Once Upon a Time When Keynes Endorsed the Fisher Effect

One of the great puzzles of the General Theory is Keynes’s rejection of the Fisher Effect on pp. 141-42. What is even more difficult to understand than Keynes’s criticism of the Fisher Effect, which I hope to parse in a future post, is that in his Tract on Monetary Reform Keynes had himself reproduced the Fisher Effect, though without crediting the idea to Fisher. Interestingly enough, when he turned against the Fisher Effect in the General Theory, dismissing it almost contemptuously, he explicitly attributed the idea to Fisher.

But here are a couple of quotations from the Tract in which Keynes exactly follows the Fisherian analysis. There are probably other places in which he does so as well, but these two examples seemed the most explicit. Keynes actually cites Fisher several times in the Tract, but those citations are to Fisher’s purely monetary work, in particular The Purchasing Power of Money (1911) which Keynes had reviewed in the Economic Journal. Of course, the distinction between the real and money rates of interest that Fisher made famous was not discovered by Fisher. Marshall had mentioned it and the idea was discussed at length by Henry Thornton, and possibly by other classical economists as well, so Keynes was not necessarily committing a scholarly offense by not mentioning Fisher. Nevertheless, it was Fisher who derived the relationship as a formal theorem, and the idea was already widely associated with him. And, of course, when Keynes criticized the idea, he explicitly attributed the idea to Fisher.

Economists draw an instructive distinction between what are termed the “money” rate of interest and the “real” rate of interest. If a sum of money worth 100 in terms of commodities at the time when the loan is made is lent for a year at 5 per cent interest, and is worth only 90 in terms of commodities at the end of the year, the lender receives back, including interest, what is worth only 94.5. This is expressed by saying that while the money rate of interest was 5 per cent, the real rate of interest had actually been negative and equal to minus 5.5 per cent. . . .

Thus, when prices are rising, the business man who borrows money is able to repay the lender with what, in terms of real value, not only represents no interest, but is even less than the capital originally advanced; that is the borrower reaps a corresponding benefit. It is true that , in so far as a rise in prices is foreseen, attempts to get advantage from this by increased borrowing force the money rates of interest to move upwards. It is for this reason, amongst others, that a high bank rate should be associated with a period of rising prices, and a low bank rate with a period of faling prices. The apparent abnormality of the money rate of interest at such times is merely the other side of the attempt of the real rate of interest to steady itself. Nevertheless in a period of rapidly changing prices, the money rate of interest seldom adjusts itself adequately or fast enough to prevent the real rate from becoming abnormal. For it is not the fact of a given rise of prices, but the expectation of a rise compounded of the various possible price movements and the estimated probability of each, which affects money rates. (pp. 20-22)

Like Fisher, Keynes, allowed for the possibility that inflation will not be fully anticipated so that the rise in the nominal rate will not fully compensate for the effect of inflation, suggesting that it is generally unlikely that inflation will be fully anticipated so that, in practice, inflation tends to reduce the real rate of interest. So Keynes seems fully on board with Fisher in the Tract.

Then there is Keynes’s celebrated theorem of covered interest arbitrage, perhaps his most important and enduring contribution to economics before writing the General Theory. He demonstrates the theorem in chapter 3 of the Tract.

If dollars one month forward are quoted cheaper than spot dollars to a London buyer in terms of sterling, this indicates a preference by the market, on balance, in favour of holding funds in New York during the month in question rather than in London – a preference the degree of which is measured by the discount on forward dollars. For if spot dollars are worth $4.40 to the pound and dollars one month forward $4.405 to the pound, then the owner of $4.40 can, by selling the dollars spot and buying them back one month forward, find himself at the end of the month with $4.405, merely by being during the month the owner of £1 in London instead of $4.40 in New York. That he should require and can obtain half a cent, which, earned in one month, is equal to about 1.5 per cent per annum, to induce him to do the transaction, shows, and is, under conditions of competition, a measure of, the market’s preference for holding funds during the month in question in New York rather than in London. . . .

The difference between the spot and forward rates is, therefore, precisely and exactly the measure of the preference of the money and exchange market for holding funds in one international centre rather than in another, the exchange risk apart, that is to say under conditions in which the exchange risk is covered. What is it that determines these preferences?

1. The most fundamental cause is to be found in the interest rates obtainable on “short” money – that is to say, on money lent or deposited for short periods of time in the money markets of the two centres under consideration. If by lending dollars in New York for one month the lender could earn interest at the rate of 5.5 per cent per annum, whereas by lending sterling in London for one month he could only earn interest at the rate of 4 per cent, then the preference observed above for holding funds in New York rather than London is wholly explained. That is to say, the forward quotations for the purchase of the currency of the dearer money market tend to be cheaper than spot quotations by a percentage per month equal to the excess of the interest which can be earned in a month in the dearer market over what can be earned in the cheaper. (pp. 123-34)

Compare Keynes’s discussion in the Tract to Fisher’s discussion in Appreciation and Interest, written over a quarter of a century before the Tract.

Suppose gold is to appreciate relatively to wheat a certain known amount in one year. What will be the relation between the rates of interest in the two standards? Let wheat fall in gold price (or gold rise in wheat price) so that the quantity of gold which would buy one bushel of wheat at the beginning of the year will buy 1 + a bushels at the end, a being therefore the rate of appreciation of gold in terms of wheat. Let the rate of interest in gold be i, and in wheat be j, and let the principal of the loan be D dollars or its equivalent B bushels. Our alternative contracts are then:

For D dollars borrowed D + Di or D(1 + i) dollars are due in one yr.

For B bushels     “       B + Bj or B(1 + j) bushels  ”   “    “   “   “

and our problem is to find the relation between i and j, which will make the D(1 + i) dollars equal the B(1 + j) bushels.

At first, D dollars equals B bushels.

At the end of the year D dollars equals B(1 + a) bushels

Hence at the end of one year D(1 + i) dollars equals B(1 + a) (1 + i) bushels

Since D(1 + i) dollars is the number of dollars necessary to liquidate the debt, its equivalent B(1 + a) (1 + i) bushels is the number of bushels necessary to liquidate it. But we have already designated this number of bushels by B(1 + j). Our result, therefore, is:

At the end of 1 year D(1 + i) dollars equals B(1 + j) equals B(1 + a) (1 + i) bushels

which, after B is canceled, discloses the formula:

1 + j = (1 + a) (1 + i)

Or,

j = i + a + ia

Or, in words: The rate of interest in the (relatively) depreciating standard is equal to the sum of three terms, viz., the rate of interest in the appreciating standard, the rate of appreciation itself and the product of these two elements. (pp. 8-9)

So, it’s clear that Keynes’s theorem of covered interest arbitrage in the Tract is a straightforward application of Fisher’s analysis in Appreciation and Interest. Now it is quite possible that Keynes was unaware of Fisher’s analysis in Appreciation and Interest, though it was reproduced in Fisher’s better known 1907 classic The Rate of Interest, so that Keynes’s covered-interest-arbitrage theorem may have been subjectively original, even though it had been anticipated in its essentials a quarter of a century earlier by Fisher. Nevertheless, Keynes’s failure to acknowledge, when he criticized the Fisher effect in the General Theory, how profoundly indebted he had been, in his own celebrated work on the foreign-exchange markets, to the Fisherian analysis was a serious lapse in scholarship, if not in scholarly ethics.

16 Responses to “Once Upon a Time When Keynes Endorsed the Fisher Effect”


  1. 1 Egmont Kakarot-Handtke December 1, 2015 at 4:35 am

    The Fisher Effect — a specimen of scientific incompetence
    Comment on ‘Once Upon a Time When Keynes Endorsed the Fisher Effect’

    The Fisher Effect is ultimately the result of a design flaw of the monetary order/institutions. As a rule, the monetary order is not consciously designed but the outcome of piecemeal institutional change in historical time. As we know from biological evolution, this leads regularly to sub-optimal outcomes with regard to structure/functionality, which, however, become only visible in hindsight. The cecum is a case in point, but biology is full of weird constructions.

    The Fisher Effect should not occur in a well-designed monetary order because it violates the principle of the neutrality of money. To see this clearly one has to change the methodological perspective.

    Our analytical framework is given as elementary consumption economy.* The business sector consists of two firms, one produces the consumption good, the other produces money and credit and is called the central bank. The central bank stands here for the whole banking industry (for details see 2015, Sec. 7).

    For simplicity, only the limiting case of a zero profit economy is considered.

    Then, in the consumption good producing firm this condition holds in the most elementary case

    (1) Pc X=W Lc

    Price Pc times quantity sold X equals wage rate W times labor input Lc. This reduces for the case of market clearing to

    (2) Pc=W/Rc

    The market clearing price is equal to unit wage costs W/Rc with Rc standing for the productivity in consumption good production.

    For the central bank holds

    (3) Jo OVD=Jd DEP+W Lb

    that is, rate of interest Jo on the asset side (here current overdrafts) times overdrafts OVD equals rate of interest Jd on the liability side (here current deposits) times deposits DEP plus wage rate W times labor input in the banking industry Lb. Strictly speaking, OVD and DEP are the average stocks per period.

    Both sides of the central bank’s balance sheet are equal, that is current overdrafts OVD equals current deposits DEP. Current deposits are here identical to the quantity of money. For simplicity, the rate of interest on the liability side Jd is set to zero. This reduces (3) to

    (4) Jo OVD=W Lb

    All real variables (labor input, productivity, output etc) remain unchanged for the time being. The real side is frozen.

    In the next period, the wage rate W in (1) and (4), which is here identical for simplicity, is doubled. As a consequence Pc in (1) doubles under the conditions of market clearing, zero profit, and no real changes.

    If W doubles in (4) on the right hand side then either Jo or OVD must double on the left hand side. The correct solution is that the interest rate Jo remains constant and the asset side=current overdrafts=OVD is doubled. Because both sides of the central bank’s balance sheet are always equal the liability side=current deposits=DEP=quantity of money has also to be doubled.

    In real terms, the situation remains unchanged for all agents. And this is as it should be according to the neutrality principle. In the historically given monetary order, however, neither the asset nor the the liability side of the consolidated balance sheet of the banking industry is properly adapted. Only for this reason the rate of interest, here Jo in (4), changes.

    Therefore, in a well-designed monetary order the interest rate Jo is like a real variable that remains ABSOLUTELY constant no matter what the rate of inflation or deflation is. It is, so to speak, the pole star of the economic firmament. The Fisher Effect is only an artifact, a historical accident, a freak phenomenon. In their analysis neither Fisher nor Keynes did ever rise above parochial realism.

    This scientific incompetence is — not a matter of ‘once upon a time’ — but the defining characteristic of the representative economist.

    Egmont Kakarot-Handtke

    References
    Kakarot-Handtke, E. (2015). Major Defects of the Market Economy. SSRN Working Paper Series, 2624350: 1–40. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624350

    * See

  2. 2 djb December 1, 2015 at 6:41 am

    “rate of return over costs”, I believe that Keynes acknowledged this as exactly equivalent to his marginal efficiency of capital

    page 141 the general theory

    one of the few times in general theory where Keynes acknowledge someone exactly pinning a concept the exact way he understood it

    that’s what I remember from general theory, him complementing fisher

  3. 3 Frank Restly December 1, 2015 at 2:32 pm

    Egmont Kakarot-Handtke,

    “Therefore, in a well-designed monetary order the interest rate Jo is like a real variable that remains ABSOLUTELY constant no matter what the rate of inflation or deflation is. It is, so to speak, the pole star of the economic firmament.”

    Except that central banks don’t do it that way and the reason is simple – the central bank can be a price giver / quantity taker OR vice versa. They can’t be both a price (interest rate) giver and a quantity (amount of debt) giver. The central bank can’t insist that a bank or anyone else take on a loan.

    Your zero profit economy presumably can still have losses – yes? And those losses can lead to bankruptcies – yes? And so, facing the potential of losses at a given interest rate, an individual firm is left to decide whether to borrow or not borrow irrespective of whether it is operating to turn a profit.

    If you meant to say – risk free economy instead of profitless economy, then ok. A profitless economy is not the same thing as a lossless economy.

  4. 4 Egmont Kakarot-Handtke December 2, 2015 at 5:01 am

    Comment on Frank Restly

    The zero profit economy is defined by the absence of profit AND loss. And this is, as I clearly stated, a ‘limiting case’ to start with. The general case is discussed in my papers. Please help yourself on SSRN
    http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1210665

    I have excluded profit/loss in my post about the Fisher Effect in order to avoid a discussion about profit theory which is defective since Adam Smith. See the post ‘Profit and the collective failure of economists’
    http://axecorg.blogspot.de/2015/11/profit-and-collective-failure-of.html

    I am well aware that a risk free economy is different from a zero profit economy and that a central bank cannot set both price and quantity. But that is not the issue here. The issue is that the Fisher Effect is ultimately caused by a constructive defect of the monetary order.

    For the other defects see ‘Major Defects of the Market Economy’
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624350

  5. 5 Frank Restly December 2, 2015 at 8:34 am

    Egmont Kakarot-Handtke,

    “The zero profit economy is defined by the absence of profit AND loss.”

    Strange economy you have there – workers live forever, equipment does not wear out, and accidents and natural disasters do not happen.

    Could it be that the Fisher Effect is caused by constraints in the real world?

  6. 6 Egmont Kakarot-Handtke December 3, 2015 at 3:28 am

    Comment on Frank Restly Dec 2

    The representative economist does not understand basic methodological principles. “There can be no doubt whatsoever that a problem which has not yet been solved in all its aspects under its simplest conditions will be still more difficult to tackle if other, ‘more realistic’ assumptions are being made.” (Morgenstern, 1941, p. 373)

    The zero profit condition is the simplest condition, therefore it is the correct starting point.

    It is the very characteristic of the representative economist that he cannot rigorously focus on one line of argument and that he has the attention span of a goldfish.*

    In my posts you will not find the statement that ‘workers live forever, equipment does not wear out, and accidents and natural disasters do not happen.’

    Could it be that you can neither read nor think but only waffle?

    By the way, that science is the art of abstraction from irrelevant detail is known since J. S. Mill “Since, therefore, it is vain to hope that truth can be arrived at, either in Political Economy or in any other department of the social science, while we look at the facts in the concrete, clothed in all the complexity with which nature has surrounded them, and endeavour to elicit a general law by a process of induction from a comparison of details; there remains no other method than the à priori one, or that of ‘abstract speculation’.” (1874, V.55)

    References
    Mill, J. S. (1874). Essays on Some Unsettled Questions of Political Economy. On the Definition of Political Economy; and on the Method of Investigation Proper To It. Library of Economics and Liberty. URL http://www.econlib.org/library/
    Mill/mlUQP5.html#EssayV.OntheDefinitionofPoliticalEconomy.
    Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political Economy, 49(3): 361–393. URL http://www.jstor.org/stable/1824735

    * See ‘One entirely sufficient reason for the shutdown of economics’
    http://axecorg.blogspot.de/2015/12/one-entirely-sufficient-reason-for.html

  7. 7 David Glasner December 3, 2015 at 9:06 am

    Egmont, Your example seems irrelevant inasmuch as there is no alternative asset to money that can be held from one period to the next, which means that the expected future price level has no effect on any decision maker in your example, so you have assumed your own conclusion.

    djb, You are right that Keynes acknowledged the connection between Fisher’s rate of return over cost and his marginal efficiency of capital. His criticism of the Fisher effect is independent of that acknowledgment of Fisher.

  8. 8 Frank Restly December 3, 2015 at 4:06 pm

    Egmont Kakarot-Handtke,

    “In my posts you will not find the statement that ‘workers live forever, equipment does not wear out, and accidents and natural disasters do not happen.”

    Then what exactly do you mean by a zero loss economy?

    When workers perish, that creates a loss.
    When equipment wears out, that creates a loss.
    When accidents and natural disasters happen, that creates losses.

    “The zero profit condition is the simplest condition, therefore it is the correct starting point.”

    Which is fine. But if I interpret a zero profit condition as also being a zero loss condition from your statement:

    “The zero profit economy is defined by the absence of profit AND loss.”

    ..then workers must live forever, equipment never wears out, and accidents and natural disasters never happen.

  9. 9 Egmont Kakarot-Handtke December 4, 2015 at 2:27 am

    Comment on David Glasner

    It seems, that not only Frank Restly can neither read nor think.

    In eq. (3) of my post of Dec 1 the rate of interest Jd on the central bank’s liability side explicitly appears and is subsequently set to zero in order to focus the argument. The rate of interest on financial assets is discussed in my papers on multiple occasions (please help yourself on SSRN).

    It should be known by now that it is rather silly to argue that a lot of phenomena are missing in an extremely simplified example and thereby to distract from the point at issue.

    Note that the introduction of the rate Jd does not change the essential point of my argument. Every serious student can verify this by following the References.

    The urgently required New Thinking in economics does not consist in the exegesis of obsolete authors (‘some defunct economist’ in Keynes’s apt terminology) and in playing old academic games. As Peirce nicely put it on a similar occasion: “[The pragmatist] is none of those overcultivated Oxford dons — I hope their day is over — whom any discovery that brought quietus to a vexed question would inevitably vex because it would end the fun of arguing around it and about it and over it.” (1931, 5.520)

    Egmont Kakarot-Handtke

    References
    Peirce, C. S. (1931). Collected Papers of Charles Sanders Peirce, volume I. Cambridge, MA: Harvard University Press. URL courses.arch.ntua.gr/fsr/138469/Peirce,%20Collected%20papers.pdf

  10. 10 Egmont Kakarot-Handtke December 4, 2015 at 4:08 am

    Comment on Frank Restly of Dec 3

    You ask: “Then what exactly do you mean by a zero loss economy?”

    I mean exactly that profit/loss is set to zero and thereby taken out of the picture for the time being in order to streamline the argument. This means that I deal with profit/loss on another occasion* and by no stretch of a feeble imagination that it escaped my notice that profit/loss occur in the real world.

    What I have shown, indeed, is that the profit theory is false since Adam Smith. If you intend to educate yourself have a look at my website.**

    Did you ever realize that the original Walrasian model (ni bénéfice ni perte) and the original Keynesian model are zero profit economies? [ni bénéfice ni perte = no profit no loss]

    In the general case, overall profit of the business sector as a whole is positive according to the Profit Law Qm=Yd+I-Sm and in this case all your objections go up in smoke. The essential point of my post of Dec 1, though, remains unaffected.

    Egmont Kakarot-Handtke

    * See for a start ‘Profit and the collective failure of economists’
    http://axecorg.blogspot.de/2015/11/profit-and-collective-failure-of.html

    ** ‘Profit is the key’
    http://www.axec.org/#!profit/c1apr

  11. 11 Henry December 4, 2015 at 10:39 am

    David,

    I am sorry to say but I think you make mountains out of molehills.

    Why is there a puzzle about Keynes’s so-called rejection of the Fisher Effect? Can’t a person change his mind? And was it a rejection or rather an embellishment of it. After all, all Keynes did was ask the question, is the inflation rate in the Fisher equation the current rate of inflation or the expected rate of inflation? He goes on to explain the reasoning behind his question.

    On the point of “contemptuously” “dismissing” the Fisher effect, I cannot detect any malice whatsoever. Keynes merely sets about making his argument without rancour.

    On the point of accreditation, in the quote you give from the Tract, the first word is “Economists”. Keynes is not claiming the Fisher Effect as his own. It is clearly the child of many parents as you point out yourself and by the time Keynes writes the Tract it was a universally accepted notion and its parentage well known and understood. I would suggest it did not need accreditation.

  12. 12 Henry December 4, 2015 at 11:19 am

    Regarding Keynes’s point about whether the inflation rate is the expected inflation rate, Fisher raises the same point on p. 86 of his “The Rate of Interest”. He takes a different view to Keynes and does not take the argument where Keynes goes ( and of course Keynes was writing 20 years later).

    I have to note that both Keynes and Fisher talk about the foreseen and unforeseen rate of inflation. Perhaps there is a subtle difference between that distinction and the expected and unexpected rate of inflation I used in my previous post?

  13. 13 David Glasner December 5, 2015 at 6:57 pm

    Egmont, I will ignore the nastiness and just say that I was not referring to a rate of interest on financial assets but to a real asset that is being held from one period to the next. As Fisher and Keynes both recognized the price ratio between the current and future price of such an asset implicitly determines an own rate of interest. In equilibrium the own rates of all assets adjusted for expected appreciation and carrying costs must be equalized. I agree that every model most involve some simplification; the question is whether the simplification excludes a factor relevant to the analysis. If there is no asset being held from one period to the next other than money, it is impossible to analyze the conditions for asset market equilibrium. Without knowing the conditions for asset market equilibrium you cannot claim to have proved anything about the rate of interest. You write a lot, which is quite admirable, but if having a conversation with you is conditional on my reading the papers you have posted on SSRN, we might as well stop at this point.

    Henry, Everyone has a right to change his mind, and I certainly don’t agree with everything I have written in the past, perhaps not even everything I have written on this blog. I think Keynes clearly did dismiss the Fisher effect. “Contemptuously” was probably not the right adverb to use. Perhaps “condescendingly” would have been a better choice. Keynes had a gift for condescension. My point was not that Keynes was claiming credit for the Fisher Effect, just that he seemed to accept it without any reservation. When he criticized it in the GT, he specifically linked it to Fisher. I didn’t suggest that Keynes was making exactly the same point as Fisher, just that he was applying Fisher’s method and logic to a different, but similar, problem.

  14. 14 Egmont Kakarot-Handtke December 7, 2015 at 8:34 am

    Comment on David Glasner of Dec 5

    Let us agree that the Fisher effect is about (i) the difference between nominal and real interest rates and (ii) that there are many real interest rates because there are many types of real assets.

    Here is the Wikipedia* definition of the Fisher effect: “…the Fisher effect is the proposition by Irving Fisher that the real interest rate is independent of monetary measures, specifically the nominal interest rate and the expected inflation rate. The term “nominal interest rate” refers to the actual interest rate giving the amount by which a number of dollars or other unit of currency owed by a borrower to a lender grows over time; the term “real interest rate” refers to the amount by which the purchasing power of those dollars grows over time — that is, the real interest rate is the nominal interest rate adjusted for the effect of inflation on the purchasing power of the loan proceeds.

    The relation between the nominal and real rates is given by the Fisher equation, which states … that the real interest rate equals the nominal interest rate minus the expected inflation rate.”

    In my example the lender rate, the borrower rate and the price of the consumption good appears. What I have shown is that in a well-designed monetary order the rate of interest is constant, no matter what the rate of inflation/deflation is. This means that the concept of expected inflation falls flat and with it the distinction between nominal and real interest rate. Therefore, the Fisher equation as a whole falls flat.

    Your answer of Dec 3 is that my example is irrelevant because the expected future price has no effect. False. My example is relevant because it shows that the Fisher equation describes a freak phenomenon that appears because of a flaw in the monetary order.

    Now, if there is something fundamentally wrong with the Fisher equation there is no need to go further and to look deeper into the concept of own rates of various real assets.

    What seems to be pretty obvious is that neither Fisher nor Keynes got the fundamental economic relationship right. This refers to interest rate/inflation, interest/profit, and profit/income. So there is no need for a lengthy elaboration of the finer points of their confusion.

    I agree, let things stay where they stay at the moment. It is certainly much more rewarding to go beyond refuted concepts and authors.

    Egmont Kakarot-Handtke

    * https://en.wikipedia.org/wiki/Fisher_hypothesis


  1. 1 Links for 12-01-15 | Economics Blogs Trackback on December 1, 2015 at 12:11 am
  2. 2 Keynes on the Theory of the Rate of Interest | Uneasy Money Trackback on December 18, 2015 at 10:10 am

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. 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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