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.
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. I will deal with this in another post.
Fixing the Economists 
The concept of multiple rates under barter is very simple.
Take an (imaginary) barter economy with a matrix of spot and future prices and loan markets for all goods. The own rate of interest for each good will be the underlying “originary” rate of interest adjusted for the price changes reflected in the sport/future price for that good. Any deviations would be eliminated by arbitrage opportunities in the market.
The “originary” rate is in this scenario would approximate to the own-rate of interest on a good whose supply and demand aren’t expected to change much (as reflected on the future markets).
The kind of supply and demand shocks you describe may well cause the originary rates as well the own-rates to shift about, but the above analysis would ensure that the relative rates would adjust and remain alligned, at least in an economy where arbitrage opportunities would be exploited. I don’t think the concept of an overall price level is meaningful under barter.
Both Keynes and Lachman in my view “rescued” Hayek (who did a bad job of defending his own theory) from Straffa on this point.
Where this gets tricky (and where Staff’s other criticism may be more valid) is when you try and apply this a money economy.
No. It does not follow. Try to explain the arbitrage market in detail and see if you can.
If demand switches from Commodity A to Commodity B and the interest rates diverge why would arbitrage cause them to move back toward one another?
This may be a bit simplistic but:
Assume I use GoodA as my unit of account, and is has a own rate of interest of 10%
On the spot market GoodB trades at 1:1 but on the futures market its 1 GoodA for 2 GoodB.
I have 100 Good A that I could trade for 100 good B on the sport market.
But if I lend the 100 A now, I get 110 A in the future, which I will be able to use to buy 220 Good B (if the futures market price is correct).
Therefore I have to be able to lend 100B now for 220 good B in the future to maintain equilibrium. The own rate for B is 120% (I think?). If its lower I can borrow in B and make a profit in A, if its higher, I can borrow in A, lend in B and again make a profit etc.
Using Rob’s example numbers, I’m not clear what you mean by real and nominal rates here, Phil.
The nominal rates in this example are 10% on A and 120% on B. This is the rate that would be specified in a loan contract in each commodity. If the inflation rate (expressed in terms of the unit of account – commodity A) is 2%, say, then the real rate of interest on loan of A is 8% (obviously) and the real rate of interest on a loan of B is 8% (less obviously). We are concerned with how much of a basket of goods one unit of B will buy, and the inflation rate expressed in terms of B is going to be much higher.
That’s how I see nominal and real rates, anyway. Are you meaning something different?
Yes, and the two rates remain different. Lachmann says this explicitly:
That is identical to what Sraffa is saying. Will have a post up on this tomorrow.
Nick,
I don’t think the authors are coherent on what they mean by “real” and “nominal” rates. See what you make of the paper. I mean what you mean.
Frome the paper:
“Fisher, himself, in Appreciation and Interest (1896) had introduced something like an own-rate analysis in discussing how the same real rate could be expressed equivalently as different nominal rates, depending on the choice of numeraire or unit of account. Keynes’s analysis in chapter 17 of the General Theory is merely a generalization of Fisher’s analysis, leading to a similar conclusion, that a unique real rate can be expressed equivalently in terms of many different nominal rates, each one depending on a different choice of numeraire or unit of account. So although it is possible to identify a unique real natural rate of interest, there is no unique nominal natural rate of interest, because, as Fisher certainly understood, the choice of a numeraire rising in value over time would imply a lower nominal interest rate than would the choice of a numeraire stable or falling in value over time”
Yeah, they get it all wrong. Will address this tomorrow.
And it is precisely this issue that the authors claim that Straffa got wrong:
“Thus, the alleged divergence of own rates to which Sraffa drew attention is simply the distinction between the real and the nominal rate of interest long recognized by economists and formally derived by Fisher (1896). 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.”
And as I point out above: that is wrong. You can’t just throw chunks of text at me. You have to engage with the argument in the post. But let’s just leave it to Glasner.
You said: ‘I don’t think the authors are coherent on what they mean by “real” and “nominal” rates’
And I thought it might be useful to supply some quotes that (to me at least) show they are quite clear on these concepts.
Anyway, I will read next your post .
And the same thing would apply no matter what good you choose as “unit of account” causing all rates to align.
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