Archive for the 'Fisher effect' Category

In the General Theory Keynes First Trashed and then Restated the Fisher Equation

I am sorry to have gone on a rather extended hiatus from posting, but I have been struggling to come up with a new draft of a working paper (“The Fisher Effect under Deflationary Expectations“) I wrote with the encouragement of Scott Sumner in 2010 and posted on SSRN in 2011 not too long before I started blogging. Aside from a generous mention of the paper by Scott on his blog, Paul Krugman picked up on it and wrote about it on his blog as well. Because the empirical work was too cursory, I have been trying to update the results and upgrade the techniques. In working on a new draft of my paper, I also hit upon a simple proof of a point that I believe I discovered several years ago: that in the General Theory Keynes criticized Fisher’s distinction between the real and nominal rates of interest even though he used exactly analogous reasoning in his famous theorem on covered interest parity in the forward exchange market and in his discussion of liquidity preference in chapter 17 of the General Theory. So I included a section making that point in the new draft of my paper, which I am reproducing here. Eventually, I hope to write a paper exploring more deeply Keynes’s apparently contradictory thinking on the Fisher equation. Herewith is an excerpt from my paper.

One of the puzzles of Keynes’s General Theory is his criticism of the Fisher equation.

This is the truth which lies behind Professor Irving Fisher’ss theory of what he originally called “Appreciation and Interest” – the  distinction between the money rate of interest and the real rate of interest where the latter is equal to the former after correction for changes in the value of money. It is difficult to make sense of this theory as stated, because it is not clear whether the change in the value of money is or is not assumed to be foreseen. There is no escape from the dilemma that, if it is not foreseen, there will be no effect on current affairs; whilst, if it is foreseen, the prices of existing goods will be forthwith so adjusted that the advantages of holding money and of holding goods are again equalized, and it will be too late for holders of money to gain or to suffer a change in the rate of interest which will offset the prospective change during the period of the loan in the value of money lent. . . .

The mistake lies in supposing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital. The prices of existing assets will always adjust themselves to changes in expectation concerning the prospective value of money. The significance of such changes in expectation lies in their effect on the readiness to produce new assets through their reaction on the marginal efficiency of capital. The stimulating effect of the expectation of higher prices is due, not to its raising the rate of interest (that would be a paradoxical way of stimulating output – in so far as the rate of interest rises, the stimulating effect is to that extent offset), but to its raising the marginal efficiency of a given stock of capital. (pp. 142-43)

As if the problem of understanding that criticism were not enough, the problem is further compounded by the fact that one of Keynes’s most important pre-General Theory contributions, his theorem about covered interest parity in his Tract on Monetary Reform seems like a straightforward application of the Fisher equation. According to his covered-interest-parity theorem, in equilibrium, the difference between interest rates quoted in terms of two different currencies will be just enough to equalize borrowing costs in either currency given the anticipated change in the exchange rate between the two currencies over reflected in the market for forward exchange as far into the future as the duration of the loan.

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 comparison. If by lending dollars in New York for one month the lender could earn interest at the rate of 5-1/2 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 in London is wholly explained. That is to say, forward quotations for the purchase of the currency of the dearer money market tend to be cheaper than the 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. (p. 125)

And as if that self-contradiction not enough, Keynes’s own exposition of the idea of liquidity preference in chapter 17 of the General Theory extends the basic idea of the Fisher equation that expected rates of return from holding different assets must be accounted for in a way that equalizes the expected return from holding any asset. At least formally, it can be shown that the own-interest-rate analysis in chapter 17 of the General Theory explaining how the liquidity premium affects the relative yields of money and alternative assets can be translated into a form that is equivalent to the Fisher equation.

In explaining the factors affecting the expected yields from alternative assets now being held into the future, Keynes lists three classes of return from holding assets: (1) the expected physical real yield (q) (i.e., the ex ante real rate of interest or Fisher’s real rate) from holding an asset, including either or both a flow of physical services or real output or real appreciation; (2) the expected service flow from holding an easily marketable assets generates liquidity services or a liquidity premium (l); and (3) wastage in the asset or a carrying cost (c). Keynes specifies the following equilibrium condition for asset holding: if assets are held into the future, the expected overall return from holding every asset including all service flows, carrying costs, and expected appreciation or depreciation, must be equalized.

[T]he total return expected from the ownership of an asset over a period is equal to its yield minus its carrying cost plus its liquidity premium, i.e., to q c + l. That is to say, q c + l is the own rate of interest of any commodity, where q, c, and l are measured in terms of itself as the standard. (Keynes 1936, p. 226)

Thus, every asset that is held, including money, must generate a return including the liquidity premium l, after subtracting of the carrying cost c. Thus, a standard real asset with zero carrying cost will be expected to generate a return equal to q (= r). For money to be held, at the margin, it must also generate a return equal to q net of its carrying cost, c. In other words, q = lc.

But in equilibrium, the nominal rate of interest must equal the liquidity premium, because if the liquidity premium (at the margin) generated by money exceeds the nominal interest rate, holders of debt instruments returning the nominal rate will convert those instruments into cash, thereby deriving liquidity services in excess of the foregone interest from the debt instruments. Similarly, the carrying cost of holding money is the expected depreciation in the value of money incurred by holding money, which corresponds to expected inflation. Thus, substituting the nominal interest rate for the liquidity premium, and expected inflation for the carrying cost of money, we can rewrite the Keynes equilibrium condition for money to be held in equilibrium as q = r = ipe. But this equation is identical to the Fisher equation: i = r + pe.

Keynes’s version of the Fisher equation makes it obvious that the disequilibrium dynamics that are associated with changes in expected inflation can be triggered not only by decreased inflation expectations but by an increase in the liquidity premium generated by money, and especially if expected inflation falls and the liquidity premium rises simultaneously, as was likely the case during the 2008 financial crisis.

I will not offer a detailed explanation here of the basis on which Keynes criticized the Fisher equation in the General Theory despite having applied the same idea in the Tract on Monetary Reform and restating the same underlying idea some 80 pages later in the General Theory itself. But the basic point is simply this: the seeming contradiction can be rationalized by distinguishing between the Fisher equation as a proposition about a static equilibrium relationship and the Fisher equation as a proposition about the actual adjustment process occasioned by a parametric expectational change. While Keynes clearly did accept the Fisher equation in an equilibrium setting, he did not believe the real interest rate to be uniquely determined by real forces and so he didn’t accept its the invariance of the real interest rate with respect to changes in expected inflation in the Fisher equation. Nevertheless it is stunning that Keynes could have committed such a blatant, if only superficial, self-contradiction without remarking upon it.


Keynes on the Theory of the Rate of Interest

I have been writing recently about Keynes and his theory of the rate of interest (here, here, here, and here). Perhaps unjustly – but perhaps not — I attribute to him a theory in which the rate of interest is determined exclusively by monetary forces: the interaction of the liquidity preference of the public with the policy of the monetary authorities. In other words, the rate of interest, at least as an approximation, can be modeled in terms of a single market for holding money, the demand to hold money reflecting the liquidity preference of the public and the stock of money being directly controlled by the monetary authority. Because liquidity preference is a function of the rate of interest, the rate of interest adjusts until the stock of money made available by the monetary authority is held willingly by the public.

I have been struggling with Keynes’s liquidity preference theory of interest, which evidently led him to deny the Fisher effect, thus denying that there is a margin of substitution between holding money and holding real assets, because he explicitly recognizes in Chapter 17 of the General Theory that there is a margin of substitution between money and real assets, the expected net returns from holding all assets (including expected appreciation and the net service flows generated by the assets) being equal in equilibrium. And it was that logic which led Keynes to one of his most important pre-General Theory contributions — the covered-interest-arbitrage theorem in chapter 3 of his Tract on Monetary Reform. The equality of expected returns on all assets was the key to Irving Fisher’s 1896 derivation of the Fisher Effect in Appreciation and Interest, restated in 1907 in The Rate of Interest, and in 1930 in The Theory of Interest.

Fisher never asserted that there is complete adjustment of nominal interest rates to expected inflation, actually providing empirical evidence that the adjustment of nominal rates to inflation was only partial, but he did show that in equilibrium a difference in the expected rate of appreciation between alternative assets must correspond to differences in the rates of interest on loans contracted in terms of the two assets. Now there is a difference between the static relationship between the interest rates for two loans contracted in terms of two different assets and a dynamic adjustment in time to a change in the expected rate of appreciation or depreciation of a given asset. The dynamic adjustment does not necessarily coincide with the static relationship.

It is also interesting, as I pointed out in a recent post, that when criticizing the orthodox theory of the rate of interest in the General Theory, Keynes focused not on Fisher, but on his teacher Alfred Marshall as the authoritative representative of the orthodox theory of interest, criticizing Fisher only for the Fisher effect. Keynes reserved is comprehensive criticism for Marshall, attributing to Marshall the notion that rate of interest adjusts to equalize savings and investment. Keynes acknowledged that he could not find textual support in Marshall’s writings for this idea, merely citing his own prior belief that the rate of interest performs that function, consequently attributing a similar belief to Marshall. But even if Marshall did mistakenly believe that the rate of interest adjusts to equalize savings and investment, it does not follow that the orthodox theory of interest is wrong; it just means that Marshall had a defective understanding of the theory. Just because most physicists in the 18th century believed in the phlogiston theory of fire does not prove that classical physics was wrong; it only means that classical physicists had an imperfect understanding of the theory. And if Keynes wanted to establish the content of the most authoritative version of the orthodox theory of interest, he should have been citing Fisher not Marshall.

That is why I wanted to have a look at a not very well known paper by Keynes called “The Theory of the Rate of Interest,” written for a 1937 festschrift in honor of Irving Fisher, The Lessons of Monetary Experience. Keynes began the paper with the following footnote attached to the title acknowledging Fisher as the outstanding authority on the orthodox theory of interest.

I have thought it suitable to offer a short note on this subject in honor of Irving Fisher, since his earliest [presumably Appreciation and Interest, Fisher’s doctoral dissertation] and latest [presumably The Theory of Interest] have been concerned with it, and since during the whole of the thirty years that I have been studying economics he has been the outstanding authority on this problem. (p. 145)

The paper is mostly devoted to spelling out and discussing six propositions that Keynes believes distill the essentials of the orthodox theory of interest. The first four of these propositions Keynes regards as unassailable, but the last two, he maintains, reflect very special, empirically false, assumptions. He therefore replaces them with two substitute propositions, whose implications differ radically from those of orthodox theory. Here are the first four propositions.

1 Interest on money means precisely what the books on arithmetic say it means. . . . [I]t is simply the premium obtainable on current cash over deferred cash, so that it measures the marginal preference . . . for holding cash in hand over cash for deferred delivery. No one would pay this premium unless the possession of cash served some purpose, i.e., has some efficiency. Thus, we can conveniently say that interest on money measures the marginal efficiency of money in terms of itself as a unit.

2 Money is not peculiar in having a marginal efficiency measured in terms of itself. . . . [N]ormally capital assets of all kinds have a positive marginal efficiency measured in terms of themselves. If we know the relation between the present and expected prices of an asset in terms of money we can convert the measure of its marginal efficiency into a measure of its marginal efficiency in terms of money by means of a formula which I have given in my General Theory, p. 227.

3 The effort to obtain the best advantage from the possession of wealth will set up a tendency for capital assets to exchange in equilibrium, at values proportional to their marginal efficiencies in terms of a common unit. . . . [I]f r is the money rate of interest . . . and y is the marginal efficiency of a capital asset A in terms of money, then A will exchange in terms of money at a price such as to make y = r.

4 If the demand price of our capital asset A . . . is not less than its replacement cost, new investment in A will take place, the scale of such investment depending on the capacity available for the production of A, i.e., on its elasticity of supply, and on the rate at which y, its marginal efficiency, declines as the amount of new investment in A increases. At a scale of new investment at which the marginal cost of producing A is equal to its demand price as above, we have a position of equilibrium. Thus the price system resulting from the relationships between the marginal efficiencies of different capital assets including money, measured in terms of a common unit, determines the aggregate rate of investment. (p. 145-46)

Keynes sums up the import of his first four propositions as follows:

These proposition are not . . . inconsistent with the orthodox theory . . . or open to doubt. They establish that relative prices . . . and the scale of output move until the marginal efficiencies of all kinds of assets are equal when measured in a common unit and . . . that the marginal efficiency of capital is equal to the rate of interest. But they tell us nothing as to the forces which determine what this common level of marginal efficiency will tend to be. It is when we proceed to this further discussion that my argument diverges from the orthodox argument.

Here is how Keynes describes the divergence between the orthodox theory and his theory:

[T]he orthodox theory maintains that the forces which determine the common value of the marginal efficiency of various assets are independent of money, which has . . . no autonomous influence, and that prices move until the marginal efficiency of money, i.e., the rate of interest, falls into line with the common value of the marginal efficiency of other assets as determined by other forces. My theory . . . maintains that this is a special case and that over a wide range of possible cases almost the opposite is true, namely, that the marginal efficiency of money is determined by forces partly appropriate to itself, and that prices move until the marginal efficiency of other assets fall into line with the rate of interest. (p. 147)

I find Keynes’s description of the difference between the orthodox theory and his own both insightful and problematic. Keynes notes correctly that the orthodox theory, abstracting from all monetary influences, treats the rate of interest as a rate of intertemporal exchange, applicable to exchange between any asset today and any asset in the future, adjusted for differences in rates of appreciation, and in net service flows, across assets. So Keynes was right: the orthodox theory is a special case, corresponding to the special assumptions required for full intertemporal equilibrium. And Keynes was right to emphasize the limitations of the orthodox theory.

But while drawing a sharp contrast between his theory and the orthodox theory (“over a wide range of possible cases almost the opposite is true”), Keynes, to qualify his disagreement, deploys the italicized (by me) weasel words, but without explaining how his seemingly flat rejection of the orthodox theory requires qualification. It is certainly reasonable to say “that the marginal efficiency of capital is determined by forces partly appropriate to itself.” But I don’t see how it follows from that premise “that prices move until the marginal efficiency of other assets fall into line with the rate of interest.” Equilibrium is reached when marginal efficiencies (adjusted for differences in expected rates of appreciation and in net services flows) of all assets are equal, but rejecting the orthodox notion that the marginal efficiency of money adjusts to the common marginal efficiency of all other assets does not establish that the causality is reversed: that the marginal efficiencies of all non-money assets must adjust to whatever the marginal efficiency of money happens to be. The reverse causality also seems like a special case; the general case, it would seem, would be one in which causality could operate, depending on circumstances, in either direction or both directions. An argument about the direction of causality would have been appropriate, but none is made. Keynes just moves on to propositions 5 and 6.

5 The marginal efficiency of money in terms of itself has the peculiarity that it is independent of its quantity. . . . This is a consequence of the Quantity Theory of Money . . . Thus, unless we import considerations from outside, the money rate of interest is indeterminate, for the demand schedule for money is a function solely of its supply [sic, presumably Keynes meant to say “quantity”]. Nevertheless, a determinate value for r can be derived from the condition that the value of an asset A, of which the marginal efficiency in terms of money is y, must be such that y = r. For provided that we know the scale of investment, we know y and the value of A, and hence we can deduce r. In other words, the rate of interest depends on the marginal efficiency of capital assets other than money. This must, however, be supplemented by another proposition; for it requires that we should already know the scale of investment. (p. 147-48)

I pause here, because I am confused. Keynes alludes to the proposition that the neutrality of money implies that any nominal interest rate is compatible with any real interest rate provided that the rate of inflation is correctly anticipated, though without articulating the proposition correctly. Despite getting off to a shaky start with a sloppy allusion to the Fisher effect, Keynes is right in observing that the neutrality of money and the independence of the real rate of interest from monetary factors are extreme assumptions. Given that monetary neutrality is consistent with any nominal interest rate, Keynes then tries to show how the orthodox theory pins down the nominal interest rate. And his attempt does not seem successful; he asserts that the money rate of interest can be deduced from the marginal efficiency of some capital asset A in terms of money. But that marginal efficiency cannot be deduced without knowledge, or an expectation, of the future value of the asset. Instead of couching his analysis in terms of the current and (expected) future values of the asset, i.e., instead of following Fisher’s 1896 own-rate analysis, Keynes brings up the scale of investment in A: “This must . . . be supplemented by another proposition; for it requires that we should already know the scale of investment.” Aside from not knowing what “this” and “it” are referring to, I don’t understand how the scale of investment is relevant to a determination of the marginal efficiency of the capital asset in question.

Now for Keynes’s final proposition:

6 The scale of investment will not reach its equilibrium level until the point is reached at which the elasticity of supply of output as a whole has fallen to zero. (p. 148)

The puzzle only deepens here because proposition 5 is referring to the scale of investment in a particular asset A while proposition 6 seems to be referring to the scale of investment in the aggregate. It is neither a necessary nor a sufficient condition for an equilibrium scale of investment in a particular capital asset to obtain that the elasticity of supply of output as a whole be zero. So the connection between propositions 5 and 6 seems tenuous and superficial. Does Keynes mean to say that, according to orthodox theory, the equality of advantage to asset holders between different kinds of assets cannot be achieved unless the elasticity of supply for output as a whole is zero? Keynes then offers a synthetic restatement of orthodox theory.

The equilibrium rate of aggregate investment, corresponding to the level of output for a further increase in which the elasticity of supply is zero, depends on the readiness of the public to save. But this in turn depends on the rate of interest. Thus for each level of the rate of interest we have a given quantity of saving. This quantity of saving determines the scale of investment. The scale of investment settles the marginal efficiency of capital, to which the rate of interest must be equal. Our system is therefore determinate. To each possible value of the rate of interest there corresponds a given volume of saving; and to each possible value of the marginal efficiency of capital there corresponds a given volume of investment. Now the rate of interest and the marginal efficiency of capital must be equal. Thus the position of equilibrium is given by that common value of the rate of interest and of the marginal efficiency of capital at which saving determined by the former is equal to the investment determined by the latter. (Id.)

This restatement of orthodox theory is remarkably disconnected from the six propositions that Keynes has just identified as the bedrock of the orthodox theory of interest. The word “saving” or “save” is not even mentioned in any of Keynes’s six propositions, so the notion that the orthodox theory asserts that the rate of interest adjusts to equalize saving and investment is inconsistent with his own rendering of the orthodox theory. The rhetorical point that Keynes seems to be making in the form of a strictly analytical discussion is that the orthodox theory held that the equilibrium of an economic system occurs at the rate of interest that equalizes savings and investment at a level of output and income consistent with full employment. Where Keynes was misguided was in characterizing the mechanism by which this equilibrium is reached as an adjustment in the nominal rate of interest. A full equilibrium is achieved by way of a vector of prices (and expected prices) consistent with equilibrium, the rate of interest being implicit in the intertemporal structure of a price vector. Keynes was working with a simplistic misconception of what the rate of interest actually represents and how it affects economic activity.

In place of propositions 5 and 6, which Keynes dismisses as special factual assumptions, he proposes two alternative propositions:

5* The marginal efficiency of money in terms of itself is . . . a function of its quantity (though not of its quantity alone), just as in the case of capital assets.

6* Aggregate investment may reach its equilibrium rate under proposition (4) above, before the elasticity of supply of output as a whole has fallen to zero. (Id.)

So in substituting 5* for 5, all Keynes did was discard a proposition that few if any economists — certainly not Fisher — upholding the orthodox theory ever would have accepted as a factual assertion. The two paragraphs that Keynes devotes to refuting proposition 5 can be safely ignored at almost zero cost. Turning to proposition 6, Keynes restates it as follows:

A zero elasticity of supply for output as a whole means that an increase of demand in terms of money will lead to no change in output; that is to say, prices will rise in the same proportion as the money demand [i.e., nominal aggregate demand, not the demand to hold money] rises. Inflation will have no effect on output or employment, but only on prices. (pp. 149-50)

So, propositions 5 and 6 turn out to be equivalent assertions that money is neutral. Having devoted two separate propositions to identify the orthodox theory of interest with the idea that money is neutral, Keynes spells out the lessons he draws from his reconstruction of the orthodox theory of the rate of interest.

If I am right, the orthodox theory is wholly inapplicable to such problems as those of unemployment and the trade cycle, or, indeed, to any of the day-to-day problems of ordinary life. Nevertheless it is often in fact applied to such problems. . . .

It leads to considerable difficulties to regard the marginal efficiency of money as wholly different in character from the marginal efficiency of other assets. Equilibrium requires . . . that the prices of different kinds of assets measured in the same unit move until their marginal efficiencies measured in that unit are equal. But if the marginal efficiency of money in terms of itself is always equal to the marginal efficiency of other assets, irrespective of the price of the latter, the whole price system in terms of money becomes indeterminate. (150-52)

Keynes is attacking a strawman here, because, even given the extreme assumptions about the neutrality of money that hardly anyone – and certainly not Fisher – accepted as factual, the equality between the marginal efficiency of money and the marginal efficiency of other assets is an equilibrium condition, not an identity, so the charge of indeterminacy is mistaken, as Keynes himself unwittingly acknowledges thereafter.

It is the elements of elasticity (a) in the desire to hold inactive balances and (b) in the supply of output as a whole, which permits a reasonable measure of stability in prices. If these elasticities are zero there is a necessity for the whole body of prices and wages to respond immediately to every change in the quantity of money. (p. 152)

So Keynes is acknowledging that the whole price system in terms of money in not indeterminate, just excessively volatile. But let’s hear him out.

This assumes a state of affairs very different from that in which we live. For the two elasticities named above are highly characteristic of the real world; and the assumption that both of them are zero assumes away three-quarters of the problems in which we are interested. (Id.)

Undoubtedly true, but neither Fisher nor most other economists who accepted the orthodox theory of the rate of interest believed either that money is always neutral or that we live in a world of perpetually full employment. Nor did Keynes show that the theoretical resources of orthodox theory were insufficient to analyze situations of less than full employment. The most obvious example of such an analysis, of course, is one in which a restrictive monetary policy, by creating an excess demand for money, raises the liquidity premium, causing the marginal efficiency of money to exceed the marginal efficiency of other assets, in which case asset prices must fall to restore the equality between the marginal efficiencies of assets and of money.

In principle, the adjustment might be relatively smooth, but if the fall of asset prices triggers bankruptcies or other forms of financial distress, and if the increase in interest rates affects spending flows, the fall in asset prices and in spending flows may become cumulative causing a general downward spiral in income and output. Such an analysis is entirely compatible with orthodox theory even if the orthodox theory, in its emphasis on equilibrium, seems very far removed from the messy dynamic adjustment associated with a sudden increase in liquidity preference.

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)


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.

Bernanke’s Continuing Confusion about How Monetary Policy Works

TravisV recently posted a comment on this blog with a link to his comment on Scott Sumner’s blog flagging two apparently contradictory rationales for the Fed’s quantitative easing policy in chapter 19 of Ben Bernanke’s new book in which he demurely takes credit for saving Western Civilization. Here are the two quotes from Bernanke:

1              Our goal was to bring down longer-term interest rates, such as the rates on thirty-year mortgages and corporate bonds. If we could do that, we might stimulate spending—on housing and business capital investment, for example…..Similarly, when we bought longer-term Treasury securities, such as a note maturing in ten years, the yields on those securities tended to decline.

2              A new era of monetary policy activism had arrived, and our announcement had powerful effects. Between the day before the meeting and the end of the year, the Dow would rise more than 3,000 points—more than 40 percent—to 10,428. Longer-term interest rates fell on our announcement, with the yield on ten-year Treasury securities dropping from about 3 percent to about 2.5 percent in one day, a very large move. Over the summer, longer-term yields would reverse and rise to above 4 percent. We would see that increase as a sign of success. Higher yields suggested that investors were expecting both more growth and higher inflation, consistent with our goal of economic revival. Indeed, after four quarters of contraction, revised data would show that the economy would grow at a 1.3 percent rate in the third quarter and a 3.9 percent rate in the fourth.

Over my four years of blogging — especially the first two – I have written a number of posts pointing out that the Fed’s articulated rationale for its quantitative easing – the one expressed in quote number 1 above: that quantitative easing would reduce long-term interest rates and stimulate the economy by promoting investment – was largely irrelevant, because the magnitude of the effect would be far too small to have any noticeable macroeconomic effect.

In making this argument, Bernanke bought into one of the few propositions shared by both Keynes and the Austrians: that monetary policy is effective by operating on long-term interest rates, and that significant investments by business in plant and equipment are responsive to relatively small changes in long-term rates. Keynes, at any rate, had the good sense to realize that long-term investment in plant and equipment is not very responsive to changes in long-term interest rates – a view he had espoused in his Treatise on Money before emphasizing, in the General Theory, expectations about future prices and profitability as the key factor governing investment. Austrians, however, never gave up their theoretical preoccupation with the idea that the entire structural profile of a modern economy is dominated by small changes in the long-term rate of interest.

So for Bernanke’s theory of how QE would be effective to be internally consistent, he would have had to buy into a hyper-Austrian view of how the economy works, which he obviously doesn’t and never did. Sometimes internal inconsistency can be a sign that being misled by bad theory hasn’t overwhelmed a person’s good judgment. So I say even though he botched the theory, give Bernanke credit for his good judgment. Unfortunately, Bernanke’s confusion made it impossible for him to communicate a coherent story about how monetary policy, undermining, or at least compromising, his ability to build popular support for the policy.

Of course the problem was even deeper than expecting a marginal reduction in long-term interest rates to have any effect on the economy. The Fed’s refusal to budge from its two-percent inflation target, drastically limited the potential stimulus that monetary policy could provide.

I might add that I just noticed that I had already drawn attention to Bernanke’s inconsistent rationale for adopting QE in my paper “The Fisher Effect Under Deflationary Expectations” written before I started this blog, which both Scott Sumner and Paul Krugman plugged after I posted it on SSRN.

Here’s what I said in my paper (p. 18):

If so, the expressed rationale for the Fed’s quantitative easing policy (Bernanke 2010), namely to reduce long term interest rates, thereby stimulating spending on investment and consumption, reflects a misapprehension of the mechanism by which the policy would be most likely to operate, increasing expectations of both inflation and future profitability and, hence, of the cash flows derived from real assets, causing asset values to rise in step with both inflation expectations and real interest rates. Rather than a policy to reduce interest rates, quantitative easing appears to be a policy for increasing interest rates, though only as a consequence of increasing expected future prices and cash flows.

I wrote that almost five years ago, and it still seems pretty much on the mark.

Is John Cochrane Really an (Irving) Fisherian?

I’m pretty late getting to this Wall Street Journal op-ed by John Cochrane (here’s an ungated version), and Noah Smith has already given it an admirable working over, but, even after Noah Smith, there’s an assertion or two by Cochrane that could use a bit of elucidation. Like this one:

Keynesians told us that once interest rates got stuck at or near zero, economies would fall into a deflationary spiral. Deflation would lower demand, causing more deflation, and so on.

Noah seems to think this is a good point, but I guess that I am less easily impressed than Noah. Feeling no need to provide citations for the views he attributes to Keynesians, Cochrane does not bother either to tell us which Keynesian has asserted that the zero lower bound creates the danger of a deflationary spiral, though in a previous blog post, Cochrane does provide a number of statements by Paul Krugman (who I guess qualifies as the default representative of all Keynesians) about the danger of a deflationary spiral. Interestingly all but one of these quotations were from 2009 when, in the wake of the fall 2008 financial crisis, a nasty little relapse in early 2009 having driven the stock market to a 12-year low, the Fed finally launched its first round of quantitative easing, the threat of a deflationary spiral did not seem at all remote.

Now an internet search shows that Krugman does have a model showing that a downward deflationary spiral is possible at the zero lower bound. I would just note, for the record, that Earl Thompson, in an unpublished 1976 paper, derived a similar result from an aggregate model based on a neo-classical aggregate production function with the Keynesian expenditure functions (through application of Walras’s Law) excluded. So what’s Keynes got to do with it?

But even more remarkable is that the most famous model of a deflationary downward spiral was constructed not by a Keynesian, but by the grandfather of modern Monetarism, Irving Fisher, in his famous 1933 paper on debt deflation, “The Debt-Deflation Theory of Great Depressions.” So the suggestion that there is something uniquely Keynesian about a downward deflationary spiral at the zero lower bound is simply not credible.

Cochrane also believes that because inflation has stabilized at very low levels, slow growth cannot be blamed on insufficient aggregate demand.

Zero interest rates and low inflation turn out to be quite a stable state, even in Japan. Yes, Japan is growing more slowly than one might wish, but with 3.5% unemployment and no deflationary spiral, it’s hard to blame slow growth on lack of “demand.”

Except that, since 2009 when the threat of a downward deflationary spiral seemed more visibly on the horizon than it does now, Krugman has consistently argued that, at the zero lower bound, chronic stagnation and underemployment are perfectly capable of coexisting with a positive rate of inflation. So it’s not clear why Cochrane thinks the coincidence of low inflation and sluggish economic growth for five years since the end of the 2008-09 downturn somehow refutes Krugman’s diagnosis of what has been ailing the economy in recent years.

And, again, what’s even more interesting is that the proposition that there can be insufficient aggregate demand, even with positive inflation, follows directly from the Fisher equation, of which Cochrane claims to be a fervent devotee. After all, if the real rate of interest is negative, then the Fisher equation tells us that the equilibrium expected rate of inflation cannot be less than the absolute value of the real rate of interest. So if, at the zero lower bound, the real rate of interest is minus 1%, then the equilibrium expected rate of inflation is 1%, and if the actual rate of inflation equals the equilibrium expected rate, then the economy, even if it is operating at less than full employment and less than its potential output, may be in a state of macroeconomic equilibrium. And it may not be possible to escape from that low-level equilibrium and increase output and employment without a burst of unexpected inflation, providing a self-sustaining stimulus to economic growth, thereby moving the economy to a higher-level equilibrium with a higher real rate of interest than the rate corresponding to lower-level equilibrium. If I am not mistaken, Roger Farmer has been making an argument along these lines.

Given the close correspondence between the Keynesian and Fisherian analyses of what happens in the neighborhood of the zero lower bound, I am really curious to know what part of the Fisherian analysis Cochrane finds difficult to comprehend.

Hawtrey’s Good and Bad Trade, Part X: Financial Crises and Asset Crashes

After presenting his account of an endogenous cycle in chapters 14 and 15, Hawtrey focuses more specifically in chapter 16 on the phenomenon of a financial crisis, which he considers to be fundamentally a cyclical phenomenon arising because the monetary response to inflation is sharp and sudden rather than gradual. As Hawtrey puts it:

It is not easy to say precisely what constitutes a financial crisis, but broadly it may be defined to be an escape from inflation by way of widespread failures and bankruptcies instead of by a gradual reduction of credit money. (p. 201)

Hawtrey’s focus in his discussion of financial crises is on the investment in fixed capital, having already discussed the role of inventory investment by merchants and traders in his earlier explanation of how variations in the lending rates of the banking system can lead to cumulative expansions or contractions through variations in the desired holdings of inventories by traders and merchants. New investments in fixed capital are financed, according to Hawtrey, largely out of the savings of the wealthy, which are highly pro-cyclical. The demand for new investment projects by businesses is also pro-cyclical, depending on the expected profit of businesses from installing new capital assets, the expected profit, in turn, depending on the current effective demand.

The financing for new long-term investment projects is largely channeled to existing businesses through what Hawtrey calls the investment market, the most important element of which is the stock exchange. The stock exchange functions efficiently only because there are specialists whose business it is to hold inventories of various stocks, being prepared to buy those stocks from those wishing to sell them or sell those stock to those wishing to buy them, at prices that seem at any moment to be market-clearing, i.e, at prices that keep buy and sell orders roughly in balance. The specialists, like other traders and middlemen, finance their holdings of inventories by borrowing from banks, using the proceeds from purchases and sales – corresponding to the bid-ask spread  – to repay their indebtedness to the banks. Unlike commercial traders and merchants, the turnover of whose inventories is relatively predictable with little likelihood of large price swings, and can obtain short-term financing for a fixed term, stock dealers hold inventories that are not very predictable in their price and turnover, and therefore can obtain financing only on a day to day basis, or “at call.” The securities held by the stock dealer serves as collateral for the loan, and banks require the dealer to hold securities with a value exceeding some minimum percentage (margin) of the dealer’s indebtedness to the bank.

New investment financed by the issue of stock must ultimately be purchased by savers who are seeking profitable investment opportunities into which to commit their savings. Existing firms may sometimes finance new projects by issuing new stock, but more often they issue debt or retained earnings to finance investment. Debt financing can be obtained by issuing bonds or preferred stock or by borrowing from banks. New issues of stock have to be underwritten and marketed through middlemen who expect to earn a return on their underwriting or marketing function and must have financing resources sufficient to bear risk of holding a large stock of securities until they are sold to the public.

Now at a time of expanding trade and growing inflation, when there is a general expectation of high profits and at the same time there is a flood of savings seeking investment, an underwriter’s business yields a good profit at very little risk. But at the critical moment when the banks are compelled to intervene to reduce the inflation this is changed. There is a sudden diminution of profits which simultaneously checks the accumulation of savings and dispels the expectation of high profits. An underwriter may find that the diminution of savings upsets his calculations and leaves on his hands a quantity of securities for which before the tide turned he could have found a ready market and that the prospect of disposing of these securities grows less and less with the steady shrinkage in the demand for investments and the falling prospect of high dividends. . . . (pp. 210-11)

It will be seen, then, that of all the borrowers from the bans those who borrow for the purposes of the investment market are the most liable to failure when the period of good trade comes to an end. And as it happens, it is they who are most at the mercy of the banks in times of trouble. For it is their habit to borrow from day to day, and the bans, since they cannot call in loans to traders which will only mature after several weeks or months, are apt to try to reduce an excess of credit money by refusing to lend from day to day. If that happens, the investment market will suddenly have to find the money which the banks want. The total amount of ready money in the hands of the whole investment market will probably be quite small, and, except in so far as they can persuade the bans to wait (in consideration probably of a high rate of interest), they must raise money by selling securities. But there are limits to the amount that can be raised in this way. The demand for investments is very inelastic. The money offered at any time is ordinarily simply the amount of accumulated savings of the community till then uninvested. This total can only be added to by people investing sums which they would otherwise leave as part of their working balances of money, and they cannot be induced to increase their investments very much in this way, however low the price in proportion to the yield of the securities offered. Consequently when the banks curtail the accommodation which they give to the investment market and the investment market tries to raise money by selling securities, the prices of securities may fall heavily without attracting much additional money. Meanwhile the general fall in the prices of securities will undermine the position of the entire investment market, since the value of the assets held against their liabilities to the banks will be depreciated. If the banks insist on payment in such circumstances a multitude of failures on the Stock Exchange and in the investment market must follow. The knowledge of this will deter the banks from making the last turn of the screw if they can help it. But it may be that the banks themselves are acting under dire necessity. If they have let the creation of credit get beyond their control, if they are on the point of running short of the legal tender money necessary to meet the daily demands upon them, they must have no alternative but to insist on payment. When the collapse comes it is not unlikely that that some of the banks themselves will be dragged down by it. A bank which has suffered heavy losses may be unable any longer to show an excess of assets over liabilities, and if subjected to heavy demands may be unable to borrow to meet them.

The calling in of loans from the investment market enables the banks to reduce the excess of credit money rapidly. The failure of one or more banks, by annihilating the credi money based upon their demand liabilities, hastens the process still more. A crisis therefore has the effect of bringing a trade depression into being with striking suddenness. . . .

It should not escape attention that even in a financial crisis, which is ordinarily regarded as simply a “collapse of credit,” credit only plays a secondary part. The shortage of savings, which curtails the demand for investments, and the excess of credit money, which leads the banks to call in loans, are causes at least as prominent as the impairment of credit. And the impairment of credit itself is not a mere capricious loss of confidence, but is a revised estimate of the profits of commercial enterprises in general, which is based on the palpable facts of the market. The wholesale depreciation of securities at such a time is not due to a vague “distrust” but partly to the plain fact that the money values of the assets which they represent are falling and partly to forced sales necessitated by the sudden demand for money. . . .[T]he crisis dos not originate in distrust. Loss of credit in fact is only a symptom. (pp. 212-14)

Let me now go back to Hawtrey’s discussion in chapter 14 in which he considers the effect of expected inflation or deflation on the rate of interest (i.e., the Fisher effect). This discussion is one of the few, if not the only one, that I have seen that consders the special case in which expected deflation is actually greater than the real (or natural) rate of interest. In my paper “The Fisher Effect Under Deflationary Expectations” I suggested that such a situation would account for a sudden crash of asset values such as occurred in September and October of 2008.

It is in order to counteract the effect of the falling prices that the bankers fix a rate of interest lower than the natural rate by the rate at which prices are believed to be falling. If they fail to do this they will find their business gradually falling off and superfluous stocks of gold accumulating in their vaults. Here may digress for a moment to consider a special case. What if the rate of depreciation of prices is actually greater than the natural rate of interest? If that is so nothing that the bankers can do will make borrowing sufficiently attractive. Business will be revolving in a vicious circle; the dealers unwilling to buy in a falling market, the manufacturers unable to maintain their output in face of ever-diminishing orders, dealers and manufacturers alike cutting down their borrowings in proportion to the decline of business, demand falling in proportion to the shrinkage in credit money, and with the falling demand, the dealers more unwilling to buy than ever. This, which may be called “stagnation” of trade, is of course exceptional, but it deserves our attention in passing.

From the apparent impasse there is one way out – a drastic reduction of money wages. If at any time this step is taken the spell will be broken. Wholesale prices will fall abruptly, the expectation of a further fall will cease, dealers will begin to replenish their stocks, manufacturers to increase their output, dealers and manufacturers alike will borrow again, and the stock of credit money will grow. In fact the profit rate will recover, and will again equal or indeed exceed the natural rate. The market rate, however, will be kept below the profit rate, since in the preceding period of stagnation the bankers’ reserves will have been swollen beyond the necessary proportions, and the bankers will desire to develop their loan and discount business. It should be observed that this phenomenon of stagnation will only be possible where the expected rate of depreciation of prices of commodities happens to be high. As to the precise circumstances in which this will be so, it is difficult to arrive at any very definite conclusion. Dealers will be guided partly by the tendency of prices in the immediate past, partly by what they know of the conditions of production.

A remarkable example of trade stagnation occurred at the end of the period from 1873 to 1897, when there had been a prolonged falling off in the gold supply, and in consequence a continuous fall in prices. The rate of interest in London throughout the period of no less than seven years, ending with 1897, averaged only 1.5 percent, and yet superfluous gold went on accumulating in the vaults of the Bank of England. (pp. 186-87)

It seems that Hawtrey failed to see that the circumstances that he is describing here — an expected rate of deflation that exceeds the real rate of interest — would precipitate a crisis. If prices are expected to fall more rapidly than the expected yield on real capital, then the expected return on holding cash exceeds the expected return on holding real assets. If so, holders of real assets will want to sell their assets in order to hold cash, implying that asset prices must start falling. This is precisely the sort of situation that Hawtrey describes in the passages I quoted above from chapter 16, a crisis precipitated by the reversal of an inflationary credit expansion. Exactly why Hawtrey failed to see that the two processes that he describes in chapter 14 and in chapter 16 are essentially equivalent I am unable to say.

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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