Sraffa vs. Hayek and the Natural Rate of Interest

September 29th, 2014
in history, macroeconomics

Fixing the Economists Article of the Week

by Philip Pilkington

David Glasner from over at the blog Uneasy Money has co-written an interesting paper on Sraffa and his critique of the natural rate of interest as it was put forward in Hayek’s business cycle theory. There is a lot that might be written about this paper as I believe that the debate has much contemporary relevance. Here, however, I will focus purely on the topic of the paper at hand. Namely, whether Sraffa’s critique of the natural rate of interest was coherent. I will also assume familiarity with the debate as, frankly, I’m too lazy to summarise it and interested people can read the paper which provides a fantastic overview.

Follow up:

Glasner and his co-author, Paul Zimmerman, quote Sraffa’s criticisms as such:

The “arbitrary” action of the banks is by no means a necessary condition for the divergence; if loans were made in wheat and farmers (or for that matter the weather) “arbitrarily changed” the quantity of wheat produced, the actual rate of interest on loans in terms of wheat would diverge from the rate on other commodities and there would be no single equilibrium rate. (p10)

Glasner and Zimmerman say that this disturbance would not persist. They write:

Deviations from equilibrium owing to fluctuations in the supply of real commodities would not persist; market forces would operate immediately to restore an equilibrium with all own rates again equalized, a tendency not mentioned by Sraffa. (p10-11)

They again quote Sraffa. In this quote Sraffa is saying that a market in which there is an increase in demand will go into backwardation. That is, a circumstance in which the forward price for a commodity is lower than the spot price.

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)

Glasner and Zimmerman claim that Sraffa dropped the ball here. They say that he has confused nominal and real interest rates. The authors write:

What Sraffa called a multiplicity of own rates, was in fact a multiplicity of nominal rates reflecting the expected appreciation or depreciation of those commodities for which demand was increasing or decreasing. The natural rate, expressed as a real rate, (i.e., abstracting from expected price changes) remains unique in Sraffa’s exercise. (p11)

But this is not at all clear. The authors appear to be confusing expected price changes with actual price changes. This can clearly be seen if we lay out the process that Sraffa imagines to occur sequentially.

  1. Demand switches from Commodity A to Commodity B.
  2. Commodity B rises in price and Commodity A falls in price.
  3. The financial market anticipates that this price discrepancy is only temporary. Thus the interest rate on Commodity B will increase and the interest rate on Commodity A will fall.

Note that the overall price level has not changed. The price increase in Commodity B has been offset by the price decline in Commodity A. In the future an increase in the supply of Commodity B will cause its price to fall and its interest rate to fall as it tends back toward equilibrium but this does not occur in the present. In the present we have a different structure of real interest rates. The overall price level has remained constant while the real interest rate on Commodity B has risen vis-a-vis the interest rate on Commodity A which has fallen.

In the period when the economy adjusts the quantity produced of Commodity A will fall and the quantity produced of Commodity B will rise. The price will fall back to equilibrium levels and so too will the interest rates. Again though, there is no actual change in the general price level. And the change in real interest rates that occurred in the previous period is still a fact that we cannot ignore.

Even in the case of a supply-shock this same mechanism will occur. If the amount of wheat produced falls below equilibrium level due to a change in the weather its relative price will rise. We then do have an increase in the overall price-level. The financial market in wheat will then go into backwardation and the wheat-interest-rate will rise. But unlike in the last example the other interest rates will not fall because demand for other goods remains constant. Thus we have a fall in real interest rates in these markets. Again the structure of real interest rates changes. The real interest rate on wheat has risen vis-a-vis the real interest rates on all other commodities by dint of the fact that the price level has risen while these interest rates remain the same in nominal terms while the nominal interest rate on wheat has risen.

As Sraffa showed in his paper this has policy implications as it completely befuddles Hayek who was trying to argue that the monetary authority should set the money rate of interest equal to the natural rate. The authors quote Sraffa on this point when he replied to Hayek’s reply:

Dr. Hayek now acknowledges the multiplicity of the “natural” rates, but he has nothing more to say on this specific point than that they “all would be equilibrium rates.” 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. (p13)

This brings up the next criticism that the authors throw at Sraffa.

 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 titled ‘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.

This article was produced from two articles posted at Fixing the Economist:









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