I thought we all had this debt burden stuff sorted out 30 years ago. Obviously we didn't.
We should have had a bigger argument about it 30 years ago, which would have sorted it all out. But we didn't. Maybe because we spent all our time arguing about other stuff 30 years ago, and didn't have time to argue about this stuff as well. Or maybe because most of us were too embarrassed to mention we had totally changed our minds on this, and that the views we used to say were uneducated views were in fact right after all. So we silently changed our beliefs, and tried to forget we had ever believed anything different. But not all of us noticed this change in beliefs, and still thought everybody else believed what we all used to. So now we are re-fighting the old ground we should have fought properly 30 years ago.
There are 4 possible positions to take on the debt. One of them doesn't make sense; the other 3 do. Which of those 3 is right is an empirical question.
Here are the 4 positions. I gave each one a name. I made up the quotes.
1. Abba Lerner. 'The national debt is not a first-order burden on future generations. We owe it to ourselves. The sum of the IOU's must equal the sum of the UOMe's. You can't make real goods and services travel back in time, out of the mouths of our grandkids and into our mouths. The possible second-order exceptions are: if we owe it to foreigners; the disincentive effects of distortionary future taxes; the lower marginal product of future labour if the future capital stock is smaller.'
2. James Buchanan/uneducated person on the street. 'The national debt is a burden on future generations of taxpayers. Foreigners are basically irrelevant. Any second order effects of distortionary taxes and lower capital stock are over and above that first order effects of the taxes themselves.'
3. Robert Barro/Ricardian Equivalence. 'The national debt is not a burden on future taxpayers (except for the deadweight costs of distortionary taxation) but only because ordinary people take steps to fully offset the burden on future generations by increasing private saving to offset government dissaving and increasing bequests to their heirs to offset the debt burden.'
4. Samuelson 1958. 'If the rate of interest on government bonds is forever less than the growth rate of the economy, the government can run a sustainable Ponzi finance of deficits, where it rolls over the debt plus interest forever and never needs to increase taxes, so there is no burden on future generations.'
I personally was taught 1 as an undergraduate. And I believed in 1 until about 1980, when I spent some time reading Buchanan and Barro arguing with each other. And I worked 4 into my own beliefs soon after.
And now, I believe 1 is false. The truth is some sort of mixture of 2,3, and 4. What precise mixture of 2,3,4 is true is an empirical question. My prior is one third-one third-one third.
Until last week, I thought that almost every macroeconomist had now realised that 1 was false. And I wrote a post arguing 1 is false. My post was triggered by Paul Krugman's recent post, which I interpret as saying that 1 is true. Paul wrote two later posts too, which I interpret as also saying that 1 is true.
Many other bloggers have now waded into this debate. Good! Finally (I was scared we were going to keep on ignoring this question)! Bill Woolsey. Greg Mankiw. Don Boudreaux. Karl Smith. Daniel Kuehn. Jim Hamilton. Noah Smith. (I must have missed some. Sorry.)
And look, just because deficits have costs doesn't mean we shouldn't do them. Like a lot of things, deficits have benefits too, and sometimes the benefits are bigger than the costs. But we shouldn't ignore those costs, just because we think the benefits are bigger than the costs.
And what we need to do more work on is this: we know Samuelson is right, if we know for sure that the interest rate on bonds is less than the growth rate of GDP forever. That is a sufficient condition for Samuelson being right, but I rather doubt it's a necessary condition. What if the interest rate will probably be less than the growth rate part of the time for a rather long time? Could Samuelson still be right, or at least partly right?
I really wish I could get my head around that question, but I can't. My hunch is that NGDP bonds would play a role in the solution, because a bond indexed to nominal GDP would resolve the uncertainty of whether the interest rate would be above or below the growth rate of GDP. And if we got the duration of those NGDP bonds right, we ought to be able to get around the problem of r being sometimes greater and sometimes less than g. Somehow, it just must be possible to eat the Samuelsonian free lunch, even if it's only a temporary and uncertain free lunch. And NGDP bonds just must be the way to eat it, somehow.
And if I could only get my head around that question, I might come up with something that would make both Scott Sumner and the MMT guys very happy indeed. Which would be neat. Plus, as a side-benefit to making both those guys happy, it might be very good for the poor ignorant uneducated slob on the street too.
But my brain just can't figure it out, yet. Maybe some of you younger, keener, brighter, people could work on this?
Worthwhile Canadian Initiative 
What about the current case, where interest rates on bonds were below the growth rate, until it reversed (Greece, Spain, Italy, etc). In this case the debts looks sustainable precisely because of 4, but after the interest rates grew above growth rates, the speed of disaster was unpredictably quick. Thoughts?
Anonymous: the Eurozone countries are a little but different, because they can’t print money and act as lenders of last resort to themselves. That means they can get stuck in a bad equilibrium where there’s a “run” on their bonds in much the same way there can be a run on a bank. The danger for “printers” like Japan, US, UK, etc., is a bit different. When/if the recession ends, and desired saving and investment return to normal, what will happen to the equilibrium real interest rate? My guess is that it will rise. If it rises above the long-term real GDP growth rate, those countries will have to increase taxes to avoid a snowballing debt/GDP ratio.
If it weren’t for the political incompetence, I wouldn’t worry much about the US. But Japan has a rather high debt/GDP ratio.
NGDP bonds could, I think, fix this problem. They would act more like equity than debt.
But I don’t understand this issue as well as I wish I did.
Well Anonymous, I guess we can say that 4 holds true… until it doesn’t hold true anymore. Of course, it is conditional on the interest rate staying below the nominal growth rate of the economy. In the case of Greece, investors really got alarmed about its debt situation when it was revealed that the Greek government had been systematically understating the amount of its borrowing. When the borrowing figures were revised upwards, there were no corresponding upward revisions to nominal economic growth. So it really was the case that deficit-funded government spending led to less GDP growth than previously stated.
Sometimes I wonder if there is a conventional economics (not involving behavioural economics) explanation for why investors seem to swing from confidence to hysteria and back over time. Keynes seemed to resort a kluge by referring to “animal spirits”. I realize that the current surge in peripheral European government bond yields can be partially rationally attributed to the need for European banks to deleverage in order to meet heightened capital requirements, which has become of a bit of a vicious cycle. Are investors and their intermediaries, such as banks, supposed to be rational economic actors? Or is there some kind of confidence explanation that can only be explained by behavioural economics and psychology?
But, wouldn’t you agree that the relevance of this debate really revolves around the more crucial question: whether the accumulation of debt (i.e. government spending) positively contributes to economic growth? (Not just positively contributes, but does so in a way that is superior to any other possible alternative given a certain set of conditions.)
Jonathan: Yep. If the government can find an investment that has a rate of return above the interest rate on bonds, then it should do it. The benefits of the investment exceed the costs of the debt. Net plus for future taxpayers.
Jonathan,
I think what’s interesting about that is that the question of whether the deficit increases growth has different relevance for different scenarios.
For example, if you accept 1, then it doesn’t really matter if deficits increase growth, since they don’t (allegedly) impose any cost. Same for 3 (because of Ricardian equivalence).
On the other hand, if you believe 2, then the possible benefit of a deficit is relevant to determining the net benefit of that deficit.
Finally, in 4, samuelson essentially incorporates the benefit of the deficit into the no-ponzi condition. Essentially this is a generalization of (1) and (2), if the deficit increases growth such that ponzi finance is feasible, you end up in 1. If not, you end up in 2.
Damn you’re good.
Thanks from your friendly neighborhood poor ignorant uneducated slob on the street.
“I really wish I could get my head around that question, but I can’t. … something that would make both Scott Sumner and the MMT guys very happy indeed”
Where’s Steve Randy Waldman when we need him? You out there Steve?
Nick, the stock market seems a clear candidate for that with an 6-8% return a year. Hell, even corporate bonds do pretty well. The trouble however is that this kind of ‘socialization of investment’ will not work. The government is not risking its own resources, the return is conditional on people selecting those stocks and bonds with their own resources at risk. And if, you cannot imagine the government to do that successfully why would you expect them to pick investment projects with a higher return outside a market setting?
What my point is, is that looking for investment opportunities that exceed the interest rate on its bond is not the job of the government and cannot be its job. Thinking about the accumulation of debt in terms of rate of return on investment seems simply wrong to me.
Regarding your original question: “What if the interest rate will probably be less than the growth rate part of the time for a rather long time? Could Samuelson still be right, or at least partly right?”
I would frame it in terms of NGDP * (1 + r_t)^t >= B * (1 + i_t)^t, where NGDP is NGDP, r_t is the growth rate of nominal spending at time t, B is the government debt and i is the rate on government debt at time t. So what you’re asking essentially is how would the path of r_t have to be relative to i_t for Samuelson to be still right? Is this what you’re asking? If so, I am not sure whether you can prove it, but you certainly should be able to run simulations of different scenario’s. You could probably reduce the simulations by making a model that relates i to r and to NGDP and B.
I attended a chat by Dr. Torben Drewes of Trent University, a macroeconomist, given to a local business gathering. He argued, in simple but clear terms, for [1]. However [1] depends on government debt being treated as akin to money in that it has no default risk. You can manage this if you print your own money but it does require work.
[4]is actually a corollary of [1], [4] relates to the interest burden and [1] relates to principal. [4] is actually of wider application because it’s the justification for defined-benefit pensions. Classically (prior to 1990) government employee pensions were invested in government bonds or simply noted as an obligation to be financed, such as the Federal Government’s Superannuation Account for Public Service pensions. Private sector pensions were financed on the assumption that the growth rate of the economy was greater than the government prime bond rate and therefore DB pensions weren’t a direct burden for the private sector either.
The trouble is that we have managed to work ourselves into cases where either [1] or [4] don’t hold for a few years and then we panic.
Bob Smith: “Same for 3 (because of Ricardian equivalence).”
Minor disagreement there. Barro would say that the government should go ahead with the investment, but it doesn’t make any difference whether it is financed by taxes or by deficits.
Steve: Thanks! (Yeah, the “poor uneducated slob on the street” bit was supposed to be ironical.)
Steve Randy Waldman might take a good crack at it. I keep trying to figure it out, then I find myself thinking about NGDP perpetuities whose value exceeds infinity, getting muddled, and giving up.
Matt Yglesias gave an interesting defense of Krugman’s position: http://www.slate.com/blogs/moneybox/2012/01/01/why_debt_doesn_t_burden.html
Krugman’s argument for #1 may be that #2 only tells half the story: “The national debt is a burden on future generations of taxpayers. … But it is also a blessing to future generations of bondholders, and the two cancel out.”
I don’t understand why Krugman ignores the distributional effects. If bondholders are on average wealthier than the uneducated person on the street, then #2 is still right when you look at important subsets of the country. Maybe he assumes that taxation will be progressive enough to offset the difference?
Martin: Yep, if the government started running a stock mutual fund, I’m not sure how well it would do, and for how long the interest rate on government bonds would be less than the returns on its portfolio. Plus, this would be a leveraged bet on the stock market with the taxpayer taking the residual risk. Would that residual risk be properly priced? Hmmm.
“Is this what you’re asking?”
I don’t know. It’s one of those cases where if I could formulate the question properly it should be easily solvable. Or, if I already knew the answer, I would be able to formulate the question properly. I’m just not clear enough on either question or answer to say.
Determinant: Torben will not be alone. My late colleague TK Rymes, an unreconstructed Keynesian, always believed 1. (And he would sometimes joke, just to tease “What’s posterity ever done for me?”
I think that 1 and 4 are very different. 4 says the government never needs to increase taxes, and that’s why it’s not a burden. 1 says it doesn’t matter whether the government does or does not need to increase taxes, because it’s never a burden in either case.
JeffreyY: Thanks for the Matt Yglesias link. Oh dear. Matt’s not getting it either. I wonder if Matt has read my post?
“If the rate of interest on government bonds is forever less than the growth rate of the economy”
Is that the nominal or real growth rate?
In point number one should the made up quote be “unless it is denominated in a foreign currency” rather than “unless we owe it to foreigners”?
What I’ve read of Lerner and others of that lineage down to current MMT’ers indicates a stance that how the debt is denominated is the determining factor, not who holds the bonds.
If 1 or 4 is true then why are we paying taxes. Let’s print (borrow) everything… Hmmm, our american friends are borrowing close to 50 cents for each dollar spent by the gov. This is pretty close to our defunct Social Credit Party’s theory.
If we follow that strategy, at one point in the future, even with all IOU issued by Canadian banks or the BoC (no outside debt), the market will lower the value of our C$ causing price inflation and eventually we will have to stop printing/borrowing or our money will be worthless. The drop in value of our C$ would most likely trigger a raise in interest rates meaning that Samuelson’s condition no.4 would not be met.
If I’m wrong then I just can’t see why the ECB is not printing more without all those governments having to cut expenses to reduce their deficit.
Nick:”if the government started running a stock mutual fund”.
It runs something much simpler and much better, the ultimate index fund aka taxing GDP.
It is more stable than interest rates and thus bond valuations ( including the not-a-burden-corporate ones), much more stable than corporate profits and avoid the wild girations in animal spirits that affect stock prices. There aren’t any of the random distributionnal effects from one individual having to sell or buy at momentarily out of whack prices. And it avoid commissions paid to the parasitic brokering services. Maybe slightly OT but Determinant opened the wedge…
W Peden: Either: nominal interest rate and growth rate of nominal GDP; or real interest rate and growth rate of real GDP. Same thing either way.
geerussell: there are times when it matters, like in the Eurozone right now. If there’s a “run” on government bonds, or if you need to loosen monetary policy in a recession, or if you want insurance against shocks, then it is much better to borrow in your own currency. But a government which borrows in its own currency still faces a budget constraint (unless 4 is true). You can inflate away the debt with a surprise inflation. But anticipated inflation simply means the nominal interest rate rises one-for-one with the inflation rate, and so printing money doesn’t help you pay down the debt. (There is a limit to the real seigniorage revenue from printing money).
Normand: If 4 is true we should not be paying taxes at the margin. We should cut taxes, and increase the debt, until the interest rate rises to just equal the growth rate of GDP.
Given the ECB faces a disinflationary recession, the ECB should be printing more money.
Jacques: I think that’s on topic. I don’t quite follow you though.
Even if the government can borrow forever at an interest rate less that the rate of GDP growth it doesn’t mean that it should be allowed to. Given a limited pool of savings then in a free market the borrowers who are prepared to bid up the interest rate to the highest level based on their current valuation of how that money should be spent will be the ones who get access to a share of it. The government will always be in a position to outbid the private sector because of its ability to tax and print money to pay future interest.
I would like to suggest the following to make sure that the government only borrows when it is optimal to do so:
1. make taxation optional
2. make currency creation open to anyone
This will ensure that when the government borrows money it is competing fairly with private borrowers.
Liquidationist: You might like this old post of mine:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/03/do-we-need-a-bubble.html
Governments that borrow in their own currency have an unfair advantage: they can’t default for lack of funds, but they can generate inflation. Therefore they have less credit risk than private businesses by structure.
Finance is sooo much easier when you operate the tax office, the central bank and the printing press.
All you need is a helicopter and away you go.
Nick: I was following Determinant’s point “4]is actually a corollary of [1], [4] relates to the interest burden and [1] relates to principal. [4] is actually of wider application because it’s the justification for defined-benefit pensions”.
That’s an interesting article but I don’t really get why there is a bubble involved. It seems to me its just a combination of altruism and self-interest that make the interest rate 0% rather than infinity. If there was a government in the picture I think there is a good chance it would inflate the money supply and reduce the value of the money savings needed to make the model work.
In any case if there was a bubble and it burst don’t the Market Monetarists know how to fix that ?
Nick:
“Would that residual risk be properly priced? Hmmm.”
I have a hunch and my reasoning is as followed:
1. Opportunity cost is the cost to the decision maker of the foregone alternative at the time of the choice.
2. If the market is perfectly competitive the opportunity cost is equal to the price.
So the price of the residual risk depends on the utility function and expectation of the decision maker and on the market structure where the risk is priced.
Assuming benevolence, the question becomes one of expectations and market structure. In the case of the EMH the risk will be properly priced and the decision maker will know what to expect. The question then is, is the presence of government on the market consistent with the EMH? I think it is not and this has to do with how capital is raised by the government: through taxation. Because of this, the decision maker can never know what the opportunity cost is to the tax payer and therefore the risk can never be properly priced.
“I don’t know. It’s one of those cases where if I could formulate the question properly it should be easily solvable. Or, if I already knew the answer, I would be able to formulate the question properly. I’m just not clear enough on either question or answer to say.”
Would it help to assume that there is some value of (B * (1+i_t)^t)/(NGDP * (1+r_t)^t) that will make a mess of things and you want r_t and i_t to be such that that value is never reached at any time t?
Nick: First, thanks for excellent post and for stirring this debate that I find more and more at the root of differences between various schools of thought about the response to the crisis.
However as for your post, I still think that Aba Lerner position is right. First thing is – how do you define “burden” and “income”? If we define burden as anything that decreases the ability of future generations to produce and income as the sum of the things they produce (and sell), then clearly position 1 is right (ignoring disincentive and distortion effects of taxation). This is the key.
So generally speaking it is not government spending that is a burden, but neglect of investment and giving up on capital formation for the sake of consumption. For example imagine a fictive state where its government has a policy that says that 30% of GDP must be in investment. And if private sector does not deliver, then government will start “spending” on infrastructure, basic research and other forms of investment to reach this ratio. Such society is clearly committed to build up the wealth to be used by their children – even if this additional investment spending is financed by deficits.
What you were saying with overlapping generations model and all that is completely different question. Imagine no growth and infinite number of generations – the worst case scenario you get is that one “winner” generation gets to consume twice or several times the product of some future generation (based on how many generations do overlap). And as a “loser” there is this future generation that in turn does not get to consume anything, it will only produce. And this is it. The effect of debt cannot get any worse – unless it somehow decreases the ability of future generations to produce – like distorting incentives, destroying capital etc. That is what I believe Paul and other people suggest. This effect is something completely else from what “ignorant uneducated slob on the street” probably thinks.
Compare this effect with the power of compound interest accruing from investment and accumulation of capital. Actually if you add growth of the overall wealth into equation, this intergeneration redistribution effect will be even lower – and it will become zero – or positive if Samuelson condition (growth above interest) applies.
Speculative answer –
Also, we know that r has to be bounded, it can never be more than the value beyond which it is expected that inflation will accelerate. For accelerating inflation will result in an excess demand for money.
Assuming that i_t =< r_t for a stable path of nominal GDP and r_t can be chosen by the monetary authority, where i_t = r_t for risk-neutrality and i_t < r_t for risk-aversion, you’d have to pick an r_t close enough to r_t that results in accelerating inflation as that maximizes the r_t – i_t with risk-averseness. With risk-neutrality you can’t do this at all I think.
Now I am assuming that the choice of r_t does not affect the ability of market participants to plan for the future and that it does not create any sorts of distortions affecting supply.
Another two notes on Samuelson position. The first and obvious one is that this condition may be stable even if interest on debt exceeds the rate of growth – given that you start with smaller debt. If you for example start with 100 production, 50 debt, 2% growth and 3% interest – you still end up with surplus production of 0,5 above interest. So to restate the condition, debt is sustainable if absolute production increase is more than absolute interest payments
However the less obvious thing is, that even if we acknowledge the validity of this position it will not pass morally as per Nick’s overlapping generation post. We still end up burdening our children. Why? Because the first generation that eats this free lunch will deprive some future generation from eating the same lunch. And the “free” lunch gets greater and greater over time as the economy grows.
So now we are getting really into philosophical ground. Is it really a burden for our children if we are the first generation that eats that free lunch? Even if we know that it is tabu and that last 1000 generations did not do it? What if every generation would keep this tabu and just let that free lunch grow? Can we even speak about the free lunch anymore? Are we making our children poorer by being the first generation that creates such tabu, prohibiting all the future generations to eat that lunch? Or it can get even better. Let’s say that we know that every generation there exist a chance – albeit a tiny one – that this tabu will be broken. Is it still amoral for us to eat that lunch, when we know for sure that some future of the infinite generations will eat it anyhow? So from the position of total well-being of all our future children it does not matter if the free lunch gets eaten now or 1000 generations later? What if there is a chance that the game may not be stable because we do not know the long-term growth of product? Would anything change if everybody believes that there is a free lunch with all other arguments valid as per stable example?
Nick,
“I think that 1 and 4 are very different. 4 says the government never needs to increase taxes, and that’s why it’s not a burden. 1 says it doesn’t matter whether the government does or does not need to increase taxes, because it’s never a burden in either case.’
So, do you disagree with number one because it contends that taxes if necessary are still not a burden?
And was your point in the apple sequence in your original post to prove that taxes if necessary must be a burden?
Is this point controversial?
Is it the central point you were originally making?
Determinant: “Finance is sooo much easier when you operate the tax office, the central bank and the printing press.”
Yep. Easier, but not trivially easy. Somebody has to pay fro stuff, eventually.
Jacques: I was following Determinant’s point “4]is actually a corollary of [1], [4] relates to the interest burden and [1] relates to principal. [4] is actually of wider application because it’s the justification for defined-benefit pensions”.”
1 and 4 both relate to the principal plus the interest burden. 1. says the taxes to cover principal+interest don’t create a burden. 4 says there never need to be taxes to pay principal+interest.
It should be PAYGO pensions, not defined benefit. The defined benefit/defined contribution distinction only matters under uncertainty. In this case what matters is the funded/unfunded distinction. 4 was indeed originally used as the rationale for an unfunded (PAYGO) US SS system.
Liquidationist: Sorry, you lost me.
Martin: “Because of this, the decision maker can never know what the opportunity cost is to the tax payer and therefore the risk can never be properly priced.”
Aha!
“Would it help to assume that there is some value of (B * (1+i_t)^t)/(NGDP * (1+r_t)^t) that will make a mess of things and you want r_t and i_t to be such that that value is never reached at any time t?”
Yes/no. In the simple case, where i and g are constant, when you write down the one-period government budget constraint, then lead it forward one period, substitute in, repeat ad infinitum, you get the Long Run Government Budget Constraint:
Existing debt + PV(Government spending) = PV(Taxes) + limit as t goes to infinity of debt at time t/(1+i)^t
(“PV” means “Present Value”)
You then use L’Hopital’s theorem to say whether that last term goes to zero or infinity in the limit. If the growth rate is less than the rate of interest, it must go to zero in the limit, and you are in the world of 2 or 3. Otherwise, you are in the world of 4.
I was actually commenting on your earlier article on the Samuelson paper that you pointed me to.
JV: Thanks!
“However as for your post, I still think that Aba Lerner position is right. First thing is – how do you define “burden” and “income”? If we define burden as anything that decreases the ability of future generations to produce and income as the sum of the things they produce (and sell), then clearly position 1 is right (ignoring disincentive and distortion effects of taxation). This is the key.”
That is indeed the key. I define “burden” as “lifetime consumption”, or, more precisely, “lifetime utility from that consumption”.
Go back to the model in my first post. You will see that output is exogenous. Every time period, and every cohort, has exactly the same exogenous output. But cohort C has lower lifetime consumption and utility as a result of the debt.
“The first and obvious one is that this condition may be stable even if interest on debt exceeds the rate of growth – given that you start with smaller debt.”
That’s not obvious to me. I would say it’s wrong. However small the existing debt/GDP ratio, if you simply rollover the debt+interest, the debt/gdp ratio will grow without limit, and eventually be impossible to rollover any more.
“However the less obvious thing is, that even if we acknowledge the validity of this position it will not pass morally as per Nick’s overlapping generation post. We still end up burdening our children. Why? Because the first generation that eats this free lunch will deprive some future generation from eating the same lunch. And the “free” lunch gets greater and greater over time as the economy grows.”
Oooh! Very interesting point! I wonder how we could share that free lunch across all generations, fairly/equally?
JKH: I answer an emphatic “Yes!” to each of your four questions. We are on the same page.
NGDP bonds or bonds pegged directly to taxation collections?
Prakash: Good question. I was implicitly assuming that taxes, or taxation capacity, was closely proxied by GDP. Bonds pegged to tax collection would be very much like equity, rather than debt. (I think this is also related to tax farming in the olden days??) But they would have a big moral hazard problem, I think.
Master Rowe, you have struck again with your apple example. Until I read that, I was firmly in Camp #1. In fact I was getting ready to write a blistering defense of Krugman against Boudreaux’s scurrilous attacks, until (fortunately) I read your post and my worldview collapsed.
Incidentally, do you know why I used to think #1? Because as a young pup I read Ludwig von Mises say somewhere that it was silly when people said deficit finance allowed the cost of World War I (?) to be foisted onto future generations. Mises pointed out that the real resources used for munitions came out of present alternative uses. I thought that was a brilliant insight and cherished it.
Bob: Wow! A totally unexpected and very welcome convert!
This just shows how wrong I was, in my estimation of what other economists believed. I had thought that all Austrians would line up with James Buchanan, like Don Boudreax. (It’s very funny, and also very good for the soul, to think of you writing to defend PK against DB!)
Is James Buchanan seen as sort of semi-Austrian? I ask out of ignorance.
I don’t remember von Mises saying that. (Which says something about my memory, and nothing about what von Mises said.)
Von Mises was perfectly correct in saying that. (IIRC, Keynes said the same thing in “How to Pay for the War”?). But the next question is: what cohort of people had lower lifetime consumption as a result of those real resources being used for munitions instead of private consumption (and/or investment)? If those resources were borrowed from the current cohort, then they had lower consumption during the war, but higher consumption after the war, when they sold their bonds to the next generation. If those resources were instead taxed from the current cohort, they had lower consumption during the war and the same consumption after the war. And if Mises failed to ask that next question, he said something correct and important, but left out something equally correct and important.
Nick: Bonds paying NGDP should settle the issue. Either they would pay NGDP flat (sustainable, I guess) or they would pay NGDP plus a spread (unsustainable) or minus a spread (sustainable). Ignoring the outlook for deep liquidity traps (ZLB => NGDP plus spread), my mind isn’t really made up how they would trade. I find it helps to ignore long term bonds, and just imagine a market made up exclusively of short term instruments: T-Bills, real T-Bills, or NGDP “bills”. Then we need to think about how risk averse investors would discount the notes vs other capital assets in a world with inflation/consumption basket price risk. And perhaps we need more that one agent to get an endogenous paradox of thrift? Something like a 2-agent Consumption CAPM might be a good place to start. Still thinking about it…
Nick, well, right, I try to defend Krugman when I think it’s appropriate, because I want to establish my street cred for when I go for his jugular.
A lot of Austrians revere Buchanan, especially (for lack of a better term) the Hayekian wing of the Austrians. In contrast, a lot of Rothbardians hate his stuff about constitutions etc. because they think he was just coming up with non sequiturs to justify a State.
K: we are on the same page, I think. I was imagining they would pay NGDP minus an epsilon spread, so it stays just barely inside the sustainable frontier. But I think they would need to be perpetuities to ensure there was never a rollover risk of refinancing at higher market rates. And then I did the PV calculation, and they came up infinitely valued. And then I gave up because I realised I was getting muddled somewhere.
Nick: You need to discount at the risk free rate plus risk premium for NGDP risk. That’s why I suggested an asset pricing framework like the CCAPM: to compute the value of that risk premium. The bonds would have to pay a coupon rate of NGDP plus a spread equal to the risk premium. The payments would be discounted by the same rate thus making the bonds par. I think that such bonds (assuming no default risk and ignoring the ZLB) would trade with zero spread since holding them would give the investor a fixed claim on a fraction of total NGDP and I don’t see why investors would either seek or be adverse to holding that risk compared to a real-return bond.
But still, I want a model. In the limit of huge debt/GDP (e.g. 100X) it ought to be possible to do something back-of-the-envelope. Basically my feeling is that in that limit the risk of swinging between inflation/deflation due to small changes in risk free rate vs expected return of capital assets ought to raise general risk and therefore market risk premium in general which would skew our choices toward consumption and away from investment, which ought to slow growth, lower rates and raise expected returns on capital assets (all from risk premium not improved outlook). So definitely bad for the economy, but I don’t see why we would get a relative shift in NGDP growth compared to T-Bill rates so no obvious impact on debt sustainability and no obvious limit to debt/GDP.
Awhile ago we (you and I) had a debate over the meaning of “crowding out” which we didn’t settle. I think this clarifies it for me. High levels of government debt crowds out real assets, raising risk premia, i.e. returns over risk-free rate which shifts the economy toward consumption, lowering growth rates and therewith the policy rate. This is how, in an economy with an endogenous central bank, high government debt levels lead to low government bond yields.
Nick,
Here is the accounting analysis I referred to earlier.
INTRODUCTION
As preamble, the “we owe it to ourselves” argument works only for assumed refinancing of outstanding debt with more debt. It doesn’t work for the case of the assumed repayment of debt with taxes. That’s pretty much what your original post demonstrates. Krugman’s point is OK if you assume there is no need to pay off debt with taxes. But I don’t think he justifies that assumption in any great way. His argument is about the nature of the liquidity issue in the assumed refinancing of debt – not the nature of the liquidity issue in the assumed repayment of debt with taxes.
The fact that “we owe it to ourselves” may be helpful in refinancing debt, all things considered, but it is not pertinent to Nick’s argument, which demonstrates the net burden effect of paying off debt with taxes. Conversely, the mere demonstration that the assumed repayment of taxes constitutes a burden on future generations does not prove there is a requirement for taxes – the calculation of the tax burden under assumed taxation is not in itself a justification for taxation. Finally, the fact that most of the debt is held domestically has little to do with any argument as to whether or not it should be paid off with taxes (see the addendum).
Summarizing what follows, the burden of paying off debt with taxes is due to the fact that in accounting terms this amounts to an equity for debt swap, because taxes in effect represent an equity infusion from the private sector into government. (The fact that no equity security is issued in the case of government is beside the point.)
So the most important question is whether or not the debt will be paid off with taxes. If the answer is yes, it is a burden along the lines of your original post. If the answer is no, it is not a burden. The tax question is the primary one; the burden flows from that. Conversely, Nick, your proof that the debt is a burden depends entirely on your assumption that it will be paid off with taxes. And to demonstrate the burden effect, it doesn’t directly matter what the argument for the tax assumption is. It only matters that there is a tax assumption.
The burden is the tax.
No tax, no burden.
I’ve attempted a presentation of your original problem, using my own form of sectoral/generational balance sheet accounting. I believe it reinforces the correctness of your presentation using reasonably pure accounting logic, for both monetary and apple economies:
…………………………….
ACCOUNTING PROOF OF NICK’S APPLE MODEL OF THE DEBT BURDEN
(Note: I’ve expressed everything in asset, liability, and equity type accounting entries here, but to keep things manageable, I’ve done this verbally, without attempting to present T accounts. It should be easy enough for the reader to mirror the verbal description with T account construction as you go along.)
So, split the world into two sectors – the government in question, and non-government (the rest of the world).
G and G’
You can assume for simplicity, for now, that it’s a closed economy, and there are no external complications (see the addendum for foreign ownership of bonds). Nevertheless, I’ll stick with the G’ notation for the sake of generality, prior to looking at the special case of foreign ownership of bonds in the addendum.
I’m going to use “cash”, “bonds”, and “tax” throughout, but just substitute apples for cash, apple bonds for bonds, and apple tax for tax, throughout, and it works quite well for an apple economy.
Here is the sequence in accounting terms:
a) G borrows for the first time. Its marginal balance sheet change now consists of cash and bonds (apples and apple bonds). G is long cash (asset) and short bonds (liability).
b) Conversely, the marginal G’ balance sheet change consists of bonds (an asset) and a cash liability. Off the top, this cash liability entry and its interpretation are critical. What we’re looking at here is a balance sheet effect at the margin. So when we say the marginal balance sheet change of G’ includes a cash liability, it means that the gross asset cash position of G’ is now reduced or “shorter” than what it would have been without G borrowing. So a short cash position at the margin reflects the draining of cash as an asset from the rest of the G’ balance sheet as it exists outside of this particular transaction.
c) IN ADDITION to the opening G’ long bond, short cash balance sheet change, there is a second balance sheet adjustment. This results from the initial government transfer of the cash that was raised by the bond issue. I.e. the cash transfer is a transfer of the initial G cash position to G’:
The opening marginal balance sheet change of G was long cash, short bonds. Following the transfer of cash to G’, G’s marginal position now gets adjusted to a net short bond position. (Complete, pure accounting would show equity as a left hand entry, not normally done in government accounting. Left hand equity is actually a negative equity position, which is logically correct here. But I won’t get into that to avoid the terminological complication. Let’s just say the G balance sheet has moved from long cash, short bonds to a net short bond position.)
Correspondingly, the G’ balance sheet now gets the cash from the transfer. The marginal balance sheet change from the cash transfer (alone) is long cash, equity. Here, the equity entry is conventional right hand side. It is positive equity in the conventional balance sheet accounting sense.
Therefore, the total cumulative marginal G’ balance sheet now has 4 entries – long bonds, short cash; long cash, equity. Consolidating that, the final cumulative marginal G’ balance sheet position at this stage is then long bonds, equity.
(BTW this position of long bonds, equity corresponds to the usual MMT designation of “net financial assets” at the margin, which is the general MMT accounting result associated with government deficit spending (or transfer). But nothing here by way of accounting presentation actually “depends” on MMT. It’s just accounting. That correspondence is only for the information of those interested in the connection.)
d) Now we can sequence G’ into time/generational G’ cohorts. Call them G’1, G’2, etc.
e) So the G’1 opening change, in total, is long bonds, equity.
f) At the transition point, G’1 sells its bonds to G’2.
g) The resulting G’1 balance sheet change is long cash, equity.
h) The resulting G’2 balance sheet change is long bonds, short cash. (The short cash position is interpreted exactly the same as it was at the beginning for G’1.)
i) Next, G’2 sells its bonds to G’3
j) The resulting G’2 balance sheet change is long cash, short cash.
Netting, the consolidated G’2 balance sheet position at the margin is then zero/zero.
k) The resulting G’3 balance sheet change is long bonds, short cash. (Again, the short cash position is interpreted exactly the same as it was for G’1 and G’2, at the stage where they also bought the same bonds.)
l) Finally, the government taxes G’3 to pay off the bonds.
m) The tax on its own has a marginal balance sheet presentation. The first step is to record the G’3 tax bill, prior to G’3 actually paying that bill. The marginal tax bill entry therefore is that of a G’3 net tax liability (short taxes). G’3 owes taxes, simply because the government says so.
n) Taking that tax liability entry into account, and adding to the position that already existed, the cumulative marginal balance sheet change of G’3 is now:
G’3 is long bonds with two different liabilities, each in the same quantity as the bonds – short cash, and short taxes.
o) G’3 now pays the taxes. Its long bond position is used to pay off the tax liability. (There are intra-G’3 bond for cash transactions etc. in order to get the cash to pay the tax, but those transactions are secondary).
p) So the G’3 long bond position nets out against its tax liability, and the resulting final cumulative marginal balance position of G’3 is net short cash.
q) That net short cash position alone is interpreted similarly as in the earlier cases. It can be viewed as G’3 ending up with that much less cash than it otherwise already had elsewhere on its total balance sheet.
r) Putting everything together then, the burden effect Nick identified in his example shows up here effectively, as position q) funding position g), through time and generations.
s) That is, the net benefit to the first cohort (the cohort receiving the transfer) is its marginal long cash, equity position as explained in g).
t) And the net cost to the final cohort (the cohort paying the tax) is its marginal short cash position (a liability, with negative equity at least implicit on the left hand side, if you will) as explained in q).
u) So the first cohort’s long cash position becomes the burden of the last cohort in the form of the last cohort’s short cash position.
v) Now replace cash with apples, bonds with apple bonds, and tax with apple tax, and that’s Nick’s example in balance sheet accounting terms.
w) The apple burden that is quite evident in Nick’s model therefore can be reflected in apple accounting. And the corresponding burden in a monetary economy as depicted more directly in the accounting above consists of the loss of the final generation’s cash and corresponding equity, by taxation, at the margin. But there is such a burden only because such a tax is assumed.
x) In relating apple accounting to monetary accounting, note that assets and liabilities (including tax) can all be depicted in either apple or money terms. Also, the balance sheet entry of equity (conventionally positive equity if a positive number on the right hand side; negative equity if a positive number on the left hand side) is the net result of assets and liabilities, depicted in either apple or money terms.
ADDENDUM REGARDING FOREIGN OWNERSHIP OF BONDS
We defined G’ at the outset as “non-government”
This general definition applies to each of the cohorts as well, G’1, G’2, and G’3. Initially, we assumed a closed economy for simplicity, so G’ was actually describing the domestic private sector. Now we extend this to the full original meaning of “non-government”, which allows for a foreign sector as well. So let’s take the case where the foreign sector buys the government bonds.
The key point here involves step n) from above:
“Taking that tax liability entry into account, and adding to the position that already existed, the cumulative marginal balance sheet position of G’3 is now:
G’3 is long bonds with two different liabilities, each in the same quantity as the bonds – short cash, and short taxes.”
So let’s assume now that G’3 does include both the domestic sector and the foreign sector and that it is the foreign sector component that has bought the bonds. And let’s suppose for simplicity that they’ve bought all of the bonds.
The first thing to recognize is that when the foreign sector buys the bonds, it creates a marginal accounting entry for itself of long bonds, short cash. This is exactly the same marginal entry as was the case when we assumed it was the domestic sector that bought the bonds.
The second thing is that this idea of marginal balance sheet effect is something that is relative to a “ceteris paribus” balance sheet otherwise. So in this case, we must think about what the balance sheet of the foreign sector itself looked like before it bought these bonds. And the pertinent thing to look at there is the nature of the pre-existing gross and net international investment position of the domestic sector interfacing with the foreign sector.
For example, suppose the domestic sector had run up a cumulative current account deficit exactly equal to the quantity of bonds purchased by the foreign sector. The foreign sector would have a corresponding cumulative current account surplus against the domestic sector. This means that the foreign sector would have been long cash to begin with (or equivalently, could have swapped its pre-existing net foreign asset position into cash). That means it uses its pre-existing cash to buy the bonds. We described the marginal balance sheet effect of the bond purchase as long bonds, short cash. Combining this with a pre-existing foreign long cash, equity position, the result of the bond purchase is a foreign balance sheet of long bonds, equity. And note that the accounting equity here corresponds to the fact that a foreign sector cumulative current account surplus is in fact a component of its collective national accounts cumulative saving, and saving is essentially equivalent to accounting equity.
As a second example, suppose the domestic sector had run a cumulative balanced current account with the foreign sector. The marginal balance sheet effect of the foreign sector bond purchase again is long bonds, short cash. There is no pre-existing foreign net asset position with the domestic sector, cash or otherwise. However, there is still a gross balance sheet position. And it is still the case that the marginal result of the bond purchase is a marginal foreign balance sheet change of long bonds, short cash. For example, the foreign sector may buy domestic bonds by simultaneously incurring some sort of liability against the domestic sector. This corresponds to a gross capital account outflow from the foreign sector (bond purchase) matched by a gross capital account inflow to the foreign sector (e.g. foreign borrowing from a domestic bank).
So all of that gets pretty complicated; i.e. the effect on the foreign sector balance sheet of the foreign sector buying domestic government bonds can get complicated.
But here’s the important point. Whatever that effect is, it arises from a pre-existing balance sheet condition that is characterized most generally in the starting point for the net and gross international investment position of either side against the other.
And that starting point has NOTHING to do directly with the fact that the domestic government has issued bonds. It has EVERYTHING to do with such matters as cumulative current account deficits and/or gross international capital flows.
And whatever that starting international position is, the fact remains that regardless of that starting position, the marginal balance sheet effect of the foreign sector buying government bonds is a marginal balance sheet entry of long bonds, short cash – the very same entry that was the case for the closed economy domestic sector purchase described earlier.
Now, returning to the main issue, remember that we are assuming G’3, the final cohort, now includes those foreigners that have bought all of the bonds. And their marginal balance sheet position as described above is long bonds, short cash.
So we come to the tax burden.
Let’s assume that the government levies the tax to pay off the bonds entirely on the domestic sector, and that the foreign bond holders escape free of any direct effect of the tax that is levied to pay off the bonds.
Remember point n) above, which describes the marginal balance sheet position of the full cohort G’3:
G’3 is long bonds with two different liabilities, each in the same quantity as the bonds – short cash, and short taxes.”
This still applies. But there is now a decomposition of this position into domestic and foreign components.
The foreign component is long bonds, short cash as described above.
The domestic component is now short taxes alone.
So what happens is that the government taxes the domestic sector to pay off the bonds. It then uses those tax proceeds to pay the foreign owners of the bonds. And the foreign owners of the bonds use that to pay off their short cash position. All of this is happening at the margin, ceteris paribus. And ALL of this is quite feasible through the mechanism of gross and/or net international capital flows. It’s the financial market.
So the net result of all of that for the final cohort is as follows:
The foreign sector part of the cohort ends up flat. Its cumulative marginal balance sheet position is zero, zero.
The domestic sector ends up short taxes.
When the domestic sector goes to pay down its tax liability, it basically swaps the tax liability for a cash liability (e.g. by borrowing the cash to pay the tax or by running down its cash position otherwise).
And the end net result for the domestic sector is EXACTLY the same as it was for the closed economy.
Now substitute apples for cash, and everything will still work.
The key point in all of this is that the starting balance sheet position is the basis for the final net apple or net cash effect on everybody. For example, it could be the case that the foreign sector started out with a net apple asset against the domestic sector, as the result of a current account apple surplus with the domestic sector. So it buys the bonds with pre-existing, domestically produced apples that it received through current account. And it gets paid back with apples that the domestic government got when it taxed the domestic sector at the other end. But that pre-existing balance sheet position, including the current account accumulation of apples by the foreign sector, has NOTHING to do directly with a government bond issue. Similarly, a pre-existing foreign sector gross international apple position, even without any net current account impact whatsoever, may also be the original source of foreign sector payment of apples for bonds. But that starting position as well has nothing to do directly with the issuance of bonds by the domestic government. And so on. So this entire issue of domestic versus foreign needs to be separated out, when considering the specific issue of burden in the form of a tax burden at the end of the whole process. And I think that’s where Krugman may be wrong, and Nick is right.
JKH: “And the end net result for the domestic sector is EXACTLY the same as it was for the closed economy.”
BINGO! Yes!
JKH: “So the most important question is whether or not the debt will be paid off with taxes. If the answer is yes, it is a burden along the lines of your original post. If the answer is no, it is not a burden. The tax question is the primary one; the burden flows from that.”
Yes! And in #4, since there is no need for future tax increases, there is no burden.
Minor quibble 1: a default on the debt would be equivalent to a tax on the bondholders, and would create a burden.
Minor quibble 2: and if future taxes are increased, not to pay off the debt, but just to pay the interest on the debt, then there is a burden, but it’s spread out over all future generations.
I was wondering if you saw my updated post here. I think it might help you to think of the real instead of the nominal side for awhile. When are real productive resources used up?
If it really is possible to consume more now at the expense of people later, why not do it as much as we can? If I convinced everyone that the singularity would happen in 30 years, would it be possible to double everyone’s real consumption today by issuing a ton of 30 year bonds? People in 30 years will be infinitely wealthy so they won’t mind. If it’s not possible, why not?
I find JKH’s laberinthine accounting unnecessary. It stikes me as obvious that Nick is right in saying (as per his original apple analogy) that IF youngsters in each generation transfer real wealth or spending power to oldies, then a real burden is passed down the generations (assuming a closed economy).
It is also true that this phenomenon actually happens with pension schemes, funded or un-funded. In both cases, youngsters effectively support oldies.
Next point is that absent government bonds, people would simply find alternative ways to fund their pensions: perhaps using other assets or perhaps making more use of un-funded schemes.
Thus the $64k question is whether people are induced to INCREASE their pension provision when government runs up extra debt, and I don’t see there being much of an effect here.
My conclusion: when government of country X incurs debt, or extra debt, there is little or no increased burden on future generations. Though if a significant portion of the extra debt is bought by foreigners (and assuming there is no singnificant increase in foreign debt bought by residents of country X) then to that extent, there will be a burden on future generations.
Nick,
“Minor quibble 1: a default on the debt would be equivalent to a tax on the bondholders, and would create a burden.”
Agreed, viewed as an isolated effect.
What I said was that debt repayment with tax is equivalent to default without tax.
Same difference.
“Minor quibble 2: and if future taxes are increased, not to pay off the debt, but just to pay the interest on the debt, then there is a burden, but it’s spread out over all future generations.”
Agreed.
Nick P.S.
The Model
You have a (performing) bond asset.
You incur a tax liability.
You pay the tax with the bond (effectively, i.e. after swapping it for cash).
Net zero.
Default Interpretation 1 (JKH)
You have a defaulted bond asset.
That is equivalent to no asset.
You have no tax liability.
Net zero.
Default Interpretation 2 (Nick)
You have a defaulted bond asset.
That is equivalent to a performing bond that is taxed away in kind.
Both are equivalent to no asset.
Net zero.
I guess I read Krugman as implying #4, but avoiding stating it in politically unpalatable terms.
I can create a model in which debt is never ever a burden. It’s a distributional, intertemporal blessing. The only change I have to make to your model is to assume that the younger cohort is unable to consume or chooses to save a portion of their apples, works with money too. I don’t even need to assume growth. And it’s not a ponzi scheme. If I want to save apples for the future but can’t store them what is the interest rate (hint it’s not 10%)? Works forever or until someone decides they want to let apples spoil.
Or am I missing something?
In all your examples the same number of apples are consumed every year. It’s the number of apples produced. Plus for consistency sake shouldn’t the final cohort tax the next cohort as was the case previously in which case cohort C refuses to buy the bonds so they are taxed to pay B and they in turn tax cohort D and so on.
Otherwise all you’ve shown is that if you buy a bond that defaults you lose money. Happens with or without government bonds taxes or whatever.
A rolling loan gathers no loss. (therefore not a burden)
That which cannot go on forever won’t. (10% interest rates in a no growth economy)
Took me a while to understand the point you’re trying to make, probably still don’t, other than you can create a model world in which debt must be paid by the people who bought the bonds. Sucks to be them. Sounds like they’re the greater fool generation.
I probably just don’t understand.
Happy new year Nick good luck in 2012 WCI
Reverend Moon: Your model is a version of #4. The real interest rate in your model (if people want to save apples for the future, but can’t) would be negative, and so less than the growth rate of the economy, even if the economy was stationary.
In my model cohort D could pay the tax, instead of cohort C. No real difference, except D rather than C bears the burden.
Adam: “I guess I read Krugman as implying #4, but avoiding stating it in politically unpalatable terms.”
Maybe, but then why does he keep talking about the disincentive effects of future taxes being a burden on future generations?
Ralph: JKH’s accounting served (for me) as a check on my intuition that it really made no difference to my argument whether we assumed an open or closed economy.
“Next point is that absent government bonds, people would simply find alternative ways to fund their pensions: perhaps using other assets or perhaps making more use of un-funded schemes.”
OK. Assume that apples can be stored, and that A was originally planning to store apples for its retirement. Then the government gives A the bonds, so A eats 100 more apples immediately because they can save they bonds instead. And B also saves the bonds rather than storing apples. But this makes no difference to the rest of my story. C still has to pay taxes to retire the bonds, so C has lower lifetime consumption.
K @1.33. My brain isn’t really up to following you, I’m afraid. But your comment has fired some (possibly random) thoughts in my brain, that may or may not lead somewhere.
Nick wrote: “something that would make both Scott Sumner and the MMT guys very happy indeed. Which would be neat. Plus, as a side-benefit to making both those guys happy, it might be very good for the poor ignorant uneducated slob on the street too.”
Funny, that. 🙂