation in t=0, since it is alive at t=0. That’s really the key to the proof – the definition of “future generation”.
Now, if the government can pre-commit to future NET transfers, my proof obviously breaks down. In this case, government debt may entail a pre-commitment at time t=0 to transfer consumption from, say, a cohort alive at t=132 to a cohort alive at t=0. In this case, the debt can impose a burden on future generations, even using my definitions of “future” and “burden”.