While writing up my post on the Keynes-Hayek debate at LSE, I visited a couple of blogs to gauge the reaction in the blogosphere to the debate. One of those was the very interesting Social Democracy for the 21st Century: A Post-Keynesian Perspective. In his post on the debate, the blogger, AKA Lord Keynes, had some interesting observations about the famous (well, maybe among Austrians and Keynesians – especially post-Keynesians — with an inordinate interest in the history of economic thought) exchange in the Economic Journal between Piero Sraffa, reviewing Hayek’s Prices and Production, a short book containing his remarkably successful LSE lectures on the nascent Austrian theory of business cycles, Hayek’s response and Sraffa’s rejoinder. The general consensus about the debate is that Sraffa got the better of Hayek in the exchange, indeed, that the debate marked the peak in Hayek’s influence, having risen steadily after Hayek’s LSE lectures and his lengthy and damaging review of Keynes’s Treatise on Money and Keynes’s ill-tempered reply. Though Hayek continued working and writing tirelessly, the decline in his influence and reputation eventually led him away from technical economics into the more philosophical writings on which his lasting reputation was built, though he received some belated recognition for his early contributions when he was awarded the 1974 Nobel Memorial Prize in economics.
Sraffa attacked Hayek’s exposition of the Austrian business cycle theory on two fronts. First, Hayek argued that monetary expansion necessarily produces a distorting and unsustainable effect on the capital structure of production, ultimately causing a costly readjustment back to the earlier capital structure. Sraffa observed that the distortion identified by Hayek was not caused by monetary expansion per se, but by a change in the distribution of money, but a distributionally neutral expansion would have no such distorting effect. Sraffa also observed that it was entirely possible that the addition to the capital structure induced by what Hayek called forced saving might actually turn out to be sustainable inasmuch as the augmented capital stock might itself imply a reduced natural rate of interest rate corresponding to the reduced money rate achieved through monetary expansion.
Sraffa’s second, and perhaps more damaging, line of attack was on the very concept of a natural rate of interest, borrowed by Hayek from the Swedish economist Knut Wicksell, though transforming it in the process. According to Hayek, the natural rate corresponds to the interest rate in a pure barter equilibrium undisturbed by the influence of money. The goal of monetary policy should therefore be to ensure that the money rate of interest equaled the natural rate, thus neutralizing the effect of money and facilitating an intertemporal equilibrium in which money is not a distorting factor, i.e., in monetary expansion by banks to finance investments in excess of voluntary savings does not drive the money rate of interest below the natural rate, a state of affairs that could never obtain in a barter equilibrium.
Sraffa, however, argued that Hayek’s use of the natural rate of interest as a benchmark for monetary policy was incoherent, because there would be no unique natural interest rate in a growing barter economy with net investment in capital goods of the kind Hayek wished to use as a benchmark for monetary policy in a growing, money-using, economy. In the barter economy, interest rates would correspond to the price ratios over time (own rates of interest, i.e., ratios of spot to forward prices) between durable or storable commodities. But these own rates would fluctuate in response to the changing demands characterizing a growing economy, implying that there is no single natural rate of interest, but a collection of natural own rates of interest. Only if Hayek were willing to follow Wicksell in defining a price level in terms of some average of prices would Hayek have been able to define a natural rate of interest as some average of own rates. But Hayek explicitly rejected the use of statistical price levels. Hayek’s reply was ineffective, leaving Sraffa the clear winner in that exchange.
However, a quarter of a century later, Hayek’s student Ludwig Lachmann in his book Capital and its Structure elegantly explained the critical point that neither Sraffa nor Hayek had quite comprehended. The natural interest rate in a barter economy has a perfectly clear meaning, independent of any statistical average, in an intertemporal equilibrium setting, because equilibrium requires that the expected return from holding all durable or storable assets be the same. The weakness of the natural-rate concept is not that it necessarily pertains to a monetary rather than to a barter economy, as Hayek supposed, but that it could only be given meaning in the context of a full intertemporal equilibrium.
In his discussion of Sraffa and Hayek on his blog, Lord Keynes insists that Sraffa got it right.
However, Piero Sraffa had already demonstrated in 1932 that outside of a static equilibrium there is no single natural rate of interest in a barter or money-using economy, and Hayek never really addressed this problem for his trade cycle theory.
Sraffa did demonstrated that there was no single natural rate of interest in a disequilibrium, but he did not do so for an intertemporal equilibrium in which price changes are correctly foreseen. Hayek actually had developed the concept of an intertemporal equilibrium in a paper originally published in German in 1929, eight years before providing a truly classic articulation of the concept in his wonderful 1937 paper “Economics and Knowledge,” so it is odd that he was unable to respond effectively to Sraffa’s critique of the natural rate in 1932.
Lord Keynes, who is aware of Lachmann’s contribution on the Sraffa-Hayek exchange, cites as authority for dismissing Lachmann, a paper by another blogger, an ardent, but surprisingly reasonable, Austrian business cycle theory supporter Robert Murphy, who has written a paper that addresses the Sraffa-Hayek debate. Lord Keynes quotes the following passage from Murphy’s paper.
Lachmann’s demonstration—that once we pick a numéraire, entrepreneurship will tend to ensure that the rate of return must be equal no matter the commodity in which we invest—does not establish what Lachmann thinks it does. The rate of return (in intertemporal equilibrium) on all commodities must indeed be equal once we define a numéraire, but there is no reason to suppose that those rates will be equal regardless of the numéraire. As such, there is still no way to examine a barter economy, even one in intertemporal equilibrium, and point to ‘the’ real rate of interest.”
Murphy is almost right in that Lachmann demonstrates that the rate of return is equalized across all investment opportunities (allowing for the usual sources of difference in rates of return) in an intertemporal equilibrium. It is not clear what he means by saying that the choice of a numeraire matters. It doesn’t matter for any real property of the intertemporal equilibrium, i.e., a real quantity or a relative price; it matters only for nominal quantities and absolute prices. But nominal quantities, by definition, depend on the choice of a numeraire and even in a static equilibrium there is no unique nominal rate of return just as there is no unique level of absolute prices. The “real” rate of interest is determined in an intertemporal equilibrium; the nominal rate is not determined. This is precisely the distinction between the real rate and the nominal rate identified in the Fisher equation. And every kindergartener knows that the natural rate is a real rate not a nominal rate.
Perhaps Murphy is made uncomfortable by the fact that Lachmann’s point shows that a Hayekian intertemporal equilibrium could be consistent with any rate of inflation as long as the nominal rate reflected the equilibrium expected rate of inflation and inflation would have no effect on relative prices. That indeed is a problem for a fundamentalist version of Austrian business cycle theory and would deny that as a matter of pure theory there cannot be an intertemporal equilibrium with inflation. But that form of Austrian fundamentalism is simply inconsistent with the basic properties of an intertemporal equilibrium and with the non-uniqueness of absolute prices in either a static or intertemporal equilibrium. So Austrians just need suck it up on that (not very important) point and move on.
Finally, to come back to Sraffa. It is worth noting that the real Keynes in the General Theory said this about the natural rate of interest.
In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest — namely, the rate of interest which . . . preserved equality between the rate of saving . . . and the rate of investment. . . .
I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate of interest for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value fo rthe rate of interest irrespective of the level of employment.
So Keynes, like Sraffa, clearly had rejected the notion of a unique natural rate of interest. But Keynes’s reasons for doing so are very different from Sraffa’s. Keynes’ makes no mention of multiple natural rates corresponding to the different commodity own rates of interest that Sraffa had introduced in his attack on Hayek’s use of the natural rate. (Keynes, of course, as editor of the Economic Journal, had selected Sraffa to write a review of Prices and Production, presumably knowing what to expect, so he knew exactly what Sraffa had said about the natural rate of interest.)
Indeed Keynes goes through Sraffa’s analysis in chapter 17 of the General Theory, “The Essential Properties of Interest and Money.” It is one of my favorite chapters, especially because its analysis of portfolio choice is so acute. I just quote one long paragraph (pp. 227-28).
To determine the relationships between the expected returns on different types of assets which are consistent with equilibrium, we must also know what the changes in relative values during the year are expected to be. Taking money (which need only be a money of account for this purpose, and we could equally well take wheat) as our standard of measurement, let the expected percentage appreciation (or depreciation) of houses be a1 and of wheat a2. q1, -c2 and l3 we have called own-rates of interest of houses, wheat and money in terms of themselves as the standard of value; i.e., q1 is the house-rate of interest in terms of houses, -c2 is the wheat-rate of interest in terms of wheat, and l3 is the money rate of interest in terms of money. It will also be useful to call a1 + q1, a2 – c2 and l3, which stand for the same quantities reduced to money as the standard of value, the house-rate of money-interest, the wheat-rate of money-interest and the money-rate of money-interest respectively. With this notation it is easy to see that the demand of wealth-owners will be directed to houses, to wheat or to money, according as a1 + q1 or a2 – c2 or l3 is greatest. Thus in equilibrium the demand-prices of houses and wheat in terms of money will be such that there is nothing to choose in the way of advantage between alternatives; i.e, a1 + q1, a2 – c2 and l3 will be equal. The choice of the standard of value will make no difference to this result because a shift from one standard to another will change all the terms equally, i.e. by an amount equal to the expected rate of appreciation (or depreciation) of the new standard in terms of the old.
In this particular post, I am happy to give Keynes the last word.