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Saturday, January 07, 2012

How Murphy Is Achieving His Result

Commentator rob, in this thread, has given a very succinct statement as to exactly the invalid maneuver Bob Murphy is using to get his "debt matters" conclusions:

"It does not matter if consumption remains the same in each period [in the counter-examples offered by myself and Steve Landsburg] 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."

Yes, rob has this exactly right. When consumption by the lender drops in period one, that doesn't count for Murphy and friends, because the lender reduced his consumption voluntarily. But when consumption by the taxpayer drops in period N, that counts, because that was an involuntary reduction.

Why is this maneuver invalid? Because judging a transactions benefits by its voluntary nature is a fine maneuver... ex ante. It's perfectly valid to judge, ex ante, that voluntary transactions are, on the whole, more likely to be beneficial for participants the involuntary ones. (Even this is not an a priori truth or anything of the sort: we may well judge that when someone is killing themselves with drink, and his friends have him involuntarily committed, that "he'll thank them later.")

But, of course, we are not looking at these scenarios ex ante, but ex post: we have Bob's whole spreadsheet, or Nick Rowe's whole example, right in front of us. And now slipping in some consideration of what someone might have anticipated at the time of some transaction is totally invalid. "Everything" (of relevance) has happened, and now, the only question is, "How did it really come out for everyone involved?" And, as Landsburg and I have shown, it came out the same (in monetary terms), whether the transfers involved occurred through taxation or debt financing.

Now, someone might protest, "But subjectively they weren't the same!" Perhaps not, but once we take such factors into account, our analysis becomes completely indeterminate. Perhaps the person taxed in period one suffers great psychological torment from being taxed. But perhaps the person receiving an unexpected transfer in a later period will experience boundless joy at this surprising bounty. All one can then say is something like, "Taxation? Debt financing? Who knows?" If we are going to run this sort of analysis at all, then we have to do so in terms of some objective results. And, objectively, Landsburg and I have shown that taxation and debt issue can have the same result in Bob's scenarios.

So, Bob is achieving his results by dropping out the loss of consumption suffered by government bond buyers because of ex ante considerations, but then looking at the entire situation ex post. This mingling of ex ante and ex post considerations invalidates the whole analysis.

UPDATE: Bob now says I am wrong, because:

"As I spelled out quite clearly, there is perfect foresight in my model. There's no distinction between ex ante and ex post, and people only derive utility from apple consumption..."

OK, I missed the place where Bob spelled this out. But it doesn't make me wrong, it makes me right for a different reason: With perfect foresight, it is wrong to ignore the deferred consumption of buying a bond but count that of being taxed because the taxpayer in period 1 will see he is getting a bigger transfer in period N that will compensate for his tax loss in period 1. It won't matter a lick to him whether his initial payment is voluntary or legally coerced. That, of course, assumes the tax burden can be made to fall on those who would have bought bonds. But the government must have perfect foresight as well, so they can do this

UPDATE II: For the life of me, I can't find where Bob spelled out "quite clearly" that the actors in his models have "perfect foresight." I searched his blog for foresight, and it doesn't appear in any of the relevant posts. Then, I re-read (re-scanned, really) the relevant posts, and didn't notice this being said through synonyms. I didn't see anything like foresight mentioned at all. But still, I am certain that Bob at least meant to put in that these actors should have perfect foresight.

19 comments:

  1. I believe the models are ignoring any subjective valuations and using consumption as the only measure.

    Changing the model slightly to have bond holders who live for ever and who will lend at 0% (for whatever reason), and everyone else living for only 1 period.

    Then: In a debt model where a bond of 100 apples is issued in period 1 and repaid in period 3.

    Generation1: Gets govt xfer and consumes 100 extra apples

    Generation2: No tax, no transfers. No additional or lost consumption

    Generation 3: Taxed 100, consumes 100 less apples

    Bond Holder: lends 100 in period 1, gets it back in period 3. No additional or lost consumption.

    We have no idea how the players felt subjectively about this. But objectively in terms of apple consumption this seems exactly as Bob and Nick describe it. Generation 1 consumes more, generation 3 consumes less and the bond-holders break even. I will let Nick and Bob comment on the ex post/ex ante aspects of this.

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  2. "Bond Holder: lends 100 in period 1, gets it back in period 3. No additional or lost consumption."

    Well, rob, that's exactly what I just said is wrong. The bondholder loses 100 units of consumption in period 1, and gains them in period 3. The subjectivity you've introduced is that, "Well, this shouldn't really count, since he *felt OK* about losing the consumption in period 1.

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  3. I thought you would say that as soon I hit send.

    The bond holder in period 1 consumes less apples but gains more bonds. It is impossible to compare bonds and apples objectively.

    If one introduces interest on the bonds back again then one can assume I think that there would be some interest rate (however high) that would make the bond holder not regret his decision to defer apple consumption ex post.

    So I conclude that there are always some scenarios where bonds allow transfers across time that depends only on the assumptions that more apples are better than less, and interest rates are possible that end up giving ex post satisfaction.

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  4. At a very simple level: Do the bond holders even matter here ?

    I am interested in the fact that one group of potential tax payers can increase their consumption at the expense of a later group of tax payers 9who may in fact be as yet unborn)

    As long as the govt can find a group of bond-holders to carry the debt through time I think this point has been demonstrated. The subjective views of the bond holders is irrelevant.

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  5. Rob, bonds are not a consumption good, they are a form of savings. If you're going to play games like that, I can claim that "Maybe the person in period N is a masochist, and loves being taxed involuntarily, and so actually gains!"

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  6. It might be a faux pas to assert it, but Bob Murphy's error seems another instance of a libertarian-style credulous belief in volunteerism (President Hoover, Salvation Army Man-style?). Unfortunately, allowing deficit spending to be declared an illicit, coercive force would not free us to use policies appropriate to the situation, and so creates a de facto coercive regime just as well (especially when one hears about balanced budget amendments and the like).

    The whole thing reminds me of Stanley Lebergott's classic example of misplacing three-and-a-half-million emergency jobs.

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  7. And rob, I never said the bond holder was unhappy about buying the bond! I said he lost consumption as a result of buying it (in the period he bought it).

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  8. As I have shown, the same result can be achieved through taxation. The bonds are irrelevant -- it is the transfers that matter.

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  9. Two things Gene:

    (1) You are right that you can give the people in my model the same amount of utility through a tax scheme (in periods 1 through 8) that I have achieved through bonds-and-one-tax-in-period-9. However, I am reluctant to say you've been right all along, because:

    (2) Everything else you say in this post is completely wrong. As I spelled out quite clearly, there is perfect foresight in my model. There's no distinction between ex ante and ex post, and people only derive utility from apple consumption; nobody cares about the government on a philosophical level.

    So, I am still quite sure you don't have a handle on this.

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  10. All you seem to see is the redistribution in consumption caused by the bond being bought and then another redistribution in consumption when the tax is levied and the bond redeemed. As you say if all you look at is the transfers in apples then all these movements can be duplicated by tax and transfer actions.

    The above is true but not very interesting. What makes it interesting is that the second transfer only happens because of the first transfer and the second transfer makes future tax payer worse off (it may make bond holders better or worse of or leave then the same, but that is not the interesting bit).

    Anyway, I think I've run out of ammo trying to explain it further.

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  11. "What makes it interesting is that the second transfer only happens because of the first transfer..."

    No doubt.

    "and the second transfer makes future tax payer worse off..."

    As I have acknowledged again and again. Why in the world you think I don't see this is beyond me. In period N, the taxpayer can consume less, and the bondholder more.

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  12. Changing the model slightly to have bond holders who live for ever and who will lend at 0% (for whatever reason)

    They would do it for the same reason people generally save: they want to defer consumption.

    As far as I can tell, that is the main motivation for saving, not the possibility of collecting interest. If that weren't true, we'd have all blown our life savings at the mall once 2008 hit. In the old days, why did farmers save a portion of their harvest over the winter? Because they didn't want to starve to death.

    I'll confess I haven't read every post and comment in this discussion, but nobody seems to be saying the obvious: the introduction of bonds into a pure apple economy introduces the possibility of deferred consumption, which is a useful thing in and of itself. Granted, in a real economy, that would presumably exist without a government intervention, but I think it's an important factor nevertheless given that we're implicitly talking about pension systems here.

    As long as the interest rate is 0% (which is actually realistic in this situation) and the system persists forever, nobody has to get the shaft until the heat death of the universe or whatever, at which point they probably won't care.

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  13. @Bob: "As I spelled out quite clearly, there is perfect foresight in my model."

    Then it is wrong to ignore the deferred consumption of buying a bond compared to getting taxed because the taxpayer in period 1 will see he is getting a bigger transfer in period N that will compensate for his tax loss in period 1. It won't matter a lick to him whether his initial payment is voluntary or legally coerced.

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  14. Gene,

    Please review this model.

    Suppose we have a population of person A and Person B (same apple economy as Nick's). The govt want to give some money to A. They have two options.

    1. Tax: They tax both A and B. They give the money to A. A clearly gains and B clearly loses.

    2. Debt.
    Period1 : They borrow half from A and half from B (via bonds) and give the money to A.
    A is clearly better off. B must be worse off because the govt favored A with a gift that meant he consumed less than A.

    A and B die and their descendants C and D inherit the bonds.

    Period 2: They tax both C and D to pay off the debt (to themselves).

    Over the 2 periods:
    A clearly does the best
    B the worst
    C and D break even


    Does this show that the transfer is the issue not the debt?

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  15. @rob: On my initial perusal, yes. But on another thread, vimothy says we have to have an Overlapping Generations model to achieve Nick Rowe's result. I am still trying to understand this point, and it seems I will soon be reading up on OLG models!

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  16. Gene wrote:

    OK, I missed the place where Bob spelled this out. But it doesn't make me wrong, it makes me right for a different reason: With perfect foresight, it is wrong to ignore the deferred consumption of buying a bond but count that of being taxed because the taxpayer in period 1 will see he is getting a bigger transfer in period N that will compensate for his tax loss in period 1. It won't matter a lick to him whether his initial payment is voluntary or legally coerced.

    Nope Gene, you still aren't getting it, and this time the mistake is clearly yours because *in the quote you have for me preceding your statement above* I say, "...people only derive utility from apple consumption."

    I know you think my libertarian dogma infects everything I do, but not on this issue.

    Tomorrow I'll post something where I literally give you the utility function--specifically, U=sqrt(a1)+sqrt(a2). So you will be able to actually plug in the numbers and see that in the endowment scenario each person gets 20 utils (100 apples in each period), but then with deficit-and-tax the first five people get more than 20 utils while the last five people get fewer than 20 utils. They don't care about ideology, they just care about apple consumption (with diminishing marginal utility in each period).

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  17. I can now see that if you just look at this in terms of transfers then you can have any volume of transfers orchestrated by the government in any period.

    It then become a trivial issue to reproduce the debt model using tax. You just substitute the words "borrowed to pay off" to "taxed to xfer to" in Bobs 9 period model and you are done.

    The interesting point (for me anyway) is lending and paying taxes are clearly very different things, not just 2 ways of transferring money. And I think for obvious reason a tax can be called a "burden" in a way that a loan is not.
    So if the govt only has taxes to carry out a transfer the "burden" has to happen straight away. If it can use debt it can defer the "burden" for many generations.

    If people feel that taxes are not a "burden" even if they are a direct xfer to someone else then I guess that they will just see the two models (tax v debt) as 2 ways of doing the same thing.

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  18. Substitute "compulsory action" for "burden" and its chrystal clear what the difference is.

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  19. Murphy can't explain why anyone would with rational expectations, perfect information etc, would buy bonds which they will themselves be taxed to retire.
    To assume otherwise is to endow agents with 'bond illusion'.
    The Govt cant do something through a bond issue, in this sort of economy, which cohorts of different generations can't do themselves by borrowing and lending to each other.
    Indeed, why is there a Govt in this economy? It serves no purpose.

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