The natural rate of interest is an unobservable hypothetical rate of interest that was conceptualized by the Swedish Economist Knut Wicksell. There were precursors to this theory, such as Henry Thorton *An Enquiry into the Nature and Effects of the Paper Credit of Great Britain* in 1802, however, it was Wicksell’s theory that can trace a direct theoretical lineage through the twentieth century (Mises, Keynes, Hayek, Woodford) to today’s central bank’s key econometric variable and policy tool R-star.

Great knowledge is often lost through time. This is why it is imperative to return to the original understanding of Wicksell’s natural rate of interest to gain insight into current definitions and uses.

## Three definitions of Wicksell’s Natural Rate of Interest

The natural rate of interest as understood by Wicksell meant three different interrelated ideas, depending on which rendition Wicksell was writing about.

**Barter Ratios**– The rate of interest that would correspond to the return on new capital if barter ratios were used.**The demand for and supply of savings and investment**– Rate of interest that would equalize savings and investment ex-ante.- T
**he rate which brings price stability**– The rate of interest that when harmonized with the market rate of interest would bring general price stability.

Subsequent economists developed or at least emphasized Wicksellian ideas based on the particular definition that worked for their model. For example, Mises, the *in *rate with relative prices, Keynes I=S *ex-post*, Michael Woodford focused on price stability through econometric estimates.

The key insight here is these three definitions are interrelated and should be synonymous, if and only if, you understand the original definition of the natural rate and the intent of Wicksell’s theory, that is it was an interest rate that was based on the capital theory of Böhm-Bawerk.

Taking one of these definitions or a part of it would lead to incorrect theoretical assumptions and models.

The purpose here is to look at the first version of this rate of interest.

### Natural Rate of Interest *in natura*

Wicksell’s definition of the natural rate of interest by Wicksell is as follows:

The natural rate of interest as understood by Wicksell was the “rate of interest which would be determined by supply and demand if no use were made of money and all lending were affected in the form of real capital goods.” (Wicksell Interest and Prices p.188).

In other words, the natural rate would “more or less correspond to the expected yield on newly created (real mobile) capital” (Wicksell, *Lectures on Political Economy* V2 p.193) if barter ratios were used.

This definition is what Wicksell deemed as more accurate and precise definition than simply the ‘real interest rate of actual business’.

Wicksell writes “A more accurate though rather abstract, the criterion is obtained by thinking of it as the rate which would be determined by supply and demand if real capital were in kind without the intervention of money” (Wicksell, *Interest and Prices* pp. 29-30).

The important point here is Wicksell’s definition of the natural rate specifically and intentionally excluded the influence of money.

That is, the natural rate of interest by definition, as understood by Wicksell, is expressed in non-monetary terms. In other words, the natural rate is the marginal productivity of capital without reference or use of money and money prices.

This is why it is called “the natural rate of interest”. If money is used or referenced, such as money prices, then this is not the natural rate. If money prices were used it would be another rate, by supported by another theory, but it does stand on a footing in the context of Wicksellian theory.

- Therefore based on the above quotes, directly from Wicksell an understanding of Knut Wicksell, the natural rate needs to be non-monetary.

### A Unified Theory of Money

A unified theory is the central point of Wicksell’s theory. The reason why Wicksell’s theory is important is not just to explain price movements or disequilibrium, it was to create a unified theory of economics, that included capital, interest, and money. Wicksell stated the issue he was trying to correct in 1898 was “there is no complete and coherent theory of money.” (Wicksell, *Interest and Prices*, p. 27).

There was a dichotomy between real-world economics and monetary economics. The quantity theory of money explained price movement in the long run, but after price adjustments occurred as a result of the increase in the supply of money, there was little else. It was again, a world of supply and demand and a world of money which had no real effects other than aggregae price level movements.

In contrast, Wicksell put his theory of interest intentionally at the center of theory because this was the linkage, the element that unifies these two rehalms of economic thought.

However, in order to unify the bifurcated theory, the two worlds need to be defined clearly and not intermingled or it would dilute or nullify its theoretical power.

Therefore, the starting point needed to be a theory of interest that was based on a natural rate, a rate without money. This is because that was the representative rate of interest for the real world, the *in * world without money. It was the rate not in money.

### Confusion in Economics in Wicksell’s time and today

Wicksell goes on to write ” Economists do not tire of impressing on their students that money and real capital are not the same , that interest on capital and interest on money are consequently different things”. But as soon as it comes to apply these ideas, almost without exception ‘the two subjects are mixed up in the most inextricable confusion’, as Mill puts it”. (Wicksell Interest and Prices p. 30)

It is this confusion that needs to be clarified. Micahel Woodford assumes a definition of the natural rate of interest, that is not congruent with Wicksellian theory. Neither the theory of Knut Wicksell of the Wicksellians that further, studied Wicksell’s ry.

Wicksell writes ” It is only with the development of a real theory of capital” (Jevons and Bohm-Bawerk)… it has become possible to make a survey of the phenomena of capital and interest, as they would be exhibited on the purely imaginary assumption that they could take place without the intervention of money and credit” (Wicksell, *Interest and Prices* p. 30).

Wicksell continues along the capital-centric lines by stating: “There is nothing so far to bring the rate of interest on money into coincidence with the rate which would be determined by the supply and demand if real capital goods were lent in kind.” (Wicksell Interest and Prices p. 30).

Therefore, we can conclude here, based on his own words, that the base of his theory of the natural rate of interest is real capital in the content of a world without money.

#### Metaphor of Water

It would be analogous to developing a complete theory and uses of hydrogen based on the properties of water, in a universe where only water existed rather than hydrogen in as an isolated periodic element. A better theory needs to understand what hydrogen and oxygen are in isolation, rather than only how hydrogen acts when oxygen is present in the form of water.

### Empirical test of Wicksell’s Natural rate of Interest

**Barter ratio natural rate estimate** – I would try to estimate the natural rate of interest as if barter ratios were used, that is Wicksell’s original understanding
of the natural rate.

For example, calculate the natural rate in a competitive market like potato seeds and potatoes. Potato seeds and Potatoes are essentially the same because a field by forgoing sale or consumption of a portion of current stock and setting it aside for seed. Therefore, the ‘seed capital’ can be calculated as a ratio based entrepreneurial inter-temporal calculations.

I could also use, sugar cane, or garlic as the seed is the same as the product.

I would sample say 100 potato farmers and determine the rate of return they would expect if they lent physical seed out of their yield. I would formalize the test. It seems like a trivial point, but if I could prove that the expected **rate of return on real mobile loanable capital under a barter ratio** was different than R-Star, then this would tell us something. Perhaps there really are multiple rates of interest, perhaps R-Star is not the real world.

**What does unobservable mean – Pretense of knowledge**

The word *unobservable *in physics (Woodford wanted to study physics) is not the same as* logically unobservable*. In physics, you can calculate an unobservable distant star though interference.

In conclusion, if you read about Federal Reserve Policy, and their R-star for monetary policy challenge the idea that perhaps their model lacks theoretical rigor because the assumptions they base it on are not tied to the theory of Wicksell as they claim it is.