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.