### Yes, Virginia, There Is a Unique Natural Rate of Interest

"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 interst rate than the choice of a numeraire stable or falling in value over time." (Emphasis mine.) -- Glasner and Zimmerman, "The Sraffa-Hayek Debate on the Natural Rate of Interest"

Now, what I did in this post was demonstrate how that unique real rate could be "pried out" of the various nominal rates.

When Bob saw the paper quoted above, he made a fuss over Glasner and Zimmerman's statement in the abstract -- was this all he read? -- that "Thus, the natural rate of interest, on Keynes's analysis in the General Theory, is well-defined, at least up to a scalar multiple reflecting the choice of numeraire."

So here is where we stand, by my lights, by analogy:

Hayek: If the central bank sets Gene's weight above Bob's weight, we will get a boom and bust.

Bob: What do you mean, "Bob's weight"? Bob's weight in grams, or pounds, or stones, or solar masses, or proton masses? Those are all different numbers!

Lachmann, Callahan, Glasner, Zimmerman: Just pick one scale. Then Gene's weight in that scale shouldn't be set above Bob's weight in that scale. Furthermore, all we need is the right multiplier and we can move the discussion into any other scale you want.

1. I think this is really about futures prices as much as interest rates. Here's why.

1. Your earlier post demonstrated that in a barter economy with spot, future and loan markets for each commodity that arbitrage would ensure that all goods in all markets would be aligned and that an underlying originary rate could be determined. If the market is efficient then all markets would be in equilibrium all the time.

2. Arbitrage would not however guarantee that futures prices are correct. If it turns out that people's expectations about future prices are wrong then we will know after the even that futures were mis-priced. As people use expectation on future prices to guide production decisions in the present the structure of production will be distorted away from the optimum.

3. Turning to a money economy. ABCT can be explained as follows: When the money supply increases unexpectedly then people's expectations about future prices will become incorrect. People will want to lend out some of the new money and having incorrect views about future prices will lend it out at real rates that will turn out to be lower than they think. The effect on borrowing will be as usually described for ABCT, with the usual distortionary effects.

4. Straffa challenges ABCT on the grounds that there is no natural rate for the market rate to fall below. However it is clear to me that the natural rate is just the rate that accurately captures originary interest plus expected changes in the future price level. If these expected future prices are accurate then they will guide the economy to the optimal structure.

5. So as long as one can show that i) there is a set of future prices that can guide the economy to equilibrium and ii) there is market clearing rate that both clears the loan market and factors in these prices then I think ABCT can not be dis-proved by Straffa's criticism.

6. In a money economy(where all loans are made in money) there is something similar to multiple own-rates of interest. This is the difference between input prices and output prices for each commodity. Entrepreneurial arbitrage will also tend to equalize these rates and align them with the real and nominal money rates. It is this process that drives ABCT through it various stages.

7. Both a barter economy and a money economy will have non-optimal structures of production if it turns out that futures prices are incorrect. I need to think about it a bit more but I suspect that in a barter economy where loans are made disproportionately in some commodities then ABCT could occur if the futures prices were wrong for those commodities.

2. Gene,

I posted a long comment on this yesterday - just curious if got filtered out somewhere or just got lost.

1. Oh, and then I saw another comment saying "Forget that last post" -- I thought you meant the long one! I have not deleted it, merely delayed posting it, as a consequence.