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Chapter Fifteen: The Sraffa-Hayek Debate on the Natural Rate of Interest (With Paul
Zimmerman)
I. Introduction
The pivotal role of Piero Sraffa’s (1932a,b) review of F. A. Hayek’s Prices and Production
(1931b) in turning opinion against Hayek’s business-cycle theory, clearing the ground for the subsequent
Keynesian ascendency, is well known to historians of economics.1 Sraffa’s criticism of Hayek’s
restatement and elaboration of Mises’s ([1913] 1934) business-cycle theory, and his failure to respond
effectively, reinforced the impression that Sraffa had exposed critical flaws in Hayek’s theory.2
Hayek’s goal was so show that the business cycle could be avoided if monetary disturbances were
eliminated and that those disturbances could be avoided by a neutral-money policy in which the monetary
authority sets the interest rate on bank loans equal to the “natural” rate of interest. Sraffa’s attack on
Hayek was two-pronged, criticizing both the idea of a neutral-money policy to stabilize or dampen the
business cycle and the coherence of the underlying concept of a natural rate of interest.3 Our attention in
this chapter is on Sraffa’s second criticism: that the concept of a “natural rate of interest” -- at least
Hayek’s version of it – is incoherent. According to Sraffa, Hayek’s conception of the natural rate of
interest -- the rate of interest determined solely by real forces in a pure barter equilibrium -- is incoherent,
because multiple commodity (or own) rates of interest exist in a growing barter economy with savings
and investment, none of them having a special claim to be the natural rate of interest. If no single
commodity rate can be identified as the natural rate to serve as the criterion for monetary policy, Hayek’s
proposal for a neutral-money policy based on the natural-rate collapses.
1 See, e.g., Lawlor & Horn’s (1992, n. 3) discussion of Lachmann’s recollection of the Hayek-Sraffa debate (stating
in part: “What is particularly interesting about Lachmann’s account . . . is his view that Sraffa’s review was a critical
factor in Hayek’s fall from stature as an economic theorist in the 1930s.”).
2 The Sraffa-Hayek exchange has been reviewed extensively, e.g., by Kurz and Salvadori (2003), Kurz (2003) and
Desai (1995).
3 Note that Hayek (1931b) referred to the natural rate as the “equilibrium” rate of interest. For Hayek, the terms
appear to have synonymous, however his use of the terms in his reply to Sraffa is problematic. See below section VI.
To show that no commodity rate of interest in a barter economy can be identified as the
natural rate, Sraffa explains that, in a barter economy in which loans cannot be executed in
monetary terms, all loans would be denominated in terms of specific commodities, with a
corresponding “own rate” of interest defined for each commodity (Lawlor and Horn, p. 392).4
Thus, the rate at which any commodity could be “borrowed” today and repaid in the future,
would define the own rate for that commodity.
Sraffa analogized such transactions to a cotton spinner that borrows money to buy spot
cotton at the current price and then to sell forward at the current forward, in effect borrowing
cotton now and contracting for future repayment. The ratio of the forward price to the spot price
of cotton would determine the cotton own rate over the term of the loan. Transactions equivalent
to such commodity loans can be executed in any economy with forward and spot commodity
markets. Arbitrage would ensure that the own rate for commodity loans would exactly
corresponds to the ratio of the forward and spot prices of that commodity in terms of money (or
any numeraire).
While Sraffa acknowledged that, in a static equilibrium, characterized by unchanging
prices over time, own rates for all commodities would be equal, he denied that the equality
would be preserved in a growing economy with changing relative prices. In a growing economy,
the resulting multiplicity of own rates renders the notion of a unique natural rate of interest
defined by pure barter relationships incoherent. And only a growing, capital-using, economy is
susceptible to the kind of business-cycle analyzed by Hayek. Because deviations from the
uniform equilibrium rate of interest can occur even in a barter economy, Hayek’s assignment of
blame for business cycles to the introduction of bank-supplied credit money was misplaced. But,
4 While Sraffa first developed the notion of the own rate, he did not call it that. Rather, as discussed later, “own rate”
is the term that Keynes used for that concept in the General Theory.
even more problematically, the very notion of a unique natural rate of interest when there could
be multiple commodity rates of interest was incoherent, there being no basis on which to select
any of those commodity rates as the natural rate of interest.
<quotation>[I]n times of expansion and production . . . there is no such thing as an equilibrium
(or unique) natural rate of interest, so that the money rate can neither be equal to, nor lower than
it: the ‘natural’ rate of interest on producer’s goods, the demand for which has relatively
increased, is higher than the ‘natural’ rate on consumers’ goods, the demand for which has
relatively fallen<end quotation> (Sraffa 1932a, 51).
Facing this challenge to the coherence of the key concept of his theory, Hayek (1932b) offered a
seemingly ineffective defense easily dismissed by Sraffa. Hayek’s weak response provided the grounds
for other economists to dismiss a theory both counterintuitive and uncongenial to their policy preferences,
but whose logic had initially seemed persuasive.
Our thesis is that Hayek’s notion of a unique natural rate is not, as Sraffa charged, incoherent.
Hayek’s understanding of the uniqueness of the natural rate is also consistent with Fisher’s (1896)
previous discussion and supported by Keynes (1936) himself, deploying by name Sraffa’s own-rate
analysis, in Chapter 17 of the General Theory, to show that individual own rates converge on an
equilibrium rate of return adjusted for the real-service yield of the asset, expected appreciation, and the
cost of storage.5 That equilibrium net rate of return corresponds to the natural rate identified by Hayek.
The correspondence between Keynes’s treatment of own rates and Hayek’s understanding of a unique
natural rate of interest, originally noted by Lachmann (1956), deepens the puzzle about Hayek’s
ineffectual response to the charge of incoherence leveled against him by Sraffa.
5 Majewski (1988) and Mongiovi (1990) discuss the influence of Sraffa’s work on the development of Chapter 17 in
the General Theory. An extensive subsequent literature on the relationship between Sraffa’s analysis of the
commodity rate and Keynes’s adaptation of that analysis in Chapter 17 has developed. See Grieve (2015) and Nardi
(2015) and citations therein. We found Grieve’s discussion especially useful and would agree with his resolution of
the apparent inconsistencies between Keynes’s discussion and Sraffa’s discussion. Grieve notes that while Sraffa
couched his analysis in the rate paid by borrowers, Keynes’s analysis focused on the expected rate of return to asset
holders. Thus, the difference between them can be reduced to a difference in perspective, not substance. We
therefore agree with Grieve that Sraffa’s criticisms of Chapter 17 were terminological rather than substantive.
To avoid misunderstanding, let us make clear what we are, and what we are not, asserting. Sraffa
lodged two arguments against Hayek: first, business cycles could result from causes other than nominal
interest-rate reductions by banks below the natural rate and rate reductions could occur without triggering
a business cycle downturn; second, and more fundamentally, the notion of a natural rate of interest,
though perhaps defensible in the sense in which Wicksell used it, was, in Hayek’s sense, incoherent.
We take issue only with the second criticism. We maintain that, even in a barter system, the
variation among own rates is constrained by arbitrage, so that, as Keynes argued in Chapter 17, borrowers
and lenders would be indifferent between borrowing and lending in terms of one commodity rate or
another. Nevertheless, readers of earlier drafts of this chapter have noted that Sraffa disagreed with
Keynes’s treatment of own rates in Chapter 17 and Keynes’s conclusion that borrowers and lenders would
be indifferent between loans whatever the commodity in which they were denominated. Perhaps so.6 But
we need not show that Sraffa would necessarily have accepted an argument by Hayek that the net
advantages of borrowing and lending under barter would be equalized in whichever commodity loans
were denominated. Sraffa did not argue that Hayek’s analysis was wrong, but that it was incoherent. We
show that Hayek could have explained that there is, under his understanding of a barter economy, an
equilibrium real own rate and that the various nominal own rates are equilibrium own rates, so that
borrowers and lenders are indifferent between borrowing or lending at any of the nominal own rates
corresponding to each commodity. Sraffa might have rejected that argument if Hayek had made it, but
there is nothing senseless or incoherent about it.
This chapter proceeds as follows. Section two discusses the historical background of Sraffa’s
review. Section three summarizes Sraffa’s critique and Hayek’s response. In Section four, noting the
6 There are two levels of ambiguity. The first is whether Sraffa disagreed with Keynes’s substantive argument as
some have alleged, or whether his disagreement was merely terminological. See Grieve (2015) and additional
references cited therein. The second is whether if Sraffa disagreed with Keynes on substance, Sraffa was right and
Keynes was wrong. But even if the latter, there is no evidence to our knowledge that Sraffa thought that Keynes’s
position was incoherent. Indeed, Sraffa argued that in Chapter 17 Keynes was inconsistent with Fisher’s own-rate
analysis; if the disagreement was substantive, Sraffa was siding with Fisher against Keynes. In section four we
restate Sraffa’s argument in Fisherian terms, but the argument of section six establishes that the Hayek’s natural-rate
concept was consistent with Fisher’s distinction between real and nominal rates and Keynes’s argument in Chapter
17.
formal equivalence between Sraffa’s treatment of own rates, and Fisher’s (1896) distinction between real
and nominal rates, we restate Sraffa’s own-rate analysis in Fisherian terms. In section five, Hayek’s
ineffectual response to Sraffa’s criticism is discussed. In section six, we argue that Hayek’s assertion of a
unique natural rate is conceptually supported by Keynes’s Chapter 17 discussion of own rates and, after
appropriate adjustments, their necessary equality in equilibrium. However, establishing that Hayek’s
position about a unique natural rate was not incoherent does not mean that the natural rate provides an
operational, much less a useful, criterion for banking and monetary policy. Section seven offers
concluding remarks including thoughts about why Hayek did not consider alternatives to the natural-rate
criterion, alternatives that would have been more consistent with his theoretical approach and more useful
than the conceptually coherent, but unobservable, natural-rate criterion.
II. Background leading up to the debate
Perhaps the key analytical concept developed by Hayek in his early work on monetary theory and
business cycles was the idea of an intertemporal equilibrium. Before Hayek, the idea of equilibrium was
confined to a stationary state in which economic agents continue doing what they have been doing.
Equilibrium represents an end state in which all adjustments to a set of initial conditions have been fully
worked out. Seeking to generalize this narrow concept to make it applicable to the study of business
cycles in which he was engaged, Hayek defined equilibrium not in terms of the stationarity of objective or
measurable magnitudes, but as the mutual consistency of the decentralized, subjectively optimal, plans of
economic agents.7 The potential consistency of these plans may be conceived of even if economic
magnitudes fluctuate, as long as fluctuations are correctly foreseen.
The meaning of correct foresight in this context relates to the need for agents making plans about
future production and consumption to either know or anticipate future prices. Insofar as forward markets
do not exist for planned future transactions, agents must formulate plans based not on observed, but
7 Hayek (1937) provided a definitive statement of his conception of intertemporal equilibrium, with a subsequent
restatement provided in Hayek (1941). But Hayek’s ([1928] 1984) first statement of the concept was published
nearly a decade earlier.
expected, prices, plans being optimized conditional on expectations of future prices. When actual prices
differ from what they had been expected to be, optimized plans are likely to be changed, but the revision
of plans after unexpected price changes is itself likely to induce further price changes, so a sequence of
revisions of once-optimal plans in response to unanticipated price changes need not lead to a new
equilibrium in which price expectations are correct and plans are optimized and mutually consistent
(Radner 1987).
The congruence of expectations is not guaranteed by a priori assumptions about the predictive
power of agents; it is merely assumed that agents at a particular moment share common price
expectations, so that, conditional on those expectations, the individually formulated plans will be
mutually consistent. Hayek therefore distinguished between correct foresight and the more commonly
used term “perfect foresight,” with its connotation of superhuman knowledge and predictive powers.8 The
assumption of correct foresight does not exclude the possibility, indeed the inevitability, that new
information falsifying previous price expectations will become available (See chapter 17). Intertemporal
equilibrium requires merely contingently correct anticipation, not perfect foresight of, future prices.9
Starting from a state of intertemporal equilibrium, Hayek traced the disturbing influence of
money on the intertemporal structure of price relationships, and hence, on the intertemporal structure of
production. An equilibrium structure of intertemporal prices corresponds to the Wicksellian natural rate
matching the rates of intertemporal substitution in production and consumption, thereby determining the
optimal length or roundaboutness of production processes via the choice among production processes of
varying degrees of capital intensity and roundaboutness. Insofar as banks provide entrepreneurs with
8 Hayek (1937) explains that the equilibrium concept can be weakened so that even correct foresight is not
necessary. All that is required is that the individual expectations of economic agents be consistent so that they could
be validated by some possible future contingency. The resulting plans would then constitute an equilibrium relative
to the information possessed by the agents at a given moment. Even if the expectations are eventually disappointed,
the plans formulated were in equilibrium with respect to each other in the sense that they were mutually consistent
and could have been realized had the expected state of the world been realized.
9 By defining correct foresight as a contingent outcome rather than as an essential property of economic agents,
Hayek elegantly avoided the problems confounding Oscar Morgenstern ([1935] 1976) in his discussion of the
meaning of equilibrium. See Chapter 17
financing for investment projects without utilizing the voluntary savings of households, the equilibrium
reconciliation of intertemporal plans to produce and consume is disturbed, implying the deviation of
future prices from the prices that were expected, thereby requiring the eventual revision of the pre-
existing network of mutually consistent plans.
Hayek posited a credit expansion induced by banks setting their lending rate10 below the natural
rate as the initiating monetary disturbance that starts the cycle. As a consequence, the prices of investment
goods would rise relative to consumption goods, reflecting increased entrepreneurial demand for
investment given the reduced interest rates charged by banks on loans. The resulting adoption of overly
roundabout production processes (termed by Hayek “malinvestments”) by entrepreneurs borrowing at
below-equilibrium interest rates would restrict the output of consumption goods, causing their prices to
rise as well, tending to reduce consumption spending overall, a phenomenon described by Hayek as
forced savings. Corresponding to “overinvestment” induced by a below-natural rate of interest, household
consumption would be restricted by the increased relative prices of current consumption goods reflecting
the shift of output from consumption to investment goods.11
For Hayek, monetarily-induced lengthening of the capital structure is the key factor generating
the business cycle, the price-level effect on which Wicksell ([1898] 1936) and Keynes (1930) had
focused, being of secondary importance. Hayek argued that, because monetarily-induced lengthening of
the capital structure is unsustainable, the crisis, or upper-turning point of a cycle, occurs when the
inconsistencies between intertemporal plans occasioned by monetary expansion cause disappointment of
expectations, making some plans prohibitively costly to execute, triggering a cascade of plan revisions
10 The bank rate of interest, sometimes referred to as the “actual,” “money,” or ‘market” interest rate, is the rate
banks charge borrowers of credit for financing capital investment
11 Our short outline of the argument in Prices and Production does not be construed to mean that Hayek viewed the
business cycle as an equilibrium phenomenon. Intertemporal equilibrium provides a benchmark of comparison
against which the disturbances introduced by credit expansion are analyzed. Deviations from an equilibrium path
create countervailing forces rendering the initial deviations unsustainable, leading to a potentially unstable
adjustment toward a new equilibrium path. The cycle reflects the path away from and back to an equilibrium path.
The natural-rate criterion was intended to avoid deviations from intertemporal equilibrium induced by monetary
forces.
and disappointments, and a state of general economic discoordination. The unraveling of plans constitutes
the downturn and the contraction phase of the cycle.
The implied policy message for banks and especially central banks is to keep the market rate of
interest equal to the natural rate corresponding to a state of intertemporal equilibrium. Hayek maintained
that such an interest-rate policy would neutralize the distorting effect of money, eliminating distortions in
the capital structure induced by monetary expansion.12 As discussed further in section six, the problem is
the unobservability of the natural rate, which renders Hayek’s policy recommendation non-operational.
III. Sraffa’s critique
Hayek developed these ideas in a series of publications in the late 1920s and early 1930s,
including most notably his 1931 lectures at the London School of Economics, subsequently published as
Prices and Production (1931b), and his review (1931a, 1932a) of Keynes’s Treatise on Money, exposing
conceptual problems in its analytical framework. Stung by Hayek’s criticisms, Keynes (1931) issued an
ill-natured response, quickly shifting from a reply to Hayek’s criticisms to an attack on Hayek and Prices
and Production, a response deplored even by Keynes’s admiring biographer Roy Harrod (1951).
Perhaps realizing that his reply to Hayek had misfired, Keynes, then editor of the Economic
Journal, enlisted the formidable Piero Sraffa to write a review of Prices and Production. It is hard to
imagine that Sraffa would have written a negative review on order, but it can be assumed that Keynes was
not displeased with the review Sraffa submitted.
Sraffa’s first criticism was to conjecture that the capital distortion identified by Hayek was caused
not by an increased quantity of money, but by a change in its distribution (Sraffa 1932a, 48-49). Sraffa
also suggested that it was possible that the accumulation of capital associated with forced saving was not,
12 That is, with the rate of interest held at the natural rate, a monetary expansion by banks to finance investments in
excess of voluntary savings would not occur, a state of affairs that could not obtain in a barter equilibrium.
as Hayek supposed, unsustainable;13 the augmented capital stock financed by monetary expansion might
well drive the natural rate of interest down to the level of the reduced money rate, an outcome whose
possibility von Mises ([1913] 1934) himself had conceded.
Our concern in this chapter is with Sraffa’s second criticism of Hayek: the incoherence of the
natural rate of interest as defined by Hayek. Sraffa observed that in a barter economy borrowing and
lending would take place not in terms of a non-existent medium of exchange, but in terms of specific
commodities. For any commodity in terms of which a loan might be contracted, an own rate of interest
for borrowing and repayment in terms of that commodity could be defined. That own (or commodity) rate
of interest would correspond to the ratio of the forward and spot prices of that commodity (Sraffa 1932a,
50-51).14 Sraffa used the ratio of forward to spot prices as a heuristic device to engage the intuition of
readers rather than an actual description of how loans would be made. Even so, the constraint of forward
prices, reflecting expectations of the future that would constrain the own rates agreed upon in a barter
setting, even absent forward markets, cannot be ignored in reasoning about the behavior of own rates in a
barter economy. And Hayek would surely have been entitled to posit their existence in framing a reply to
Sraffa.
The ratio of the forward to the spot prices of any commodity being market-determined, Sraffa
argued that, in some circumstances, those ratios would not be equalized across commodities. If so,
Hayek’s claim that it is the operation of the banking system that causes the market interest rate to diverge
from the natural rate is meaningless, because no single own rate of interest toward which all other own
rates would gravitate could be identified. If there are different own rates for different commodities, then
none of them is uniquely natural, so deviations of the market rate from the natural rate cannot be
attributed, as Hayek did, to operation of the banking system.
13 The meaning of “unsustainable” in Austrian business-cycle is both vague and problematic.
14 As noted by Hagemann (2008) and discussed further below, the concept of an own rate of interest can be traced
back to Fisher (1896). Fisher’s concept was adopted by Sraffa and then by Keynes.
It will be instructive to follow the own-rate analysis Sraffa uses against Hayek, his argument
being more complicated than a bare assertion that the distinct own rates for individual commodities may
be unequal. After quoting Hayek’s assertion that, in a money economy, the money rate of interest may
diverge from the equilibrium (natural) rate, Sraffa observed:
<quotation>An essential confusion, which appears clearly from [Hayek’s] statement, is
the belief that the divergence of rates is a characteristic of a money economy: and the confusion is
implied in the very terminology adopted, which identifies the “actual” with the “money” rate, and
the “equilibrium” with the “natural” rate. If money did not exist, and loans were made in terms of
all sorts of commodities, there would be a single rate which satisfies the conditions of
equilibrium, but there might be at any one moment as many “natural” rates of interest as there are
commodities, though they would not be “equilibrium” rates. The “arbitrary” action of the banks is
by no means a necessary condition for the divergence; if loans were made in wheat and farmers
(or for that matter the weather) “arbitrarily changed” the quantity of wheat produced, the actual
rate of interest on loans in terms of wheat would diverge from the rate on other commodities and
there would be no single equilibrium rate.<end quotation> (Sraffa 1932a, 49)
Sraffa correctly observes that, owing to a change in demand or supply, particular own rates might
deviate from their (static) equilibrium values. However, such deviations are not, as Sraffa suggested,
analogous to the deviations from equilibrium associated with a monetary disturbance, the deviations
toward which Hayek directed his attention. Deviations from equilibrium caused by fluctuations in the
supply of real commodities would not persist; market forces would operate immediately to restore an
equilibrium with all own rates again equalized, a tendency not mentioned by Sraffa, though two
paragraphs later Sraffa acknowledged that, in equilibrium, all own rates must be equal.
<quotation>In equilibrium the spot and forward prices coincide, for cotton as for any
other commodity; and all the “natural” or commodity rates are equal to one another, and to the
money rate. But if, for any reason, the supply and the demand for a commodity are not in
equilibrium (i.e. its market price exceeds or falls short of its cost of production), its spot and
forward prices diverge, and the “natural” rate of interest on that commodity diverges from the
“natural” rates on other commodities.<end quotation> (Sraffa 1932a, 50)
Perhaps thinking of a stationary equilibrium in which prices do not change rather than the
intertemporal equilibrium analyzed by Hayek, Sraffa, positing a change in demand, traced the effect of
the change in demand on the relationship between spot and forward prices.
<quotation>Suppose there is a change in the distribution of demand between various
commodities; immediately some will rise in price, and others will fall; the market will expect
that, after a certain time, the supply of the former will increase, and the supply of the latter fall,
and accordingly the forward price, for the date on which equilibrium is expected to be restored,
will be below the spot price in the case of the former and above it in the case of the latter; in other
words, the rate of interest on the former will be higher than on the latter<end quotation>. (Id.)
Inferring from the shift in demand and consequent price adjustment that own rates of interest
need not be equalized, Sraffa argued that a unique natural rate does not exist. But Sraffa overlooked that
the divergence in own rates in his example might be accounted for by anticipated changes in the prices of
individual commodities. Thus, the alleged divergence of own rates to which Sraffa drew attention could
be understood as reflecting Fisher’s (1896) distinction between the real and the nominal rate of interest.
What Sraffa called a multiplicity of own rates, might be viewed as a multiplicity of nominal own rates
reflecting the expected appreciation or depreciation of those commodities for which demand was
increasing or decreasing. Given those expectations, borrowers and lenders would be indifferent between
contracting loans at own rates corresponding to either commodity. If Sraffa’s example exposed a flaw in
the theory of interest, the flaw is not only Hayek’s; it is also Irving Fisher’s. Sraffa’s thought experiment
did not show that the natural rate, expressed as a real rate (adjusted for expected price changes) is not
unique.
Sraffa further observed that Hayek could have avoided the problem of a non-unique natural rate
by adopting Wicksell’s definition of a price level as an appropriately weighted average of the money
prices of individual commodities. By extension, Hayek could then have defined the natural rate as a
weighted average of the own rates of individual commodities (Sraffa 1932a, 51). But that option, as
Sraffa (1932b, 251) noted, had been foreclosed to Hayek by his rejection of statistical price levels in his
review of Keynes’s Treatise on Money.15 The observation is correct, but Sraffa overstated its significance,
overlooking the distinction between the unique (real) natural rate and the multiplicity of nominal rates
consistent with the unique natural rate, depending on expected appreciation or depreciation of the
commodity whose (nominal) own rate is being determined. Defining the natural rate in terms of a
constant price level pins down a nominal rate; the real rate was already pinned down by Fisher’s analysis.
IV Deconstructing Sraffa’s Critique
It may be helpful, using Fisherian terminology, to restate our argument about the uniqueness of
the real own rate of interest under Sraffian barter conditions. Consider a barter economy with two
commodities, tomatoes and cucumbers, whose prices are expressed in terms of a third commodity, say,
onions serving as the numeraire. We begin with an initial equilibrium, expressing own rates of interest for
tomatoes and cucumbers, as follows:
(1 + it) = (1 + rt) x (ft /st)16
(1 + ic) = (1 + rc) x (fc/sc),
Where it and rt are the nominal and real own rates of interest for loans in terms of tomatoes and ft and st
are the forward and spot prices for tomatoes expressed in terms of the numeraire, onions. Similarly, ic and
15 See Hayek (1931a).
16 In Fisher (1896), the ratio of the forward price to the spot price is expressed as (1 + a), where “a” denotes the
expected rate of appreciation in the price of the commodity, i.e., the ratio of the forward to the spot price.
rc are the nominal and real own rates of interest for loans in terms of cucumbers and fc and sc are the
forward and spot prices for cucumbers in terms of onions.
In a static equilibrium with unchanging prices, spot and forward prices are the same, so the above
equations reduce to the following:
it = rt
ic = rc.
If borrowers and lenders are indifferent between borrowing or lending in terms of one commodity
or another, then the real own rates are equal, i.e., rt = rc. The equality of real rates established by arbitrage
implies that it = ic.
Thus, in static equilibrium all real and nominal own rates are equal, and a unique natural rate of
interest is well-defined. However, Sraffa argued that a deviation from static equilibrium, causing a
temporary increase in the price of one commodity, say tomatoes, and a decrease in the price of another,
say cucumbers, would be expected to be temporary, causing the spot and forward prices of the
commodities to diverge, and, therefore, the real own rates of the two commodities to diverge. From the
inequality between two or more own rates, Sraffa concluded that Hayek’s conception of the natural rate of
interest is incoherent.
Sraffa’s argument for the multiplicity of own rates hinged on an argument that borrowers and
lenders would expect the future price of tomatoes to fall and the future price of cucumbers to rise. But
given that expectation, borrowers would prefer to borrow from lenders offering to lend in terms of
cucumbers and lenders would prefer to lend in terms of tomatoes. Competition between borrowers to
borrow and lenders to lend would constrain the terms at which borrowers and lenders were making loans
to adjust until, at the margin, borrowers and lenders, given their expectations of the appreciation of
cucumbers and depreciation of tomatoes, were indifferent between borrowing and lending in terms of
either commodity. The tomato own rate on loans would have to be sufficiently greater than the cucumber
own rate to compensate for the expected difference between the expected rates of appreciation of two
commodities.
The argument can be restated formally by assuming that forward prices for tomatoes and
cucumbers are posted in forward prices, but the tendency toward elimination of differential incentives to
borrow or lend in terms of either commodity exists even without observable forward prices. The
assumption of explicit forward prices shows the outcome to which incentives to profit from expected
differences in the prices of tomatoes and cucumbers lead, by converting speculative profit opportunities
into arbitrage opportunities. The consequent indifference between borrowing and lending in terms of
either commodity undermines Sraffa’s argument that there is a multiplicity of own rates.
Consider the sort of case posited by Sraffa: a shift in demand between tomatoes and cucumbers
raising the spot price of cucumbers and lowering that of tomatoes. Sraffa asserted that the deviation from
long-term equilibrium would be temporary, implicitly assuming constant long-run costs for both
commodities (Arrow and Starret, 1973). Given that deviations of the prices of cucumbers and tomatoes
from their long-run equilibrium values are only temporary, the forward and spot prices for both
commodities would no longer be equal, forward cucumber prices being below and forward tomato prices
above their spot values.
The following relationships must hold after a demand shift causes tomato and cucumber spot
prices to diverge from long-run equilibrium values:
(1 + i*t) = (1 + r*t) x (ft/s*t)
(1 + i*c) = (1 + r*c) x (fc/s*c),
where starred variables represent post-demand-shift values. Because the shift in demand raises the spot
price of cucumbers and reduces the spot price of tomatoes, while leaving forward prices unchanged, we
have
(ft/s*t) > (ft/st)
(fc/s*c) < (fc/sc).
Since (ft/st) = (fc/sc), it follows that (ft/s*t) > (fc/s*c). From this inequality, Sraffa inferred that, after
a temporary disturbance of a static equilibrium, not all own rates of interest are equal, so that there is no
natural rate. But Sraffa overlooked the arbitrage constraint on real own rates. When fully effective, the
arbitrage constraint ensures that r*t = r*c. If that equality holds, given the forward prices of cucumbers and
tomatoes, borrowers and lenders would be indifferent between contracting loans in terms of cucumbers or
tomatoes.
Let r*t = r*c = r*. Thus, a unique real own rate of interest can be identified after the demand shift
posited by Sraffa, namely r*, and it can also be defined as the natural rate of interest. Hayek’s conception
of the natural rate therefore is not incoherent; it is consistent with Fisher’s distinction between the real
and nominal rates of interest, corresponding to the real own rate whose existence is ensured by the
arbitrage constraint. Sraffa’s critique of Hayek was ultimately a critique of Fisher’s distinction between
real and nominal rates; the critique of Fisher was not explicit, only implied.
Such a critique might have taken either of two forms. First, it might deny that the concept of a
real rate of interest is coherent. After all, loans are contracted in terms of nominal, not real rates. But
Sraffa, himself, acknowledged that, given expectations of differential rates of appreciation, nominal rates
adjust to reflect differences in expected appreciation. The adjustment to expected appreciation is evidence
that real rates matter. Second, it might deny that the unique real rate that existed before the hypothesized
demand shift equals the unique real rate, r*, that obtains after the demand shift. If the unique real rate is
not invariant to demand shifts, then Sraffa’s critique would only have been conjectural, not absolute. We
shall have more to say about this question below in section six.
V Hayek’s Response
Hayek’s (1932b) response to Sraffa seemed ineffectual, appearing to concede Sraffa’s point that
multiple own rates of interest are possible in a barter economy. While conceding the point, Hayek denied
that the concession compromised his position, thereby appearing to ignore, or not even to grasp, how
damaging the concession was for his position.
<quotation>I think it would be truer to say that . . . there would be no single rate which, applied
to all commodities, would satisfy the conditions of equilibrium rates, but there might, at any
moment, be as many “natural” rates of interest as there are commodities, all of which would be
equilibrium rates; and which would all be the combined result of the factors affecting the present
and future supply of the individual commodities, and of the factors usually regarded as
determining the rate of interest.<end quotation> (Hayek 1932, emphasis in original)
Without elaboration, Hayek simply withdrew behind an evasive statement (“The inter-relation between
these different rates of interest is far too complicated to allow of detailed discussion within the compass
of this reply”), suggesting that he was incapable of framing a counterargument to Sraffa’s attack. The
previous two sections have shown that the interrelation between the different rates of interest was less
complicated than Hayek suggested.
From his terse commentary about multiple natural rates, Hayek shifted to a discussion of the
related, though possibly second-order, issue of whether the effects following from any one natural (own)
rate of interest in a barter economy being “out of equilibrium” would be comparable to the effects arising
in a monetary economy when the money rate diverged from the natural rate.17 Silent on how to implement
his policy rule in a monetary economy with multiple natural rates, Hayek left unanswered Sraffa’s
criticism that, in the ideal barter economy serving as his conceptual benchmark, a multiplicity of natural
rates is possible, with none having a claim to serve as the criterion for a neutral monetary policy.
17 Hayek (1932, p. 246) maintains that the latter, but (in general) not the former, will lead to disequilibrium
outcomes (“I certainly believe that it is possible in this case to change ‘artificially’ the rate of interest in a sense in
which this . . . cannot be said of any commodity”).
Sraffa’s (1932b, p. 251) rejoinder chided Hayek for conceding the existence of multiple natural
rates without responding to his substantive criticism:
<quotation>Dr. Hayek now acknowledges the multiplicity of the “natural” rates, but he has
nothing more to say on this specific point than that they “all would be equilibrium rates.” The
only meaning (if it be a meaning) I can attach to this is that his maxim of policy now requires that
the money rate should be equal to all these divergent natural rates<end quotation>.
In other words, Hayek’s new position on the natural rate was either unresponsive or nonsensical.
But Hayek’s response may be interpreted more charitably than Sraffa did; it could be interpreted
in a way that is at least suggestive of our criticism of Sraffa’s own-rate analysis and of Lachmann’s
(1956) argument that, even under barter, arbitrage would force the distinct own rates to converge on a
common equilibrium value, with due allowance for differences in real service yields, expected
appreciation, and storage costs.
We digress briefly to note a terminological ambiguity. We showed in the previous section that the
existence of a unique real own rate follows immediately from the existence of forward markets providing
a tight arbitrage constraint. Even without forward markets, a tendency toward a unique real own rate
follows from the expectations of future price changes that Sraffa himself invoked to establish the
existence of multiple own rates. The arbitrage constraint operating even without the existence of an
intertemporal equilibrium, Lachmann’s argument for a unique real own rate holds even without a full
intertemporal equilibrium.18
Having himself previously ([1928] 1984) argued that anticipated price changes are not
inconsistent with intertemporal equilibrium, Hayek did not deny the divergence of nominal own rates of
interest. Hayek’s response was problematic in not distinguishing between the unique real own rate
18 See F.M. Fisher (1983) who used the arbitrage constraint as an alternative to tâtonnement in proving the stability
of a general equilibrium.
embedded in divergent nominal own rates constrained by arbitrage and the differential anticipated rates of
appreciation.
But such a response would have required Hayek to enlarge his conception of what constitutes a
neutral-money policy. This was a concession he was unable or unwilling to make. He would have had to
acknowledge that multiple rates of monetary expansion are consistent with a neutral-money policy
provided that price expectations are correct. But Hayek’s conception of a neutral monetary policy did not
allow him to do so.
VI Keynes to the Rescue?
Given Keynes’s stake in refuting Hayek’s analysis in Prices and Production, his selection of
Sraffa to write a review of Prices and Production, and his adoption in Chapter 17 of the General Theory
of Sraffa’s own-rate analysis, it is remarkable that Chapter 17 actually provided the analytical tools with
which Hayek could have responded to Sraffa’s criticism of his conception of the natural rate of interest.19
This curiosum went unnoticed for over twenty years until Lachmann (1956), Hayek’s student at LSE, but
also an admirer of Keynes, relied on Chapter 17 to explain that, even in a barter system, the expected
return (including the pecuniary and non-pecuniary yields plus price appreciation, net of storage costs)
tend to be equalized for all assets held from period to period. Three decades later, commenting on his
earlier defense of Hayek, Lachmann (1986, 238; first emphasis added) wrote:
<quotation>If there is a multiplicity of commodity rates, it is evidently possible for the money
rate of interest to be lower than some but higher than others. What, then, becomes of monetary
equilibrium? . . .
19 Fisher (1896) had already provided the basic framework for Keynes’s analysis, earlier exploited by
Keynes (1923) in his analysis of covered interest arbitrage. Chapter 17 generalized the framework to
encompass liquidity preference, providing a theory of the interaction between the demand for money and
the yield on assets held from period to period. Although he claimed too much for his liquidity preference
theory, his analysis of liquidity preference and liquidity premium remains foundational for the theory of
asset valuation and interest-rate determination.
It is not difficult, however, to close this particular breach in the Austrian rampart. In a barter
economy with free competition commodity arbitrage would tend to establish an overall
equilibrium rate of interest. Otherwise, if the wheat rate were the highest and the barley rate the
lowest of interest rates, it would become profitable to borrow in barely and lend in wheat. Inter-
market arbitrage will tend to establish an overall equilibrium in the loan market such that, in
terms of a third commodity serving as numéraire, say, steel, it is no more profitable to lend in
wheat than in barley.<end quotation>
Lachmann (id.) went on to conjecture what arbitrage activity implies for the expected own rates of return
in intertemporal equilibrium:
<quotation>This does not mean that actual own-rates must all be equal, but that the disparities are
exactly offset by disparities between forward prices. The case is exactly parallel to the way in
which international arbitrage produces equilibrium in the international money market, where
differences in local interest rates are offset by disparities in forward rates. In overall equilibrium,
it must be impossible to make gains by “switching” commodities as in currencies.<end
quotation>
Thus, while own rates in intertemporal equilibrium may differ, the differences are subject to the condition
that the expected returns from holding every asset must be equalized, any divergence of expected returns
triggering readjustments of asset valuations. Lachmann argued that the weakness of the natural-rate
concept is not that it pertains to a barter, rather than a monetary, economy, but that it can be defined
uniquely only in the context of full intertemporal equilibrium, which, Lachmann believed, rendered it
useless as a policy criterion.
But Lachmann conceded too much, because, in the presence of forward markets, the arbitrage
constraint operates without intertemporal equilibrium. Sraffa, himself, related the divergence of own rates
to the ratios between forward and spot prices in commodity markets, because own rates are constrained
by those ratios.20
While Keynes adopted Sraffa’s own-rate analysis and rejected the natural-rate concept, which he
had expounded upon in the Treatise, his reasons for doing so differed from Sraffa’s:
<quotation>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 the 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 for
the rate of interest irrespective of the level of employment. <end quotation>(Keynes 1936, 242)
(emphasis in original)
Thus, for Keynes, “non-uniqueness” of the natural rate refers not to a multiplicity of own rates, but to the
possibility that different natural rates of interest hold in different equilibrium states corresponding to
differing levels of employment. That is to say, while there is a particular natural rate corresponding to the
full-employment equilibrium, there may be different “natural” rates corresponding to equilibria at less
than full employment. Thus, for any level of employment, the real own rates of interest would all
converge to the same “unique” rate corresponding to a particular level of equilibrium employment. As we
noted in discussing Sraffa’s argument against a unique own rate of interest, it is entirely possible for the
unique real own rate to change after a shift in demand.21
20 Murphy (2010), though a devoté of Austrian business-cycle theory, defends Sraffa’s criticism of Hayek’s use of
the natural rate of interest, rejecting Lachmann’s defense that there is a tendency even in a pure barter economy for
equality among own rates, as Keynes explained in Chapter 17. The problem with Murphy’s discussion is that he
mistakenly believes that there is real significance to the choice of the numeraire in terms of which prices are quoted.
21 See Glasner (2018b) for a criticism of the implicit assumption that the real interest rate in the Fisher equation is
unique. The assumption is clearly untenable when expected inflation falls at zero lower bound. In such cases the
This view of multiple natural rates is different from Sraffa’s criticism of Hayek’s conception of
the natural rate, which concerned differing own rates of interest across commodities and assets held from
period to period, a possibility Keynes dismissed in Chapter 17. No divergence between real own rates
would be observed if expectations of differential returns caused asset prices to change.22 Even if
(nominal) gross own rates of return differ across commodities held from period to period, anticipated net
real rates of return across these assets must be equalized; otherwise, profits are being foregone. Taking
money as the standard measure of value, Keynes (1936, 227; emphasis added) made this very point:
<quotation>To determine the relationships between the expected returns on different assets which
are consistent with equilibrium . . . let the expected percentage appreciation (or depreciation) of
houses be
a1
and of wheat
a2
.
q1
,
−c2
, and
l3
we have called the own-rates of interest of houses,
wheat and money in terms of themselves as the standard of value . . . with this notation it is easy
to see that the demand of wealth owners will be directed at houses, to wheat or to money
according as
a1+q1
,
a2−c2
, or
l3
is greatest.<end quotation>
This realization in turn leads Keynes (pp. 227-28; first emphasis added) to the following unambiguous
conclusion:
<quotation>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 the alternatives, i.e.,
a1+q1
,
a2−c2
, and
l3
will be equal.<end quotation>
Of course, there are reasons why such a result might not hold, e.g., informational imperfections discussed
by Grossman and Stiglitz (1980), but Sraffa was not implicitly relying on such notions in his review of
Hayek.
nominal rate, being bound from below the Fisher equation can only be satisfied by an increase in the real rate.
22 And if there are reasons to believe that the adjustment of “disequilibrium” natural (own) rates would be sticky, one
will not find them laid out in the General Theory.
Viewed in this light, it may be possible, as we suggested in the previous section, to construe
Hayek’s seemingly ineffectual response to Sraffa in a more favorable light than has been customary. His
apparent concession that own rates might indeed be different may have been no more than an
acknowledgement that differences in service flows or storage costs or expected appreciation could
account for differences in nominal own rates. However, for equilibrium to obtain, such differences would
be such as to equalize the net expected real returns from holding different assets. But if Hayek had fully
grasped the distinction, he ought to have articulated the difference less cryptically than he did. So, while
we cannot be confident that Hayek perceived the gist of Keynes’s argument, there may be reason to
reconsider the received view that Hayek’s response to Sraffa was ineffectual.
VII Conclusion
Although we have argued that Sraffa’s criticism of Hayek’s business-cycle theory and his
criterion for a neutral-money policy was less damaging than it seemed to subsequent commentators, we
make no claim to have rehabilitated Hayek’s cycle theory or his natural-rate criterion. We claim only that
Sraffa’s charge that Hayek’s conception of the natural rate of interest is incoherent was not proven,
because the natural rate referenced by Hayek was simply the unique Fisherian real rate of interest of
which Keynes himself provided a generalized exposition in Chapter 17 of the General Theory.
It may be worth mentioning that the Fisherian basis of Keynes’s own-rate analysis in Chapter 17,
on which Keynes (1923) had previously relied in his theory of covered interest-rate arbitrage, is difficult
to reconcile with Keynes’s (1936, 142) strident criticism of the Fisher equation relating the nominal rate
of interest to the real rate plus expected inflation. Presumably, Keynes directed his criticism at the
implicit assumption in the Fisher equation that the real rate is independent of expected inflation.
However, the reasoning behind Keynes’s attack on the Fisher equation remains difficult to grasp and
seems, at least superficially, at odds with his own-rate discussion in Chapter 17.23
23 The reconciliation would presumably focus on the distinction between the relation between different nominal rates
at a point in time, reflecting different rates of expected depreciation at that time of different assets, and how an
exogenous change in expected appreciation would change the previous relationship between the nominal and the
In fact, the source of intertemporal disequilibrium identified by Hayek – equality between the
market rate and the natural rate of interest -- could not serve as a criterion for neutral money, because
neutral money could be achieved at any nominal rate of interest if price expectations are aligned with the
nominal rate of interest set by the monetary authority. Hayek, one of the originators of the concept of
intertemporal equilibrium, was equipped to grasp that point, but failed to transcend a reflexive attachment
to the notion of a unique nominal natural rate.
But even within his limitations, Hayek was groping for an alternative to equality between the
nominal interest rate and a nominal natural rate as the criterion for neutral money. Hayek (1931b, chap. 4)
introduced an alternative criterion of neutral money: a constant stream of spending (
MV ¿
. If the quantity
of money were adjusted to keep total spending constant, changes in the money stock (
M
) would just
offset changes in the demand to hold money
(
1
V
)
.
Under such circumstances, Hayek felt that money
would have no disturbing effect on economic activity. Excess cash would not drive up prices, nor would a
deficiency of cash drive them down. Prices would adjust only to changes in productivity implying
corresponding changes in cost. Unlike the equality between the nominal interest rate and a supposedly
unique nominal natural rate, the constant-total-spending criterion was at least defined in terms of an
observable magnitude.
To Hayek’s discredit, and later regret, and despite the reasons he himself had advanced for
constant
MV
as a policy criterion, he relentlessly advocated deflationary policies to counter the Great
Depression (Chapter 15).24 Had he followed the implications of his own analysis, Hayek would have
supported reflation during the Great Depression to restore MV to its pre-crash level, and would have been
allied with, rather than opposed to, Keynes and other supporters, like Hawtrey, Cassel, and Fisher, of
monetary easing to promote recovery from the Great Depression. Exactly why Hayek chose to advocate
real rates.
24 On Hayek’s conflicting policy positions during the Great Depression, see the interesting recent discussion by
Lawrence White (2008).
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