The natural rate of interest and the own-rate argument

The Austrian vs Keynesian end of the blogosphere often battle over the existence of a natural rate of interest. The Keynesian side typically points to Piero Sraffa's argument that there are many natural rates of interest, or own-rates, and therefore an Austrian sort of monolithic natural rate of interest simply doesn't exist.

Over the last few weeks I've participated in the comments here at Jonathan Finegold Catalan's blog and here at Daniel Kuehn's blog. Here is an older comment in this vein on "Lord Keynes" blog. Bob Murphy also has a paper (pdf) on this subject and has commented on the above blogs on this subject.

Sraffa's point that there are different own-rates was not a new one. Irving Fisher pointed this out many years before, in Appreciation and Interest (1896):

If we seek to eliminate the money element by expressing the rate of interest in terms of real " capital," we are immediately confronted with the fact that no two forms of capital maintain or are expected to maintain a constant price ratio. There are therefore just as many rates of interest on capital as there are forms of capital diverging in value.

Fisher called this the multiple theory of interest.

In my opinion, the seminal blog post on this debate is still David Glasner's Sraffa v Hayek, especially the comments section. I think that a lot of the above commentators have not been able to understand David's point:

...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. 

On Daniel's recent post, I left this comment, which explains this in different words:

A natural rate is an own-rate - the difference between an asset's present price and its future price. Own-rates differ markedly. Looking at today's futures markets, the future price of Chicago wheat is above the spot price, whereas the future price of Minneapolis wheat is below the spot price. This means that the own-rate on Minneapolis wheat is negative whereas the own-rate on Chicago wheat is positive. In other words, you get financial compensation for holding Chicago wheat for a few months whereas you get penalized for holding Minneapolis wheat over that same time period. So on the surface, it appears there are two natural rates for very similar commodities. Odd, yes?

But this difference between own-rates does not mean that holding Chicago wheat provides a superior overall return to Minneapolis wheat. In equilibrium, all returns are equalized by arbitrage.

So what accounts for the different observable own-rates on Chicago and Minneapolis wheat? First, you have to take into account storage. Sure, you may earn more holding Chicago wheat, but storage costs may be far higher in Chicago so that final returns are equalized. You also have to think about risk. Perhaps holding Minneapolis wheat is far less risky than Chicago wheat (maybe an outbreak of locusts in Chicago), and therefore markets have to compensate Chicago-area speculators with a higher own-rate to compensate for the risk. Lastly, you have to think about liquidity. If Minneapolis wheat is, for the moment at least, more liquid ie. marketable than Chicago wheat, this constitutes a service provided to holders of Minneapolis wheat. As such investors do not need a high own-rate on Minneapolis wheat to encourage them to hold it, since liquidity constitutes its own reward.

So in sum, you are probably right to not be too concerned about this. Yes, there are an infinite number of observable own-rates in the economy. But an asset's own-rate only constitutes one component of its overall return. When you adjust for all the other factor that constitute an asset's return, Minneapolis wheat and Chicago wheat are providing speculators with the same expected return, despite their different own-rates. If they aren't, their prices will soon adjust. What is that economy wide rate-of-return? We can't see it. It's somewhere out there.

The above is really just a restatement of John Maynard Keynes's Chapter 17 of the General Theory. Here is Keynes:

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.

Keynes then proceeds to decompose expected returns on an asset into a liquidity component, the expected output that the asset will yield, an expected appreciation (relative values during the year) component, and storage costs.

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 the alternatives; — i.e. a1 + q1, a2 - c2 and l3 will be equal.

All of this goes beyond Sraffa's critique of the natural rate. In this paper, Grieve points this out:

Keynes certainly (as acknowledged by footnote, Keynes, 1936, p.223) took Sraffa’s bare and abstract conception and developed it into his most ‘general’ statement of the General Theory – in the form of a theory of asset returns, asset choice and economic activity in the context of a real world production economy operating under conditions of uncertainty.

What Keynes created was  a portfolio choice theory of assets in which all returns are equalized in equilibrium. Using this framework, one can back out all sorts of useful ideas about interest rates, term structures of interest rates, and the liquidity premium on assets. It's a very useful way of thinking about the world. I'd say its the best theory on interest rates we have.

Note that I have no opinions on how this affects the various business cycle theories- I'm only interested in the general ideas of interest and asset returns. Nor is this about Keynes vs Hayek. It's more like Hayek + Fisher + Sraffa = Keynes. We are all jointly working on arriving at the truth.