When we teach students economics, we sometimes use numerical examples to help them understand general principles. Sometimes we make them work through those numerical examples by themselves, as an assignment. It's the only way they will really get it, and see what's really going on. But once they get it, they don't need the numbers any more, they can see the general principle that doesn't depend on any particular numbers.
As an undergraduate at Stirling I took a course on Merleau-Ponty's Phenomenology of Perception. One book for one course. Looking back on it, I have no idea what it was about. I think I learned something, but I couldn't really tell you what it was.
But I remember (I think I remember) one of Merleau-Ponty's examples. There is a row of light bulbs. The first bulb lights up, then goes out. Then the second bulb lights up, then goes out. Then the third, and so on. And we see a light moving from left to right along the row, even though none of the bulbs is moving.
I think it was Roger Farmer who first explained Samuelson 1958 to me, back in grad skool at Western. He used a numerical example. I think it went something like this:
1. Imagine an infinite line of people, each holding one beer. One equilibrium is where each person drinks one beer. But there is a second equilibrium, where each person gives his beer to the person in front. The person at the front of the line drinks two beers, and everyone else drinks one. The second equilibrium is Pareto Superior to the first, because the person at the front of the line drinks more beer, and everyone else is the same. You can imagine the first person in line giving the person second in line a bit of paper, in exchange for the beer. That bit of paper (money) travels down the line in exchange for the beers traveling up the line.
2. Now change Roger's example, so there is one person first in line, two people second in line, four people third in line, and so on. The population doubles every generation. If every individual gives his beer to the person in front, every individual can drink two beers. The paper money becomes twice as valuable every generation, or pays 100% interest per generation (same thing). But if the population ever starts to decline, somebody is going to be stuck drinking less than one beer.
3. Now change the example again. Let the population be constant, and assume each person lives two periods. He produces 100 beers when young, and none when old. He would like to save half his beer to drink when old, but beer does not keep. If each young person gives 50 beers to the old person in front, everyone is better off. The old people at the front of the line get to drink 150 beers over their lifetime (100 when young, and 50 when old). Everyone else gets to drink the same 100 beers over their lifetime, but now drinks 50 when young and 50 when old, which they prefer.
The total number of beers consumed over one's lifetime tells us something, but it doesn't tell us everything. If beer has diminishing Marginal Utility, and if people do not discount future utility, they will always prefer drinking 50 when young and 50 when old to any other combination of drinking 100 beers over their lifetime. For example, let:
lifetime utility = log(beers consumed when young) + log (beers consumed when old)
4. Now change the example again. Same utility function, constant population, but now assume people produce 50 beers when young and also produce 50 beers when old. If each individual consumes what he produces, and consumes it when he produces it, it looks like this:
A 50 50
B 50 50
C 50 50
D 50 50
E 50 50
etc.
Each row represents a generation (or cohort). Generation A is followed by generation B is followed by generation C and so on, forever.
Each column represents a period in time. By assumption, each column must add up to 100 beers, because it is impossible to make beers travel in time. You are not allowed to move beers horizontally.
But you can move beers vertically. You can take 10 beers away from the young in generation B and give them to the old in generation A. And you can imagine that you give the young a bit of paper in exchange for their 10 beers. And you can repeat this, so that the young in generation C give 10 beers to the old in generation B. And then stop, so that the young in generation D give no beers to the old in generation C (the debt is redeemed).
You can make it look like those 10 beers are traveling back in time from generation C to generation A. Just like Merleau Ponty's row of light bulbs.
There are two ways to aggregate: aggregate by columns (years); aggregate by rows (generations). You get different perceptions of reality depending on which way you aggregate. You can't see beers travel back in time horizontally, but you can see beers travel back up the generations vertically.
[Update: if we use natural logs, then lifetime utility is 7.824 for every row; and the aggregate utility in any period (if you are comfortable with adding two people's utilities) is also 7.824 for every column.]
Play with this numerical example by yourself. Because I can't teach you anything. You can only teach yourself this stuff. And the best way to teach yourself is by playing with numerical examples. That's how I learned it. That's how Bob Murphy learned it. See what happens to the lifetime consumption, and lifetime utility, of future generations, if you use debt to finance transfers to the old in generation A. There is no way you can do it without making some future generation have lower lifetime utility.
[The equilibrium rate of interest in this model will be determined by:
1+r = (consumption when old/consumption when young)
Because Marginal Utility of consumption = dlog(C)/dC= 1/C
At the initial equilibrium drawn above, r=0. But if the debt is positive, r will be strictly positive.]
I would be indebted to anybody who knows how to set this thing up on a spreadsheet, with the lifetime utility calculator built right in, and can put it up on the web somehow. Young people can do that sort of thing, right? [Update: thanks to rpl for creating this spreadsheet; which you should be able to copy and edit! I think rpl used base 10 logs, which is why his utility numbers are different from mine.]
Have fun.
Worthwhile Canadian Initiative 
Krugman, as quoted by Donoghue:
“[When people speak about the burden of the debt on future generations] what they mean is that America as a whole will be poorer, just as a family that runs up debt is poorer thereafter. Does this make any sense?”
As I thought, Krugman is addressing the propaganda, which relies upon the lack of systemic thinking on the part of the populace. The thing is, Nick Rowe and Bob Murphy, et al., being systemic thinkers and not propagandists, do not, repeat, not mean that when they talk about the burden of debt upon future generations. What we have is a non-conversation, a “failure to communicate”.
It helps to connect balance sheets with income statements to see this.
Krugman hasn’t demonstrated a strength in this type of accounting in the past – particularly in some of the debates on banking.
Krugman’s post is fine – assuming there is never a surplus in the future.
And specifically this is OK if that is the case:
“Debt has distributional implications, and it may have macroeconomic effects because of those distributional issues. But again, all this is within the current generation; it’s not about the present versus the future.”
But its not OK if there is a surplus in the future.
That’s what Nick’s models show (or at least one of the things).
Thanks, JKH. I will
play with that idea in my version of the toy model and leave Nick alone.
I should add that it looks like its also not OK according to the effect of debt on the distribution of utility over time (Nick, Bob Murphy, others), although that seems to me to be an additional layer of analysis that I’m not sure I fully understand yet
Ah I think I see. In PK world the music never stops, but it is not a Ponzi scheme because the music never has to stop. But in fact it will stop either by fiat or by some future surplus. The game is infinitely lived only in the set up. At least for certain assumptions in a toy model regarding r, g, and impossibility of shocks to the level of debt.
If that is still wrong I give up.
Michael S.
Murphy has an interesting model where there is a surplus effect at the end, but he focuses instead on explaining the utility effect (I think):
http://consultingbyrpm.com/blog/2015/02/krugman-defenders-0-murphyrowe-324.html
So it seems to me like an additional type of intergenerational effect, whether or not there is a surplus at the end
(I think Nick has done something similar)
Krugman made a slip in the initial round of this debate 3 years ago when he acknowledged in one of the essays he wrote that it matters whether or not foreigners are the ones Americans are borrowing from, rather than other Americans. So, yes, I think Krugman is basing his entire argument on the “we owe it to ourselves” meme.
“Odie: you can play with the model yourself, or change the assumptions and see how the answers change. That way you will really learn it.”
Ok, I give it a try. The first generation reduces its consumption in order to generate some real (physical and human) capital. If subsequent generations continue doing that the capital wealth of each generation is larger than the previous one. Thus, the last generation may realize that the claims on consumption the are holding may not be exchangeable in the amount they were expecting. However, they still have the large capital base to draw from that previous generations built by foregoing their consumption. Does that sound about right?
“A national debt is like an unfunded pension plan”
Would an unfunded pension plan not more be like social security? In your beer example the government taxes one generation to transfer consumption to another generation there would be no government debt, would it? Debt is acquired when some people decide to not consume their entire production and the government instead of taxing it borrows it so that other people can consume more than they produce. However, when those “over-consumers” produce some real capital subsequent production/consumption will be higher and the borrowing becomes justified. (Which would also justify my job in academics; so that’s at least how I like to think about this topic.)
Michael S: you are getting close.
If the debt stays at 10 beers, and the government never pays it down, every generation has a lifetime consumption of 100 beers, the same as if there were no debt.
But their utility is lower, because they consume 40 when young and 60 when old, and this gives them less lifetime utility than if they consumed 50-50. (That’s because of diminishing marginal utility.)
Yancey: “Krugman made a slip in the initial round of this debate 3 years ago when he acknowledged in one of the essays he wrote that it matters whether or not foreigners are the ones Americans are borrowing from, rather than other Americans.”
If the 10 beer debt were owed to foreigners (rather than a 10 beer debt in a closed economy like my example), and the interest payments were made to foreigners, and if the debt were constant over time, total consumption in any year would be lower, but lifetime utility would actually be higher. So it does matter, but in the opposite way that Paul intended.
Nick Rowe: “But their utility is lower, because they consume 40 when young and 60 when old, and this gives them less lifetime utility than if they consumed 50-50. (That’s because of diminishing marginal utility.)”
But when you are old, every beer is like the first. (You forget the others. ;))
I applaud everyone who has chipped in on this debate. All of the issues that have been raised on Nick’s blog were the topic of frontier research in economics journals in the 1950s — 1970s.
The paper that started all of this (at least in the English speaking world) was by Paul Samuelson. “An exact consumption-loan model of interest with or without the social contrivance of money”, Journal of Political Economy 1958, Vol 66 No. 6. The French lay claim to an earlier version by Maurice Allais, but that’s another story. Samuelson’s paper was a revelation to economists because it provided an example where markets don’t work. In Samuelson’s example there is an equilibrium, (people optimize taking prices as given and all markets clear) that can be improved upon by a government institution. Samuelson’s paper is a good starting point for those who would like to read more about this.
Samuelson provided a model of pure exchange, like the examples Nick has developed. In a pure exchange model there is no production. In 1965, Peter Diamond introduced capital to this model and he discussed the role of government debt in “crowding out” private capital. His paper was published in the American Economic Review, Vo. 55, no 5 under the title “National Debt in a Neoclassical Growth Model”. Peter uses a mathematical tool called a ‘difference equation’; and if you are sticking with my reading program, you will need to know a little bit about difference equations. There are many good undergraduate books on the topic; I like “Fundamental Methods of Mathematical Economics” by Chiang, but that probably dates me.
The next paper I would recommend in this literature is by a mathematician, David Gale, “Pure Exchange Equilibria of Dynamic Economic Models” Journal of Economic Theory 6 (1973). I include David’s paper on the reading list of my first year Ph.D. class. In it, David distinguishes what he calls a “Samuelson economy’ from a ‘classical economy’ and he shows that every overlapping generations model has at least two steady state equilibria; one in which the interest rate equals the population growth rate and one in which the aggregate saving by the young is zero. This divide is the key to understanding when government debt is a burden in the sense we have been discussing.
Throughout the 1960s and 1970s there was a very muddled discussion in the journals, trying to understand why markets can sometimes fail to be optimal. Some people thought that it was because not everybody can meet, due to the one way flow of time. That issue was cleared up by Karl Shell in 1971, “Notes on the Economics of Infinity”, Journal of Political Economy, Vol. 79. Karl attributed the problem to what he called the ‘double infinity’ of people and goods. This is the paper to cite at parties if you want to appear knowledgeable about the topic. It probably won’t enlighten you much unless you’re enrolled in an economics Ph.D. program.
Any question that you have has, almost surely, been answered already in the literature. How do the conclusions of the model depend on the assumption of no bequests? What happens if some people live forever? What happens if there are multiple goods in each period? Many of these questions are answered in my book “The Macroeconomics of Self-Fulfiling Prophecies”.
I’m sorry if the answers are not always obvious, or the papers I have cited seem impenetrable to you. But realize that mathematics is a language and often it is the best language for answering questions of logic.
If you think that we are debating esoteric issues that are unrelated to the real world; you are entitled to that opinion. An economic model is only useful if helps us to understand the world. I happen to think that the overlapping generations model contains a great deal of useful insight. If you read, and understand, all of the papers I have cited. You will never again utter the phrase: “debt is money that we owe to ourselves”.
Roger: You know much more about the OLG literature than I do.
One paper you may or may not know about, that i would recommend: Stefan Homburg’s “Interest and Growth in an Economy with Land” CJE 1991
Nick,
Here is my write up of a model in which no burden is applied across generations as a result of optimal taxation policy to redeem debt.
rjs, let’s use beer instead of fruit.
“An economic model is only useful if ?it? helps us to understand the world.”
Let’s add “money” to your model. Assume the beer supply grows by 3% per year. Assume beer demand is not unlimited. Assume wealth/income inequality.
Now what does your model look like?
@ Roger Farmer
Many thanks for your very informative note, and for all the references. 🙂
Since you are here, in paragraph 1. of the text Nick Rowe makes an argument that he attributes to you about the Pareto Superiority of one distribution of a countably infinite number of beers among a countably infinite number of people. If you believe that the argument as Nick presents it is not fallacious and applies to finite economies, would you please defend it; if you do not believe those things, would you please correct the argument? Thanks. 🙂
The argument resembles that of the Infinite Hotel, which we know to be valid. The Infinite Hotel has an infinite number of rooms. Someone shows up at the hotel and asks for a room. The desk clerk replies that the hotel is full, but then says that they can accommodate the new guest. The guest is placed in room 1, while the guest who is currently in room 1 is placed in room 2, the guest who is currently in room 2 is placed in room 3, and so on. Almost miraculously a full hotel can add another guest.
We started out with one more person than the hotel had rooms, and then . . . . Stop right there! That is not so. In fact, the argument is a proof that infinity plus one is not greater than infinity, but is equal to infinity. The room assignment is, in fact, a way of counting the number of guests. There were never more people wanting rooms than rooms. Despite appearances.
Similarly, finding a room for the new guest appears to be welfare enhancing. After all, she started out without a room and then got one. But again, that is an illusion which is the result of our familiarity with finite hotels and our unfamiliarity with infinite hotels. There was always room in the inn. 🙂
Does the Infinite Hotel tell us about finite hotels? Of course not. If we reassign rooms in a finite hotel which is full, we accommodate the new guest by ejecting a current guest.
Well, what about situations in which we do not know the future? By analogy, does the Infinite Hotel tell us about situations in which we are ignorant?
Suppose that we are ignorant of the number of rooms, but we do know that the hotel is full. Then we know that we cannot add the new guest without ejecting another. (OC, for the sake of the puzzle we are not allowing room sharing. ;)) Suppose that we are ignorant of whether the hotel is full or not. Then we could reassign rooms and cross our fingers. But in real life we do not bother the current guests and simply search for an empty room. (True, in the case of a temporal sequence we might act in the present and cross our fingers regarding the future. ;))
Now, what about the argument in paragraph 1? Passing the beers forward appears to be welfare enhancing because there now seems to be one more beer than people. But now we know that that is an illusion. The number of beers and the number of people are the same. The argument also requires an unstated assumption that there is no last person in line, because that person ends up with no beer. In the Infinite Hotel argument there may or may not be a last room. It does not matter. The reassignment of rooms is just a way of ordering (and counting) the guests. You could have an infinite number of guests who stay in their rooms. Passing a beer forward is a different kind of operation. It is crucial to the argument that there is no last person in line.
Does the argument apply to the real world? Real, finite lines have a last person who ends up with no beer. Therefore the infinite analog, if it has any application to the real world, should also have a last person in line. Just because the natural numbers have no greatest member does not justify not having a last person in line.
Instead of jumping to the infinite case, isn’t it better to start with finite cases and then approach the infinite case in the limit? Doing so for this argument shows that the case where the first person in line ends up with two beers while everybody else has a beer is not, repeat, not the limiting case for finite lines. We’re not in Kansas anymore.
Now, I will note that in one of this week’s essays, Krugman was now saying the “world economy owes the debt to itself”. So he is trying to define away the distribution problem again.
I keep coming back to this, however- if the debt really doesn’t matter and isn’t paid off- just rolled over-, why do we have taxes at the federal level?
I just Googled “krugman overlapping generations”, and got this:
http://krugman.blogs.nytimes.com/2012/10/22/things-that-arent-bubbles/
It either proves Nick’s point about Krugman, or it justifies Kevin Donaghue’s discomfort with Nick’s point about Krugman.
Or it just shows that Samuelson’s was such a grand synthesis that it can justify any two opposing views.
Seems to me that debt is irrelevant to the issue of can inter-generational transfers occur. US Social Security system got started at a point in time, at that point the recipients, because they hadn’t paid in over their lifetimes, received a generational transfer. Whether the startup of social security was debt financed or not is irrelevant to the fact of the transfer.
A post on taxes can be a burden on past generations should probably follow this one.
Andy: an unfunded government pension plan is just like a debt. Both create intergenerational transfers. An unfunded pension plan is a debt that is not on the books. But that doesn’t mean that debt is irrelevant for intergenerational transfers.
“An unfunded government pension plan is just like a debt. Both create intergenerational transfers. An unfunded pension plan is a debt that is not on the books. But that doesn’t mean that debt is irrelevant for intergenerational transfers.”
That needed to be said, because quite a few people are floating that particular objection. It’s a red herring as a distinction, and irrelevant as a challenge to the valid point being made about debt.
It is somewhat mysterious to me that otherwise reasonable people would (intentionally? unintentionally?) misrepresent Krugman’s argument that ‘debt is money we owe ourselves’ as ‘debt doesn’t matter at all’, and then spend so much time and effort trying to refute it. Especially when he makes it very obvious what canards he is trying to skewer with the statement, and has mentioned the distributional aspects a number of times, if only to say that they are a separate problem, and are solvable in a world where solving them is considered to be a net positive.
It’s a very strange phenomenon.
Neither an unfunded plan like social security, nor a debt like a fixed coupon payment creates intergenerational transfers. Whether or not debt creates an intergenerational transfer is the issue under debate. You cannot define debt as something that creates intergenererational transfers because it begs the question.
Both can be extinguished without any intergenerational transfers. For the pension you can tax the old to extinguish the pension liability just as you can tax the bondholders to extinguish the bond liability. Whether or not an intergenerational transfer occurs depends on how the liability is extinguished. We have in the past raised the social security retirement age and raised FICO taxes as well as paid for social security out of the general budget. We may not have gotten the right mix, but all the tools are there to avoid intergenerational transfers. Of course in real life, we have a growing economy and interest rates below the growth rate, so overall social welfare may be increased with intergenerational transfers, but the existence of the debt does not obligate that these transfers occur — the two issues are separate.
Yancey Ward: “if the debt really doesn’t matter and isn’t paid off- just rolled over-, why do we have taxes at the federal level?”
Well, first, the debt is paid off, even if it is rolled over. The exception being consuls, which are never paid off, and for that reason may not be considered debt. But bonds and bills are paid off.
And as for taxes, consider the case of the Continental Dollar. The states did not grant Congress the right to tax, despite the warnings of Benjamin Franklin. Nor were they obligated to accept Continentals, either. As a result, the value of the Continental virtually evaporated in a few years.
Let’s look at a social security type transfers.
In our OLG model, the young collect 10 apples every period. 5 apples are taxed and given to the old every period. These are real resources, so if we stop the social security payments, the very last generation will get screwed because they paid in 5 apples but didn’t get a benefit. That is an argument to not stop the transfers. In this sense, we can think of social security as a moral obligation to continue, even though it is not a legal obligation — e.g. the government would not be in default if it stopped paying social security, but it would be stealing from the future. In this way, social security is “like a debt” — e.g. the payouts made by generation n at least morally obligate generation n+1 to also make a payout.
But as long as the economy is able to produce enough goods ands services, we can arrange for taxation in such a way as to continue the transfer — i.e. it is not inevitable that social security will be stopped as a program. Therefore it is not inevitable that the debt will be a burden. But suppose the economy is not able to produce enough? That would be a real constraint on the program.
Suppose, in the future, a shock occurs, and for a single period only 8 apples are collected. After that 10 apples will again be collected.
The socially optimal thing to do is to give only 4 apples to the old, and let the young eat 4. Now the older generation paid in 5 apples but only got 4. The young eat 4 and are taxed 4 during the depression, but in the next period, the young (now old) will get 5 apples, but they only paid in 4.
So the consumption of the generations is smoothed out: , …, 10, 9, 9, 10, 10, …
This is a net transfer to the future from generation n-1 to generation n so that both generations share equally the burden of the depression. In this way, we can think of social security as an investment, or as an asset. Generation n-1 invests in the welfare of generation n.
If there was a storage technology possible and everyone could store their own apples, then generation n-1 would eat 10 apples (5 and 5), and generation n would eat 8 apples (4 and 4), and generation n+1 would be back to 10 apples. The sequence of total consumption would be: …, 10, 10, 8, 10, 10, …
This sequence has less total utility than the previous sequence as generation n bears the full brunt of the recession.
Individual savings results in more volatility and reduced welfare than collective transfers. Collective transfer programs like social security can, and in practice are a benefit to the future and form cohesion among overlapping generations.
So, in practice, is a transfer system a debt imposed on future generations or is it an investment made by past generations? It really depends on how we operate the system, but in practice, social security has been more like the latter than like the former. And the irony is how critics are calling to end social security because they call it a burden on the future. It will only be a burden if they end it! Paul Krugman has made this point several times.
Moreover, if we were to design a system choosing a veil of ignorance — e.g. not knowing whether we would be born into the lean years or the fat years, we would opt for social security rather than individual savings.
Me: “Public debt is neither necessary nor sufficient for an intergenerational stitch-up.”
Nick: “An unfunded pension plan is a debt that is not on the books. But that doesn’t mean that debt is irrelevant for intergenerational transfers.”
Note that Nick is not actually contradicting me. Similarly, his posts on this issue, for the most part, do not contradict Paul Krugman’s point. What Krugman is saying about the “burden” of debt is not affected by the undeniable fact that senior citizens can avoid taxes, by persuading the government to postpone collection by selling debt to the young.
If this issue is really so important, let’s give it an appropriate name: The Crumblies Problem, perhaps? But whatever you call it, let’s be clear that it’s a different issue, even if there is some overlap in the arguments.
K-man:
“Debt has distributional implications, and it may have macroeconomic effects because of those distributional issues. But again, all this is within the current generation; it’s not about the present versus the future.”
Nick’s posts absolutely reject that (according to my reading). That’s what this is all about, IMO.
There are enough straw men in this debate (in total) to fill a barnyard to standing room only.
I think Krugman’s phrase “within the current generation” is vague. It could do with clarification. If the government starts providing free nursing-home care for the elderly and finances it by borrowing, it’s trivially true that these transactions involve only the current generation. But obviously that doesn’t mean “it’s not about the present versus the future.” It must be, since it benefits people who have no future to speak of. Note however that such spending and borrowing means increasing debt. Whether the debt:GDP ratio was 20% or 70% when the Free Nursing Homes Act came into force doesn’t much odds AFAICT. In that sense the level of debt is irrelevant.
From Paul Krugman’s point of view, Nick Rowe’s Lucky Crumblies Critique is a straw man, but I suppose Nick Rowe could say that Krugman’s focus on fallacious VSP arguments is a straw man. I say: let’s distinguish clearly between the two topics and avoid reading a post about one as a post about the other.
So Krugman is saying:
a) there may be macroeconomic effects because of distributional issues
b) those issues and effects are only about the current generation – the future is not involved
And I believe Rowe is saying:
a) there may be macroeconomic effects because of distributional issues
b) those issues and effects can definitely involve both the present and the future
Note Krugman’s use of the words “may” and “not” respectively in the quote above.
It is the b) “not” point that is wrong according to Rowe (how I read it)
And it looks to me like about 97 per cent of the total discussion is an unnecessary deflection away from that central point. Interesting issues, but peripheral to that point.
I think the following comment by Nick elsewhere is a very good summation:
1. Debt does not reduce aggregate consumption in any future year, by assumption (it might do if it crowds out real investment, or if distorting taxes have disincentive effects so people produce less, but those were never at issue, so we are assuming those away).
2. If the government pays down the debt at some future period, the lifetime consumption of those paying the higher taxes to pay down the debt will be reduced, even though aggregate consumption in any year is unchanged.
3. If the government just taxes enough to pay the interest on the debt, but not pay down the debt itself, the lifetime consumption of those paying the taxes is unchanged, but their lifetime utility is reduced.
from:
http://mainlymacro.blogspot.ca/2015/02/the-burden-of-government-debt-again.html?showComment=1423761385753#c7804259090841953369
I would still like to know what distinguishes government debt from private debt. What about a business issuing shares to workers to fund their pension plans?
Has anyone ever made the analysis whether real capital is not a burden on past generations to the benefit of future ones? Kind of the counterfactual to the government debt debate.
In a way, the point being contested is an isolated one, because there are so many interesting issues around it that can change a given scenario as a starting point. But on the other hand its a major point because the analytical framework for generational accounting is pretty tricky. There’s a lot of important accounting embedded it – so you have to understand that a bond that is sold or bequeathed from one cohort to another does not have the same effect as when there is also a tax that effectively claws back either the interest or the interest plus principal. And it seems to me that the opinion of some of these professional economists such as Rowe and Wren-Lewis and Farmer is that there is a way of teaching things so these effects and the various larger issues around it can be clearly unpacked. And PK has confused things in his style of explanation. The way I see it, “we owe the debt to ourselves” is fine – except that the world changes from one second to the next. The “we” changes. So “we owe it to ourselves” simply becomes a way of saying that balances sheets reveal that a liability is also an asset at a moment in time. But that’s not good enough to understand what goes on over time.
Kevin: “Whether the debt:GDP ratio was 20% or 70% when the Free Nursing Homes Act came into force doesn’t much odds AFAICT. In that sense the level of debt is irrelevant.”
Compare two possible worlds:
World A is just like my example above, with zero debt, where each individual consumes 50 apples when young and 50 apples when old, and r = 0%.
World B has a debt of 10 apples. Nobody remembers when that debt was incurred, but it exists now. The government holds the level of debt constant, and just pays the interest on the debt. Each individual consumes 40 apples when young and 60 apples when old (they buy a 10 apple bond when young, and sell it again when old). The interest rate is 50% per period (because 60/40 = 1.50). The government taxes each old person 5 apples and gives 5 apples back as interest.
Individuals in World A have a lifetime utility of 7.824
Individuals in World B have a lifetime utility of 7.783
If the level of the debt is 20 apples in World C, individuals consume 30 when young and 70 when old, and have a lifetime utility of 7.686
So if we start in World A and then increase the debt by 10 apples to finance the nursing home, lifetime utility drops from 7.824 to 7.783. That’s a drop of 0.041
And if we start in world B and then increase the debt by 10 apples to finance the nursing home, lifetime utility drops from 7.783 to 7.686. That’s a bigger drop of 0.097
We learn two lessons from this:
1. the level of debt matters (comparing world A to World B) even if it never changes.
2. the level of debt also matters for changes in the level of debt (comparing the difference between A and B to the difference between B and C).
Starting at r = g = 0, the marginal cost of debt is initially zero, but is an increasing function of the level of the debt.
(And notice, by the way, that individuals would be better off in terms of lifetime utility if they could sell some of the bonds to foreigners, if the foreign interest rate were less than the domestic autarky interest rate. Foreign debt is less of a burden than domestic debt, in that sense.)
Odie: “1. I would still like to know what distinguishes government debt from private debt.”
Oh Christ. how many times have I answered that question? I can’t force my kids to pay my private debts after I die. The government can force my kids to pay taxes to pay government debts.
Odie: “I would still like to know what distinguishes government debt from private debt.”
Most gov’ts have printing presses.
Nick Rowe: “I can’t force my kids to pay my private debts after I die. The government can force my kids to pay taxes to pay government debts.”
Within living memory, and perhaps even now (I don’t know), debts were inherited in India.
Nick,
I’ll think about your example. At present I must admit I can’t make sense of it. For example, “the interest rate is 50% per period (because 60/40 = 1.50)” loses me completely. I suppose some OLG optimization problem could come out that way but I don’t see how. And the government undertakes to give bondholders what, exactly? Is it a perpetuity with a nominal value of 10 apples and a coupon of 5 apples payable once per generation? If so that’s fine, but I don’t see why the young will buy it at par, if they have the log+log utility function you set out with.
Having said that, I’m quite ready to believe that with given endowments and tax arrangements (say, as in your example, only the old are taxed) the debt:GDP ratio will matter in an OLG model. I’m less convinced that welfare will always be lower at higher debt levels.
Just to note that Simon Wren-Lewis has a handy addition to the vocabulary for avoiding ambiguity in the discussion of OLG type effects, IMO.
He refers to the aggregation of co-existing generations in a given period as “societies”.
That clears up the meaning “future generation” as one of several that may co-exist at different life stages in the same future period – but not the entire population or “society” at that time.
That seems helpful because the word “generation” is still being used in different ways in different discussions.
e.g.
Robert Skidelsky is using the word “generation” in the sense of SWL’s “society” here:
“The national debt is not a net burden on future generations. Even if it gives rise to future tax liabilities (and some of it will), these will be transfers from taxpayers to bond holders.”
from:
That is wrong in the sense of OLG of course.
JKH: Simon Wren-Lewis “refers to the aggregation of co-existing generations in a given period as “societies”.
“That clears up the meaning “future generation” as one of several that may co-exist at different life stages in the same future period – but not the entire population or “society” at that time.
“That seems helpful because the word “generation” is still being used in different ways in different discussions.”
Or we might use English instead of redefining common terms. For example: “Cohort” applies to people born at the same time. “Cross-section” applies to people alive at the same time.
Kevin: “At present I must admit I can’t make sense of it. For example, “the interest rate is 50% per period (because 60/40 = 1.50)” loses me completely.”
OK. This is crucial. There’s a debt of 10 apples (by assumption). So the young person buys the 10 apple bond, and so only has 50-10=40 apples left to consume. And the old person sells the 10 apple bond, so gets to consume 50+10=60 apples. (He also gets paid interest, but is taxed to pay the interest, so that’s a wash). In equilibrium, he must be just willing to consume {40;60}, otherwise there will be an excess supply or demand for bonds. At what rate of interest will {40;60} be his choice? It’s where (1+r) = MU(40)/MU(60). (The relative price of two goods must equal the ratio of the Marginal Utilities of those two goods, and in this case the two goods are: beers when young and beers when old.) And with U=log(C), we know that MU = 1/C (because dU/dC = 1/C.). So in the new equilibrium, the interest rate is given by 1+r=60/40, so r= 0.5, or 50%.
If people eat the same 100 apples over the lifetime, they prefer consuming 50,50 to consuming 40,60. But an individual who does not buy a bond still pays the tax, so consumes 50,45, which gives him lower utility than 40,60.
min:
what’s the definition of generation?
Thanks Nick. OK, so I’m born with no bonds and a (50,45) endowment (after tax). When my hair goes grey I sell my bonds ex-div to a youngster and collect the coupon of 5 apples per bond from the government. Fine, I’ll think about that model and some minor variations on it.
It may be worth noting at the outset what I expect to find, to see whether I’m learning anything. I’m guessing that the level of debt does matter, but that zero debt doesn’t maximize welfare (weighting the utility of all cohorts equally). The optimal level of debt will depend on the initial endowments. But hopefully there will be some surprises.
Kevin: you are very nearly there with your guess. Zero debt may or may not maximise welfare. In my particular example above, where people have equal endowments when young and old, and where they weight their utility equally when young and when old (zero time preference proper), then zero debt is optimal.
If I changed my example, so that they were endowed with 60 when young and 40 when old, a debt of 10 would be optimal. (And the rate of interest r would be negative 50% initially, and would increase to 0% with a debt of 10). With negative r, the government would need negative lump-sum taxes to pay interest on the debt (it would be paying lump sum subsidies).
@jkh
According to Webster, a generation is “a group of people born and living during the same time”. It is vague enough to be used for people born at the same time and for people living at the same time. IIUC, demographics uses the term, “generational cohort” for the former. 🙂
I am not proposing to do away with the term as used in the OLG literature, which is apparently the same as a generational cohort. But to try to impress a very vague term like “society” into service as a precise term seems misguided. “Cross-section” may not be the best term, but it is already used to specify part of a flow at a given point in time. If you look at Nick’s vertical relation above, it is a cross-section.
And when the propagandists talk about the National Debt being a “burden on future generations”, they are not using “generation” in any but a vague sense. They are certainly not talking about generational transfers.
I hope that it is clear that I am not trying to tarnish Nick nor his arguments by association. 🙂
Min: I prefer the word “cohort” too. But we seem to be stuck with “generation X” rather than “cohort X”.
Min,
That all makes sense. I’ve used the term “cross-sectional” myself in comment.
Generational cohort and generational cross section might make sense as terms.
As do horizontal and vertical as descriptors.
I think my point is that “generation” alone is a potentially ambiguous word that is unfortunately embedded in the term OLG itself.
So, for purposes of avoiding ambiguity in discussion, unpacking it somehow makes some sense ….
It would make discussion a lot easier if standardized
Nick Rowe: “we seem to be stuck with “generation X” rather than “cohort X”
No, we do not have to adopt vernacular terminology. In fact, if we communicate with the general public while using words in a different sense than that of common usage, we invite misunderstanding. In fact, that is part of what is going on with “burden on future generations”.