While writing up my post on the Keynes-Hayek debate at LSE, I visited a couple of blogs to gauge the reaction in the blogosphere to the debate. One of those was the very interesting Social Democracy for the 21^{st} Century: A Post-Keynesian Perspective. In his post on the debate, the blogger, AKA Lord Keynes, had some interesting observations about the famous (well, maybe among Austrians and Keynesians – especially post-Keynesians — with an inordinate interest in the history of economic thought) exchange in the *Economic Journal* between Piero Sraffa, reviewing Hayek’s *Prices and Production*, a short book containing his remarkably successful LSE lectures on the nascent Austrian theory of business cycles, Hayek’s response and Sraffa’s rejoinder. The general consensus about the debate is that Sraffa got the better of Hayek in the exchange, indeed, that the debate marked the peak in Hayek’s influence, having risen steadily after Hayek’s LSE lectures and his lengthy and damaging review of Keynes’s *Treatise on Money* and Keynes’s ill-tempered reply. Though Hayek continued working and writing tirelessly, the decline in his influence and reputation eventually led him away from technical economics into the more philosophical writings on which his lasting reputation was built, though he received some belated recognition for his early contributions when he was awarded the 1974 Nobel Memorial Prize in economics.

Sraffa attacked Hayek’s exposition of the Austrian business cycle theory on two fronts. First, Hayek argued that monetary expansion necessarily produces a distorting and unsustainable effect on the capital structure of production, ultimately causing a costly readjustment back to the earlier capital structure. Sraffa observed that the distortion identified by Hayek was not caused by monetary expansion per se, but by a change in the distribution of money, but a distributionally neutral expansion would have no such distorting effect. Sraffa also observed that it was entirely possible that the addition to the capital structure induced by what Hayek called forced saving might actually turn out to be sustainable inasmuch as the augmented capital stock might itself imply a reduced natural rate of interest rate corresponding to the reduced money rate achieved through monetary expansion.

Sraffa’s second, and perhaps more damaging, line of attack was on the very concept of a natural rate of interest, borrowed by Hayek from the Swedish economist Knut Wicksell, though transforming it in the process. According to Hayek, the natural rate corresponds to the interest rate in a pure barter equilibrium undisturbed by the influence of money. The goal of monetary policy should therefore be to ensure that the money rate of interest equaled the natural rate, thus neutralizing the effect of money and facilitating an intertemporal equilibrium in which money is not a distorting factor, i.e., in monetary expansion by banks to finance investments in excess of voluntary savings does not drive the money rate of interest below the natural rate, a state of affairs that could never obtain in a barter equilibrium.

Sraffa, however, argued that Hayek’s use of the natural rate of interest as a benchmark for monetary policy was incoherent, because there would be no unique natural interest rate in a growing barter economy with net investment in capital goods of the kind Hayek wished to use as a benchmark for monetary policy in a growing, money-using, economy. In the barter economy, interest rates would correspond to the price ratios over time (own rates of interest, i.e., ratios of spot to forward prices) between durable or storable commodities. But these own rates would fluctuate in response to the changing demands characterizing a growing economy, implying that there is no single natural rate of interest, but a collection of natural own rates of interest. Only if Hayek were willing to follow Wicksell in defining a price level in terms of some average of prices would Hayek have been able to define a natural rate of interest as some average of own rates. But Hayek explicitly rejected the use of statistical price levels. Hayek’s reply was ineffective, leaving Sraffa the clear winner in that exchange.

However, a quarter of a century later, Hayek’s student Ludwig Lachmann in his book* Capital and its Structure* elegantly explained the critical point that neither Sraffa nor Hayek had quite comprehended. The natural interest rate in a barter economy has a perfectly clear meaning, independent of any statistical average, in an intertemporal equilibrium setting, because equilibrium requires that the expected return from holding all durable or storable assets be the same. The weakness of the natural-rate concept is not that it necessarily pertains to a monetary rather than to a barter economy, as Hayek supposed, but that it could only be given meaning in the context of a full intertemporal equilibrium.

In his discussion of Sraffa and Hayek on his blog, Lord Keynes insists that Sraffa got it right.

However, Piero Sraffa had already demonstrated in 1932 that outside of a static equilibrium there is no single natural rate of interest in a barter or money-using economy, and Hayek never really addressed this problem for his trade cycle theory.

Sraffa did demonstrated that there was no single natural rate of interest in a disequilibrium, but he did not do so for an intertemporal equilibrium in which price changes are correctly foreseen. Hayek actually had developed the concept of an intertemporal equilibrium in a paper originally published in German in 1929, eight years before providing a truly classic articulation of the concept in his wonderful 1937 paper “Economics and Knowledge,” so it is odd that he was unable to respond effectively to Sraffa’s critique of the natural rate in 1932.

Lord Keynes, who is aware of Lachmann’s contribution on the Sraffa-Hayek exchange, cites as authority for dismissing Lachmann, a paper by another blogger, an ardent, but surprisingly reasonable, Austrian business cycle theory supporter Robert Murphy, who has written a paper that addresses the Sraffa-Hayek debate. Lord Keynes quotes the following passage from Murphy’s paper.

Lachmann’s demonstration—that once we pick a numéraire, entrepreneurship will tend to ensure that the rate of return must be equal no matter the commodity in which we invest—does not establish what Lachmann thinks it does. The rate of return (in intertemporal equilibrium) on all commodities must indeed be equal once we define a numéraire, but there is no reason to suppose that those rates will be equal regardless of the numéraire. As such, there is still no way to examine a barter economy, even one in intertemporal equilibrium, and point to ‘the’ real rate of interest.”

Murphy is almost right in that Lachmann demonstrates that the rate of return is equalized across all investment opportunities (allowing for the usual sources of difference in rates of return) in an intertemporal equilibrium. It is not clear what he means by saying that the choice of a numeraire matters. It doesn’t matter for any real property of the intertemporal equilibrium, i.e., a real quantity or a relative price; it matters only for nominal quantities and absolute prices. But nominal quantities, by definition, depend on the choice of a numeraire and even in a static equilibrium there is no unique nominal rate of return just as there is no unique level of absolute prices. The “real” rate of interest is determined in an intertemporal equilibrium; the nominal rate is not determined. This is precisely the distinction between the real rate and the nominal rate identified in the Fisher equation. And every kindergartener knows that the natural rate is a real rate not a nominal rate.

Perhaps Murphy is made uncomfortable by the fact that Lachmann’s point shows that a Hayekian intertemporal equilibrium could be consistent with any rate of inflation as long as the nominal rate reflected the equilibrium expected rate of inflation and inflation would have no effect on relative prices. That indeed is a problem for a fundamentalist version of Austrian business cycle theory and would deny that as a matter of pure theory there cannot be an intertemporal equilibrium with inflation. But that form of Austrian fundamentalism is simply inconsistent with the basic properties of an intertemporal equilibrium and with the non-uniqueness of absolute prices in either a static or intertemporal equilibrium. So Austrians just need suck it up on that (not very important) point and move on.

Finally, to come back to Sraffa. It is worth noting that the real Keynes in the *General Theory* said this about the natural rate of interest.

In my

Treatise on MoneyI defined what purported to be a unique rate of interest, which I called thenatural rate of interest— namely, the rate of interest which . . . preserved equality between the rate of saving . . . and the rate of investment. . . .I had, however, overlooked the fact that in any given society there is, on this definition, a

differentnatural rate of interest for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus it was a mistake to speak ofthenatural rate of interest or to suggest that the above definition would yield a unique value fo rthe rate of interest irrespective of the level of employment.

So Keynes, like Sraffa, clearly had rejected the notion of a unique natural rate of interest. But Keynes’s reasons for doing so are very different from Sraffa’s. Keynes’ makes no mention of multiple natural rates corresponding to the different commodity own rates of interest that Sraffa had introduced in his attack on Hayek’s use of the natural rate. (Keynes, of course, as editor of the Economic Journal, had selected Sraffa to write a review of *Prices and Production*, presumably knowing what to expect, so he knew exactly what Sraffa had said about the natural rate of interest.)

Indeed Keynes goes through Sraffa’s analysis in chapter 17 of the *General Theory*, “The Essential Properties of Interest and Money.” It is one of my favorite chapters, especially because its analysis of portfolio choice is so acute. I just quote one long paragraph (pp. 227-28).

To determine the relationships between the expected returns on different types of assets which are consistent with equilibrium, we must also know what the changes in relative values during the year are expected to be. Taking money (which need only be a money of account for this purpose, and we could equally well take wheat) as our standard of measurement, let the expected percentage appreciation (or depreciation) of houses be

a1and of wheata2.q1, -c2andl3we have called own-rates of interest of houses, wheat and money in terms of themselves as the standard of value; i.e.,q1is the house-rate of interest in terms of houses, -c2is the wheat-rate of interest in terms of wheat, andl3is the money rate of interest in terms of money. It will also be useful to calla1+q1,a2–c2andl3, which stand for the same quantities reduced to money as the standard of value, the house-rate of money-interest, the wheat-rate of money-interest and the money-rate of money-interest respectively. With this notation it is easy to see that the demand of wealth-owners will be directed to houses, to wheat or to money, according asa1+q1ora2–c2orl3is greatest. Thus in equilibrium the demand-prices of houses and wheat in terms of money will be such that there is nothing to choose in the way of advantage between alternatives; i.e,a1+q1,a2–c2andl3will beequal. The choice of the standard of value will make no difference to this result because a shift from one standard to another will change all the terms equally, i.e. by an amount equal to the expected rate of appreciation (or depreciation) of the new standard in terms of the old.

In this particular post, I am happy to give Keynes the last word.

Very informative. Thank you.

This is a very good post.

“Sraffa did demonstrate that there was no single natural rate of interest in a disequilibrium, but he did not do so for an intertemporal equilibrium in which price changes are correctly foreseen. “Your operative words are “correctly foreseen”.

But such a “intertemporal equilibrium” seems to be a condition that will never exist in the real world (just like Mises’s ERE) when you face fundamental uncertainty – uncertainty in the sense of Frank Knight and Keynes in his 1937 article:

Keynes, “The General Theory of Employment,” Quarterly Journal of Economics 51 (1937): 209–223.

You say above in your “About Me” section:

“In my book

Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money”Out of interest, does this mean that you support Hayek’s notion of competing private currencies?

One final point, I think I have covered some points here relevant to your discussion:

http://socialdemocracy21stcentury.blogspot.com/2011/06/hayek-on-flaws-and-irrelevance-of-his.html

Nice blog and thoughtful posts, though I will have to read more.

I was very impressed by Murphy’s paper but after this post I think I need to give it another look. It did seem odd to me at the time of reading it but he had me convinced (I had been wondering about Austrian insights into the predictive power of the yield curve for some time so I was quite ready to accept anything I read, and I have often admired much of Murphy’s work). Arguing in terms of intertemporal equilibrium and ERE (as Lord Keynes points out) are always disconnected from reality, though often necessarily though. I’m wondering (as I guess our royal commenter is as well) what your comments are about the effects “Knightian” uncertainty and things for which risk is impossible to measure.

That post cleared up a number of things I have been wondering about. In particular, you have confirmed my interpretation of what Sraffa was saying about the natural rate on wheat being different from the natural rate on barley. And you and Lachmann are right. It’s no biggie.

Can you relate this discussion with the intertemporal equilibrium in general equilibrium and Ramsey pricing!

You: “Sraffa did demonstrated that there was no single natural rate of interest in a disequilibrium, but he did not do so for an intertemporal equilibrium in which price changes are correctly foreseen.”

That’s not true (and I’m no Sraffa-fan)! In a barter economy with perfect foresight, intertemporal equilibrium characterized by diverging own rates of interest are the norm; stationarity is just a special case. Christopher Bliss is the literature you should consult.

John Hawkins is wondering about Knightian uncertainty, I am too. But more generally I’m wondering where you think Frank Knight’s views on capital and interest fit into this debate, if at all. It seems to me that Knight’s ‘perpetual fund’ of capital implies a stable Wicksellian natural or real rate of interest, contra both Hayek and Sraffa/Keynes.

It is pretty obvious why Hayek never used the argument of a general intertemporal equilibrium to defend his natural rate, equilibrium in the sense of correctly foreseen price changes. In his noble speech he makes it clear that he believes “imperfect knowledge” and the utter, irreducible uncertainty it both reflects and creates is indispensable to understanding the purpose and functioning of markets. Rational expectations/ assuming omnipotence on the part of market participants is a cope out to the real vision of economics Hayek, Keynes and Knight all discussed.

“History is bunk. History of economic thought is bunk on stilts.” — greg ransom

Hayek in 1931-1932 was still caught between 2 worlds — an attempt to extend marginalist and relative price thinking across time & into production across time, and an attempt to use the aggregated “average period of production” as a Ricardo-type aggregate measure in trade cycle theory. Hayek was aware early on that this was not a satisfactory blend — but in the 1931-1934 period Hayek came to see it was a complete failure as a short-cut make-shift.

The interchange with Sraffa was only one small bit in the transformation of Hayek’s who approach — leading up to what he did in his 1941 book _The Pure Theory of Capital_, which utterly rejected the Bohm-Bawerk / Ricardio tradition shortcut of aggregate measuring of the “average period of production”.

Note well — Sraffa’s critique come out of the Ricardian frame, Hayek’s seminal effort in the history of economic science in this period is to pioneer the extension of marginalism into the real of time & production thru time, abandoning the category of measured “capital” as an aggregated class entity.

Hayek was abandoning the last vestiges of Ricardian objectively measured and physically characterized aggregated values when he abandoned the average period of production linked to the “natural rate of interest”.

Sraffa, famously, went in a different direction.

Hayek takes up some of these “own rate of interest” issues again in his 1941 book .. I may add more later.

[closing the italic tag left open above…

Bill, You’re welcome. I’m glad that you found what I wrote to be helpful.

LK, Thanks. I agree that the natural rate of interest is neither directly observable nor operational. But I think Sraffa went further and argued that the very notion of a natural rate, at least for Hayek owing to his aversion to index number, was incoherent. Lachmann showed that Sraffa was wrong because in an intertemporal equilibrium the net rate of return on every asset held over time must be equalized. But Lachmann himself was only applying the analysis of Keynes in chapter 17 of the GT. So it was Keynes, who got Sraffa to write the review of Hayek, in the end rejected Sraffa’s point about the natural rate of interest. Even though Keynes also rejected the idea of a natural rate of interest as unworkable, he clearly says that there is a natural rate in equilibrium (i.e., full employment), but that there may be different natural rates corresponding to non-equilibrium (i.e., less than full employment) levels of income. I haven’t looked at the paper you cite, at least not for a long, long time, but I think chapter 17 settles the point. But I would welcome hearing your take.

About my view of Hayek and competing currencies, in my book I criticized Hayek’s argument that competing currencies would engage in competitive discovery process in selecting the standard most preferred by the public. I pointed out that his argument completely neglected the network externality (though I didn’t use that term which was not yet familiar when I was writing my book) associated with a monetary standard, so that there could be no presumption that the standard emerging from a competitive process would be optimal and that, in any case, competing suppliers of currency would choose to link their currencies to an already existing standard to internalize those externalities. I therefore argued that the government should create a standard through a form of indirect convertibility aimed at stabilizing the expected money wage level, thus cushioning employment from adverse supply shocks.

I agree that Hayek’s discussion of monetary policy was not always on target, and I don’t think his argument that inflation would necessarily lead to a crisis is historically or theoretically correct. That is not to say that inflation may not be destabilizing, just that Hayek’s theoretical account was highly problematic. I have learned more from Hayek than I think anyone else, I had the utmost admiration, and personal affection (though we were never really close) for him. What I liked best about him was his amazing tolerance and open-mindedness and consideration. He never tried to create a school and cultivate disciples. And I believe that his political and philosophical ideas could potentially be adapted to a more center-left orientation than is usually recognized.

John, I liked Murphy’s paper as well, and my criticism is not that he adopts the perspective of intertemporal equilibrium, but doesn’t quite get it right, otherwise he wouldn’t have criticized Lachmann. On Knightian uncertainty, I don’t think that we have a systematic way of dealing with it, or, if we do, it doesn’t fit in with the kinds of modeling strategies that people are used to. Lachmann and G.L.S. Shackle both tried to carry through some kind of revision of economic theory to take into account uncertainty with very interesting but very unoperational results. But it is at least worthwhile to remember that our models generally just pretend that we can reduce all uncertainty to a normal distribution and then apply the methods of DSGE.

Nick, It’s good to know that you think my discussion was on target. It’s always nice to have authority on your side. But see amv’s comment and my response below.

Prakash, I’m not sure that I can. At any rate, you would have to give me a much more focused question before I could even try.

amv, Sorry to be demanding, but it would really be nice if you gave me a specific citation that you think contradicts my argument rather than just invoke the name of Christopher Bliss.

knapp, See my response to John above about Knightian uncertainty. I don’t know that much about Knight’s capital and interest theory. My vague impression is that he viewed capital as just a single undifferentiated commodity. That would tend to imply a flat yield curve in simple one or two good intertemporal GE model, but if you introduce money and expectations I think that you can derive fluctuating short-term interest rates and a rising or falling yield curve. My view is that in these matters it is not a question of whether one model is right or wrong; it is whether the model is appropriate for the particular problem that you are trying to solve or explain.

JR, Your premise is incorrect. Hayek’s early work was totally situated in the context of intertemporal equilibrium analysis. Even his last important piece of theoretical analysis The Pure Theory of Capital was intertemporal equilibrium analysis from start to finish. It is true that he later became increasingly skeptical of whether equilibrium analysis was capable of yielding useful insights but that skepticism was part of the reason that he gave up high economic theory for broader more philosophical research. I am sure that he would have been unhappy with the way in which rational expectations models have developed, but in 1932 he was still working in the context of intertemporal equilibrium models.

Greg, I look forward to seeing your citations of further points of inconsistency between Ricardo and Hayek in the Pure Theory of Capital. But as a general matter, I don’t see the relevance of these issues to the particular interchange between Sraffa and Hayek.that I am discussing.

You argue that diverging own rates indicate disequilibrium in barter models that predict intertemporal equilibrium. But this is not the case. Hayek introduced the notion of intertemporal equilibrium (in 1928, not 1929) to expand the equilibrium notion beyond the case of stationarity, and even beyond the case of steady state. Own rates of interest are equal, iff all goods grow at the same rate. If relative scarcities vary over time, his barter model (or rather numeraire model) predicts an intertemporal equilibrium that takes account of this change. Some rates are higher than others. Some are even negative, indicating an increase of relative scarcities over time. No disequilibrium here. Just standard equilibrium reasoning by means of dated commodities. Equal own rates are just a special case. In general, there is no single natural rate that could be compared with the own rate of money. Sraffa is right.

Lachmann confuses the logic described above with the Smithian logic of profit equalization. Bliss has a short New Palgrave entry on “equal rates of profits” that clarifies this point. The no-arbitrage opportunity you are referring to applies to sequence economies, where financial asset(s) reduce(s) the number of open markets necessary to implement intertemporal equilibrium allocations (# dynamically complete markets < # complete markets in static notions of equilibrium). But this is not Hayek!

ah, the evidence … you can find it in almost all of Hayek works up to and including the Pure Theory of Capital where he talks about equilibrium notions that do not specify constant relative prices and utility levels, including his 1928 paper. See also Utility Analysis and Interest (1936), and his Copenhagen lecture (first held in 1933). He was well aware of the fact that perfect foresight in non-stationary equilibrium can by no means be an legitimate individual restriction (as many forerunners still believed because stationary equilibria are learnable). This led him to his famous statements in ‘Economics and Knowledge’ (1937) that perfect foresight is no individual characteristic but a general equilibrium condition.

This is a weird situation, where you guys are prepared to give the Austrian (Lachmann) a pass in his argument against Sraffa, and I’m going to dig in my heels and say no, Sraffa’s objection has yet to be met.

Glasner wrote:

Murphy is almost right in that Lachmann demonstrates that the rate of return is equalized across all investment opportunities (allowing for the usual sources of difference in rates of return) in an intertemporal equilibrium. It is not clear what he means by saying that the choice of a numeraire matters….In the Hayek/Sraffa debate–with the relevant sections quoted in my paper linked above–Sraffa basically said, “Hayek is an idiot. He says the central bank needs to set the money rate of interest equal to the natural rate. But there’s no such thing as a unique natural rate of interest in an economy.”

So Lachmann chimes in and says, “There is too a unique natural rate of interest in the economy! Arbitrage ensures that the rate of return, measured in reference to a commodity, is equalized across all investments.”

Right, but that hasn’t answered Sraffa’s challenge. Suppose the own-rate of interest on apples is 10%, and the own-rate of interest on oranges is 5%. So should the central bank set the money rate of interest at 5% or 10%?

(You can introduce another layer of complexity by talking about a general price inflation level, but that just pushes back the problem one step. There isn’t a unique way of defining what the change in the purchasing power of money is; it depends on how we define the commodity basket.)

Bob, so is the idea that since the rate of interest is constantly changing among commodities, entrepreneurs haven’t had time to reallocate in a way that would equalize the interest rates (basically: oh, apples are doing better, and I believe this trend will continue. Let me sell my orange-futures and buy some apple-futures, or some scenario like that). If this is not your point, I may need to re-read your paper to remember why it made sense then. I have a feeling this is not your point, and the intuitive problem I’m having is: why would the orange owners continue to tolerate the lower rate of return?

John, no that’s not the point. There’s nothing about uncertainty here. For example, if the output of apples rises at 10% per year (for whatever reason), while the output of oil steadily declines at 10% per year (because there’s only so much to go around), even if everybody at time=1 can forecast perfectly for the next 100 years, then you are not going to get a unique “real” rate of interest in this economy. It depends how you define the commodity basket to determine the “price level” in a given time period.

The choice of price basket won’t affect entrepreneurial decisions; this is the germ of truth in Lachmann’s argument. If you earn x% per year, when using apples as the standard of value, or you earn y% when using oil, you don’t care. Alternate investments will be correspondingly affected by the change of numeraire. Whatever it makes sense for you to do, using apples as the numeraire, it will also make sense for you to do if you switch your accounting and reckon in barrels of crude oil.

But that’s not the issue here. Hayek said that the banks must set the money rate of interest to the natural rate, to avoid a boom-bust cycle. So Sraffa said, “How do we compute ‘the’ natural rate? There is no such thing.”

Lachmann hasn’t answered that problem.

amv, I think that I understand Hayek’s concept of intertemporal equilibrium. Own rates in an intertemporal equilibrium don’t have to be equal, but differences in own rates must reflect some compensating advantage such as a real service provided by an commodity held or a cost of storing a commodity held. The net return from holding assets must be equal in equilibrium otherwise prices would have adjusted to eliminate the difference in the net return. Otherwise, we are not working with the same equilibrium concept. This is straight out of chapter 17 of the General Theory. I haven’t had a chance to look up Bliss in the New Palgrave yet, but I will try to do so. There is no single own rate of interest that can be compared to the money rate of interest only if you mean that there is no own rate that uniquely corresponds to the money rate of interest, but in a barter equilibrium, no matter which own rate is used, there will be a unique optimum length of time which the owner of a bottle of wine will allow that bottle to age. That is the unique natural real rate of interest for that barter equilibrium.

Obviously I do not understand your point about sequence economies versus Hayek’s intertemporal equilibrium. If you can explain it to me, I would of course be greatly indebted to you, but as of now, I don’t understand your point.

Bob, You said:

“This is a weird situation, where you guys are prepared to give the Austrian (Lachmann) a pass in his argument against Sraffa, and I’m going to dig in my heels and say no, Sraffa’s objection has yet to be met.”

Well, obviously that what makes you the charming guy that you are.

Bob, the rate of return from holding all assets net of their storage costs and their current service flows must be equal in equilibrium. If not, you’re not in equilibrium. So all you have to do is find an asset with no storage cost and no current service flow and calculate its expected rate of appreciation and you have the real natural rate of interest. That is independent of your choice of numeraire. If you don’t believe me, read chapter 17 of the General Theory and you will be amazed to learn something from Keynes that you never learned from any Austrian economist. Of course, that is subject to amv explaining to us why Keynes was wrong.

John and Bob, Just to reiterate the point. If, in equilibrium, apples are appreciating relative to oranges, say because it is more costly to store apples than to store oranges, so apples must appreciate relative to oranges otherwise no one would be willing to store the apples, if we declare apples to be the numeraire we can compute the pure real rate of interest by finding whatever asset provides no current yield and has no current storage cost and finding its rate of appreciation. We can do the same with oranges as numeraire and we will come up with the same answer.

David Glasner wrote:

“John and Bob, Just to reiterate the point. If, in equilibrium, apples are appreciating relative to oranges, say because it is more costly to store apples than to store oranges, so apples must appreciate relative to oranges otherwise no one would be willing to store the apples, if we declare apples to be the numeraire we can compute the pure real rate of interest by finding whatever asset provides no current yield and has no current storage cost and finding its rate of appreciation. We can do the same with oranges as numeraire and we will come up with the same answer.”OK this is really a dangerous situation, because one of us is making a really dumb mistake here. Fortunately for me, if I turn out to be the one who’s wrong, then at least it makes the Austrians right all these decades. (It’s sort of like I bet against my favorite team in the Superbowl. I’m hedged emotionally.)

OK so the own-rate of interest on apples is 1% and the own-rate of interest on oranges is 10%. First let’s use apples as the numeraire. That means the rate of return on any investment, measured in apple prices, has to be 1%. So we look at bars of gold, which have no current yield and no appreciable storage cost. The spot price of gold, measured as pounds of apples per ounce of gold, changes over time such that the rate of return on holding gold is 1%.

Now we switch our numeraire to oranges. The spot exchange rates of all goods against oranges change over time such that the rate of return in any investment is 10%. In particular, if I buy and hold gold, the orange-price of gold rises at 10%.

So now I ask you: What is the natural, real, rate of interest in this economy? When Hayek says the central bank must set the money-rate of interest equal to the natural rate, what number should the central bankers use?

Welcome back from Japan!

ad “Own rates in an intertemporal equilibrium don’t have to be equal, but differences in own rates must reflect some compensating advantage such as a real service provided by an commodity held or a cost of storing a commodity held.”

I disagree. Even at zero storage costs and zero convenience yields, own rates may differ in a barter economy due to changing relative scarcities over time. An intertemporal market economy with equal primitives displays the same result by changing relative prices over time. A positive own rate of commodity X in the barter model corresponds to decreasing decreasing relative prices over time in the market model (and vice versa). Hayek innovated the notion of intertemporal equilibrium to escape Böhm-Bawerk’s stationary equilibrium, which equates stationary primitives with stationary outcomes (constant utility, constant prices, …). Instead, he wants a broader equilibrium notion that can predict different prices at different dates. In fact, Hayek innovates a proto Arrow-Debreu model. Different prices at different dates for each commodities corresponds to diverging own rates in a barter model.

ad “The net return from holding assets must be equal in equilibrium otherwise prices would have adjusted to eliminate the difference in the net return. Otherwise, we are not working with the same equilibrium concept.”

Where is your asset coming from. The clue of an intertemporal equilibrium notion is that it incorporates time in a purely static framework by means of dated commodities. If, however, you argue with dated commodities, there is no rationale to introduce assets (or financial markets). We are not working with the same equilibrium concept indeed.

ad “Obviously I do not understand your point about sequence economies versus Hayek’s intertemporal equilibrium. If you can explain it to me, I would of course be greatly indebted to you, but as of now, I don’t understand your point.”

It is widely acknowledged that the number of markets required by intertemporal equilibrium analysis is far too large to be realistic. Even in Hayek’s deterministic variant, an infinite time horizon suggests infinitely many markets. Assets are means to reduce the number of markets necessary to implement efficient allocations. Instead of dated commodities – traded in an initial period before the physical history of the economy -, we have a sequence of open spot markets, including financial markets. This is called a sequence economy: http://www.newschool.edu/nssr/het/essays/sequence/sequence.htm .

My point is that you attempt to discuss Sraffa’s critique of Hayek, who attempts to discuss monetary policy issues by means of the ill-suited intertemporal equilibrium notion, by switching to sequence economies. Thus, your conclusions do not apply to the debate.

Bob, OK I’m going to make your day. My previous response was not as clear as it should have been. I should have known better than to try to write a response at 1:30 AM. It’s only 12AM now, so I should be OK. At any rate the idea is simple. If we have an intertemporal equilibrium, we can calculate, for any numeraire, the own-interest rate for any commodity in terms of that numeraire. Given the own-interest rate in terms of a numeraire, we can derive the natural rate in terms of the numeraire by subtracting the cost, if any, of holding the commodity in terms of the numeraire and adding the service yield, if any, from holding the commodity in terms of the numeraire to the own interest rate of that commodity in terms of the numeraire. The natural own-interest rate for each commodity is equal to the natural own-interest rate for every other commodity in terms of a given numeraire, because the rate of price appreciation in intertemporal equilibrium is equal to the natural interest rate plus holding cost minus yield or service flow. The natural own-interest rate in terms of every other numeraire can be found by the standard equation for covered interest arbitrage. Thus for whatever commodity we choose as numeraire, we can immediately calculate through the covered interest arbitrage equation the corresponding natural interest rate in terms of every other choice of numeraire. You ask which natural interest rate is the central bank supposed to set? You might as well ask which temperature are you supposed to set your thermostat, celcius or farenheit? The answer is it doesn’t matter. Setting the thermostat at 72 degrees farenheit is the same as setting the thermostat as 22.22 degrees celcius. The interest rate is the same, the only difference is whether you are quoting the interest rate in terms of apples or oranges, but for any interest rate quoted in terms of apples, you get the same interest rate quoted in terms of oranges. There will be a different numerical structure of interest rates for every choice of numeraire, but they all reduce to the same structure after adjusting for the choice of numeraire just as you can measure the same distance in terms of feet, inches, yards and miles, and meters, centimeters and kilometers. The actual distance is the same whichever way it is measured.

Consider a model with apples, oranges which are costly to hold and a third commodity which is costless to hold. No commodity provides any yield until it is finally consumed. If apples and oranges are being held from one period to the next, then the net yield on both must be the same. Suppose that pples are more costly to store than oranges, so apples must be appreciating faster than oranges otherwise it wouldn’t pay to incur the extra cost of storing the apples. So if apples increase in price by say 10% in terms of some arbitrary unit of account and oranges increase by 5% in terms of that unit of account, then if apples were the numeraire, then the own-apple interest rate would be zero, and the own-orange interest rate quoted in apples would be approximately -5%. If oranges were the numeraire, then the own-orange interest rate would be zero and the own-apple interest rate quoted in oranges would be approximately 5%. Now if there is an asset, say gold (or aging wine), that is costless to hold, and provides no real yield — in this model gold does not glitter — then gold is appreciating more slowly than apples or oranges, so the own-gold interest rate quoted in apples would be -7.5% and the own-gold interest rate quoted in oranges would be 2.5%. But the natural rates adjusting for holding cost and yield would all be equivalent, and you, or anyone else, would be indifferent between contracting in terms of any of these rates, because the rates are equalized by the formula for covered interest arbitrage.

amv, Thanks, it’s really good to be back.

Again I am sorry to admit that I am really having trouble following your explanations, and it could very well be my fault because I seem to be missing some relevant background knowledge. But I just don’t seem to be following your argument. Let me just try it this way. Are you saying that there is no restriction in intertemporal equilibrium on the variation of prices of commodities through time because prices in each period are determined by the demand and supply for the commodity in that period? If so, how do you distinguish that case from the restriction on the variation on prices between different locations as a result of transportation costs? The analysis is completely symmetric except that commodities can only be transported from the present to the future not from the future to the present (except insofar as there is intertemporal substitution in demand). So why wouldn’t intertemporal arbitrage should eliminate any price differences? Maybe we can get somewhere working through the analysis this way.

David,

I think part of what’s going on here, is that you and I might be using different terminology. By “own-rate of interest” I mean the real rate of exchange between units of a given commodity at time T and time T+1.

So for example, if I hold an orange at time T, I can sell it for some money, then use the money to buy a claim on an orange to be delivered at time T+1. (For concreteness, you can picture me buying a call option on 1 orange with expiration in T+1 with a strike price of zero.)

So in my approach, I actually think about the (gross) own-rate of interest as the ratio of two different prices *in time T*: Namely, spot price divided by the price of the above-mentioned call option. It shows how many future oranges you can buy right now, if you sell 1 present orange.

Is that the same definition you are using? Obviously with perfect foresight, we can get the same number by (say) selling the orange in period 1 for money, investing the money into some asset (which could be a bond), and then using the accumulated money in period T+1 to then buy orange(s) at their new spot price.

Bob, Perhaps we are using different definitions, amv was suggesting a different definition of equilibrium, but I couldn’t figure it out. I’m sorry to admit this, but I have absolutely no intuition when it comes to option pricing, so it doesn’t help me to translate into that language so I am going to stick to the ratio of spot prices. In intertemporal equilibrium, the today’s forward equals tomorrow’s spot price. Are we on the same page?

This is a classic post and…well, it helped me think through a problem I’ve been working on for a long time. It’s not done yet, and I would like to have something like a real model.

The key point here is that of uncertainty, I think — which Lord Keynes sharply pointed out in his first post. David then admitted that, if uncertainty is accepted “the natural rate of interest is neither directly observable nor operational.” And went on to say:

“But I think Sraffa went further and argued that the very notion of a natural rate, at least for Hayek owing to his aversion to index number, was incoherent.”

But that’s NOT what Sraffa was saying. His point was more humble. It was the same one as Bob made below, namely: show me the rate!

Bob asked David to point out an observable natural interest rate that the central bank could use for regulatory purpose — David did so, but in the process ignored the dimension of fundamental uncertainty.

My reading is that David did this by exploring the idea of ‘inter-temporal equilibrium’, but this seems means something very specific which Lord Keynes pointed out in his first post. Quoting directly from the original piece, Lord Keynes points out that David’s inter-temporal equilibrium is a situation “in which price changes are correctly foreseen”. But this is no good for Hayek. Quoting from the blog post Lord Keynes linked to, Caldwell says:

“by the middle of the 1930s, problems with [Hayek’s] static equilibrium theory had become ever more evident, as questions of the role of expectations came to the fore and, and, with them, the recognition that earlier models had assumed perfect foresight”

Done and dusted, if you ask me. Sneaking in the ‘perfect foresight’ circumstance of inter-temporal equilibrium is, at a deeply theoretical level, doing precisely the same thing as taking up a ‘God’s Eye’ view of a statistical price level ala Wicksell — something Hayek explicitly rejected due to his realism (and dislike of planners, perhaps?).

So, we can take Hayek together with his realism and then the theory falls apart. Or we can turn Hayek into something different entirely and allow some central banker to guess at some highly theoretical inter-temporal natural rate of interest. I don’t think I need to say that Hayek would loath the latter option. Indeed, it would, in many ways, be similar to what happens today when central bankers try to set a ‘perfect’ rate of interest to stop inflation. Pure technocracy, to Hayek’s mind, I should think!