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

moneyrate of interest was 5 per cent, therealrate of interest had actually been negative and equal tominus5.5 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

factof a given rise of prices, but theexpectationof 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 +

abushels at the end,abeing therefore the rate of appreciation of gold in terms of wheat. Let the rate of interest in gold bei, and in wheat bej, and let the principal of the loan beDdollars or its equivalentBbushels. Our alternative contracts are then:For

Ddollars borrowedD+DiorD(1 +i) dollars are due in one yr.For

Bbushels “B+BjorB(1 +j) bushels ” “ “ “ “and our problem is to find the relation between

iandj, which will make theD(1 +i) dollars equal theB(1 +j) bushels.At first,

Ddollars equalsBbushels.At the end of the year

Ddollars equalsB(1 +a) bushelsHence at the end of one year

D(1 +i) dollars equalsB(1 +a) (1 +i) bushelsSince

D(1 +i) dollars is the number of dollars necessary to liquidate the debt, its equivalentB(1 +a) (1 +i) bushels is the number of bushels necessary to liquidate it. But we have already designated this number of bushels byB(1 +j). Our result, therefore, is:At the end of 1 year D(1 + i) dollars equals

B(1 +j) equalsB(1 +a) (1 +i) bushelswhich, after B is canceled, discloses the formula:

1 +

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

j=i+a+iaOr, 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.