Wednesday, October 8, 2014

Another Example of Wicksell’s Second Definition of the Natural Rate of Interest

That is, as discussed in this earlier post.

The new passage comes from Wicksell’s article “The Influence of the Rate of Interest on Prices” (1907), where the “natural rate” is called the “normal” rate:
“According to the general opinion among economists, the interest on money is regulated in the long run by the profit on capital, which in its turn is determined by the productivity and relative abundance of real capital, or, in the terms of modern political economy, by its marginal productivity. This remaining the same, as, indeed, by our supposition it is meant to do, would it be at all possible for the banks to keep the rate of interest either higher or lower than its normal level, prescribed by the simultaneous state of the average profit on capital?” (Wicksell 1907: 214).
This appears to be an earlier formulation of the definition given in Wicksell’s later work Vorlesungen über Nationalökonomie. Band 2: Geld und Kredit (1922). In the English translation of this called Lectures on Political Economy. Volume 2: Money (trans. E. Classen; 1935) we have this definition:
“The rate of interest at which the demand for loan capital and the supply of savings exactly agree, and which more or less corresponds to the expected yield on the newly created capital, will then be the normal or natural real rate. It is essentially variable.” (Wicksell 1935: 192–193).
In this definition the “natural” or “normal” rate of interest is determined by the marginal productivity of capital.

Laidler (1999: 53) points out that the Stockholm School contemporaries of Wicksell had already, by the late 1920s, understood the problems with identifying the natural rate of interest defined in these terms:
“[sc. the Stockholm School] … understood that the idea of an aggregate stock of capital with a well-defined marginal product that existed independently of the value of the market rate of interest was, except under very special circumstances, theoretically indefensible. Hence they rejected just that aspect of Wicksell’s analysis that lay at the very foundation of Austrian cycle theory.” (Laidler 1999: 53).
Laidler (1999: 29–31) also has an interesting discussion of the ambiguity in how Wicksell defined the natural rate in different passages in his writings.

To speak of a single, or unique, “natural” rate would seem to entail that an economy is in an equilibrium state where the marginal productivity of capital is the same on all capital. Indeed, in Wicksell’s Interest and Money it is a simple stationary-equilibrium model that is the starting point of Wicksell’s monetary theory (Donzelli 1993: 57), an unrealistic assumption for real world economies.

Moreover, though I am no expert on the capital controversies, it would seem to me that on this point members of the Stockholm School also anticipated aspects of the Cambridge Capital Controversies well before the early founders of Post Keynesianism in the 1960s, at least with respect to the natural rate and problems with defining the quantity of capital K in the neoclassical production function.

Colin Rogers’ analysis (Rogers 1989: 22, 30–32) confirms this: he argues that the Cambridge capital critique applies to Wicksell’s theory of capital, and shows that Wicksell’s natural rate of interest is untenable outside a purely abstract one-commodity world (Rogers 1989: 22).

Furthermore, capital as measured in the neoclassical production function Q = f(K,L) is ambiguous, given the circularity involved in defining the quantity of capital K, when to determine K one needs to know the rate of interest, but to determine the rate of interest one needs to know the value of capital K (Rogers 1989: 31).

Further Reading
“Colin Rogers’ Money, Interest and Capital, Chapter 2,” June 12, 2014.

“Hayek’s Trade Cycle Theory, Equilibrium, Knowledge and Expectations,” January 4, 2012

Donzelli, F. 1993. “The Influence of the Socialist Calculation Debate on Hayek’s view of General Equilibrium Theory,” Revue européenne des sciences sociales 31.96.3: 47–83.

Hansson, Bjorn A. 1990. “The Swedish Tradition: Wicksell and Cassel,” in Klaus Hennings and Warren J. Samuels (eds.), Neoclassical Economic Theory, 1870 to 1930. Kluwer Academic, Boston and London. 251–279.

Kompas, T. 1992. Studies in the History of Long-Run Equilibrium Theory. Manchester University Press, Manchester.

Laidler, David E. W. 1999. Fabricating the Keynesian Revolution: Studies of the Inter-War Literature on Money, the Cycle, and Unemployment. Cambridge University Press, Cambridge.

Rogers, C. 1989. Money, Interest and Capital: A Study in the Foundations of Monetary Theory. Cambridge University Press, Cambridge.

Wicksell, K. 1907. “The Influence of the Rate of Interest on Prices,” The Economic Journal 17.66: 213–220

Wicksell, K. 1922. Vorlesungen über Nationalökonomie. Band 2: Geld und Kredit. Fischer, Jena.

Wicksell, K. 1935. Lectures on Political Economy. Volume 2: Money (trans. E. Classen). Routledge & Kegan Paul, London.


  1. LK, if you could get over or Wicksells closets adept Erik Lindahl´s 1939 book:
    "Studies in the Theory of Money and Capital"
    and also maybee Erik Lundbergs 1937 dissertation "Theory of Economic Expansion" and his
    The Development of Swedish
    and Keynesian Macroeconomic Theory and
    its Impact on Economic Policy "
    Cambridge University Press, Cambridge 1996
    there is an rather good overview of the different uses of Wicksell´s natural rate by him others.They also interesting in the sence, since they write about how Wicksell, Keynes and Hayek etc use the natural rate framework. And yes it´s true,Wicksell never really gave any clear definition of the natural rate.In his writings in swedish you could find i think at least even 10 more definitions of this "magical" natural rate.In his more policy directed writings,he did not hardly use the term.

  2. In the Cambridge Capital Controversies, frequent reference is made to "Wicksell effects". I think that Wicksell had a good grasp on price Wicksell effects and why, therefore in equilibrium, the marginal product of capital would be unequal to the interest rate. I would be surprised to find in Wicksell, however, a recognition of the possibility of perverse Wicksell effect.

    I, too, like Myrdal's Monetary Equilibrium. I do not find it as clearly revolutionary as Keynes General Theory, perhaps because I do not understand the context well enough. Which follower of Wicksell - was it Lindah? - came up with the phrases "ex ante savings" and "ex post" savings? This, I gather, leads to a clearer way of distinguishing between the equality of savings and investment as an equilibrium condition and as an accounting definition - a distinction one can criticize Keynes as none too clear on in his exposition.

    I find Myrdal's book makes clear that Wicksell thought the natural rate of interest had multiple implications that Myrdal argued might not all hold at once: clearing the market for the supply and demand of "real" capital, clearing the market for loanable funds (savings and investment in money terms), and keeping the price level stable. I probably never had an opinion on which of these was supposed to be a definition in Wicksell and which were supposed to follow.

  3. Quick question: When speaking of "interest" does Wicksell mean interest on loans or does he mean unlevered cost of capital?

    If he means the former (which is the impression I get) then the theory is subject to another criticism. For the expected (mean) rate of profit at best would be an upper limit for which funds would be borrowed.

    If the interest rate is the same as the rate of profit, then all else being equal, I would always prefer loaning money than investing in capital. It allows me to get the same expected rate of return at a much lower risk.

    From a financing standpoint, if the rate of profits are certain, then I might borrow up to (but just below) the rate of profit. But even if we ignore Knightian uncertainty, we might still insist that profits are a random variable following some distribution in which case profits aren't certain.

    I, and any sensible business person, would want to include a margin of safety between the expected rate of return on the capital asset and the interest paid for financing that asset.

    And my guess is there's a lot of "wiggle room" in how much of a margin of safety is required. If there's a good deal of perceived uncertainty, borrowers will be reluctant to borrow unless they're confident that there's a decent margin of safety between expected returns and the interest rate.

    So if there is a "natural rate of interest" (in the above sense), I doubt it would be a precise value but at some discount to the ("uniform") rate of profit.

    The rate of profit would, at best, be an unstable equilibrium.

    . . .

    Regarding the circularity you mention at the end, what about newly created capital? I realize the value of existing capital will depend upon the interest rate but the value of new capital will give a potentially different price.