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Friday, January 06, 2012

Nick Rowe's Model Cannot Prove Anything

because it is logically incoherent. (Hey, everyone else is blogging about this, so I felt I had to as well. In my next post, I will show why Bob Murphy's post on this prove the exact opposite of what he thinks they prove.)

But first let's see why Rowe's model falls apart"

"Assume: closed economy; no investment or real capital of any kind; lump-sum non-distorting taxes with zero collection costs; positive real interest rate and zero real growth; exogenous full-employment level of output; apples are the only output good; apples cannot be stored; identical agents; overlapping generations; no funny stuff.

"Suppose the government makes a transfer of 100 apples to the current cohort, financed by borrowing. Does that create a burden on future generations? Yes or no? B or NB?"

There is no correct answer to the question, because there is no possibility that what Rowe describes could happen. Why?

From where did the 100 apples come?

Well, not from overseas: we have a closed economy. Not from seed stock: there is no investment or real capital. And not from savings: "apples cannot be stored."

The transfer is impossible. All apples were already being consumed, and necessarily by the current cohort. The government has been made into a magical apple-making machine.

At this point we can stop reading: from an incoherent model, any conclusion whatsoever can be drawn. But it is interesting to note that the exact opposite nonsensical move occurs at the end of the post, when the government taxes cohort C 121 apples to retire its debt.

To where did the 100 apples go?

They can't be sent overseas: it's a closed economy. They can't be put in seed stock: there's no investment. And they can't be stored. The only thing that can be done with them is to... eat them! And who is around to eat them? Well, only cohort C is! So the 121 apples of consumption they "lost" by being taxed they got back because they must be eaten immediately.

The whole construction is nonsensical, and can't be used to prove anything, other than that, if the government is magical black box, and can make apples appear from nowhere for one generation, and disappear into the mystic during another, then the one with more apples will like that, and the one with fewer apples won't, in whatever order those generations appear.

UPDATE: I think I gave a reasonable interpretation to the paragraph I quote above. But Nick Rowe has explained that was not what he meant, and has explained what he did mean. So look for a post soon on this newly interpreted model.

9 comments:

  1. I think Rowe made a mistake, but it's much more minor than you think. The apples he initially talks about are apples because he wants to emphasize that these are real resources and that everything is perfect and frictionless.

    The apples he later talks about are dollar bills, not the numeraire good.

    So it was technically wrong to slip between the numeraire good and money, but it doesn't make what he is saying incoherent. I can pretty easily read what he is saying and imagine how it would play out in the math and a typical neoclassical model.

    I don't think he should have played fast-and-loose with those words, but the effects he is talking about are real. I am also pretty sure that he was phrasing it the way he was to help communicate more effectively with neoclassicals, not to confuse.

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  2. But Ryan, where did the new consumption apples come from? And where did the taxed apples go away to? You haven't addressed these questions at all!

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  3. "The apples he later talks about are dollar bills, not the numeraire good."

    And that's just totally irrelevant: he is trying to show C is hurt because they can consume fewer apples. But they can't consume fewer apples, because there is no place for the apples to go but in there mouths, but the very logic of his model. What he did was make the government a magic box that sucked the apples out of existence.

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  4. "was make the government a magic box that sucked the apples out of existence"

    Wasn't that the point (of his analysis)? My question: where's the capital coming from? Surely, debt is not the source of capital... Somebody must produce enough to pay it back, and that requires capital.

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  5. "Wasn't that the point (of his analysis)?

    No.

    "My question: where's the capital coming from?"

    In Rowe's model, there is no capital.

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  6. Gene: there were no new apples.

    Cohort A got to eat some of cohort B's apples, and cohort B got repaid by eating some of cohort C's apples. And then cohort C didn't get repaid, because the government decided to pay off the debt.

    Bob Murphy lays out a neat numerical example:

    http://consultingbyrpm.com/blog/2012/01/future-generations-will-be-indebted-to-me-for-the-clarity-of-this-exposition.html

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  7. But Nick, cohort C's apples are not even buds yet. It is simply physically not possible for cohort A to eat them, anymore than they can eat their own great-great-great-great-grandchildren, or the favorite newly created food of the year 2500!

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  8. Gene: see my comment on your most recent post, where I spell it out a little more.

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  9. OK. If this entire model is based upon consumption debts (no capital), then there simply is no way to pay down the debt, nor is there a way for subsequent cohorts to have a higher standard of living than the very first.

    Essentially, every generation will need to consume more and more into perpetuity.

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