# Multiple Natural Rates of Interest – Pierro Straffa

The natural rate of interest is a rate of interest is a rate of interest that exists in natura, that is, if there were no use of money. The Wicksellian marginal productivity on capital in a barter economy.

This posts looks at the significance of multiple natural rates and offers one avenue to pursue for a solution.

### R-Star the singular empirical natural rate of Interest

Why this is important? The Federal Reserve Bank targets R-star an empirical proxy for this rate to try to create equilibrium in the economy. That is, if the observable market rate, (the fed funds rate) equals the natural rate, (R-star for the central bank), then money should be neutral. This means prices will neither go up or down for monetary reasons and the economy should avoid a business cycles for monetary reasons.

These are generalizations and there are many contributors to this theory, however, you can find these ideas in Knut Wicksell, Friedrich Hayek, and Michael Woodford.

Therefore, if the natural rate of interest equals the market rate of interest the Federal Reserve generally postulates we will have money macro equilibrium. This point is debatable. However, it is a mainline Federal Reserve opinion and operational policy. It is important because it is core theory the central banks operate on.

For a more detailed discussion of R-star directly from the Federal Reserve you can find it here: R-Star the empirical Natural Rate of Interest.

However, despite the intricate models and mathematical proofs, there is a theoretical problem that has not been addressed. Specifically, there are multiple natural rates of interest.

In other words, instead of one wholly empirically derived rate of interest, there exists multiple natural rates of interest for each commodity. Each good, particularly capital goods has its own rate of interest.

This means that the central bank targeting one interest rate is an incorrect policy. What might be good for one capital good is not good for another. Therefore, at some point there will be a distortion in the entrepreneurial use of capital that can create a business cycle. The result is the natural rate of interest as a theoretical construct and its representative in the empirical world R-Star is on unsure footing to use for policy. Central banks around the world like the US Fed and the ECB do just that.

### Multiple natural rates of interest issue for theory

This objection of multiple rates of interest was raised by Piero Sraffa (1932) specifically in response to Hayek’s Austrian business cycle theory (ABCT) developed from Mises (Theory of Money and Credit 1912).

The idea of multiple natural rates of interest by Sraffa was so devastating to ABCT theoretically it was never directly addressed. It was circumvented by both the Austrians and the Federal Reserve and notably when Michael Woodford (Interest and Prices 2003) resuscitated the Wicksellian idea.

Woodford does discuss multiple rates on interest is his paper on Financial Intermediation in 2010, but this is not the Sraffa’s multiple rates of interest. Rather this is simple a spread rate to account for frictions. Woodford focuses on rigidities and frictions into his model. However, his model is still based on an equilibrium rate of interest which has theoretical issues, such as multiple rates. Therefore, the model which the central bank bases policy has a weakness. Specifically articulated by Pierro Straffa in 1932.

It is not addressed by mainstream economists or Austrian Economists.

### Is Straffa’s natural rate a Wicksellian rate?

The own rate of interest– the rate at which something exchanges for itself. A commodity rate of interest.

Straffa’s own rate is not a natural rate of interest as understood by Wicksell. However, for the critique of the theory the same argument would hold if it was a Wicksellian natural rate or an Straffa own rate.

That is, shoes, are not a form of capital that is generally used in the production process. Better are potatoes seeds. Potato seed would be something I see as mobile capital that could approximate a natural rate as understood by Wicksell. It is homogeneous but also functions as a commodity and capital for the production process.

### Straffa on Multiple natural rates:

An essential confusion, is the belief that the divergence of rates is characteristic of a money economy […] If money did not exist, and loans were made in terms of all sorts of commodities, there would be a single rate which satisfies the conditions of equilibrium, but there might be at any one moment as many “natural” rates of interest as there are commodities, though they would not be “equilibrium” rates. […] if loans were made in wheat and farmers […] “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.

(Sraffa 1932 p.49)

This divergence and the existence of multiple rates was a common phenomenon in a barter economy. Sraffa’s sees the divergence of the money rate and the natural rate as the divergence between the spot rate and the forward rate. However, in this case, it is still observed in a monetary economy. Money is still ubiquitous and flowing in every part of this economy. Even though he is analyzing essential commodities like cotton or wheat, it feels like a natural rate. But it is not, it is still in a world where all we see is money prices.

• Sraffa does understand the dynamic nature of the economy that, changes in the production of a particular commodity can at least temporarily create changes in the natural rate between, so there are multiple natural rates.
• Sraffa did see a convergence of commodity rates of interest when the economy was in equilibrium, in which all commodity rates were equal as well as the money rate.
• Sraffa critiques Hayek by stating that the multiple naturals rates are not equilibrium, only when unified as one rate.

This is my first pass at an understanding of the multiple natural rate problem. A more in-depth article I might review latter is by Robert P. Murphy. Murphy has a suggested solution.

Multiple Interest Rates and Austrian Business Cycle Theory

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