Wednesday, March 27, 2013

How Hayek solved Sraffa's own-rate problem

It turns out it is the same way that Keynes solved it:
But Hayek had indeed, like Keynes, absorbed the lessons of the Sraffa exchange, and accordingly acknowledges that whereas the rate of increase of the physical amount of anyone input invested at an earlier date and the physical amount of the same input obtained at a later date may, and indeed will, differ for any two commodities, "the value equivalence in terms of the 'numéraire' at the two dates must bear the same ratio to one another for all commodities...

This elucidation, we should note, is precisely the same as Keynes's own-rate setup in chapter 17." -- Tyler Beck Goodspeed, Rethinking the Keynesian Revolution, p. 120-1
The fact that Keynes, Hayek and Lachmann all see Sraffa's own-rate challenge as having been answered, and by the same answer that I see as meeting that challenge, gives me a fair amount of confidence I am on sound footing here!


  1. Hayek clearly states in the Pure Theory of Capital (where I assume that quote is from)

    "But it will still be true that, measured in terms of anyone commodity, the rate of increase will have to be the same for all commodities. The actual numerical value of this rate of increase will, however, be different, according as one commodity or another is chosen as the standard of comparison or "numeraire "."

    It could scarcely be more clearly stated.

    Very odd then that so many commentators seem of the opinion that Hayek never really addressed Staffa's criticism on this point.

    1. Yes, from the Pure Theory of Capital.

  2. Whoa whoa whoa. Keynes was the editor of the Hayek/Sraffa exchange, wasn't he? I seem to recall him chiming in at some point and saying that Sraffa's understanding of Keynes was fine, contradicting Hayek's assertion.

    Your exclamation point notwithstanding, Lachmann, Goodspeed, and you are wrong. Hayek himself realized Sraffa had raised a very good objection and switched to an analogy to try to answer it. He didn't give the trivial fact that once you pick a numeraire, the rate is pinned down. The problem was, the choice of numeraire was arbitrary.

    1. 1) "saying that Sraffa's understanding of Keynes was fine, contradicting Hayek's assertion."

      Huh? I don't get what time frame you are using, or what Hayek asserted.

      2) "The problem was, the choice of numeraire was arbitrary."

      This merely shows you have still not properly understood the Hayek/Keynes/Lachmann response: this choice *makes no difference*.

    2. Hayek addresses the arbitrary nature of the numeraire - again in PTC, which was written quite some time after the Straffa debate and I assume contains Hayek's considered opinion on the matter.

      'It is probably unnecessary to emphasize that there is no way in which this multitude of different own rates of interest" (as Mr. Keynes has called these rates of increase in terms of particular commodities) can reduced to one single rate which has a stronger claim than any other to be regarded as the rate of productivity of investment'

    3. Not sure if the "and?" was aimed at my comment - but just in case: I was responding to Bob who said (speaking of Hayek's views on the issue)

      'The problem was, the choice of numeraire was arbitrary.'

      Any my quote was meant to show that Hayek clearly didn't see that as a problem but just a feature.

  3. You guys are something else.

    SRAFFA: There is no single thing which can be called the natural rate of interest. So how can you tell the banks to set the money rate equal to the natural rate to avoid a boom?

    GENE and rob 600 years later: BOOM! Hayek pointed out there is so single thing which can be called the natural rate. Suck it, Sraffa!

    1. Bob, you really, really are missing what is going on here.

  4. I don't think its a matter of "So how can you tell the banks to set the money rate equal to the natural rate to avoid a boom?". The banks won't be able to do that. Its about identifying a market process that would allow the natural rate to emerge - which can only happen if there is a natural rate to emerge!

    Gene has shown how in a barter economy where we assume that each good has a spot and a futures market the "own rate of interest" for each good will be the underlying originary rate of interest adjusted for expected price change in that commodity.

    So: I don't see why you could not take any one of those goods and use it as money and the model stays the same. Am I missing something here ?

    In addition I think Hayek describes processes by which any deviations in pricing or interest rates will be corrected and there will be a tendency for prices and rates to adjust so that the actual rate will move towards the natural rate.

    I can see some additional complexities:

    - What happens if you use fiat and not commodity money ?
    - What happens if the futures darkest is wrong about what future prices will actually be ?
    - What about risk as a factor in interest rates ?

    But I think those complexities can be addressed in a more sophisticated model.

  5. "Am I missing something here ?"

    Someone is, but it's not you!

  6. Gene, Rob just said "I don't think its a matter of "So how can you tell the banks to set the money rate equal to the natural rate to avoid a boom?"

    OK do you agree that Rob is now disagreeing with what Sraffa's whole point was?

    If Rob wants to take that route, fine, that may be a good answer.

    But all you guys are doing is repeating Sraffa's own objection, back to him, and thinking that solves it.

    Gene, you are misunderstanding my (fairly modest) point. Sraffa's objection *relies* on the fact that you can have an equilibrium (in the intertemporal, no-arbitrage sense) regardless of choice of numeraire. That's crucial to his very objection. So you don't answer it, by pointing out one-half of his objection. That makes no sense.

    Remember, I *believe in* ABCT. So I think Sraffa's conclusion was wrong. All I have been pointing out, lo these many years, is that you don't answer Sraffa by repeating back the premise of his objection to him.

  7. But isn't the debate more like:

    Sraffa: In a barter economy there will as as many own-rates as there are goods. ABCT is based on a single natural rate so that theory cannot hold.

    Lachmann: But all those own-rates are linked based on expectations of future price changes. The existence of multiple rates is not a serious challenge to ABCT.

    I think Lachmann understands and addresses Straffa's objection. Why do you see that as just restating the problem ?

    1. That is how I understand the issue too, rob. But maybe I need to read Sraffa again!


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