Teaching, OLG models, and the phenomenology of perception

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.

Log calculator is here.

[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.

Comments

[JKH]

"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."

Assuming it stops, right?

(i.e. analogous to tax / primary surplus)

[rpl]

Nick, is this the kind of spreadsheet you were looking for?

[Link Here NR]

NB: The shared doc itself won't be editable (e.g. to change the generational transfer amount) by people other than me, but you should be able make a copy that you can edit (I think...)

[Vladimir]

If everyone in line has a beer and passes a beer forward ,for the first person to have two doesn't that mean she must retain her beer? Doesn't it then follow that the last person will have no beer, having passed her beer forward? The last person will merely have the scrip.

[Odie]

Two questions:
1. "There is no way you can do it without making some future generation have lower lifetime utility."
Does that also hold when you introduce the production of real capital like a beer-producing machine in addition to just changing the distribution of consumption goods?

2. How would public debt be any different here from private debt?

[Frances Woolley]

Vladimir - it's an infinite line, there is no last person (by definition of infinity).

Nick: "I can't teach you anything. You can only teach yourself" Is this self-evidently true? Those 10 words merit a blog post in their own right.

[Kevin Donoghue]

What happens to the lifetime consumption, and lifetime utility, of future generations, if you use sawn-off shotguns to enforce transfers to the old in generation A? Am I right in thinking that there is no way you can do it without making some future generation have lower lifetime utility? If that is so, do we need a treatise on The Burden of Shotguns?

[Nick Rowe]

JKH: "Assuming it stops, right?
(i.e. analogous to tax / primary surplus)"

We don't need to *assume* it stops. If you try to run a Ponzi scheme in this model, r rises above g (the growth rate is 0%), you will eventually get to a point where the debt can't grow any more, because if it did it would be bigger than 50, so the young would be drinking negative beers. It has to stop.

(It would be different if I assumed r < g, for example by having the young produce 60 beers and the old produce 40, which would make r < 0%.)

rpl: that's exactly what I had in mind (I think), if people can find some way to copy then edit it. Thanks!

Vladimir: it doesn't work if the line is finite. It also doesn't work if someone breaks the chain.

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.

Frances: Hmmm. Probably not self-evidently true, and not 100% true, but from experience (as student and teacher) I think there's a lot of truth in it, especially when it comes to OLG models.

Kevin: we do use sawn-off shotguns. Or the government does. To collect taxes. Debt and taxes are related. If r < g, there need be no taxes, and there needn't be a burden of the debt.

[Nick Rowe]

Kevin: want to call it "the deferred burden of deferred taxes? OK.

[Kevin Donoghue]

Nick, I'll stick with the answer I gave you in comments at Mainly Macro: The Perils of Aggregation.

There's no good reason why a policy which benefits Generation A and screws Generation Z should be called a burden, nor why the reverse policy should be called a boon.

[JKH]

Nick

"We don't need to *assume* it stops."

Can't you sustain it with primary surplus of 0?

In which case you do have to assume it stops (with a positive primary surplus)?

[Nick Rowe]

JKH: "Can't you sustain it with primary surplus of 0?"

No. If the debt is positive, then (Cold/Cyoung) > 1 so r > 0, so you need to run a primary surplus to pay the interest and stop the debt growing over time.

[JKH]

Oh right .. got that backwards

I guess I intended a primary surplus equal to the interest

thx

[Nick Rowe]

Kevin: if the government puts a tax on apples, is it the seller of apples or the buyer of apples who bears the tax burden? And is there an excess burden of taxation? That's how we normally talk about tax incidence. We use the word "burden". I don't see why I'm not allowed to use the same word the same way to talk about intertemporal taxation.

[Kevin Donoghue]

Odie: "How would public debt be any different here from private debt?"

There's no way Generation A can borrow from Generation B, since they only coexist for one period. But of course government can tax Generation B and subsidize Generation A and then repeat the process until (in Nick's example) it decides to not tax Generation E or subsidize Generation D (the one that gets screwed).

In other words, we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this. That's probably one reason why Paul Krugman is ignoring Nick Rowe & Co.; he knows a red herring when he sees one.

[Nick Rowe]

You can't force future generations to pay your private debts, unless you leave thenm an asset in return.

You wait Kevin. Any day now, Paul will see The Light, and will be converted to The Truth.

[Donald Pretari]

My Phenomenology of Perception course was taught by Dreyfus. It was very good. Speaking of times past:

"Nick, I might ask something else, but this puzzles me:

"because the domestic and foreign central banks want to push interest rates lower, but can't.'

I don't understand why the Fed couldn't"
1) Add a fee to these bonds
2) Discount them over time

In other words, add a disincentive to buy and hold them.
Posted by: Don the libertarian Democrat | February 03, 2009 at 04:51 PM

"Hi Don: it's technically possible. But people would just hold cash under the mattress, or in safety deposit boxes, and get zero interest rates that way. (There are various schemes always floated to tax cash, or make it expire, etc., but they always come across as a bit sci-fi.)

Posted by: Nick Rowe | February 03, 2009 at 05:27 PM"

Welcome to the future:

http://www.nytimes.com/2015/02/13/business/international/sweden-cuts-interest-rate-and-announces-bond-buying-program.html?partner=rss&emc=rss

[Nick Rowe]

Don! The one person who might read this and know if I'm talking nonsense about Merleau-Ponty! (My course was very good too, but man that was a difficult book.) I just Googled and found this. I don't really understand it, but bits of it are very slowly coming back to me, out of a 40 year old haze.

Yep, if there are costs to storing currency (fear of fire and theft) you can get interest rates a little bit negative. Until someone figures out a cheaper way to store currency. (I think they are already onto the "pay your taxes in advance" gambit.)

[Peter Dorman]

Am I missing something obvious here? Since you have diminishing marginal utility in beer in each period, additive utility across individuals, and an equal division of beer consumption across time periods in the initial state, a transfer of beer consumption from one time period to another, even between different people, is utility-reducing. This is more or less tautological. The transfer of beer from Gen B to Gen A in the second column (period) is a dumb idea. The model shows that you can compensate the Gen B’s loss of ten beers in the first half of its life by getting Gen C to donate 10 beers in the following period, but it can’t be fully compensating in utility terms, nor can subsequent compensations to Gen C, Gen D etc.

Similarly, with the same utility functions, if people are more productive in the first half of their lives, producing 60 beers in the first period and 40 in the next, you would get an aggregate utility boost from the same transfer program, assuming an infinite time horizon.

So the moral of the story is, if the old and young are equally well off, don’t force the young to transfer some additional portion of their consumption to the old. I’ll buy that.

[Jussi]

If the old owns everything, let's say an apple tree (there is no beer trees I know of). Let's say he needs to pay the young a price to pick the apples (a market clearing price) - assume the old cannot pick the apples.

The old wants to sell the apple tree to buy some extra apples as he knows he will be soon gone. What is the price of the apple tree? I think there is no such price because after the trade there is no market for apples anymore. What is the price of government debt? I think it is zero, the young will not buy it at any price. The young knows he would be worse off. The old cannot hand over a piece of paper to make the young comply. The young will get everything by just waiting.

The old needs more than economical means to get extra amount of apples. This is not an economical model at the micro level?

This is not exactly Nick's model but does it give any insight? Can we relax the assumptions that the old cannot pick the apples?

[Avon Barksdale]

OLG with an infinite number of agents is done well in Romer's Advanced Macroeconomics (an upper year undergraduate text). The Welfare Theorems are violated when you expand to an number of infinite agents. What you are talking about in this post is the possibility of dynamic inefficiency.

The best way to learn this is NOT by numerical examples, it's by writing down the specification and working out the Pareto efficient equilibriums. As I learned in high school, numerical examples confuse, they don't help. Units disappear making it impossible to track mistakes, and the arithmetic is just mechanical. Insight comes from understanding relationships, that's why we use algebra!

This is a useful exercise for undergraduates so that they can see how it is possible to get a Pareto efficient outcome that a competitive market cannot reach.

[Jussi]

"get a Pareto efficient outcome"

It looks to me as an inefficient outcome? And I think competitive market will do better.

@Peter
I think you are exactly right, the young will not buy the burden (it can be forced, by taxation but not in voluntary terms).

[Min]

"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."

This illustrates the danger of reasoning from infinities. The amount of beer drunk is the same in each "equilibrium", yet one more beer is drunk in the "Pareto Superior equilibrium". Economies are finite, and there is no reason to think that reasoning from infinities applies to them. Besides which, it matters how the infinity is generated.

Let us start with two people and two beers. In one "equilibrium" each person drinks a beer. In the other "equilibrium" the first person drinks two beers and the second person drinks none. The second "equilibrium" is not Pareto Superior to the first. Now let us add one person and one beer. In the first "equilibrium" each person drinks one beer. In the second "equilibrium" the first person drinks two beers, the middle person drinks one beer, and the last person drinks none. The second "equilibrium" is not Pareto Superior to the first. Now let us add another person and one more beer. It is obvious that the "equilibrium" where the first person drinks two beers and the last person drinks none is not Pareto Superior to the other one. If we keep on adding people, we will never reach a situation where one "equilibrium" is Pareto Superior to the other. That relation between the two "equilibria" is always the same, and it remains the same in the limit.

So is the second "equilibrium" Pareto Superior to the first or not at infinity? There is no way to tell. The original reasoning assumes that when you have an infinite number of people and beers, there is no last person. But that assumption is not justified. It is perfectly possible to have an infinity of people and beers with or without a last person. The reasoning from infinity of the quoted argument is fallacious. Reasoning from infinity is dangerous.

[JKH]

But reasoning from infinity is fun.

[Jussi]

Nick constructed a model which is not infinite because r>g (g=0). I'm not sure this is a consistent model because with certainty (no volatility) and zero growth I think r == 0. If r>0 this is a ponzi scheme, so who is willing to buy the bond in the first place? Both r>0 and r==0 cannot be true - market doesn't clear?

[Jussi]

Hmm. it might be infinite but the effect kicks in at some point of time. This happens when a generation recognizes the ponzi scheme. Assuming rationality it will be the first and second generations.

[Phil Koop]

This illustrates the danger of reasoning from infinities.

It is perfectly true that reasoning from infinities has many pitfalls for the naive; that is why an innocuous-looking series like Grandi's series diverges. It is also true that the reasoning given in the post is fallacious.

But it is possible to reason about infinities and in fact your inductive approach is the right way to go about it: construct a sequence of arbitrary length and then ask whether it converges, and if so what to? But I don't agree with "no way to tell"; every term in the series is Pareto Inferior, assuming convex utility. The average utility converges (from below) to the original average.

[Phil Koop]

But once they get it, they don't need the numbers any more, they can see the general principle ...

Your posts so often make me nostalgic!

The introduction to the textbook for my first exposure to abstract algebra ("Modern Algebra with Applications", by Gilbert) ran, in paraphrase:

Algebra is the manipulation of symbols ... the ancient Greeks knew the technique of using an abstract symbol, such as x, to represent an unknown number ... the symbol could be manipulated just like a known number to solve a problem ... but in the 19th century, it was gradually realized that the symbols did not have to stand for numbers; in fact, they didn't have to stand for anything at all!

And so the path was opened to Stone's representation theorem and all that followed.

[Bob Murphy]

Kevin wrote: "If that is so, do we need a treatise on The Burden of Shotguns?"

If a Nobel laureate in firearms kept writing blog posts saying, "It's impossible to shoot yourself" then yes, we would definitely need such a treatise.

[Bob Murphy]

Kevin wrote:

"we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this. That's probably one reason why Paul Krugman is ignoring Nick Rowe & Co.; he knows a red herring when he sees one."

And yet, Krugman has never once made this particular argument, Instead, he keeps saying "we owe it to ourselves," which is utterly irrelevant if he has been trying to make the point you bring up here. One almost gets the sense that Krugman thinks "we owe it to ourselves" is the crucial factor, since he keeps saying it is. Nick is simply taking Krugman at face value, rather than inventing arguments for his position that Krugman has never made.

[Min]

Phil Koop: "But it is possible to reason about infinities and in fact your inductive approach is the right way to go about it. . . . But I don't agree with "no way to tell"

IMO, for scientific purposes the inductive approach is correct, as a rule. However, it is quite possible for something to be true for each finite instance and yet false for the infinite case. But if you reason from infinity there is no way to tell if that is so. IOW, you have to make an assumption.

[Min]

Bob Murphy: "Krugman has never once made this particular argument, Instead, he keeps saying "we owe it to ourselves,"

I don't follow Krugman, so I am not exactly sure what he means. But as far as future debt is concerned, people in the future owe it to other people in the future. If both the future debtors and future creditors belong to "us", then "we" do owe it to "ourselves". ("Do" in the sense of the timeless indicative. ;))

[Nick Rowe]

Peter: "Similarly, with the same utility functions, if people are more productive in the first half of their lives, producing 60 beers in the first period and 40 in the next, you would get an aggregate utility boost from the same transfer program, assuming an infinite time horizon."

True. But in that case, r < 0. With a negative interest rate, an increase in the debt would imply no future taxes. Ponzi finance would be sustainable, because the debt would diminish over time by itself. All future generations would gain (and you can make that statement without adding interpersonal utilities).

And where does this case leave "We owe it to ourselves, so debt doesn't matter at the aggregate level"?

[Too Much Fed]

Odie said: "2. How would public debt be any different here from private debt?"

With private debt, entities have a pretty good idea who will/should pay the interest and principal and when the principal and interest will/should be paid.

With gov't debt, not so much.

[Too Much Fed]

rpl, thanks for the spreadsheet. It appears the key in this particular scenario is B2,C2 and E5,F5.

Anyone, is there "money" in this model?

[Bob Murphy]

Min, if you look carefully at what my statement again, you'll see that I didn't argue, "Krugman is wrong when he says we owe it to ourselves." Rather, I said that that is irrelevant to the argument Kevin Donoghue was making about why the debt is a red herring.

It's like Krugman has been running around for 3 years saying, "Whales are actually mammals, not fish, because their name starts with 'w.'" And all the biologists are saying, "Yep, good job, clearing up that confusion with the public."

(I realize I destroyed any comprehension you may have had, with that analogy. My audience is Nick at this point.)

[Min]

@ Bob Murphy

No, you didn't destroy anything. What Krugman says may be irrelevant to what Donoghue is saying, but Krugman is addressing fears of the public and propaganda that has been around as long as I have been alive. Maybe everybody needs to go to an Esalen weekend retreat and communications workshop. ;)

[rjs]

Nick,

I'm just wondering, why do you only tax the young and not the old in these models?

Suppose, for example, that the government taxes the public and uses the proceeds to fund Public Television for one period. Don't the old also watch TV? But they were not taxed when young to watch TV in the current period -- Public Television was only provided in the current period, not the past. Wouldn't this be a transfer from the young to the old? Exactly the same kind of transfer as if the government sold bonds to pay for public television for one year, and then redeemed the bonds in the future. In other words, the transfers you describe are due to a poor taxation system, whether this is part of pay-as-you go or part of coupon redemption. In this case, you may want to pay for public TV by imposing a tax on consumption that is paid for by both the young and the old, rather than a tax on labor income that is only paid for by the young. A tax on consumption, in your model, is identical to a tax on savings as the old consume all of their savings and only their savings.

You have only shown that with a bad taxation policy, it's *possible* for government debt to result in a transfer. Just as it's possible for a pay-as-you go government expenditure to result in an intergenerational transfer! The financing method is not the culprit here, but the taxation policy.

But you have not shown that it is required. E.g. that by taxing both the young and the old, an intergenerational transfer necessarily arises. It does not arise with an optimum taxation policy, regardless of whether the spending is deficit financed and redeemed in a distant future period or pay-as-you go.

[JKH]

Nick,

In your original post (this year’s) you make the basic point about intergenerational distribution.

Which you label as “time travel”.

But you do not talk about utility there, until subsequent posts.

I’m trying to piece these together – versus Krugman for example.

These are analytically separate pieces aren’t they?

Independent? Interdependent?

Is Krugman denying both of them?

[Jussi]

"True. But in that case, r < 0"

But Nick in your example r > 0 and it is a ponzi scheme, why do you assume someone is buying ponzi-bonds in the first place??

[Nick Rowe]

JKH: adding utility to the model doesn't really change the model, but it lets you see additional things. It lets you see that debt can make someone worse off (or better off, if r < 0) even if their lifetime consumption is unchanged. It's a better, more accurate way to talk about the burden of the debt.

rsj: there are two ways for the government to implement my 10 beer example:

1. Set up an unfunded pension plan where each period the government taxes the young 10 beers and gives 10 beers to the old (then stops doing it after 2 periods).

2. Issue bonds to borrow 10 beers from the young in the first period and give them to the old. The rate of interest will be (60/40)-1 = 50% per period. The government taxes the old 5 beers to pay the interest. Next period the old sell their bonds to the young. Then the government pays off the debt.

Both 1 and 2 give exactly the same result. A national debt is like an unfunded pension plan.

Yes, it is possible for the government to tax the old to benefit the young in each period. That's like a negative unfunded pension plan, or a negative national debt. A student loan program is like a negative national debt, because students owe the government. Funding for high schools is like a negative unfunded pension plan. Lots of things are possible.

[Nick Rowe]

JKH: but if you say that debt makes people worse off if it reduces the *Present Value* of their lifetime consumption, then adding utility to the model doesn't really let you see much more. You get the same answers with PV as you get with Utility, for small changes in debt. (For large changes, the sign of the effect is the same, but the magnitude is different.) So if you want to think in terms of *PV* of lifetime consumption, you are fine. (It gets tricky for large changes, because r will change too.)

[JKH]

"A national debt is like an unfunded pension plan"

right

which is why those who are saying this is not about debt are introducing a straw man

the "time travel" idea obviously requires/assumes a time period longer than zero

and some form of liability over that period

an unfunded pension plan still has a liability, which amounts to contingently structured debt

[Kevin Donoghue]

Many thanks to Bob Murphy for giving me some idea what it feels like to be Paul Krugman. Against uncharitable readings the gods themselves contend in vain.

Sez Bob: Krugman has never once made this particular argument, Instead, he keeps saying "we owe it to ourselves," which is utterly irrelevant if he has been trying to make the point you bring up here.

My point being: "we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this."

Here's Krugman making precisely that point:

[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?

Well, let’s do a thought experiment that doesn’t, at least initially, seem to have anything to do with debt. Suppose that instead of gifting seniors with debt, President Santorum passes a constitutional amendment requiring that from now on, each American whose name begins with the letters A through K will receive $5,000 a year from the federal government, with the money to be raised through extra taxes. Does this make America as a whole poorer?

He goes on to argue that it doesn't.

http://krugman.blogs.nytimes.com/2012/10/12/on-the-non-burden-of-debt/

[Roger Sparks]

The infinitely long line of beer holders, each passing his beer forward, ignores the effect of time. This is a serious departure from economic reality.

Assume the infinite line of beer holders, each with a beer in hand. The first in line shouts the order to "Pass Beer Forward!" The order travels down the line at the speed of sound . As the order travels down the line at the speed of sound, each beer begins movement when the order reaches the beer location. It is obvious that beer movement begins later in time when the beer holder is farther from the front. The effect can be considered as a traveling hole . Each beer holder becomes beer deficient when he makes the transfer of his beer.

The effect of debt is the traveling hole that each person in the line experiences. Except for the first in line, there is always a period where the beer holder actually has no beer.

[JKH]

Nick,

I think the deficit/surplus intergenerational transfer and the utility intergenerational transfer are separate analytical issues.

Because utility is still an issue (I think) even if there is no “stop” effect from a surplus as otherwise assumed at the far end of your model.

And I think this is one point of confusion – e.g. it shows up in comments in Murphy’s post.

A sub-point is that some people seem to believe that the front end deficit alone is enough for an intergenerational transfer – which it is not in terms of intergenerational transfers from the future to the present, which is the point of your model - which also leads them to think that debt (liability more generally) is not an issue, which is also wrong - again this shows up in comments in Murphy’s post.

And then there’s the extremely basic point that some people don’t seem to understand that a steady state GDP is assumed in the model – to make the other points clearer. It is absolutely no revelation at all to understand that aggregate consumption in a period is unchanged, notwithstanding the intergenerational analysis that is done beyond that. It is a simplifying assumption – not a Eureka insight – as to what’s going on. Similarly, Krugman’s “we owe it to ourselves” should be obvious enough to anybody who understands that a government debt obligation is somebody’s asset. For those to whom that is not obvious, Krugman shouldn’t be making sweeping generalizations that are incorrect in other specific ways.

The key strike against Krugman is still the very last sentence in his post, which is what your model addressed.

What a mess, still, after 3 years.

[Nick Rowe]

JKH: "Because utility is still an issue (I think) even if there is no “stop” effect from a surplus as otherwise assumed at the far end of your model."

Yes. Utility can be reduced, if taxes to pay interest are positive, even if the debt is constant over time. But then Present Value of lifetime consumption is reduced by those taxes too.

[Scott Sumner]

Nick, I haven't followed this closely, but Krugman is obviously smart enough to understand what you are saying. He would have grasped the point more quickly than I did. It seems to me that either:

1. He hasn't read any of your posts on this.

2. He has, but prefers to think in terms of the consumption of cohorts alive at various dates (is that the right term?), not generations.

[Michael S.]

Nick,

If PK were led to the Truth after reading your posts over a light lunch of apples and beer, he might feel duty bound to say "If I define intergenerational transfer in a particular way, as a transfer between old and young at the time they coexist on this earth, then debt can transfer wealth across generations. However, 125 years later, this debt will have no impact on the aggregate wealth of old and young combined." Would that end the debate on this particular topic, or is there something deeper that I ( and others asking the same question) are missing?

I realize it is frustrating for you when multiple people ask the same question, as though some new phrasing of it will suddenly make you change your mind. I am just trying to understand.
I have played with the arithmetic as you advised, and am no clearer. I cannot create a cascading loss of wealth or utility.

Michael

[Min]

"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."

And, I may add, the best way to play around with the numbers is with computer simulation. I just did a quick web search, and I do not mean the sophisticated computer programs that solve massive systems of equations, or those that compute equilibria, but something like NetLogo, which lets you create simple models and run them. :)

[JKH]

“And then STOP, so that the young in generation D give no beers to the old in generation C … 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”

A deficit starts the process.
Time elapses
A surplus stops the process.

The intergenerational burden is due to:

a) The initial deficit
b) The passage of time
c) The surplus tax event

Krugman simply doesn’t address this

utility is a separate measurement dimension, IMO

[Min]

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".

[JKH]

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.

[JKH]

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).

[Michael S.]

Thanks, JKH. I will
play with that idea in my version of the toy model and leave Nick alone.

[JKH]

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

[Michael S.]

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.

[JKH]

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)

[Yancey Ward]

One almost gets the sense that Krugman thinks "we owe it to ourselves" is the crucial factor, since he keeps saying it is.

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]

"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.)

[Nick Rowe]

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.)

[Nick Rowe]

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.

[Min]

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. ;))

[Roger Farmer]

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".

[Nick Rowe]

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

[rjs]

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.

https://windyanabasis.wordpress.com/2015/02/15/is-government-debt-a-burden-on-future-generations-not-in-fruitopia/

[Too Much Fed]

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?

[Min]

@ 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.

[Yancey Ward]

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?

[Michael Sigman]

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.

[Andy Wall]

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.

[Lord]

A post on taxes can be a burden on past generations should probably follow this one.

[Nick Rowe]

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.

[JKH]

"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.

[Fred Fnord]

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.

[rjs]

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.

[Min]

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.

[rjs]

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.

[Kevin Donoghue]

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.

[JKH]

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.

[Kevin Donoghue]

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.

[JKH]

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

[Odie]

1. 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?

2. 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.

[JKH]

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.

[Nick Rowe]

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.)

[Nick Rowe]

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.

[Min]

Odie: "I would still like to know what distinguishes government debt from private debt."

Most gov'ts have printing presses.

[Min]

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.

[Kevin Donoghue]

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.

[JKH]

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.

[JKH]

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:

https://larspsyll.wordpress.com/2015/02/16/debt-myths-debunked/

That is wrong in the sense of OLG of course.

[Min]

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.

[Nick Rowe]

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.

[JKH]

min:

what's the definition of generation?

[Kevin Donoghue]

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.

[Nick Rowe]

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).

[Min]

@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.

[Min]

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. :)

[Nick Rowe]

Min: I prefer the word "cohort" too. But we seem to be stuck with "generation X" rather than "cohort X".

[JKH]

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

[Min]

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".