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Friday, January 06, 2012

Revised Go at Nick Rowe's Model

Nick Rowe's model, as I now understand it, with taxation instead of borrowing:

The government taxes cohort B to give each person in cohort A an extra 110 apples, which he eats. Cohort A then dies.

Cohort A is better off. Each member of cohort A eats an extra 110 apples.

Cohort B eats 110 fewer apples when young, but then the government taxes cohort C 121 extra apples when cohort B is old, so that cohort B eats 11 extra apples. We could adjust the present value of the consumption so that these just balance out.

Cohort C is out 121 apples.

We have achieved the exact same result with taxation as with debt. It is the transfer payments that matter.


34 comments:

  1. Now you are starting to argue just like Steve Landsburg! (Not that there's anything wrong with that, because Steve is a *very* smart economist.)

    http://www.thebigquestions.com/2012/01/06/debt-the-never-ending-topic/

    When my colleague and co-blogger read my post, she commented that it was exactly like an unfunded government pension plan. Which it is. But the government can do exactly the same thing with debt.

    In the first period, the government borrows 100 apples from A, when A is young. Then it gives the apples straight back to A, as a freebie. A get's old, and the government repays the old As 110 apples. Where does the government get those 110 apples? It borrows them from young B. And so on.

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  2. Without capital, the transfer payments don't really matter (in fact, they may increase costs). Supply must shrink or demand must increase in order for this model to work. In either case, you're still SOL.

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  3. Yes, I responded to Murphy's model, and then saw in his comments section that Landsburg had made the exact same point I did.

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  4. In your example you just have transfers between living people.

    Bob's and Nick's examples show how debt can transfer the burden inter-generationally even if all the original beneficiaries are dead and even with output and consumption the same in every period

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  5. No, Rob, you are incorrect. Both of my models are exactly equivalent to Murphy's and Rowe's, but with taxes substituted for loans. It is logically impossible to transfer anything to the dead. What I have *shown* is that their models also only include transfers amongst the living.

    You might note that Rowe has essentially granted the equivalence of our models (with taxes substituted for debt) in his comment above.

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  6. "It is logically impossible to transfer anything to the dead"

    I never said anything to suggest that was happening, rather that the current living can transfer the burden to the yet unborn.

    Maybe I am missing something in your model. Why does the government keep increasing the size of the transfer? This model would be self-sustaining if they just repeated the transfer of 110 apples for ever.

    In Nick and Bob's model you had a whole generations (everyone alive at a certain time) where every member either lost (if they were taxed) or broke even (if they were involved in a bond transaction). In your model every generation always breaks even. Cohort C is 121 worse of in the last period and cohort B 121 better off. The fact that Cohort B started off 10 apples down is simply a carry over from the transfer of the previous period.

    In the bond=based models the distance between beneficiary and losers can be separated in time for many generations (bounded by the size of the rolled-over debt getting too high).

    I'm not an expert in precisely what issue they are all trying to resolve in this discussion but this is my understanding of the differences in the models.

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  7. I agree that it is the transfer payments that matter. Using debt just separates the beneficiary and loser in time in a way that taxation does not.

    I guess in theory you could do a reverse model where the govt taxes, saves the money for many generation and the spends it to benefit them.

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  8. Gene,

    It's clear from your example that you can use the time profile of taxes to replicate the distribution that would obtain under bond financed deficit spending.

    But that doesn't mean that it's only the transfer payments that are important.

    To see this, note that any current govt expenditure or transfer payments paid for out of current taxes will have no intergenerational redistributive effect (at least, as a first order approximation).

    In order to burden future generations, you need both the expenditure or transfer and the borrowing (and the assumption that this is paid for out of future taxes).

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  9. vimothy, my example burdens future generations in the same way that Rowe's does! Each person could give up or receive money from the government at the exact same moment. And the transfers payments could be promised in advance.

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  10. Gene,

    Yes, I agree!

    As a wrote in my previous comment, it's clear from your example that you can use the time profile of taxes to replicate the effect of debt funded govt expenditure and/or transfers.

    But that doesn't disprove the OLG argument. It's still the case that any debt financed expenditure and/or transfer payments that requires higher future taxes are redistributive across generations (leaving aside Ricardian Equivalence).

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  11. Take the proposition, it's the fact of transfers and not the method of financing.

    This is false because:

    (Assume increased future taxes from any current borrowing and no RE)

    1, The intergenerational effect is the same if we let the borrowing finance expenditure and not transfer payments.

    2, If we finance current transfers from current taxes, there is no intergenerational effect.

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  12. vimothy, I have shown how *the exact same intergenerational effect* can be achieved through taxation as through debt financing. I am not comprehending how you can both agree that I have done that, and insist that the principle this obviously demonstrates, that it is the transfers that matter and not the financing, is false.

    For instance, your point two is very obviously false: Social Security, the taxing of current workers to pay current retirees, very obviously has an inter-generational effect.

    I keep saying "very obviously" because I really don't get how you could comprehend the example and deny the very point it illustrates.

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  13. Gene,

    You're right, that was sloppy language on my part. Point 2 should read,

    "2, If we finance current transfers from current taxes, there is no effect on future generations."

    The fact that you can replicate the burden which current borrowing imposes on future generations (per our assumptions) with taxes, cannot as a point of logic, disprove the proposition that current borrowing burdens future generations. At least, as far as I can see.

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  14. The tax transfer used to fund SS is intergenerational but happens immediately.

    To do an integenerational transfer that does not happen immediately then one needs either govt borrowing (if the transfer of the burden is from the present to the future) or govt savings (if the present bears the burden).

    It does not matter if consumption remains the same in each period because we are assuming that those who buy or sell bonds are not bearing any burden or making any gains if they voluntarily adjust their consumption as a result of the bond transactions.

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  15. vimothy, I have shown it is the transfer between generations that creates the burden, and not the borrowing. Why don't *you* create an example that shows a burden on future generations that cannot be duplicated by taxing and transfers, since I have defeased Murhpy's and Rowe's examples?

    Again this should be rather obvious: let's say the government borrows a million ounces of gold in 1500 from the Smiths by issuing them bonds. Does this, in and of itself, create some burden on future generations? Plainly and obviously not. Imagine the government spends the gold on a war. One hundred years later, the government decides to retire the debt, now valued at 10 million ounces. It taxes the Joneses 10 million ounces of gold, and pays the descendants of the Smiths back. The generation is not one ounce poorer: the Joneses are 10 million worse off, while the Smiths are 10 million better off.

    Debt, in and of itself, is no "burden on future generations." It will represent a transfer between future taxpayers and future bondholders.

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  16. "To do an integenerational transfer that does not happen immediately..."

    Is impossible. One cannot suck future resources back into the present!

    "It does not matter if consumption remains the same in each period because we are assuming that those who buy or sell bonds are not bearing any burden or making any gains if they voluntarily adjust their consumption as a result of the bond transactions."

    And this is the bogus ideological way that Bob is making his examples work. If consumption is the same in each period, there was no intergenerational transfer, period.

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  17. But rob, I will say you have isolated exactly the invalid move that Bob is using to make his examples work. I will have a post up explaining his error soon.

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  18. Gene, A further point: I don't find it surprising in the least that you can do this with the future path of taxes--it seems obvious that you should be able to (although it sees less obvious to me that anyone should want to in practice).

    But regardless, if we finance current transfers with current taxes, we impose no future burden. So it must be the case that it's "transfers + borrowing". But it's also true that if we financed govt expenditure (for example, govt consumption) via borrowing, we would impose a future burden (per our assumptions).

    Therefore it must be the borrowing. And if course, if there's no transfer or expenditure, then there's no need to borrow or tax, and hence no issue from either direction. But that is question begging.

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  19. vimothy, did you bother looking at the example I just posted, showing how funding a current transfer with borrowing imposes no future burden?!

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  20. Gene, Sorry, it's certainly not my intent to cause offence. I started writing my last comment immediately after the one that preceded it, so I hadn't seen you reply then.

    I don't believe that it is possible to create an example that is not replicable by adjusting the time path of taxes, because that suggests a some kind of inexplicable phenomena. If we can describe the payoffs accruing to different actor in the model, then it should be relatively trivial to replicate them using a particular time profile of taxes.

    Moreover, I believe that there are already an unnecessary number of examples floating round of what is at the end of the day a standard result of a standard macro model.

    let's say the government borrows a million ounces of gold in 1500 from the Smiths by issuing them bonds. Does this, in and of itself, create some burden on future generations? Plainly and obviously not.

    Well, not necessarily--you need some extra assumptions.

    Say that the the borrowing finances govt consumption. Then the debt is rolled over across overlapping generations. Eventually, taxes are raised to retire the debt. Then generation who pay the extra taxes bare the burden of the original borrowing.

    Remember that we are describing an overlapping generations model. Without overlapping generations, this result doesn't make any sense.

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  21. @vimothy: You're not offending me, but I am getting a little crazy that you are not actually thinking through the examples, because:

    "Say that the the borrowing finances govt consumption. Then the debt is rolled over across overlapping generations. Eventually, taxes are raised to retire the debt. Then generation who pay the extra taxes bare the burden of the original borrowing."

    Aaaaaaah! I just gave you a very straightforward example where the borrowing finances govt consumption, and showed you that it imposes no burden on future generations whatsoever.

    And your response is to ignore my model and just re-assert what my model shows to be false?!

    "Exasperated" is the right word, not "offended."

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  22. Is impossible. One cannot suck future resources back into the present!

    But you can transfer them across overlapping generations.

    In fact, you demonstrate that this is possible in your post.

    The issue is, does govt borrowing redistribute resources across generations. It's obvious that it does, if it a future generation faces higher taxes as a result of present borrowing. This could occur regardless of whether the govt uses the funds for transfers, consumption, or investment (just net out the value of the capital asset).

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  23. Gene,

    Aaaaaaah! I just gave you a very straightforward example where the borrowing finances govt consumption, and showed you that it imposes no burden on future generations whatsoever.

    Apologies, I tried to address that. In your example, generations do not overlap. At the point of borrowing, there is one generation. At the time the debt is retired, there is another. But nothing links them.

    You need overlapping generations to pass the burden between them.

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  24. Let me try one final time and phrase it like this:

    In every period, there are two generations, say an old and a young.

    In the first period, when the borrowing occurs, one generation has, at the margin, higher consumption.

    At every successive time period, the distribution of resources between the two current generations can take any form. In particular, as the generations overlap through time, they can each pass on the debt to the next generation, and smooth their lifetime consumption.

    Then, in the final period, when the debt is retired, the original flow is reversed and the other generation has higher consumption at the margin.

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  25. "In the first period, when the borrowing occurs, one generation has, at the margin, higher consumption."

    Only if there is a transfer to them. If the money is spent on ice cream for child care centers, it would be the younger generation that got higher consumption.

    It is the transfers that matter.

    "Then, in the final period, when the debt is retired, the original flow is reversed and the other generation has higher consumption at the margin."

    And I've just offered an example that shows that that is not (necessarily) true, and in a straightforward case, it is false.

    And you simply post again and again as if I had not offered that example at all.

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  26. Gene,

    Sorry, there is a post gone missing between my post @ 3:25 PM and my post @ 2:27 PM.

    Perhaps it is stuck in your spam filter? I'll try to recreate the jist of it.

    Aaaaaaah! I just gave you a very straightforward example where the borrowing finances govt consumption, and showed you that it imposes no burden on future generations whatsoever.

    I tried to address this in my previous comment. In your example, the generations do not overlap. You just have one generation at t1 and another generation at t2. But there's nothing connecting them.

    What happens in Nick's stylized OLG model is that current consumption of current resources is redistributed between the current overlapping generations as a result of previous borrowing, just as in your version the same result occurs because the government recreates that redistribution using taxes.

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  27. It is the transfers that matter.

    When you say transfer, I'm assuming that you mean "transfer payments".

    In fact it's how the government changes the distribution of real resources more generally between the two currently existent generations that matters, and how it finances that change.

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  28. @vimothy:

    Sometimes blogger does not send me e-mails about comments. I have never understood why.

    "In your example, the generations do not overlap."

    Who says? I jsut didn't mention them. Do you really think I can't fancy the model up with lots of overlapping generations?

    In any case, we have shown already that the overlapping generations is a red herring, because I can duplicate the exact result with taxes. And pure simple debt to finance consumption is a red herring, since I have just given you an example (which you accept, I see) that shows that creates no burden.

    So there is nothing left to your position.

    It is the transfers that matter.

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  29. Gene,

    Sometimes blogger does not send me e-mails about comments. I have never understood why.

    No worries.

    I want you to know that I'm not here trying to defend a particular political position. I'm trying, perhaps not very successfully, to explain a basic and well known result of a workhorse macro model.

    I'm not from the LvMI. I'm just an econ post grad.

    I'm sure you can fancy up an OLG model for your govt consumption example. But you will find, when you do this, that you get the same result as Nick, assuming you keep his assumptions about taxes rising at some point and RE.

    If you model a transfer plus borrowing plus higher taxes then one generation gains at the expense of a later generation.

    But it's equally true that you could model govt consumption or investment and get the same result. What's important is how the govt changes the allocation of resources between the two existing generations at any given time.

    What you can't do, is model borrowing paid with future tax rises so that a later generation doesn't lose out, unless RE holds.

    Or you junk the whole OLG framework. For obvious reasons, you won't get this result in an infinite horizons model.

    Thanks

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  30. @vimothy:

    1) At the end, don't you mean "if RE holds"?

    2) I have recognized from the beginning that this is not (generally) an ideological debate: we have Krugman and Landsburg on the same side, after all.

    3) In any case, you are now telling me I need to understand the world of OLG models if I want to see this point. I am willing to concede that may be so. But Murphy and Rowe have been trying to contend that we can just follow a model any non-specialist can grasp and get this.

    In any case, where is the best discussion of OLG models and government debt finance for a beginner?

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  31. Still not getting how the beginning and end of Rowe's model tie together.

    1. It's a "simple model."

    2. In the beginning there's "zero real growth."

    3. There's ONE "apple bond" ever discussed, that keeps getting rolled over.

    4. At the end, we're told "debt is rising faster than GDP?"

    4a. What "rising GDP?" We were told there's zero real growth, so isn't GDP flat?

    4b. What "rising debt?" We've seen one loan ever, for the hundred apples, and it keeps getting rolled over.

    So how is "debt is rising faster than GDP" consistent with, first, what we were told about initial conditions, and second, the model being "simple?"

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  32. Where have you gone, Mr. Vimothy?
    Our blogger turns his lonely eyes to you
    Ooh-ooh-ooh

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  33. "What's important is how the govt changes the allocation of resources between the two existing generations at any given time."

    Yes, my point exactly.

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  34. Here, Daniel Kuehn produces an OLG model in which the later generations benefit at the expense of the earlier ones.

    I think that is a case closer.

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