That Oh So Elusive Natural Rate of Interest

Last week, I did a short post linking to the new draft of my paper with Paul Zimmerman about the Sraffa-Hayek exchange on the natural rate of interest. In the paper, we attempt to assess Sraffa’s criticism in his 1932 review of Prices and Production of Hayek’s use of the idea of a natural rate of interest as well as Hayek’s response, or, perhaps, his lack of response, to Sraffa’s criticism. The issues raised by Sraffa are devilishly tricky, especially because he introduced the unfamiliar terminology of own-rates of interest, later adopted Keynes in chapter 17 of the General Theory in order to express his criticism. The consensus about this debate is that Sraffa got the best of Hayek in this exchange – the natural rate of interest was just one of the issues Sraffa raised, and, in the process, he took Hayek down a peg or two after the startling success that Hayek enjoyed upon his arrival in England, and publication of Prices and Production. In a comment to my post, Greg Ransom questions this conventional version of the exchange, but that’s my story and I’m sticking to it.

What Paul and I do in the paper is to try to understand Sraffa’s criticism of Hayek. It seems to us that the stridency of Sraffa’s attack on Hayek suggests that Sraffa was arguing that Hayek’s conception of a natural rate of interest was somehow incoherent in a barter economy in which there is growth and investment and, thus, changes in relative prices over time, implying that commodity own rates of interest would have differ. If, in a barter economy with growth and savings and investment, there are many own-rates, Sraffa seemed to be saying, it is impossible to identify any one of them as the natural rate of interest. In a later account of the exchange between Sraffa and Hayek, Ludwig Lachmann, a pupil of Hayek, pointed out that, even if there are many own rates in a barter economy, the own rates must, in an intertemporal equilibrium, stand in a unique relationship to each other: the expected net return from holding any asset cannot differ from the expected net return on holding any other asset. That is a condition of equilibrium. If so, it is possible, at least conceptually, to infer a unique real interest rate. That unique real interest rate could be identified with Hayek’s natural rate of interest.

In fact, as we point out in our paper, Irving Fisher in his classic Appreciation and Interest (1896) had demonstrated precisely this point, theoretically extracting the real rate from the different nominal rates of interest corresponding to loans contracted in terms of different assets with different expected rates of price appreciation. Thus, Sraffa did not demonstrate that there was no natural rate of interest. There is a unique real rate of interest in intertemporal equilibrium which corresponds to the Hayekian natural rate. However, what Sraffa could have demonstrated — though had he done so, he would still have been 35 years behind Irving Fisher – is that the unique real rate is consistent with an infinite number of nominal rates provided that those nominal rates reflected corresponding anticipated rate of price appreciation. But, instead, Sraffa argued that there is no unique real rate in intertemporal equilibrium. That was a mistake.

Another interesting (at least to us) point in our paper is that Keynes who, as editor of the Economic Journal, asked Sraffa to review Prices and Production, borrowed Sraffa’s own-rate terminology in chapter 17 of the General Theory, but, instead of following Sraffa’s analysis and arguing that there is no natural rate of interest, Keynes proceeded to derive, using (without acknowledgment) a generalized version of Fisher’s argument of 1896, a unique relationship between commodity own rates, adjusted for expected price changes, and net service yields, such that the expected net returns on all assets would be equalized. From this, Keynes did not conclude, as had Sraffa, that there is no natural rate of interest. Rather, he made a very different argument: that the natural rate of interest is a useless concept, because there are many natural rates each corresponding to a different the level of income and employment, a consideration that Hayek, and presumably Fisher, had avoided by assuming full intertemporal equilibrium. But Keynes never disputed that for any given level of income and employment, there would be a unique real rate to which all commodity own rates had to correspond. Thus, Keynes turned Sraffa’s analysis on its head. And the final point of interest is that even though Keynes, in chapter 17, presented essentially the same analysis of own rates, though in more general terms, that Fisher had presented 40 years earlier, Keynes in chapter 13 explicitly rejected Fisher’s distinction between the real and nominal rates of interest. Go figure.

Bob Murphy wrote a nice paper on the Sraffa-Hayek debate, which I have referred to before on this blog. However, I disagree with him that Sraffa’s criticism of Hayek was correct. In a post earlier this week, he infers, from our statement that, as long as price expectations are correct, any nominal rate is consistent with the unique real natural rate, that we must agree with him that Sraffa was right and Hayek was wrong about the natural rate. I think that Bob is in error on the pure theory here. There is a unique real natural rate in intertemporal equilibrium, and, in principle, the monetary authority could set a money rate equal to that real rate, provided that that nominal rate was consistent with the price expectations held by the public. However, intertemporal equilibrium could be achieved by any nominal interest rate selected by the monetary authority, again provided that the nominal rate chosen was consistent with the price expectations held by the public. In practice, either formulation is very damaging to Hayek’s policy criterion of setting the nominal interest rate equal to the real natural rate. But contrary to Sraffa’s charge, the policy criterion is not incoherent. It is just unworkable, as Hayek formulated it, and, on Hayek’s own theory, the criterion is unnecessary to avoid distorting malinvestments.

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13 Responses to “That Oh So Elusive Natural Rate of Interest”


  1. 1 Rob Rawlings February 28, 2013 at 3:05 pm

    “However, intertemporal equilibrium could be achieved by any nominal interest rate selected by the monetary authority, again provided that the nominal rate chosen was consistent with the price expectations held by the public”

    This seems misleading. If the nominal rate chosen has to be consistent with “the price expectations held by the public” – doesn’t that limit it to one rate ?

    In addition as well as price expectations held by the public surely the natural rate must also factor in time preferences held by the public ?

    So at any point in time the public will hold

    1) expectations about future prices
    2) time preference valuations between future and present goods

    Both of these will surely combine to give a unique natural rate.

    In addition why is setting such a rate unworkable ? Didn’t Hayek argue for holding MV constant ? if so then if the monetary authorities adjusted the interest rate to achieve that goal they would hit the “natural” rate, as long as they had successfully led the public to expect this . If the public expects constant MV then they should expect any price changes to be due to real factors and the interest rate should get set to the “natural” rate via market forces.

    Isn’t this more or less what modern Market Monetarists are calling for ?

  2. 2 Ritwik March 1, 2013 at 2:00 am

    David

    I take Keynes’s use of Fisher equation to be consistent because it seems to me that he’s saying :

    1) Given a nominal rate, one can always derive a real rate. Moreover, there is an arbitrage relation between own rates of interest AT a given point of time.

    2) There is no consistent relationship between inflation and nominal rates ACROSS time that is independent of real rates i.e. money is not super-neutral.

    So he accepts the Fisher equation *mechanistically* but refutes the monetarist paradox. This seems like a perfectly consistent set of views to hold.

    Also, I think his addition of commodity yields to the analysis of own rates of interest is critical. I’d always thought it was strange that Keynes tried so hard to establish money in terms of a commodity when he had earlier accepted and appreciated more creditist conceptions of it (like that of Mitchel Innes, e.g.). But some recent discussions made me realise that he was trying to establish the critical *numeraire* properties of money and derive a theory of liquidity premium from there, and for this it was important for him to cover the standard commodity theory of money.

  3. 3 Greg Ransom March 1, 2013 at 8:55 pm

    Hayek explicitly *rejects* this as a policy criterion:

    “Hayek’s policy criterion of setting the nominal interest rate equal to the real natural rate.”

    Hayek says it’s impossible to do this, and in any case, there are other factors involved that must be taken into consideration.

    Hayek is crystal clear about rejecting this as a real world policy criterion in the real world.

  4. 4 Greg Ransom March 1, 2013 at 9:12 pm

    See Hayek’s “Appendix: Some Supplementary Remarks on ‘Neutral Money’” for an account of the impossibility of securing ‘Neutral Money’, including an account of many of the factors which make this impossible.

    Hayek explains elsewhere why real interest rates don’t simply reflect value ratios in the time structure of production — which makes it impossible to read off the “real natural rate” from any prices found in the market, making it impossible for any central bank to identify or ‘set’ the nominal interest rate based on information derived from the market.

    The knowledge problem begins right here — as does Hayek’s discussion of real world prices as imperfect signals which are *never* exactly like anything in any economist’s math construct. This stuff dates back to the 1920s.

  5. 5 Greg Ransom March 1, 2013 at 9:14 pm

    To be clear, the “Appendix” mentioned above is in “Prices and Production”.

  6. 6 David Glasner March 3, 2013 at 9:12 pm

    Rob, You are right in pointing out that there is an ambiguity in what it means to say that central bank can choose any rate it wants to provided that the rate is consistent with the price expectations held by the public. The monetary authority does not have unlimited discretion in choosing its policy rate, on the other hand, the monetary authority is able to affect the public’s expectations by its actions, so some exercise of discretion is possible.

    The time preference of the public is reflected in the real rate; price expectations are reflected in the nominal rate. The full intertemporal equilibrium real rate is unique, price expectations are not necessarily unique.

    Yes, Hayek advocated holding MV constant, but he also expressed the view that it really was not a workable policy either. Hayek thought that if the central bank did set the policy rate equal to the natural rate, the result would be constant MV, but he was unable to formulate a method by which the monetary authority could know what rate to set or how to keep MV constant.

    Market Monetarists believe that the monetary authority can come tolerably close to keeping MV equal to a desired target path. Hayek at times thought that it would be good if the monetary authority could do so, but was skeptical whether it could do so.

    Ritwik, You make a good point, and I think it’s true that Keynes has to be arguing that it is the real rate that adjusts to a change in inflation expectations not the nominal rate, but I am not so sure that if you put the argument of chapter 13 side by side with the argument of chapter 17, that a reader will not be confused about what is going on. But the question requires further study.

    Greg, I think that I generally agree with you about this inasmuch as I believe that Hayek regarded the “natural rate” as an unobservable magnitude. I think that he was explicit about that in Trade Theory and the Trade Cycle, possibly less so in Prices and Production. I will try to have a look at the appendix to Prices and Production and see what he says. The upshot of what you are saying seems to support David Laidler’s characterization of Hayek’s position in the 1930s as “policy nihilism.”

  7. 7 Frank Restly April 1, 2013 at 6:10 pm

    “Yes, Hayek advocated holding MV constant, but he also expressed the view that it really was not a workable policy either. Hayek thought that if the central bank did set the policy rate equal to the natural rate, the result would be constant MV, but he was unable to formulate a method by which the monetary authority could know what rate to set or how to keep MV constant.”

    Using a credit based currency:

    Debt * Velocity = Nominal GDP = Income * ( 1 – Liquidity Preference ) + Change in Debt with Respect to Time

    D * V = I * ( 1 – LP) + dD/dt = ( D * V + INT * D ) * ( 1 – LP ) + dD/dt
    D = exp ( f(t) )
    dD/dt = f’(t) * exp ( f(t) )

    D * V * LP = INT * D * ( 1 – LP ) + dD/dt
    V * LP = INT * ( 1 – LP ) + f’(t)

    V = [ INT * ( 1 - LP ) + f'(t) ]

    Monetary policy affects the interest rate (INT), tax policy affects f’(t). Hitting any given D * V should be easy enough. The problem lies here:

    Productivity = Real GDP / Total Debt = Velocity / ( 1 + Inflation Rate )
    PR = RGDP / D = V / ( 1 + IR )

    PR = [ INT * ( 1 - LP ) + f'(t) ] / [ 1 + IR ]

    Here there are two government influenced variables ( nominal interest rate and f’(t) ) and three exogenous variables ( inflation rate, liquidity preference, and productivity ). To generate a unique solution, government equity is required.

  8. 8 David Glasner April 10, 2013 at 5:58 pm

    Frank, Sorry, but I can’t figure this out.

  9. 9 JW Mason November 23, 2013 at 6:20 pm

    Sorry to be commenting on such an old point, but I think you have missed two important parts of Sraffa’s criticism.

    Yes, it is possible to identify a unique intertemporal rate of substitution that, in equilibrium, will be incorporated into every transaction that involves goods in more than one period. I even think Sraffa recognized that. The problems are:

    (1) There is no reason to identify this “time-substitution” interest rate with the natural rate of interest in the Wicksellian sense, or indeed with any interest rate at all. Any intertemporal price we observe in reality incorporates risk, liquidity, carrying costs, and expected relative price changes as well as the pure time-substitution rate, and there is no particular reason to think the money-bond price is closer to the true time-substitution rate than, say, the rent-home price ratio, or the deflation rate, or the ratio of tuition costs to the college wage premium, or any other intertemporal price. In fact, as Keynes shows in the GT, there is good reason to think the bond-money price reflects the time-substition rate LESS than those three examples do.

    (2) Assuming equilibrium assumes away exactly the questions we are interested in, namely what interest rate will preserve price stability in an economy in which development is taking place. Suppose some new production technique becomes available. Then the expect return on engaging in this new technique must be greater than the expected return on existing techniques — this difference in returns is precisely the price signal that leads to adoption in the new technique. An interest rate rule that applies only to a static economy is irrelevant to the problem Hayek was addressing.

  10. 10 David Glasner November 30, 2013 at 7:58 pm

    JW, I am a bit rusty on this topic at the moment. Here a couple of off the cuff reactions. 1) I was not trying to defend Hayek’s natural-rate position as an operational rule for economic policy, but simply trying to show that Sraffa was overstating his objections to Hayek (e.g., calling Hayek’s notion of a natural rate of interest incoherent) in a way that even Keynes was not willing to accept when he wrote chapter 17 of the GT. I also agree that the natural rate exists only in an equilibrium setting. A change in the underlying equilibrium can change the natural rate. Again that makes the natural rate criterion difficult if not impossible to operationalize, but not incoherent. The most damaging argument against Hayek is one that Sraffa did not make, which is that the unique natural real rate is consistent with (in principle) an infinite number of nominal natural rates corresponding to different expectations of future nominal prices.


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About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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