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Charlie: you forgot to include the lump sum tax when old in the budget constraint. It should be 100(1+r) + 100 - T = Cy(1+r) + Co. (That assumes the lump sum tax is paid by old people). You got the FOC right. If the government then sets T=r(100-Cy) (so the tax equals the interest on the debt), the resource constraint is not compromised, even by an infinitely high interest rate.

Yes, I picked the consumption stream I wanted, and then solved for the r that satisfied the FOC. But T gives me an extra degree of freedom.

BTW: are you the same Charlie I was having a good argument with on Scott Sumner's blog? In any case, stick around, because I appreciate commenters who are actually checking my stuff, and who have read stuff.

Intuitively (because I'm no good at arithmetic):

choosing (1+r) determines the ratio Co/Cy

Choosing T determines the level of Cy or Co

And if I set T=rF, then I get Cy+Co=200 . It is as if the young agents lent the government F apples, and get F apples back when old, gross of interest, net of taxes. As long as F < 100, it's always resource-compatible.

Nick,

I didn’t really have the time to look at this properly on first go around, but excellent post. I think you’ve compartmentalized a number of issues that were swirling around the original point of your future generation burden model, but which were distractions from the real point and focus of it. I think the challenge with that entire discussion going back to January was the continuous spilling over the boundaries of such compartmentalization, which got in the way of people getting your point. It’s like a serial straw man disputation (I think that's a problem with a lot of economics discussion on the internet). And the answer is decomposing and segregating all the partial derivatives, so to speak, to get full clarity on the main point being made.

BTW, I liked W. Stephenson’s post, but was puzzled over his algebra, as here: (I’m probably the one that’s wrong)

http://newmonetarism.blogspot.ca/2012/10/government-debt-and-intergenerational.html?showComment=1350523934204#c7167952927911582545

Nick: "Think about it: if I persuade you to postpone some of your consumption by offering you interest, and then take that interest away, you are worse off."

It's irrelevant: they had an option not to buy. If I sell you an adjustable-rate mortgage, you're worse off if the rate goes up, but you could have bought a fixed-rate.

I've written this elsewhere, but here's another way of looking at this: the government can borrow at a rate of interest over a hundred percent of GDP in the first period. Since GDP is constant it's impossible to pay this back and the government defaults. As a result no taxes get raised and no future generations are burdened.

To me this clearly shows the absurdity of looking at debt as a burden on future generations.

rsj: "we don't really know what the real burden of debt will be by looking at current nominal interest rates."

Very important point.

Hi Nick,

Yes, that is me.

I was assuming the young generation was paying the lump sum taxes on the interest [and I set it to zero for that cohort B, since I thought the first tax was on the young of cohort C], not the old.

If you tax the old, it works:

max Co*Cy

Cy + b = 100
Co = 100 + (1+r)b - T

FOC:

Co = Cy(1+r)

100 + (1+r)b - T = (100-b)(1+r)

which simplifies to:

b = (T + 100r) / 2(1+r)

With your tax rule:

T = r(100-Cy) = rb [the interest on the bonds]

b = (rb +100r) / 2(1+r)

Solving for b yields:

b = 100r / (2+r)

Maybe that's why we disagreed on whether there could be taxes that weren't a burden. I was putting taxes on the young, so the taxes can be used to move consumption forward in time. I actually don't even need the debt to do that.

I can do something like tax the young 50 apples and transfer to old, then tax 75 apples and transfer to the next old, then tax 87.5 apples and transfer to the next old...

If Utility is equal to lifetime consumption, then every generation is better off. Everybody gets more than they gave in taxes.

Nick,

I suppose explanations for why bad arguments are wrong may be questioned too, can't they?

E.g. Your explanation # 0:

"There is no burden on future generations because the extra taxes to service the debt will be paid to those same future generations that inherit (sic) the bonds." That is a really bad argument. It's just plain wrong, unless you believe in Barro-Ricardian Equivalence, which the people making that argument do not believe.”

You qualify that further, but in fact it’s not wrong because of any of that, IMO. The internal contradiction you identity tends to obscure why it’s really wrong.

It doesn’t matter whether the future generation that holds the bonds bought or inherited them. And of two co-existing future generations, it doesn’t matter who holds the bonds at the point in time when the taxes are imposed. As I’ve said repeatedly, this all depends only on the fact that taxes service the debt. That means there is a primary budget surplus. That’s the indicator of the burden and that alone. And whoever pays the tax bears the burden, under any configuration of bond holdings or prior bond purchases or inheritances.

Consider the generations co-existing at the time of the tax, young and old. The fact is that no matter who holds the bonds, no matter whether the bonds were purchased or inherited by whoever currently holds them, or who pays the tax – regardless of all of that, the simple fact is that whoever pays the tax that ends up paying off the bonds ends up being worse off. And that is the only criterion for the burden. The burden is the tax.

For example, if all the bondholders are old when the tax is imposed, and if the tax is imposed entirely on the young, then the young are going to be worse off – whether or not they even buy the bonds from the old before they mature and given the possibility that the old may simply mature their bonds with the government. And provided that the young generation at that time is sufficiently time removed from whoever received the original transfer when the bonds were issued, that separation will satisfy your criterion for demonstrating that a future generation can suffer the burden of the debt. And the point works similarly with all conceivable permutations of who gets taxed, who holds the bonds, etc.

The burden is the tax that created the primary surplus. Full stop – nothing else matters, and that’s all that any of your models depend on. All the stuff about r and g and all other issues are in the background of the actual decision of government to fund debt service with taxation at a given point in time. The decision creates the burden, regardless of the reason for the decision. And there is no absolutely predictable reason for the decision. It could come at any time. There are numerous scenarios possible for the reason to tax, which I think in fact you've demonstrated yourself, and they are all background to the act of taxation itself and the creation of the corresponding burden.

^ He's right! Everyone is over-complicating this issue. If there's a tax, there's a burden. End of story. And duh.

You want to complicate it? Now argue when taxes may occur! Nick, you seem to keep agreeing with me and JKH on this, but when you go to re-state the issues, this idea gets obscured. Why?

wh10: "If there's a tax, there's a burden. End of story. And duh."

That's like saying that if I go to the store and pay cash for something, my payment is a burden. That's not English. Double duh! ;)

OK. Next question: What are good arguments for surpluses? :)

Min: "Next question: What are good arguments for surpluses? :)"

Excellent question!

I think most of my arguments are symmetric?

JKH: "The burden is the tax that created the primary surplus."

Agreed. But r and g matter because they tell us whether or not there must eventually be such a tax. I r > g, there must eventually be such a tax. If r > g, the (expected) present value of the primary surpluses must equal the existing value of the debt.

Min- but it is that simple. Everyone's trying to sort out who gets what and when, but it doesn't have to do with any of that. The burden is defined by whether or not there will be a tax. If we take your store example, it's like focusing on whether or not you hand the cashier the money first or she hands you the candy bar first, or if you use your right or left hand to accomplish the task etc. No, the question is - do you hand over the cash or not?

(And what's not simple is figuring out whether or not there will be a tax. Your dismissal of my comment seems to potentially have arisen from an assumption that there will always be a tax.)

wh10: "The burden is defined by whether or not there will be a tax."

Not in English. A tax is a cost. A cost is not a burden unless it is burdensome.

Okay, so we're playing a semantics game now. What is your definition of burdensome? A tax, individually, is a cost, and I am calling that a burden. I've been speaking English all my life, so you'll have to do a bit better. Just because the tax is a burden/cost doesn't mean it can't be outweighed by other benefits.

Man Nick, sorry but you are still confused about the "real" and the "financial" burden.
For an economy (the macro perspective) the financial burden is always a matter of political choice (ie distribution of obligations between various LIVING interests groups).

Nick thinks it's OK to ignore every argument he's ever come across that doesn't jive with his own views. So next year, even if he's agreed with something here, he will have forgotten whether he actually said "agreed" and just say the same thing he's said here again. It's a neverending cycle with him. he has no arguments against the more heterodox stuff he really doesn't agree with, he just chooses to ignore it and act like people *really* respect his opinions on economics even though he's completely wrong theoretically (ie his economic/theoretical models, etc) and wrong factually 90% of the time. Really, Nick, how long has rsj and JKH been here trying to pound the same points into you? and yet they come back to you every time you sing your siren song, pretending they've just started arguing with you when in reality it's been 2-4 years since then. When are you going to actually listen to their factual arguments? I mean, forget the theoretical stuff, you're hopelessly lost there, we're just debating facts at this point.

wh10: "Okay, so we're playing a semantics game now. What is your definition of burdensome? A tax, individually, is a cost, and I am calling that a burden."

I am not the one calling the deficit a burden on future generations. If the debt/deficit hawks cried, "The debt is a cost for future generations," nobody would be frightened. Romney would not be calling the debt a moral issue. "Burden" is an emotional term. That's why it is being used as propaganda.

Often the same tax that is a burden during hard economic times is not a burden during good economic times. The debt/deficit hawks do not make that distinction. Instead, they take the perceived burden of the debt now, during hard times, and project it into the future. They do that to scare people. The generally sensible thing is a counter-cyclical policy, no? Run surpluses during good times, deficits during bad times.

Payam: funny you say that. I don't think you have been following. JKH and I are pretty much in total agreement on this debt thing, as far as I can see. Right JKH? Yep, rsj and I disagree on some things. If I spent all my time arguing with rsj, I would never get anything else done.

Yes, Payam. Never did I post here really believing that I would convince anyone of anything. The goal of making an argument is to see if first someone can understand your position, second to see if someone can come up with a better counterargument, one that you didn't think of if you were debating in front of a mirror.

If I convince myself that there are no good counterarguments presented, then I am happy with my position, regardless of what the other side continues believes. Sometimes there are good counterarguments, and I have to re-asses. So information is transmitted from one person to the other, like the consumption being shifted from one generation to another, without anyone needing to say "I no longer believe X because Y has convinced me of Z".

In this particular debate, I just don't think that Nick is making a very good case against Keynesian-style deficit spending. There is no multiplier that would cause tax receipts to rise as a result of successful income management policy, no risk that government insurance can smooth and no sense that this is a repeated game, so that all generations are subject to this risk and benefit, ex-ante, from the smoothing even if some may pay disproportionately more, ex-post. If there is only one recession at the beginning of the model, then every generation will avoid the recession with probability 1 and there is no ex-ante benefit realized.

The core story of deficit spending is that it does smooth recessions, and yet the core argument here is that deficit spending causes consumption to be more volatile. That can't be right. Nick is missing something fundamental to this story if he believes the harm of deficit spending is excess consumption volatility.

While there may well be arguments against deficit spending -- for example, I think you can make a good case that nations that deficit spend more tend to be more unequal and experience a greater deterioration in median wage shares -- in order to capture those arguments, you need a richer model.

The model presented here doesn't convince me, for the reasons I already stated -- when the interest rate is too high (which is the *only* reason for recessions in this model) deficit spending can reduce that rate, partly by taxing back some of the interest payments in the next generation, and partly by creating more inflation in the next generation. Both of these techniques can be used to undo the effects of the rate being too high.

Given that the model has no other possible causes for a recession, this would be the only reason why a government would deficit spend. Clearly if the deficit spending is *random* then this can cause as much harm as *random* interest rate management policy.

Nick: You are ignoring JKHs point and begging the question.

"JKH: we don't know the future, and don't know whether, at the margin, the present value of extra taxes will equal the extra deficit."

This assumes that extra deficit now somehow requires or limits the ability of extra taxes in the future. You are assuming there is some tradeoff between them, and there is not.

The consequence of extra/insufficient deficit is inflation/recession. This is always felt in the period. There is no tradeoff.

Winterspeak: please don't make me do the math! I don't like doing math! Whether or not the extra debt must equal the PV of extra taxes depends on whether or not the rate of interest is above or below the growth rate. If r is always above g, then debt = PV of primary surpluses. If r is always below g, then we are in the Samuelson case, where the government can rollover the debt+interest forever, and never raise taxes. I have said this a number of times.

"The consequence of extra/insufficient deficit is inflation/recession. This is always felt in the period. There is no tradeoff."

That isn't correct. We know that both theoretically and empirically. Theoretically, because the central bank can tighten or loosen monetary policy to offset loosening or tightening of fiscal policy. Empirically, because (to give just one example) this is exactly what we have seen in Canada over the last 20 years, where there have been massive changes in fiscal policy but the Bank of Canada kept inflation on target. Take the mid-90's, where the government decided it really needed to stop the debt/GDP ratio growing and make it shrink. So we went from big deficits to big surpluses. The BoC loosened monetary policy, so interest rate and exchange rate fell, and there was no recession and inflation kept close to target.

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