Can Lachmann’s Arbitrage Save the Austrian Theory of the Interest Rate?

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This is the second part of my criticism of Glasner and Zimmerman’s paper. The first part can be found here and should be read and understood before proceeding with the second part. Glasner and Zimmerman note that Ludwig Lachmann tried to rescue Hayek’s theory by introducing market arbitrage. They quote Lachmann as such:

If there is a multiple of commodity rates, it is evidently possible for the money rate of interest to be lower than some but higher than others. What, then, becomes of monetary equilibrium? . . . It is not difficult, however, to close this particular breach in the Austrian rampart. In a barter economy with free competition commodity arbitrage would tend to establish an overall equilibrium rate of interest. Otherwise, if the wheat rate were the highest and the barley rate the lowest of interest rates, it would become profitable to borrow in barely and lend in wheat. Inter-market arbitrage will tend to establish an overall equilibrium in the loan market such that, in terms of a third commodity serving as numéraire, say, steel, it is no more profitable to lend in wheat than in barley. (p15)

This seems to not be a criticism of Sraffa at all. The own rates of interest still differ it is just that the differences are perfectly reflective of the knowledge that prices will fall in the future as the market equilibrates. Lachmann says this explicitly when he writes:

This does not mean that actual own-rates must all be equal, but that the disparities are exactly offset by disparities between forward prices. The case is exactly parallel to the way in which international arbitrage produces equilibrium in the international money market, where differences in local interest rates are offset by disparities in forward rates. In overall equilibrium, it must be impossible to make gains by “switching” commodities as in currencies. (p15 — My Emphasis)

It is interesting to note that Lachmann is invoking the empirically untrue theory of Purchasing Power Parity (a critique can be found here), but let us ignore this for the moment. Anyway, the above quote is not a critique of Sraffa. This is exactly what Sraffa was arguing. What is so surprising is that Glasner and Zimmerman actually quoted Sraffa saying this four pages beforehand. Here is that quote again:

Suppose there is a change in the distribution of demand between various commodities; immediately some will rise in price, and others will fall; the market will expect that, after a certain time, the supply of the former will increase, and the supply of the latter fall, and accordingly the forward price, for the date on which equilibrium is expected to be restored, will be below the spot price in the case of the former and above it in the case of the latter; in other words, the rate of interest on the former will be higher than on the latter. (p11 — My Emphasis)

Remember that this is a quote from Sraffa that the authors themselves provide! Yet Glasner and Zimmerman nevertheless write:

In contrast, Sraffa’s critique of the (unique) natural rate can apply only under intertemporal disequilibrium, but not under an intertemporal equilibrium in which future prices are correctly foreseen. (p16)

I do not know what to make of this at all. Even if the future prices are correctly foreseen — that is, in the case of a so-called ‘intertemporal equilibrium’ — the interest rates on various commodities will change in relation to one another when changes in the distribution of demand (or changes in supply) cause price changes that will, in the future, call forth changes in the structure of production. Thus Lachmann’s defence appears to have arisen from a simple misreading of Sraffa! Sraffa had already put forward Lachmann’s defence as a criticism!

All that Sraffa is saying is that as The Market directs resources through time the interest rates on various commodities will change in order to shift resources in various directions (if corn is undersupplied the interest rate on corn will rise etc.). In such a case there is no unique ‘natural rate of interest’.

In his paper Sraffa makes this point directly when he points out that there will be no unique ‘natural’ rate on producers goods and consumers goods. They will each have their own ‘natural’ rate:

But in times of expansion of production, due to additions to savings, there is no such thing as an equilibrium (or unique natural) rate of interest, so that the money rate can neither be equal to, nor lower than it: the “natural” rate of interest on producers’ goods, the demand for which has relatively increased, is higher than the ” natural ” rate on consumers’ goods, the demand for which has relatively fallen. (p51)

This is what does the damage to Hayek’s theory. Thus, Sraffa says, we are on far safer grounds with Wicksell. Wicksell used a price index to understand what he meant by the natural rate. Sraffa notes this clearly and contrasts it with Hayek’s approach:

This, however, though it meets, I think, Dr. Hayek’s criticism, is not in itself a criticism of Wicksell. For there is a ” natural ” rate of interest which, if adopted as bank-rate, will stabilise a price-level (i.e. the price of a composite commodity): it is an average of the “natural ” rates of the commodities entering into the price-level, weighted in the same way as they are in the price-level itself. (p51)

This is what Lachmann also wanted to do. Which gives a further sense that he had not read the debate properly. Recall that he wrote:

Inter-market arbitrage will tend to establish an overall equilibrium in the loan market such that, in terms of a third commodity serving as numéraire, say, steel, it is no more profitable to lend in wheat than in barley.

But this approach, while obviously more coherent, is not without its own problems. As Sraffa points out there will still be no unique rate because there will be a different structure of interest rates for each numeraire chosen as the basis of our price index (note that Sraffa refers to the numeraire as the ‘composite commodity’).

What can be objected to Wicksell is that such a price-level is not unique, and for any composite commodity arbitrarily selected there is a corresponding rate that will equalise the purchasing power, in terms of that composite commodity, of the money saved and of the additional money borrowed for investment. Each of these monetary policies will give the same results in regard to saving and borrowing as a particular non-monetary economy-that is to say, an economy in which the selected composite commodity is used as the standard of deferred payments. (p51)

Sraffa then points out that, since the selection of the numeraire is arbitrary, we may as well have just introduced a monetary standard. He writes:

It appears, therefore, that these non-monetary economies retain the essential feature of money, the singleness of the standard; and we are not much the wiser when we have been shown that a monetary policy is “neutral” in the sense of being equivalent to a non-monetary economy which differs from it almost only by name. (p51)

And so we are back to a monetary economy. The problem then becomes: what is the interest rate on money? Introducing money at different interest rates will have different effects on the interest rates on various commodities. If I open a bank in a barter economy and set the rate of interest equal to 2% the structure of interest rates that pertain across the economy will be very different to the structure of interest rates that pertain across the economy if I set the rate of interest equal to 5% or 0%. In Wicksellian terms: we are now talking not about the ‘natural’ rate of interest but rather the money rate of interest.

Well, now we are at the point where we must ask what sets the interest rate on money. Keynes, who is arguing against Hayek, says that the rate of interest on money is determined by ‘liquidity preference’; that is, the desire on the part of people to hold liquidity as opposed to interest-bearing investments. Some economists complained that Keynes was therefore allowing the interest rate to ‘hang by its own bootstraps’. But after the above discussion we see clearly that it could not have been otherwise. The money rate of interest must necessarily be autonomous of the various commodity rates of interest and so it will be set arbitrarily vis-a-vis the market system. In the real world it might be set by the markets in line with their confidence-levels, by central banks in line with either their confidence-levels or in line with an internally incoherent ‘policy rule’ that they use to absolve themselves from the responsibility of making a judgement or possibly in line with some rather arbitrary law like the usury laws of the Middle Ages.

Before signing off on this issue I should note a point of historical interest: Karl Marx actually realised this point when he investigated the money markets in Das Kapital: Volume III. In Chapter 23, aptly title ‘Division of Profit. Rate of Interest. Natural Rate of Interest.‘, Marx wrote:

The average rate of interest prevailing in a certain country — as distinct from the continually fluctuating market rates — cannot be determined by any law. In this sphere there is no such thing as a natural rate of interest in the sense in which economists speak of a natural rate of profit and a natural rate of wages.

I’m not the biggest fan of Marx but he was way ahead of the curve here. Echoing Keynes’ theory of liquidity preference he quotes Joseph Massie who wrote:

The only thing which any man can be in doubt about on this occasion, is, what proportion of these profits do of right belong to the borrower, and what to the lender; and this there is no other method of determining than by the opinions of borrowers and lenders in general; for right and wrong, in this respect, are only what common consent makes so.

The rate of interest hangs by its own bootstraps or it does not hang at all. There is no alternative.

 

 

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About pilkingtonphil

Philip Pilkington is a London-based economist and member of the Political Economy Research Group (PERG) at Kingston University. You can follow him on Twitter at @pilkingtonphil.
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7 Responses to Can Lachmann’s Arbitrage Save the Austrian Theory of the Interest Rate?

  1. ivansml says:

    I think the main point against Sraffa here is that although own rates of interest on different commodities may differ (looks like all agree on that point), he didn’t fully appreciate that intertemporal equilirium (or more precisely, lack of arbitrage, a weaker assumption) imposes additional structure across those differences. Once we understand the structure, it becomes clear that unique natural rate can be defined provided we choose the numeraire commodity. To apply the concept for monetary policy, the numeraire will be simply a basket of goods used to define the price level index (if Hayek had problems with defining price indices, so much worse for Hayek, but the logic remains behind natural rate remains unaffected). Everything works out.

    PS: Lachmann likely refered to covered interest rate parity (essentially, no-arbitrage condition for forward rates), not PPP.

    • But Sraffa DID recognise the arbitrage outcome. The quote I provided above shows that beyond a shadow of a doubt. His point was that you had to choose a numeraire ala Wicksell. Hayek refused to do this because he (presumably) recognised that the choice of numeraire would be arbitrary (as Sraffa then goes on to point out). This can lead to problems of its own that I did not deal with in this piece but which Keynes’ liquidity preference theory hints at.

      Also, PPP is required to get Real Interest Rate Parity which is clearly what Lachmann is referring to. That’s what I meant.

      • ivansml says:

        Sure, Sraffa recognized the point, but didn’t think it through, else he wouldn’t write: “The only meaning (if it be a meaning) I can attach to this is that his maxim of policy now
        requires that the money rate should be equal to all these divergent natural rates.” No, it’s enough to set money rate to the natural rate associated with price index basket, no-arbitrage will then ensure that various own rates of interest, although different, will be compatible with equilibrium where the price level (as measured by choice of numeraire) is stable.

        Purchasing power parity relates price levels and exchange rates across countries. Lachmann makes no reference to price levels and instead speaks of spot and forward rates only, so I highly doubt he refers to PPP.

      • (1) No. That comment is addressed to HAYEK. Sraffa clearly states:

        This, however, though it meets, I think, Dr. Hayek’s criticism, is not in itself a criticism of Wicksell. For there is a ” natural ” rate of interest which, if adopted as bank-rate, will stabilise a price-level (i.e. the price of a composite commodity): it is an average of the “natural ” rates of the commodities entering into the price-level, weighted in the same way as they are in the price-level itself.

        He fully recognised that Wicksell produced a justification for his theory but Hayek didn’t. The reason that Hayek is uncomfortable with the Wicksell formulation is because he recognises that he is introducing money and this can lead to Keynes’ theory which uncouples the interest rate from any ‘real’ rate.

        (2) Read the paper. The authors recognise that what is at issue here is also price levels. If Lachmann was being consistent he would have taken this into account (did he? I don’t know and I don’t really care…). What we are interested in here is a sort of “Fisher effect”. That includes changes in relative prices.

  2. Rob Rawlings says:

    Straffa gives his example of changing relative supply and demand and concludes ‘in other words, the rate of interest on the former will be higher than on the latter.’ He sees this as an example of a situation where multiple natural rates could emerge and this was one of his main points of attack on Hayek.

    My reading of this is that he recognized the conditions for which the arbitrage outcome would arise, but I do not see any evidence that he understood that the arbitrage outcome explained these different own-rates (along the lines identified by both Keynes and Lachman) and rescued that part of Hayek’s theory.

    • He recognised in Wicksell what you call the “arbitrage” argument (actually it has to do with price indices). But this requires the introduction of money which Hayek was uncomfortable with (rightly, because the introduction of money leads directly to Keynes’ theories which Hayek was trying to compete with).

  3. Bastien says:

    “I do not know what to make of this at all.”

    Well, that the debate may be difficult, but that the authors could have been more careful in order not to make false criticisms, especially when you quote something that refutes or invalidates your own argument. As you said, even if prices are correctly foreseen, interest rates will diverge anyway.

    “This is what does the damage to Hayek’s theory.”

    What I find even more interesting is that Sraffa’s criticisms also showed that you don’t even have to introduce a monetary part in Hayek’s parable in order to obtain business cycles : they can be explain by divergence between own-rates in a “barter” economy, as you (and the authors of the paper…?) rightly pointed out in the first post with the first quote. A unique natural interest rate does not exist and so it is useless for monetary policy to pursue it, but it even seems that Hayek explanation of business cycles as a discrepancy between the money rate and the natural rate is not needed for them to exist.

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