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But if we want to maximize utility - why not simply tax and redistribute? That choice is still open for those living in the future time period. If you do that, there might be a second order cost in terms of reduced efficiency, but no one has ever denied that.

The implicit assumption that someone will tax and redistribute is the basis for pretty much every cost benefit analysis ever done. It is definitely ALWAYS required for pareto optimality, and is almost always needed if you use some cardinal logarithmic social welfare function (since when your voting right is determined by wealth, the “best” actions is usually those who benefit the wealthy).

nemi: if in every year you tax the old and give it to the young, the young will save the transfer payment to pay their future taxes when old. It won't affect consumption in my model.

"Each young person therefore consumes 100-B when young and 100+B when old"

Strange. Isn't it the opposite? Young people consume more than old people which is the reason why they take loans?

"Now suppose the government issues bonds and gives each person in the first cohort a bond worth B apples"

This is also a very strange statement. The correct one is "young and old people together decide to move some apples around and for that reason issue bonds". In such statement the act of moving applies around is by definition neutral to the total utility. Making the rest of arithmetic redundant. Or I am wrong?

In the second period, you tax the first cohort B units (or default on the bonds). -> utility max in period 2 and every future time period -> no burden under current definition.)

Sergei: "Young people consume more than old people which is the reason why they take loans?"

From my observations, young people *invest* more than old people (who disinvest), which is why they take out loans. Houses, education, cars, etc. But if I put investment in the model, I would get crowding out of investment, which we all agree can be a burden.

Sergei: "This is also a very strange statement. The correct one is "young and old people together decide to move some apples around and for that reason issue bonds"."

The kids, and the unborn, don't have the vote.

nemi: that's like saying: the debt won't be a burden any more if you pay it off. Sure, if you give the young in the first cohort a bond, then take it away from them when they get old, nothing happens.

Nick: Yes - that is the point. They have the choice to remove the so called burden. If the goal of their society is to maximize social welfare, they will do that – unless they are stupid, but then it is the stupidity that is the real burden and not the debt.

PS: We could of course introduce some assumptions about power distribution, but if the old are more powerful and want 100+B when they are old – they will get that whether they hold a bond or not. (or 100 + X if they cant get everyting they want, but that X will be the same with or without bonds)

nemi: OK. But if they falsely think it is impossible for debt to create a burden on the future, they will probably make stupid decisions.

Ah but Nick Rowe, all you've really shown here is that debt can reduce utility. What if the government decided to shoot random people in the head? That would reduce utility too. More red herrings from the Canadian...

(This is a joke for people who don't know what I'm talking about.)

What would be funny Nick is if you combined this type of model with a social choice mechanism, and showed that the government would issue debt if only early generations can "vote," but it will run a balanced budget if all generations have a say in the government's policy in each period. (I'm not sure you could make the debt outcome subgame perfect, but I think you could make it a Nash.)

And a good one Bob!

Let's see if some of our critics can do any better!

Of course debt, or shooting random people in the head, can reduce utility – but it does not create a burden on future time periods since they retain the option to stop shooting random people in the head.

If they keep on shooting random people in the head, even though no one likes the policy, they are simply stupid.

It is not the past policy of shooting people in the head that creates the burden of current random executions. It is their stupidity. How can this not be clear?

Bob. I think (I'm not sure) it would depend on population growth rate. If the growth rate is just slightly positive, so there are more young than old, the young would eventually at time T agree to default on the bonds, and the whole thing unravels backwards. I vaguely remember we had a good discussion of this in comments a year ago. But now my memory has failed.


Another model that works for the "debt is a burden" side is via balance sheet analysis:


Utility can be decreased for entire generations when taxation is introduced to pay back the debt, in the form of total property declining without any replacement (money + goods + asset (bond).

We don't even need to derive a "convenient" utility model that just so happens to output a lower utility for a different cross-sectional consumer good allocation between young and old when debt is present.

We can show debt burdens the future by tracking all property titles, including money, goods, and assets (bonds).

"total consumption in any year is held constant in your examples "

Thanks, Nick. That's exactly the issue I keep banging up against, no matter how many times I go through this.

Two things:

1. Isn't the problem with this model that consumption *is* held constant? Because higher consumption drives higher production, so the whole question is whether there are mutual incentives causing higher GDP over time. We want to ask: does this grow the economy? By holding consumption constant, that question can't even be asked. The model seems to preclude both the question and the answer. Or: it's become so stylized and assumption-constrained in its attempt to tease out one (arguably tiny or at least quite uncertain and far-off) effect, that it's making it impossible to see several elephants in the room. ??

2. If you want to start on MUC, transfer between cohorts, then I'm expecting posts on how we should be transferring a lot more money from the rich to the poor, maximizing aggregate utility. No names, just initials: EITC.) I'd also expect some MPC-based posts on how such policies increase velocity and AD, encouraging more production and GDP growth.

M_F: I think you are right. One of our regular commenters here, JKH, has done something similar. But I have also seen people use balance sheet analysis to "prove" the opposite.

I still remember a published paper I was shown as an undergraduate. The proof went:

I's = Me's

Multiply both sides by "OU"

IOU's = UOMe's


1. well, I did build a model with unemployment where the deficit caused total consumption to rise. But I still got a burden on future generations.

2. Yep, but it would hardly be new or controversial. That's the standard argument in economics for redistributive tax/transfer policies. Everyone would just yawn if I did a post on that. And I have done lots of posts on whether and how fiscal policy works to increase AD.

"From my observations, young people *invest* more than old people (who disinvest), which is why they take out loans"

Nick, do you say that all private debt is good because it is investment or what? I do not understand what you want to say with "they take out loans to invest"

"The kids, and the unborn, don't have the vote"

They also do not get the bonds neither they get the apples. And *nobody* can force them to either buy the bonds or sell the apples when unborns get to vote. Because when they get to vote they can also decide on who gets apples and who gets bonds.

@Nick: "a model with unemployment where the deficit caused total consumption to rise"

1. Is that the right link? The post doesn't mention consumption or employment.

2. A. Is an MUC (hence MPC) function commonly included in economic models? Like the Fed's? B. How about one of your (excellent) simplified thought-experiment posts on how redistribution and MPC curves affect velocity, AD, production, and the investment necessary for that production? "Imagine the top 1% give 1% of their wealth to the 99% every year. Compare to 0%." Or some such.

Steve: Ooops! Wrong link. Sorry. I've fixed it now.

Gotta go. Back later.

This post is related to another case about which I have thought, where some people are liquidity constrained and others behave according to Ricardian equivalence (for standard Barro reasons). The debt then burdens the poor of future generations (those whose ancestors were liquidity constrained and therefore didn't leave bequests), forcing them to cede consumption to the rich people who have inherited bonds. If we believe that the marginal utility of consumption is diminishing and that it's meaningful to compare utility across people (which is a standard argument for income/wealth redistribution, I think), then the debt again reduces the total utility of future generations.

It's an interesting case, I think, because it seems to be the case that a lot of Keynesians have in mind, when they argue that (1) the tax multiplier is positive but (2) debt doesn't burden future generations (in aggregate). Dean Baker, for example, suggests that most people (unlike me, who I gave as an example) do have bequest motives. If asked why he doesn't then believe in Ricardian equivalence, I assume his main argument would be to bring up liquidity constraints. But if you follow that idea to its logical conclusion, it has the ugly implication that debt burdens the poor of future generations but not the rich.

I've gotten old enough to remember when all the right leaning parties were telling Canadians that paying down the debt means a socialists paradise, money for all the programs we could ever want.

But each time those parties got in and made cuts to "Fight The Deficit" (and debt) instead of real reductions to the deficit or debt we instead saw tax cuts. Tax cuts for corporations, tax cuts for the wealthy, tax cuts even for the middle class and poor. Although the tax cuts for the middle class and poor were offset by various consumption taxes, fees and reduction in government services like employment insurance and pensions, old age pension, increases in medical premiums, etc.

And each of those tax cuts further inflated the deficit and debt. None of them paid for themselves, each had to be paid for by cuts in services that have impacted real people. And our debt continues to increase.

So I propose the the rights continual screaming about debt is nothing but a canard, a ruse, because every time they have the opportunity to reduce the debt they instead reward their political supporters and corporate masters.

And for the record I'm not for debt. But the time to scrimp on healthcare isn't when the breadwinner has cancer. Instead you do what you need to to get the breadwinner back to work. When he/she is working, then you pay down the debt.


Yeah I've read that post a couple of times. Unlike you I couldn't do much of the resolving in my head, and like you I wanted a math wonk to sort out the final implications.

Even better, I want an agent-based simulation model that lets us turn the various dials and watch what happens over the generations.

Nick: Once again, if you really feel this way you - you should start a crusade against microeconomics – since pretty much any real world application of it rest on the assumption that the issue of efficiency can be separated from the issue of distribution (which we are supposed to achieve through taxes and redistribution).

And the one you really should direct this discussion towards is not Krugman, but Delong, since the assumption above is the very core of Neoliberalism (where Delong is the high priest).

I really do not see why you would put this discussion in some little box and label it “thoughts about debt”, when it is a very general issue and a (if not THE) fundamental part of both applied microeconomics and Neoliberalism.

"My counterexample is obvious really. What matters for economic welfare in any given year is not consumption in that year but the utility people get in that year from consumption in that year. If debt causes total utility to go down, even if total consumption stays the same, it seems reasonable to say there is a burden in that year. But why should debt cause total utility to go down, if it doesn't reduce total consumption? Because it may create or increase inequality of (marginal utility of) consumption between young and old. (Or it may reduce it, it depends)."

But this is the point of using total consumption instead of welfare. Welfare requires knowledge of the pre-redistribution (by debt) distribution (of income). It also depends on the form that we presume the welfare function to take.

To be frank, as a microeconomist I find that it is precisely the tendency to infer too much from these sorts of bare-bones macromodels any kind of welfare effect that bothers me the most about what macroeconomists do. Remember the Lucas (or I remember it being a Lucas... been a while since I did macro) paper estimating tiny welfare loss from allowing business cycle fluctuations? Yeah... not plausible.

You can't know what you claim to know about the system. As you rightly point out, redistribution could be improving welfare. By all means, use your welfare analysis to see what happens between cohorts, since in that case welfare analysis is not doing the heavy lifting for your argument--but if you want to change that, I'm going to have to cry foul.

BSE: Hey, I thought the whole of micro was about those little triangles! Only macroeconomists get to look at rectangles! And here I am, doing micro triangles, and you complain???

Sure, like all models, it's only an example. There could always be something else going on, like borrowing to build schools, which goes in the other direction. But if a microeconomist build a model of (say) welfare loss triangles due to distorting taxes, would you say it has no insights to offer? I could change many of my assumption, but as long as r > g, you are still going to get the effect I'm illustrating here.

nemi: "...since the assumption above is the very core of Neoliberalism (where Delong is the high priest)."

I thought "Neoliberalism" was some sort of lefty poli sci word used to demonise freemarket righties. And I thought that Brad Delong was a little bit left of centre? His name is not one that comes to my mind as a high priest (or any sort of priest) of "neoliberalism". Maybe I'm wrong about Brad DeLong. Or maybe I don't understand what you mean by "neoliberalism". (But, dear God, let's not get into that, please.)

Andy Harless: "But if you follow that idea to its logical conclusion, it has the ugly implication that debt burdens the poor of future generations but not the rich."

You don't even need time travel for that.

Chicago plan, anyone?

"I thought "Neoliberalism" was some sort of lefty poli sci word used to demonise freemarket righties"

Yes - but the only people I know who call themselves neoliberals are progressives - and if I remember correctly Delong is using that term to describe himself.

What it means to be a neoliberal is basically that you think that the first welfare theorem has a lot to tell us, and if you are a progressive neoliberal you would add that the second welfare theorem is there for us to exploit.

There is a Nobel winning physicists who insists that the earth goes round the Sun. I have built a counterexample , made out of clay , to prove to him that it is possible that the sun in fact goes round the earth. Unfortunately he still does not seem convinced.

After reading most of this huge discussion here and elsewhere, much of it multiple times, I'd like to suggest that Nick Rowe's conclusions could be summarized as follows.

"Government deficit spending today might impose a burden on future generations. They might be less prosperous because of it. But they might be more prosperous because of it. The effect in either direction might be very small or nonexistent. It is certainly uncertain and far off. Anybody who makes "the burden of government debt on future generations" the centerpiece of their economic ideology and rhetoric either doesn't understand economics, or is choosing to ignore that understanding."

That's what I get from all your writingson this. (Though being more good-natured than me, you would express it more gently.) Please let me know if I'm misreprenting the gist; it's certainly possible that I'm doing so.

Oh and I have to ask: imagine a counterfactual in which the U.S., the U.K., or Canada had not run up government debt over previous centuries. Do you think their peoples would be more or less prosperous today? Thx.

I have a great deal of difficulty with this discussion, as savings without investment makes up only half of the process. Plus, all of this bobbing around with apples, people need bananas too! Oops, that one has been done, alas, twice. I think it is time you graduated this discussion to the next level, Keynes' Parable of the Banana. There is a good article by Rick Holt at on the subject in the Encyclopedia of the Social Sciences.
Any Reactions?

"OK Nick. Your previous counterexamples have shown that debt can be a burden on future cohorts even if future national income is not affected. But that's not what we meant by 'future burden of the debt'. Those counterexamples don't show the country as a whole being worse off in future years. Obviously it isn't, because total consumption in any year is held constant in your examples"

The counterexamples show that in the current period debt is one of the one of the ways that income can be redistributed between living cohorts. However to have either of the effects you have identified (be a burden on future cohort, or show the country as a whole being worse off in future years) actually happen I don't think that debt alone can do the job. At the start of the next period the government always has the option of using tax to prevent the debt from having any further inter-generational effect. This will limit the effects of the bond-issue to the period in which it was issued (it will affect the present not the future).

So: Do these counterexamples show that there is at least a theoretical possibility that debt can cause the effects described ? I guess they do but only if one adds additional assumptions about how the govt will act in periods after the bond has been issued. I have not seen these assumption in the models. Further, as bond-issue is only one of the ways that the govt can redistribute income between cohorts in the present I think that once one adds the additional assumptions about government actions one ends up with the conclusion that it is in fact these actions themselves (bond and tax policy) not debt that causes the affects shown in the the counter-examples.

Even if government debt would be a burden on future generations, changes in private debt could reverse the effect.

Steve: That is not how I would summarise it. I would say: the debt will impose a burden on future cohorts, if r > g, and it won't if r < g. The burden will equal the size of the debt itself, which is big, if it's a big debt. There may be offsetting benefits if the government borrows to invest in things that benefit future generations.

Ronald Calitri: Here is my own version of the burden of the debt in a model where Keynes' "banana parable" is true.


Re: "What if the government decided to shoot random people in the head? That would reduce utility too."

Within the context of your model (where there is no loss of utility attached to sudden death) it wouldn't be the shooting per-se that caused the loss of utility but the inter-generational affects it created. Are they shooting old people or young people and what happens to their endowment ?


" They have the choice to remove the so called burden. If the goal of their society is to maximize social welfare, they will do that – unless they are stupid, but then it is the stupidity that is the real burden and not the debt. "

This is a matter of game theory. There is an advantage from reliable enforcement of contracts and also one from stable assumptions about future redistribution. You couldn't have a modern society where these were unpredictable over an interval much shorter than the life of a cohort.

Moreover these gains are not uniformly distributed. A future burden in some sense represents an equilibrium between the costs of a particular set of obligations and assumptions and the sum of the direct costs of repudiation, the indirect costs of destabilizing the system of mandates in which the obligations are embedded and the gain in utility from the difference between obligated distribution and the replacement distribution.

This is complicated, hard to calculate and there is a considerable danger to tinkering with a system for which you have no good model particularly with uncertainties about future demographics, technology and resources.

The reluctance to tinker and lobbying by any groups with a vested interest in the current system (who are by definition economically advantaged and thus good at lobbying) creates a resistance to removing burdens.

Evolution throws up these problems of optimal response all the time, and we really are only beginning to understand how to model them.

I'm pretty sure that ruthlessly and systematically replacing any stupid burdens when they arise with maximized social welfare will prove an incredibly bad idea. And haven't we seen this movie before?

Econ 101 -- you can't meaningfluply sum over 'utils'.

Economists have known this for well over 100 years.

When did the dramatic loss of scientific knowledge take place?

Economists -- demonstratively -- understand economic science less well than they did in 1912.

Andy, that is a very interesting observation. However, what if taxation is highly progressive and only wealthy Ricardian heirs pay taxes in the future when the debt is being paid off? In that case, would the existence of current liquidity constrained poor imply a transfer payment multiplier greater than 1?

"what if taxation is highly progressive and only wealthy Ricardian heirs pay taxes in the future when the debt is being paid off? In that case, would the existence of current liquidity constrained poor imply a transfer payment multiplier greater than 1?"

The wealthy heirs would not have to be Ricardian, right? They would not have to save in order to pay the eventual taxes, because they get more money out of the economy than they put in. The world is their piggy bank, eh?

Nick, thank you for pointing out your own banana case, written out in the previous post on this topic. I've looked through it, and can see some resemblance to Keynes' Banana Parable. Unfortunately, the model you are using doesn't incorporate the price level, wages, or investment, so it doesn't quite work as a full banana. Nothing final about what I'm about to say, since it's an active subject in "Keynesianistics."

However, in your model the fiscal authority has perfect foresight, while in Keynes' the initial trigger is the withdrawal of spending, followed by a paradox of thrift intensified by downward stickiness of wages. The government takes steps to renew investment. It may do this directly, anticipating that the ensuing wages will restore demand; but I don't think that would be accommodated in your model without production.

The case you render is purchasing power provided directly to consumers, your "F."
The stimulus F is paid for with bonds carrying interest "r," and this induces consumption disparities F( 1 +or- r). Well, yes, but suppose, the interest rate r = 0.0, in that case the variations flatten. Secondly, consider the motives of the bond purchasers. Due to the recession, they now anticipate future consumption lower than before the recession. Accordingly, they are willing to _pay_ the government to restore the growth path, anticipating that the costs in negative interest will be returned through future consumption. So, the appropriate interest rate is zero or less. The same could be accomplished by taxes, provided the government expenditure multiplier is adequate, as we all know it is given last week's IMF outlook.

This is partial, but seemingly applicable in our present liquidity trap. There is one further issue though, worth considering separately.

My impression is that Keynes considered wages downward sticky because labor unions were a structural feature of his economy. Even as late as the early '90s, B.O.E. econometric models, among others, identified union wages as the leading indicator of general wages. This, definitely has changed, as Mr. Romney crows over cutting $4,000 out of Obama's median income. In part, the election next week is over the fear of Republicans, that, instead of moribund unions, the government sector will attain wage leadership. I'm afraid most of the debate stands off from this question; but, in the absence of some leader in bargaining, I'm afraid wages will continue downwards!

Best of course, the government will take up the most difficult jobs itself, as it ever must do, "to close the virtuous circle."

Your getting to the heart of the matter. Future burdens come from different marginal utilities. Just take

" Because it may create or increase inequality of (marginal utility of) consumption between young and old."

and for young and old substitute the pair of your choice. If a social commitment has been made which future society chooses to honor, and this commitment affects the marginal utilities of certain groups in a suboptimal way, then you have a burden.

With burdensome debt (debt which exceeds assets and for which the negative effects are large). the burden of debt includes the debt itself, the difference in marginal utility of the money owed between debtor and creditor and the important but usually overlooked burden of the state of being in debt.

This last is extremely important. For example people with burdensome debt have trouble obtaining credit. They pay increased costs for goods and services because of their lack of good credit. Until recently, it was impossible to refinance a house with an underwater mortgage at a lower interest rate. People with underwater mortgages can't move in order to take a better job elsewhere.

You can easily make your own list. In particular, if you have a debt you can't pay and that can't be discharged in bankruptcy, your situation is like a debtors prison without walls.

Also debtors and creditors have different preferences, and there have to be all sorts of economic effects from decreasing the demand for debtor goods while increasing the demand for creditor goods, and when creditors are worried about the economy, safe assets are at the top of their shopping list.

I don't believe in debt in and of itself as a burden. I believe in the negative incentives that debt incurs. Debt in any capital structure is a senior level claim on a cash flow or asset. As such it engenders a legal protection above junior level claims (for instance equity). If that legal protection is not counterbalanced with productive enterprise, then some combination of slow economic growth and/or higher inflation will result.

Overproduction financed with debt is self defeating. The prices of goods produced fall when production creates more of a good than what is demanded, but the cost of servicing the debt remains fixed. And so equity is required to handle production smoothing.

Unfortunately, politicians and other members of the political arena have yet to figure this out. They still believe that deficits must be funded with debt.

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