Last September, after Robert Murphy and Lord Keynes wrote about the Sraffa-Hayek debate of 1932 about the natural rate of interest, I wrote a post about that controversy in which I took an intermediate position defending Hayek against Sraffa’s charge that his use of the natural-rate concept was incoherent, while observing as well that the natural rate of interest in nominal terms is not unique, because any real intertemporal equilibrium is consistent with any choice of price level and any rate of inflation. The condition for a real intertemporal equilibrium with money is simply that the level and rate of change of prices be foreseen correctly. In such an equilibrium, own rates could differ, but by no more than necessary to compensate for different real service flows and different costs of storage associated with different assets, inasmuch as the expected net real return from holding every asset must be equal in equilibrium. But while expected real returns from holding assets must be equal, that unique real return is consistent with any nominal return reflecting any arbitrary rate of price change. It is not by choosing a particular nominal rate of interest — a rate that equals the natural rate — that the monetary authority brings about intertemporal equilibrium. Rather, it is the consistency between whatever nominal interest rate the monetary authority has chosen and the expectations by economic agents of future prices that is the necessary and sufficient condition for intertemporal equilibrium. Any nominal interest rate can become the natural rate if it is supported by an equilibrium set of price expectations. Hayek almost, but not quite, understood this point. His incomplete understanding seems to have prevented him from responding effectively to Sraffa’s charge that his concept of a natural rate of interest was incoherent based on the potential existence of many different own rates of interest in a barter equilibrium.

As a result of last September’s post about Sraffa and Hayek, my colleague Paul Zimmerman and I wrote a paper about the Sraffa-Hayek debate and Keynes’s role in the debate and his later discussion of own rates in chapter 17 of the *General Theory*. I gave a talk about this paper at Brock University in St. Catherines, Ontario on Sunday at the annual meeting of the History of Economics Society. At some point in the near future, I hope the paper will be ready to circulate on the internet and to submit for publication. When it is I will provide a link to it on the blog. So it was an interesting coincidence that two days after the conference, the Sraffa-Hayek debate about the natural rate and about own rates was the subject of renewed interest in the blogosphere.

The latest round was started by Andrew Laiton who wrote about multiple own rates of interest. Laiton apparently thinks that there could be multiple real own rates, but seems to me to overlook the market forces that tend to equalize own rates, market forces wonderfully described by Keynes in chapter 17. Nick Rowe followed up with a post in which he seems to accept that real own rates could differ across commodities, but doesn’t think that that matters. All that matters is that the monetary authority choose a particular own rate and sets its nominal rate to match the chosen own rate. (Daniel Kuehn agrees with Nick here.)

Nick is right that there is no natural rate that can be defined apart from a particular choice of a nominal price path for at least one commodity over time. But in an economy with* n* commodities and* t* time periods, there are *nt* possible choices (actually many more possible choices if we take into account all possible baskets of commodities and all possible rates of price change). The job of the monetary authority is to pin down a path of nominal prices. Given that nominal choice, the natural rate consistent with intertemporal equilibrium would find expression in a particular nominal term structure of interest rates consistent with the equilibrium price expectations of agents. Hayek himself proposed constant NGDP as a possible monetary rule. What Hayek failed to see is that it was the choice of a particular value or time path of nominal GDP that would determine a particular nominal value of the natural rate, not, as Hayek believed, that by choosing a nominal interest rate equal to the natural rate, the monetary authority would ensure that NGDP remained constant over time.

“own rates could differ, but by no more than necessary to compensate for different real service flows and different costs of storage associated with different assets”

Agreed. But the same thing is true of all financial securities, including those used as money. That seems to pin down the price path and nominal interest rate, and contradicts this:

“Any nominal interest rate can become the natural rate if it is supported by an equilibrium set of price expectations.”

Yes, the natural nominal rate is not unique, as the price level is theoretically indeterminate in Wicksellian and neo-Wicksellian models, as many have noted. But history (of the price level itself, as in New Keynesian models, or of the quantity of money, as in monetarist models) and/or the commercial legitimacy of the state (commodity backing/ fiscal stance/ ability of set unit of account/ whatever) pin down the price level and expectations of the price level.

So the Sraffian challenge is purely one of ‘prove logical consistency in all states of the world’. I don’t know why you would let Sraffa have half the credit. If the aim is to answer the question ‘does the current monetary regime have a unique short term risk free nominal rate that clears the market ( for the short term risk free real rate)’, the answer is plainly and simply yes.

My reading of Sraffa, from Nick’s post, is that while his aim may have been to contest that the economy could ever be in equilibrium (the limits to arbitrage and the market forces describe din Ch. 17), his anti-monetary bias led him to posit that as saying that the natural nominal rate is not unique – which is different and more theoretical point about a Wicksellian price level being indeterminate in theory.

The basic difference between Keynes and Sraffa is that the Keynesian disequilibrium is a story of capital and investment, but Sraffa wants to extend it to consumption as well, and that too for commodities.

The correct challenge to Hayek is the more mainstream Keynesian/Post-Keynsian one. That there is a zero lower bound, that risk may be mispriced, and that even if there was no ZLB/risk mis-pricing, because of radical uncertainty and animal spirits, the term structure of interest rates may be out of whack. Thus business investment is in dynamic disequilibrium.

And a plausible response to this challenge is the Fischer Black one – that while this may be true of the time that Keynes spoke of, modern financial markets that have created more avenues for making and expressing inter-temporal decisions have changed that. And a good response to this response is the Minsky one – that finance may by itself be destabilising, and that at the very least the monetary authority has to confront two price levels, goods prices and asset prices.

Sraffa is a distraction, it’s price theory uninformed by Marshall.

Perhaps I should say :

Does the current monetary regime have a unique path of short term risk free nominal rates contingent on expectations that clears the market ( for the short term risk free real rate)

David: “In such an equilibrium, own rates could differ, but by no more than necessary to compensate for different real service flows and different costs of storage associated with different assets, inasmuch as the expected net real return from holding every asset must be equal in equilibrium.”

I think about that bit very differently. The “own rate of interest on apples” is the nominal rate of interest minus the rate of inflation of apple prices. If apples cost $1 each this year, and I lend someone $100 (or $100 apples), and if the interest rate on money is 5% and the rate of inflation on apples is 2%, then next year I get back $105, which is worth (approx) 103 apples (or I get paid back 103 apples) so the own rate of interest on apples is 3%.

Maybe apples can’t be stored, because they rot. And the borrower just eats the apples. Who knows. But if technological progress in growing apples is causing the price of apples to fall relative to the price of bananas, then if the apple inflation rate is 2% the banana inflation rate could be 4%, so the own rate on apples would be 3% while the own rate on bananas is 1%.

David: “What Hayek failed to see is that it was the choice of a particular value or time path of nominal GDP that would determine a particular nominal value of the natural rate…”

Leaving aside the question of what Hayek saw (I don’t trust my knowledge of Hayek) I would make a stronger claim:

Even in a world in which money is long run superneutral, with sticky prices and real shocks the choice of a particular target variable, whether NGDP, the CPI, the price of apples, bananas, gold, whatever, will affect the whole pattern of own real rates. (But the choice of a particular numerical value for that target variable, whether it is a 2% or 3% or 4% target, will not affect that pattern of own real rates, given superneutrality. And that is the sense in which there exist natural rates.)

In other words, given superneutrality, the choice of a 3% vs 4% NGDP target doesn’t matter for any real variables, including the whole pattern of own rates. But the choice of an NGDP target vs a CPI target does matter for real variables. It will affect the variance of those real variables, and will probably affect the means of those real variables too (unless the model is linear).

Nick

Your’s and David’s different formulations of the multiple own real rates of interest is interesting. David’s formulation is that multiple own real rates of interest = real disequilibrium. Your formulation is that multiple own real rates of interest = different evolution of individual supply curves.

In David’s formulation, Sraffa is denying the market mechanisms that cause equilibrium in product markets, while (perhaps) holding aggregate supply constant. In your formulation, he is simply denying the concept of an AS curve. In either case, his challenge seems weak.

If Sraffa were to shift his gaze from commodities to the ‘means of commodities’, he would find the multiple own real rates of interest that don’t quite clear through the logic of arbitrage. Capital goods and labour. There is not much that Sraffa adds to Keynes. And Keynes was at least as, if not more, Wicksellian as Hayek. At least that’s my take on the whole thing.

Nick:

“the own rate on apples would be 3% while the own rate on bananas is 1%.”

Then everyone would invest in apples and nobody would invest in bananas, (or they would lend apples and borrow bananas) until the own rates equalized.

Not everyone would invest in apples if the banana market is more liquid. But I must admit I’m not sure if that matters in such a theoretical discussion. As so often with economists, I’m not sure what the ground-rules are for the debate.

Kevin:

Interest rates naturally differ when there are differences in storage costs, convenience yield, risk, or liquidity. David sort of took care of that when he said “own rates could differ, but by no more than necessary to compensate for different real service flows and different costs of storage associated with different assets”

Odd ‘debate’.

Hayek strictly distinguished between two theoretical contexts for talking avout two very different concepts of ‘interest’.

One notion is meant to capture a value across tiem relation in the pure logic of choice involving the trade-offs between alternative output potentials & alternative lengths of production — a construct where ‘money’ is completely absent.

This notion of ‘interest’ is preliminary to any discussion of the real world of the real money economy and the real world of the everyday stuff in which we have interest rates in the market & set by the central banks.

To muddle these two contexts is to do botch any attempt to address the work of Hayek or his engagement with Sraffa.

The debate is a cross paradigm engagement, where many terms are not grounded in common theoretical settings, and where conversation is routinely at cross purposes.

Sme backgound differences — Hayek was attempting to extend the Menger / Jevon’s pure logic of marginal valuation coherently into choice across time and involving production goods of alternative time lengths and output.

Sraffa was working in a non-marginalist objective cost frame inherited from Smith, Ricardo & Marx (Sraffa was involved in the Italian communist party), attempting to solve some of its problem.

Mike, For any nominal interest rate, there is a set of price expectations that would be consistent with that interest rate being an equilibrium. I don’t see what the problem is.

Ritwik, But the nominal rate that clears the market depends on price expectations, so I don’t see why it is unique. For given price expectations it’s unique, but price expectations aren’t given. I don’t really follow your identification of the difference between Sraffa and Keynes, but I think that your list of weaknesses in Hayek’s theory is pretty much on target. I am not concerned with Sraffa except as he offered a critique of Hayek that is regarded as having been dispositive. I don’t think his critique was that damage, but that doesn’t mean that Hayek’s theory as presented was not seriously flawed.

The answer to your alternative question is it depends on whether expectations are given or not.

Nick, My problem is that in equilibrium the expected net return from holding each asset must be equalized across all assets that are held. The expected return on some assets may be less than the natural rate, but those assets are not held, they are consumed. Think of the optimal aging of wine.

I am not sure what you mean by the choice of a particular value affecting the whole pattern of own real rates. Do you mean nominal own rates? By positing sticky prices, you are violating the assumption of intertemporal equilibrium. In intertemporal equilibrium all future prices are correctly foreseen, so price stickiness is not an option. The choice of an NGDP target vs. a CPI target can affect the real equilibrium only if future prices are not correctly foreseen. Why are prices correctly foreseen under one target and not another?

Ritwik, Sraffa actually exempted Wicksell from his critique of Hayek’s use of the natural rate, because he said you could calculate a natural rate as an average of individual own rates, but since Hayek rejected the use of index numbers, he was stuck with multiple own rates. From the broader perspective, that argument now seems a bit lame.

Mike, Yes, that was my point in my response to Nick above.

Kevin, Differences in liquidity offer compensating non-pecuniary returns for a difference in pecuniary yield. That is actually Keynes’s point in Chapter 17.

Mike, Again you anticipated my response to Kevin as well.

Hayek distinguished between two different tasks, which look to be muddled in your discussion, David.

The ‘debate’ with Sraffa overlaps and muddles these two different tasks.

The core Hayek even say should not be called ‘interest’, but the term is only used by Hayek due to convention.

In the first context, there is no money, and hence no actual prices and no price expectation.

This first problem situation involves the pure logic of choice, the choices of an all knowing and all pwoerful dictator in an imaginary world.

The problem is to make sense of the value differential across time when considering the choice between production goods producing more,of less output and taking more of less time.

This is a value structure in the relation of all goods across time whcih cannot be eliminated (Wieser).

The next step is to consider the effect of the fact of this valuational structure on the pricing of production goods and the credit used for production and consumption in the real world, ie the world of money and uncertainty and differential judgments of what the world is like or will be like.

Sraffa comes out another world when it comes to considering all of these thing — ie he come out of the objective cost tradition of Ricardo.

It looks like my earlier posting was filtered by the comments robot,

David:

“For any nominal interest rate, there is a set of price expectations that would be consistent with that interest rate being an equilibrium. I don’t see what the problem is.”

The problem is that the forward price F of a security is related to the spot price S by the following:

F=Se^(r-i+c)t

where r=interest rate, i=income (including convenience yield) yielded by the security, c=costs like storage, handling, etc.), e=natural log base, and t=time. Given these parameters, the price path of the security is pinned down, and if the equality in the equation does not hold, there will be arbitrage opportunities. Money is a financial security with a convenience yield, handling and storage costs, etc, and those things pin down the value of money just like anything else.

Way above my head.

Greg, Sorry, but I cannot really grasp your argument or understand what it has to do with my discussion of the natural rate and own rates.

Mike, I guess I still don’t understand what the problem is. I agree that spot and forward prices are governed by the relation you specify. I am saying for any nominal interest rate set a central bank there is a potential set of present and future expected prices under which that nominal interest rate would be consistent with intertemporal equilibrium. The actual set of present and future expected prices need not correspond to the equilibrium set of present and future expected prices for that nominal interest rate, but such a set could exist, and if it did exist, the nominal interest rate would be a natural rate. The point is a central bank trying to set its nominal rate equal to the natural rate is confronting a pretty daunting task.

Tas, I know the feeling.

This is getting more confusing rather than less.

Combining you and Nick, this is what I get:

So there are many commodities and financial instruments, each with a unique own rate, cost of storage, convenience yield, and liquidity premium. In equilibrium, the net return (sum of own rate, convenience yield, liquidity premium less storage) of each asset is equal. By own-rate, I mean expected price appreciation over time plus any dividends or interest.

One of the many assets in an economy are the notes issued by a central bank. A central bank tries to set the own rate on its notes at -2% or so per year. It does this by ensuring that the price of a basket of assets (CPI) which a note can buy rise by 2% a year i.e. the central bank tries to set the own-rate on the CPI basket at 2%. Rather than buying CPI assets directly– and this is somewhat confusing – it does so indirectly by buying and selling bonds as certain rates and prices, adjusting those buying rates over time to keep CPI rising at 2%/notes falling at 2%. Notes are still willingly held despite falling in value relative to goods because they provide superior liquidity services that more than compensate for their declining purchasing power.

The prices of all assets in the economy are measured in terms of central bank notes. In calculating an asset’s real return, one must subtract the own-rate on central bank notes from that asset’s own rate, subtract storage costs, and add back convenience yields and liquidity services provided by that asset. Doing this for all assets, you’d see that all returns are equal.

If a central bank decides to change the own-rate on notes so that they fall faster, say at 4% a year rather than 2%, then all that happens is that the own-rates of other assets must adjust, rising by 2%. Storage costs, convenience yields, and liquidity services all stay constant so that, as a result, the real return is not affected by the change in the own-rate on notes.

As long as the change from 2% to 4% a year is foreseen, and all prices are fluid, there will be no real effects. If not, there will be real effects.

What do you think?

David and JP:

Take some extreme examples: Say the Fed sets an inflation target of 50%/year. People would soon find a substitute money that doesn’t inflate so badly. The Fed and its money would disappear. Or if the Fed targeted a deflation rate of -50%/year, the demand for the Fed’s money would be enormous, but since the Fed could not possibly get enough assets to back up that rate of return on holding dollars, the Fed collapses again.

I’ll bet you wouldn’t dispute the above. I’d go further, and say that the range from -50% to +50% is many times wider than what is realistically possible.

So when David says: “For any nominal interest rate, there is a set of price expectations that would be consistent with that interest rate being an equilibrium.” I ask myself: ANY nominal interest rate?? ANY set of price expectations?? No. They don’t have that latitude. They are constrained by market interest rates, convenience yield, handling costs, etc.

David, have you read Hayek’s _Pure Theory of Capital_?

The distinctions I make regarding two notions of ‘interest’ embedded in two different conceptual constructs are discussed there.

@ Mike Sproul and David Glasner

I do not understand your response to Nick Rowe. Whether you save bananas or apples you end up with 105 $ in period t+1. (Obviously Nick´s use of “inflation” simply refers to the “price change”, i.e. general as well as relative)

The tradeoff/return in terms of apples today for apples tomorrow might differ from the tradeoff in terms of bananas today for bananas tomorrow. Assume that you calculate the real return as nominal return minus the change in the price level. Given a fixed nominal return, this real return will differ depending on whether you calculate the change in the price level from a basket containing only apples, only bananas, or any specific mix of bananas and apples.

It is also true that absent storage cost etc., ketchup economics assure that it does not matter which asset you use to transfer wealth from today to the future – i.e. whether you hold apples or bananas. This says that all assets give the same return, but not which level of return that is.

Isn´t it clear that the general level of real return is undefined, or rather specific for each individual (depending on preferences) for the same reason that changes in e.g. “the cost of living” is different for different individuals (depending on preferences)?

JP, Why do you say it’s getting more complicated? You seem to get the idea pretty well, except that liquidity premium refers to the increase in the asset’s value as a result of its monetary/liquidity services not to the real rate of return associated with those services.

Mike, I’m not so sure that people would stop using dollars at a 50% rate of inflation, though you would certainly see a shift out of non-interest bearing cash into other instruments that did pay interest, but I conjecture that they would still be dollar denominated. But I take your point that there are limits on the upside and the downside to the rates of inflation that could potentially be consistent with an intertemporal equilibrium

Greg, I will try to check the Pure Theory of Capital, but , off the top of my head, I don’t see the relevance of your point to the Sraffa-Hayek debate.

Nemi, In intertemporal equilibrium, the expected net yield form holding every asset has to equal the expected net yield from holding every other asset. If there is a difference in expected yields, the relative prices of higher yielding assets would rise and the prices of lower-yielding assets would fall until expected yields were equalized. The expected net yield could be measured in different numeraires, but the real yield would be identical regardless of which numeraire was chosen.

Glasner: Ok – you are right.

I was thinking infinite storage cost (you have to sell your fruit and transfer your wealth in money form) while I wrote no storage cost. How am I supposed to be able to act as a rational agent?

However, I will change my claim to say that there has to be no storage cost etc. for all goods (and services) if there is to be an identical real rate of return between different individuals.

Say that the price of apples increase by three percent, no storage cost. The price of bananas increase by four percent with one percent storage cost. If I save 100 $ of assets today, I will have 103 dollar of assets in t+1.

In t+1, person A only want to buy apples. His real return were zero.

In t+1, person B only wants to buy bananas. His real return was minus one percent.

Show me the errors of my way.

nemi, Real returns are equalized net of storage costs. The gross return for bananas has to exceed the gross return for apples by enough to justify incurring the added storage costs. So if bananas are held their price has to rise fast enough to make it worthwhile to incur the storage cost.

“JP, Why do you say it’s getting more complicated? You seem to get the idea pretty well, except that liquidity premium refers to the increase in the asset’s value as a result of its monetary/liquidity services not to the real rate of return associated with those services.”

Ok, good to hear. Sometimes I need to get a reality check to make sure I’m on the right track. Both your post and Nick’s are tough to integrate but I think I’m getting there.

Mike: “I ask myself: ANY nominal interest rate?? ANY set of price expectations?? No. They don’t have that latitude. They are constrained by market interest rates, convenience yield, handling costs, etc.”

I don’t disagree. It seems to me at very high rates of inflation, calculation using the unit of account gets very difficult and people will spontaneously choose a new unit.

Hayek moved to a ‘stream’ metaphor with elements in the production goods coordination process which would never be reproduced. I.e. it’s not a traditional ‘equilibrium’ construct.

The differential valuation structure across time depending upon differences in output and difference in production time gives a valuational structure to the whole stream of goods as it flowed across time.

This stream can be thought of in a pure ‘barter’ economy — ie a pure goods and NO MONEY picture, like Menger’s most primitive examples of valuation relations at the margin involving individual choice over just one or two consumption goods.

ONE use of the term ‘interest’ — a use that dates back to Bohm-Bawerk and before, is for this embedded valuation structure.

There are NO PRICES, and hence no rates of inflation or price levels in this construction which illustrates the structured logic of marginal valuation across time.

David writes,

“the natural rate of interest in nominal terms is not unique, because any real intertemporal equilibrium is consistent with any choice of price level and any rate of inflation.”

For a popular account of Hayek’s more mature ‘non-equilibrium’ picture see his 1981 LSE lecture on macroeconomics, in Hayek’s _Monetary Economics, Part II_.

My understanding is that Wicksell’s notion of a ‘natural’ rate of interest derives from and is grounded in Bohm-Bawerk’s ‘barter economy’ / no money theory of ‘interest’, i.e. the valuational structure within the production goods sector.

” The gross return for bananas has to exceed the gross return for apples by enough to justify incurring the added storage costs.”

In my last example it did. The net nominal return (using the same numeraire – money) was equal. The different real return is due to what they are saving for, i.e. due to preferences. Since one person wanted to buy a good whose price had increased more, “nominal return – cost of living increase =real return” was less for this person.

If one good/asset has a storage cost that is one percent higher than other goods, the price of this good has to increase by one percent more (given that it is used to transfer wealth between periods). If your preferred consumption basket contain a relatively big share of this good, the nominal cost of buying a basket that gives this person some fixed level of utility will increase faster than for a person whose preferred consumption basket contain relatively little of the good. The only way these two persons could face the same real return is if the first got a higher nominal return (which he will not).