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.

Thompson’s Reformulation of Macroeconomic Theory, Part V: A Neoclassical Black Hole

It’s been over three years since I posted the fourth of my four previous installments in this series about Earl Thompson’s unpublished paper “A Reformulation of Macroeconomic Theory,” Thompson’s strictly neoclassical alternative to the standard Keynesian IS-LM model. Given the long hiatus, a short recapitulation seems in order.

The first installment was an introduction summarizing Thompson’s two main criticisms of the Keynesian model: 1) the disconnect between the standard neoclassical marginal productivity theory of production and factor pricing and the Keynesian assertion that labor receives a wage equal to its marginal product, thereby implying the existence of a second scarce factor of production (capital), but with the market for capital services replaced in the IS-LM model by the Keynesian expenditure functions, creating a potential inconsistency between the IS-LM model and a deep property of neoclassical theory; 2) the market for capital services having been excluded from the IS-LM model, the model lacks a variable that equilibrates the choice between holding money or real assets, so that the Keynesian investment function is incompletely specified, the Keynesian equilibrium condition for spending – equality between savings and investment – taking no account of the incentive for capital accumulation or the relationship, explicitly discussed by Keynes, between current investment and the (expected) future price level. Excluding the dependence of the equilibrium rate of spending on (expected) inflation from the IS-LM model renders the model logically incomplete.

The second installment was a discussion of the Hicksian temporary-equilibrium method used by Thompson to rationalize the existence of involuntary unemployment. For Thompson involuntary unemployment means unemployment caused by overly optimistic expectations by workers of wage offers, leading them to mistakenly set reservation wages too high. The key idea of advantage of the temporary-equilibrium method is that it reconciles the convention of allowing a market-clearing price to equilibrate supply and demand with the phenomenon of substantial involuntary unemployment in business-cycle downturns. Because workers have an incentive to withhold their services in order to engage in further job search or job training or leisure, their actual short-run supply of labor services in a given time period is highly elastic at the expected wage. If wage offers are below expectations, workers (mistakenly = involuntarily) choose unemployment, but given those mistaken expectations, the labor market is cleared with the observed wage equilibrating the demand for labor services and supply of labor services. There are clearly problems with this way of modeling the labor market, but it does provide an analytical technique that can account for cyclical fluctuations in unemployment within a standard microeconomic framework.

In the third installment, I showed how Thompson derived his FF curve, representing combinations of price levels and interest rates consistent with (temporary) equilibrium in both factor markets (labor services and capital services) and two versions of the LM curve, representing price levels and interest rates consistent with equilibrium in the money market. The two versions of the LM curve (analogous, but not identical, to the Keynesian LM curve) correspond to different monetary regimes. In what Thompson called the classical case, the price level is fixed by convertibility of output into cash at a fixed exchange rate, with money being supplied by a competitive banking system paying competitive interest on cash balances. The LM curve in this case is vertical at the fixed price level, with any nominal rate of interest being consistent with equilibrium in the money market, inasmuch as the amount of money demanded depends not on the nominal interest rate, but on the difference between the nominal interest rate and the competitively determined interest rate paid on cash. In the modern case, cash is non-interest bearing and supplied monopolistically by the monetary authority, so the LM curve is upward-sloping, with the cost of holding cash rising with the rate of interest, thereby reducing the amount of money demanded and increasing the price level for a given quantity of money supplied by the monetary authority. The solution of the model corresponds to the intersection of the FF and LM curves. For the classical case, the intersection is unique, but in the modern case since both curves are upward sloping, multiple intersections are possible.

The focus of the fourth installment was on setting up a model analogous to the Keynesian model by replacing the market for capital services excluded by Walras’s Law with something similar to the Keynesian expenditure functions (consumption, investment, government spending, etc.). The key point is that the FF and LM curves implicitly define a corresponding CC curve (shown in Figure 4 of the third installment) with the property that, at all points on the CC curve, the excess demand for (supply of) money exactly equals the excess supply of (demand for) labor. Thus, the CC curve represents a stock equilibrium in the market for commodities (i.e., a single consumption/capital good) rather than a flow rate of expenditure and income as represented by the conventional IS curve. But the inconsistency between the upward-sloping CC curve and the downward sloping IS curve reflects the underlying inconsistency between the neoclassical and the Keynesian paradigms.

In this installment, I am going to work through Thompson’s argument about the potential for an unstable equilibrium in the version of his model with an upward-sloping LM curve corresponding to the case in which non-interest bearing money is monopolistically supplied by a central bank. Thompson makes the argument using Figure 5, a phase diagram showing the potential equilibria for such an economy in terms of the FF curve (representing price levels and nominal interest rates consistent with equilibrium in the markets for labor and capital services) and the CC curve (representing price levels and nominal interest rates consistent with equilibrium in the output market).

Thompson_Figure5A phase diagram shows the direction of price adjustment when the economy is not in equilibrium (one of the two points of intersection between the FF and the CC curves). A disequilibrium implies a price change in response to an excess supply or excess demand in some market. All points above and to the left of the FF curve correspond to an excess supply of capital services, implying a falling nominal interest rate; points below and to the right of the FF curve correspond to excess demand for capital services, implying a rising interest rate. Points above and to the left of the CC curve correspond to an excess demand for output, implying a rising price level; points below and to the right of the CC curve correspond to an excess supply of output, implying a falling price level. Points in between the FF and CC curves correspond either to an excess demand for commodities and for capital services, implying a rising price level and a rising nominal interest rate (in the region between the two points of intersection – Eu and Es — between the CC and FF curves) or to an excess supply of both capital services and commodities, implying a falling interest rate and a falling price level (in the regions below the lower intersection Eu and above the upper intersection Es). The arrows in the diagram indicate the direction in which the price level and the nominal interest rate are changing at any point in the diagram.

Given the direction of price change corresponding to points off the CC and FF curves, the upper intersection is shown to be a stable equilibrium, while the lower intersection is unstable. Moreover, the instability corresponding to the lower intersection is very dangerous, because entering the region between the CC and FF curves below Eu means getting sucked into a vicious downward spiral of prices and interest rates that can only be prevented by a policy intervention to shift the CC curve to the right, either directly by way of increased government spending or tax cuts, or indirectly, through monetary policy aimed at raising the price level and expected inflation, shifting the LM curve, and thereby the CC curve, to the right. It’s like stepping off a cliff into a black hole.

Although I have a lot of reservations about the practical relevance of this model as an analytical tool for understanding cyclical fluctuations and counter-cyclical policy, which I plan to discuss in a future post, the model does resonate with me, and it does so especially after my recent posts about the representative-agent modeling strategy in New Classical economics (here, here, and here). Representative-agent models, I argued, are inherently unable to serve as analytical tools in macroeconomics, because their reductionist approach implies that all relevant decision making can be reduced to the optimization of a single agent, insulating the analysis from any interactions between decision-makers. But it is precisely the interaction effects between decision makers that create analytical problems that constitute the subject matter of the discipline or sub-discipline known as macroeconomics. That Robert Lucas has made it his life’s work to annihilate this field of study is a sad commentary on his contribution, Nobel Prize or no Nobel Prize, as an economic theorist.

That is one reason why I regard Thompson’s model, despite its oversimplifications, as important: it is constructed on a highly aggregated, yet strictly neoclassical, foundation, including continuous market-clearing, arriving at the remarkable conclusion that not only is there an unstable equilibrium, but it is at least possible for an economy in the neighborhood of the unstable equilibrium to be caught in a vicious downward deflationary spiral in which falling prices do not restore equilibrium but, instead, suck the economy into a zero-output black hole. That result seems to me to be a major conceptual breakthrough, showing that the strict rationality assumptions of neoclassical theory can lead to aoutcome that is totally at odds with the usual presumption that the standard neoclassical assumptions inevitably generate a unique stable equilibrium and render macroeconomics superfluous.

Thinking about Interest and Irving Fisher

In two recent posts I have discussed Keynes’s theory of interest and the natural rate of interest. My goal in both posts was not to give my own view of the correct way to think about what determines interest rates,  but to identify and highlight problems with Keynes’s liquidity-preference theory of interest, and with the concept of a natural rate of interest. The main point that I wanted to make about Keynes’s liquidity-preference theory was that although Keynes thought that he was explaining – or perhaps, explicating — the rate of interest, his theory was nothing more than an explanation of why, typically, the nominal pecuniary yield on holding cash is less than the nominal yield on holding real assets, the difference in yield being attributable to the liquidity services derived from holding a maximally liquid asset rather than holding an imperfectly liquid asset. Unfortunately, Keynes imagined that by identifying and explaining the liquidity premium on cash, he had thereby explained the real yield on holding physical capital assets; he did nothing of the kind, as the marvelous exposition of the theory of own rates of interest in chapter 17 of the General Theory unwittingly demonstrates.

For expository purposes, I followed Keynes in contrasting his liquidity-preference theory with what he called the classical theory of interest, which he identified with Alfred Marshall, in which the rate of interest is supposed to be the rate that equilibrates saving and investment. I criticized Keynes for attributing this theory to Marshall rather than to Irving Fisher, which was, I am now inclined to think, a mistake on my part, because I doubt, based on a quick examination of Fisher’s two great books The Rate of Interest and The Theory of Interest, that he ever asserted that the rate of interest is determined by equilibrating savings and investment. (I actually don’t know if Marshall did or did make such an assertion.) But I think it’s clear that Fisher did not formulate his theory in terms of equating investment and savings via adjustments in the rate of interest rate. Fisher, I think, did agree (but I can’t quote a passage to this effect) that savings and investment are equal in equilibrium, but his analysis of the determination of the rate of interest was not undertaken in terms of equalizing two flows, i.e., savings and investment. Instead the analysis was carried out in terms of individual or household decisions about how much to consume out of current and expected future income, and in terms of decisions by business firms about how much available resources to devote to producing output for current consumption versus producing for future consumption. Fisher showed (in Walrasian fashion) that there are exactly enough equations in his system to solve for all the independent variables, so that his system had a solution. (That Walrasian argument of counting equations and unknowns is mathematically flawed, but later work by my cousin Abraham Wald and subsequently by Arrow, Debreu and McKenzie showed that Fisher’s claim could, under some more or less plausible assumptions, be proved in a mathematically rigorous way.)

Maybe it was Knut Wicksell who in his discussions of the determination of the rate of interest argued that the rate of interest is responsible for equalizing savings and investment, but that was not how Fisher understood what the rate of interest is all about. The Wicksellian notion that the equilibrium rate of interest equalizes savings and investment was thus a misunderstanding of the Fisherian theory, and it would be a worthwhile endeavor to trace the genesis and subsequent development of this misunderstanding to the point that Keynes and his contemporaries could have thought that they were giving an accurate representation of what orthodox theory asserted when they claimed that according to orthodox theory the rate of interest is what ensures equality between savings and investment.

This mistaken doctrine was formalized as the loanable-funds theory of interest – I believe that Dennis Robertson is usually credited with originating this term — in which savings is represented as the supply of loanable funds and investment is represented as the demand for loanable funds, with the rate of interest serving as a sort of price that is determined in Marshallian fashion by the intersection of the two schedules. Somehow it became accepted that the loanable-funds doctrine is the orthodox theory of interest determination, but it is clear from Fisher and from standard expositions of the neoclassical theory of interest which are of course simply extensions of Fisher’s work) that the loanable-funds theory is mistaken and misguided at a very basic level. (At this point, I should credit George Blackford for his comments on my post about Keynes’s theory of the rate of interest for helping me realize that it is not possible to make any sense out of the loanable-funds theory even though I am not sure that we agree on exactly why the loanable funds theory doesn’t make sense. Not that I had espoused the loanable-funds theory, but I did not fully appreciate its incoherence.)

Why do I say that the loanable-funds theory is mistaken and incoherent? Simply because it is fundamentally inconsistent with the essential properties of general-equilibrium analysis. In general-equilibrium analysis, interest rates emerge not as a separate subset of prices determined in a corresponding subset of markets; they emerge from the intertemporal relationships between and across all asset markets and asset prices. To view the rate of interest as being determined in a separate market for loanable funds as if the rate of interest were not being simultaneously determined in all asset markets is a complete misunderstanding of the theory of intertemporal general equilibrium.

Here’s how Fisher put over a century ago in The Rate of Interest:

We thus need to distinguish between interest in terms of money and interest in terms of goods. The first thought suggested by this fact is that the rate of interest in money is “nominal” and that in goods “real.” But this distinction is not sufficient, for no two forms of goods maintain or are expected to maintain, a constant price ratio toward each other. There are therefore just as many rates of interest in goods as there are forms of goods diverging in value. (p. 84, Fisher’s emphasis).

So a quarter of a century before Sraffa supposedly introduced the idea of own rates of interest in his 1932 review of Hayek’s Prices and Production, Fisher had done so in his first classic treatise on interest, which reproduced the own-rate analysis in his 1896 monograph Appreciation and Interest. While crediting Sraffa for introducing the concept of own rates of interest, Keynes, in chapter 17, simply — and brilliantly extends the basics of Fisher’s own-rate analysis, incorporating the idea of liquidity preference and silently correcting Sraffa insofar as his analysis departed from Fisher’s.

Christopher Bliss in his own classic treatise on the theory of interest, expands upon Fisher’s point.

According to equilibrium theory – according indeed to any theory of economic action which relates firms’ decisions to prospective profit and households’ decisions to budget-constrained searches for the most preferred combination of goods – it is prices which play the fundamental role. This is because prices provide the weights to be attached to the possible amendments to their net supply plans which the actors have implicitly rejected in deciding upon their choices. In an intertemporal economy it is then, naturally, present-value prices which play the fundamental role. Although this argument is mounted here on the basis of a consideration of an economy with forward markets in intertemporal equilibrium, it in no way depends on this particular foundation. As has been remarked, if forward markets are not in operation the economic actors have no choice but to substitute their “guesses” for the firm quotations of the forward markets. This will make a big difference, since full intertemporal equilibrium is not likely to be achieved unless there is a mechanism to check and correct for inconsistency in plans and expectations. But the forces that pull economic decisions one way or another are present-value prices . . . be they guesses or firm quotations. (pp. 55-56)

Changes in time preference therefore cause immediate changes in the present value prices of assets thereby causing corresponding changes in own rates of interest. Changes in own rates of interest constrain the rates of interest charged on money loans; changes in asset valuations and interest rates induce changes in production, consumption plans and the rate at which new assets are produced and capital accumulated. The notion that there is ever a separate market for loanable funds in which the rate of interest is somehow determined, and savings and investment are somehow equilibrated is simply inconsistent with the basic Fisherian theory of the rate of interest.

Just as Nick Rowe argues that there is no single market in which the exchange value of money (medium of account) is determined, because money is exchanged for goods in all markets, there can be no single market in which the rate of interest is determined because the value of every asset depends on the rate of interest at which the expected income or service-flow derived from the asset is discounted. The determination of the rate of interest can’t be confined to a single market.

Talk about Sound Money: Heckuva Job, Bitcoin

One of the buzzwords of assorted right-wing libertarians and conservatives is sound money. What’s interesting about their advocacy of “sound money” is that they typically identify “sound money” with restoring gold standard, or, more edgily, adoption of some new privately created currency like the bitcoin.

The past couple of months have seen a rapid run-up in the value of bitcoins which, after shooting up to over $1000 in 2014, had fallen back to the $200-300 range where it had been wallowing until for some reason it recently started a steady rise until shooting up to over $400 last week.

So I was interested in reading Dan McCrum’s piece in the Financial Times the other day in which he compared bitcoins to a pyramid scheme, providing a lot of historical background on similar schemes going back to General Gregor MacGregor in 1821. McCrum also points out an inherent flaw in the bitcoin which is that the very feature that is supposed to ensure its stability — the absolute limit on the total number of bitcoins — will ultimately cause its failure.

The inherent flaw of pyramid schemes is that they must always suck in new converts to avoid collapse, and the exponential growth in users is impossible to sustain. Bitcoin shares some of these features. It requires constant evangelism because its value derives from its use.

The limited supply of bitcoins then becomes a fatal constraint. The more people use it, the greater the price must rise, dissuading its use as a currency.

Of course, after each run-up in the value of the bitcoin, a reaction sets in, people then shifting away from bitcoins as a medium of exchange, causing its value to drop, so the bitcoin is naturally beset by sharp swings in its value – just what you want from sound money. Yeah, right. So, after a price increase of over 60% in less than a month, bitcoins have lost 20% of their value in a week. Have a look:


Doesn’t get much sounder than that.

I especially liked this quotation from Walter Bagehot provided by McCrum:

One thing is certain, that at a particular time a great deal of stupid people have a great deal of stupid money.

The Well-Defined, but Nearly Useless, Natural Rate of Interest

Tyler Cowen recently posted a diatribe against the idea monetary policy should be conducted by setting the interest rate target of the central bank at or near the natural rate of interest. Tyler’s post elicited critical responses from Brad DeLong and Paul Krugman among others. I sympathize with Tyler’s impatience with the natural rate of interest as a guide to policy, but I think the scattershot approach he took in listing, seemingly at random, seven complaints against the natural rate of interest was not the best way to register dissatisfaction with the natural rate. Here’s Tyler’s list of seven complaints.

1 Knut Wicksell, inventor of the term “natural rate of interest,” argued that if the central bank set its target rate equal to the natural rate, it would avoid inflation and deflation and tame the business cycle. Wicksell’s argument was criticized by his friend and countryman David Davidson who pointed out that, with rising productivity, price stability would not result without monetary expansion, which would require the monetary authority to reduce its target rate of interest below the natural rate to induce enough investment to be financed by monetary expansion. Thus, when productivity is rising, setting the target rate of interest equal to the natural rate leads not to price stability, but to deflation.

2 Keynes rejected the natural rate as a criterion for monetary policy, because the natural rate is not unique. The natural rate varies with the level of income and employment.

3 Early Keynesians like Hicks, Hansen, and Modigliani rejected the natural rate as well.

4 The meaning of the natural rate has changed; it was once the rate that would result in a stable price level; now it’s the rate that results in a stable rate of inflation.

5 Friedman also rejected the natural rate because there is no guarantee that setting the target rate equal to the natural rate will result in the rate of money growth that Freidman believed was desirable.

6 Sraffa debunked the natural rate in his 1932 review of Hayek’s Prices and Production.

7 It seems implausible that the natural rate is now negative, as many exponents of the natural rate concept now claim, even though the economy is growing and the marginal productivity of capital is positive.

Let me try to tidy all this up a bit.

The first thing you need to know when thinking about the natural rate is that, like so much else in economics, you will become hopelessly confused if you don’t keep the Fisher equation, which decomposes the nominal rate of interest into the real rate of interest and the expected rate of inflation, in clear sight. Once you begin thinking about the natural rate in the context of the Fisher equation, it becomes obvious that the natural rate can be thought of coherently as either a real rate or a nominal rate, but the moment you are unclear about whether you are talking about a real natural rate or a nominal natural rate, you’re finished.

Thus, Wicksell was implicitly thinking about a situation in which expected inflation is zero so that the real and nominal natural rates coincide. If the rate of inflation is correctly expected to be zero, and the increase in productivity is also correctly expected, the increase in the quantity of money required to sustain a constant price level can be induced by the payment of interest on cash balances. Alternatively, if the payment of interest on cash balances is ruled out, the rate of capital accumulation (forced savings) could be increased sufficiently to cause the real natural interest rate under a constant price level to fall below the real natural interest rate under deflation.

In the Sraffa-Hayek episode, as Paul Zimmerman and I have shown in our paper on that topic, Sraffa failed to understand that the multiplicity of own rates of interest in a pure barter economy did not mean that there was not a unique real natural rate toward which arbitrage would force all the individual own rates to converge. At any moment, therefore, there is a unique real natural rate in a barter economy if arbitrage is operating to equalize the cost of borrowing in terms of every commodity. Moreover, even Sraffa did not dispute that, under Wicksell’s definition of the natural rate as the rate consistent with a stable price level, there is a unique natural rate. Sraffa’s quarrel was only with Hayek’s use of the natural rate, inasmuch as Hayek maintained that the natural rate did not imply a stable price level. Of course, Hayek was caught in a contradiction that Sraffa overlooked, because he identified the real natural rate with an equal nominal rate, so that he was implicitly assuming a constant expected price level even as he was arguing that the neutral monetary policy corresponding to setting the market interest rate equal to the natural rate would imply deflation when productivity was increasing.

I am inclined to be critical Milton Friedman about many aspects of his monetary thought, but one of his virtues as a monetary economist was that he consistently emphasized Fisher’s  distinction between real and nominal interest rates. The point that Friedman was making in the passage quoted by Tyler was that the monetary authority is able to peg nominal variables, prices, inflation, exchange rates, but not real variables, like employment, output, or interest rates. Even pegging the nominal natural rate is impossible, because inasmuch as the goal of targeting a nominal natural rate is to stabilize the rate of inflation, targeting the nominal natural rate also means targeting the real natural rate. But targeting the real natural rate is not possible, and trying to do so will just get you into trouble.

So Tyler should not be complaining about the change in the meaning of the natural rate; that change simply reflects the gradual penetration of the Fisher equation into the consciousness of the economics profession. We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.

Keynes made a very different contribution to our understanding of the natural rate. He was that there is no reason to assume that the real natural rate of interest is unique. True, at any moment there is some real natural rate toward which arbitrage is forcing all nominal rates to converge. But that real natural rate is a function of the prevailing economic conditions. Keynes believed that there are multiple equilibria, each corresponding to a different level of employment, and that associated with each of those equilibria there could be a different real natural rate. Nowadays, we are less inclined than was Keynes to call an underemployment situation an equilibrium, but there is still no reason to assume that the real natural rate that serves as an attractor for all nominal rates is independent of the state of the economy. If the real natural rate for an underperforming economy is less than the real natural rate that would be associated with the economy if it were in the neighborhood of an optimal equilibrium, there is no reason why either the real natural rate corresponding to an optimal equilibrium or the real natural rate corresponding to the current sub-optimal state of economy should be the policy rate that the monetary authority chooses as its target.

Finally, what can be said about Tyler’s point that it is implausible to suggest that the real natural rate is negative when the economy is growing (even slowly) and the marginal productivity of capital is positive? Two points.

First, the marginal productivity of gold is very close to zero. If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest. If you look at futures prices for gold you will see that they are virtually the same as the spot price. However, storing gold is not costless. According to this article on Bloomberg.com, storage costs for gold range between 0.5 to 1% of the value of gold, implying that expected rate of return to holding gold is now less than -0.5% a year, which means that the marginal productivity of real capital is negative. Sure there are plenty of investments out there that are generating positive returns, but those are inframarginal investments. Those inframarginal investments are generating some net gain in productivity, and overall economic growth is positive, but that doesn’t mean that the return on investment at the margin is positive. At the margin, the yield on real capital seems to be negative.

If, as appears likely, our economy is underperforming, estimates of the real natural rate of interest are not necessarily an appropriate guide for the monetary authority in choosing its target rate of interest. If the aim of monetary policy is to nudge the economy onto a feasible growth path that is above the sub-optimal path along which it is currently moving, it might well be that the appropriate interest-rate target, as long as the economy remains below its optimal growth path, would be less than the natural rate corresponding to the current sub-optimal growth path.

Keynes on the Theory of Interest

In my previous post, I asserted that Keynes used the idea that savings and investment (in the aggregated) are identically equal to dismiss the neoclassical theory of interest of Irving Fisher, which was based on the idea that the interest rate equilibrates savings and investment. One of the commenters on my post, George Blackford, challenged my characterization of Keynes’s position.

I find this to be a rather odd statement for when I read Keynes I didn’t find anywhere that he argued this sort of thing. He often argued that “an act of saving” or “an act of investing” in itself could not have an direct effect on the rate of interest, and he said things like: “Assuming that the decisions to invest become effective, they must in doing so either curtail consumption or expand income”, but I don’t find him saying that savings and investment could not determine the rate of interest are identical.

A quote from Keynes in which he actually says something to this effect would be helpful here.

Now I must admit that in writing this characterization of what Keynes was doing, I was relying on my memory of how Hawtrey characterized Keynes’s theory of interest in his review of the General Theory, and did not look up the relevant passages in the General Theory. Of course, I do believe that Hawtrey’s characterization of what Keynes said to be very reliable, but it is certainly not as authoritative as a direct quotation from Keynes himself, so I have been checking up on the General Theory for the last couple of days. I actually found that Keynes’s discussion in the General Theory was less helpful than Keynes’s 1937 article “Alternative Theories of the Rate of Interest” in which Keynes responded to criticisms by Ohlin, Robertson, and Hawtrey, of his liquidity-preference theory of interest. So I will use that source rather than what seems to me to be the less direct and more disjointed exposition in the General Theory.

Let me also remark parenthetically that Keynes did not refer to Fisher at all in discussing what he called the “classical” theory of interest which he associated with Alfred Marshall, his only discussion of Fisher in the General Theory being limited to a puzzling criticism of the Fisher relation between the real and nominal rates of interest. That seems to me to be an astonishing omission, perhaps reflecting a deplorable Cambridgian provincialism or chauvinism that would not deign to acknowledge Fisher’s magisterial accomplishment in incorporating the theory of interest into the neoclassical theory of general equilibrium. Equally puzzling is that Keynes chose to refer to Marshall’s theory (which I am assuming he considered an adequate proxy for Fisher’s) as the “classical” theory while reserving the term “neo-classical” for the Austrian theory that he explicitly associates with Mises, Hayek, and Robbins.

Here is how Keynes described his liquidity-preference theory:

The liquidity-preference theory of the rate of interest which I have set forth in my General Theory of Employment, Interest and Money makes the rate of interest to depend on the present supply of money and the demand schedule for a present claim on money in terms of a deferred claim on money. This can be put briefly by saying that the rate of interest depends on the demand and supply of money. . . . (p. 241)

The theory of the rate of interest which prevailed before (let us say) 1914 regarded it as the factor which ensured equality between saving and investment. It was never suggested that saving and investment could be unequal. This idea arose (for the first time, so far as I am aware) with certain post-war theories. In maintaining the equality of saving and investment, I am, therefore, returning to old-fashioned orthodoxy. The novelty in my treatment of saving and investment consists, not in my maintaining their necessary aggregate equality, but in the proposition that it is, not the rate of interest, but the level of incomes which (in conjunction with certain other factors) ensures this equality. (pp. 248-49)

As Hawtrey and Robertson explained in their rejoinders to Keynes, the necessary equality in the “classical” system between aggregate savings and aggregate investment of which Keynes spoke was not a definitional equality but a condition of equilibrium. Plans to save and plans to invest will be consistent in equilibrium and the rate of interest – along with all the other variables in the system — must be such that the independent plans of savers and investors will be mutually consistent. Keynes had no basis for simply asserting that this consistency of plans is ensured entirely by way of adjustments in income to the exclusion of adjustments in the rate of interest. Nor did he have a basis for asserting that the adjustment to a discrepancy between planned savings and planned investment was necessarily an adjustment in income rather than an adjustment in the rate of interest. If prices adjust in response to excess demands and excess supplies in the normal fashion, it would be natural to assume that an excess of planned savings over planned investment would cause the rate of interest to fall. That’s why most economists would say that the drop in real interest rates since 2008 has been occasioned by a persistent tendency for planned savings to exceed planned investment.

Keynes then explicitly stated that his liquidity preference theory was designed to fill the theoretical gap left by his realization that a change income not in the interest rate is what equalizes savings and investment (even while insisting that savings and investment are necessarily equal by definition).

As I have said above, the initial novelty lies in my maintaining that it is not the rate of interest, but the level of incomes which ensures equality between saving and investment. The arguments which lead up to this initial conclusion are independent of my subsequent theory of the rate of interest, and in fact I reached it before I had reached the latter theory. But the result of it was to leave the rate of interest in the air. If the rate of interest is not determined by saving and investment in the same way in which price is determined by supply and demand, how is it determined? One naturally began by supposing that the rate of interest must be determined in some sense by productivity-that it was, perhaps, simply the monetary equivalent of the marginal efficiency of capital, the latter being independently fixed by physical and technical considerations in conjunction with the expected demand. It was only when this line of approach led repeatedly to what seemed to be circular reasoning, that I hit on what I now think to be the true explanation. The resulting theory, whether right or wrong, is exceedingly simple-namely, that the rate of interest on a loan of given quality and maturity has to be established at the level which, in the opinion of those who have the opportunity of choice -i.e. of wealth-holders-equalises the attractions of holding idle cash and of holding the loan. It would be true to say that this by itself does not carry us very far. But it gives us firm and intelligible ground from which to proceed. (p. 250)

Thus, Keynes denied forthrightly the notion that the rate of interest is in any way determined by the real forces of what in Fisherian terms are known as the impatience to spend income and the opportunity to invest it. However, his argument was belied by his own breathtakingly acute analysis in chapter 17 of the General Theory (“The Properties of Interest and Money”) in which, applying and revising ideas discussed by Sraffa in his 1932 review of Hayek’s Prices and Production he introduced the idea of own rates of interest.

The rate of interest (as we call it for short) is, strictly speaking, a monetary phenomenon in the special sense that it is the own-rate of interest (General Theory, p. 223) on money itself, i.e. that it equalises the advantages of holding actual cash and a deferred claim on cash. (p. 245)

The huge gap in Keynes’s reasoning here is that he neglected to say at what rate of return “the advantages of holding actual cash and a deferred claim on cash” or, for that matter, of holding any other real asset are equalized. That’s the rate of return – the real rate of interest — for which Irving Fisher provided an explanation. Keynes simply ignored — or forgot about — it, leaving the real rate of interest totally unexplained.

Keynes and Accounting Identities

In a post earlier this week, Michael Pettis was kind enough to refer to a passage from Ralph Hawtrey’s review of Keynes’s General Theory, which I had quoted in an earlier post, criticizing Keynes’s reliance on accounting identities to refute the neoclassical proposition that it is the rate of interest which equilibrates savings and investment. Here’s what Pettis wrote:

Keynes, who besides being one of the most intelligent people of the 20th century was also so ferociously logical (and these two qualities do not necessarily overlap) that he was almost certainly incapable of making a logical mistake or of forgetting accounting identities. Not everyone appreciated his logic. For example his also-brilliant contemporary (but perhaps less than absolutely logical), Ralph Hawtrey, was “sharply critical of Keynes’s tendency to argue from definitions rather than from causal relationships”, according to FTC economist David Glasner, whose gem of a blog, Uneasy Money, is dedicated to reviving interest in the work of Ralph Hawtrey. In a recent entry Glasner quotes Hawtrey:

[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.

This is a very typical criticism of certain kinds of logical thinking in economics, and of course it misses the point because Keynes is not arguing from definition. It is certainly true that “identity so established cannot prove anything”, if by that we mean creating or supporting a hypothesis, but Keynes does not use identities to prove any creation. He uses them for at least two reasons. First, because accounting identities cannot be violated, any model or hypothesis whose logical corollaries or conclusions implicitly violate an accounting identity is automatically wrong, and the model can be safely ignored. Second, and much more usefully, even when accounting identities have not been explicitly violated, by identifying the relevant identities we can make explicit the sometimes very fuzzy assumptions that are implicit to the model an analyst is using, and focus the discussion, appropriately, on these assumptions.

I agree with Pettis that Keynes had an extraordinary mind, but even great minds are capable of making mistakes, and I don’t think Keynes was an exception. And on the specific topic of Keynes’s use of the accounting identity that expenditure must equal income and savings must equal investment, I think that the context of Keynes’s discussion of that identity makes it clear that Keynes was not simply invoking the identity to prevent some logical slipup, as Pettis suggests, but was using it to deny the neoclassical Fisherian theory of interest which says that the rate of interest represents the intertemporal rate of substitution between present and future goods in consumption and the rate of transformation between present and future goods in production. Or, in less rigorous terminology, the rate of interest reflects the marginal rate of time preference and the marginal rate of productivity of capital. In its place, Keynes wanted to substitute a pure monetary or liquidity-preference theory of the rate of interest.

Keynes tried to show that the neoclassical theory could not possibly be right, inasmuch as, according to the theory, the equilibrium rate of interest is the rate that equilibrates the supply of with the demand for loanable funds. Keynes argued that because investment and savings are identically equal, savings and investment could not determine the rate of interest. But Keynes then turned right around and said that actually the equality of savings and investment determines the level of income. Well, if savings and investment are identically equal, so that the rate of interest can’t be determined by equilibrating the market for loanable funds, it is equally impossible for savings and investment to determine the level of income.

Keynes was unable to distinguish the necessary accounting identity of savings and investment from the contingent equality of savings and investment as an equilibrium condition. For savings and investment to determine the level of income, there must be some alternative definition of savings and investment that allows them to be unequal except at equilibrium. But if there are alternative definitions of savings and investment that allow those magnitudes to be unequal out of equilibrium — and there must be such alternative definitions if the equality of savings and investment determines the level of income — there is no reason why the equality of savings and investment could not be an equilibrium condition for the rate of interest. So Keynes’s attempt to refute the neoclassical theory of interest failed. That was Hawtrey’s criticism of Keynes’s use of the savings-investment accounting identity.

Pettis goes on to cite Keynes’s criticism of the Versailles Treaty in The Economic Consequences of the Peace as another example of Keynes’s adroit use of accounting identities to expose fallacious thinking.

A case in point is The Economic Consequences of the Peace, the heart of whose argument rests on one of those accounting identities that are both obvious and easily ignored. When Keynes wrote the book, several members of the Entente – dominated by England, France, and the United States – were determined to force Germany to make reparations payments that were extraordinarily high relative to the economy’s productive capacity. They also demanded, especially France, conditions that would protect them from Germany’s export prowess (including the expropriation of coal mines, trains, rails, and capital equipment) while they rebuilt their shattered manufacturing capacity and infrastructure.

The argument Keynes made in objecting to these policies demands was based on a very simple accounting identity, namely that the balance of payments for any country must balance, i.e. it must always add to zero. The various demands made by France, Belgium, England and the other countries that had been ravaged by war were mutually contradictory when expressed in balance of payments terms, and if this wasn’t obvious to the former belligerents, it should be once they were reminded of the identity that required outflows to be perfectly matched by inflows.

In principle, I have no problem with such a use of accounting identities. There’s nothing wrong with pointing out the logical inconsistency between wanting Germany to pay reparations and being unwilling to accept payment in anything but gold. Using an accounting identity in this way is akin to using the law of conservation of energy to point out that perpetual motion is impossible. However, essentially the same argument could be made using an equilibrium condition for the balance of payments instead of an identity. The difference is that the accounting identity tells you nothing about how the system evolves over time. For that you need a behavioral theory that explains how the system adjusts when the equilibrium conditions are not satisfied. Accounting identities and conservation laws don’t give you any information about how the system adjusts when it is out of equilibrium. So as Pettis goes on to elaborate on Keynes’s analysis of the reparations issue, one or more behavioral theories must be tacitly called upon to explain how the international system would adjust to a balance-of-payments disequilibrium.

If Germany had to make substantial reparation payments, Keynes explained, Germany’s capital account would tend towards a massive deficit. The accounting identity made clear that there were only three possible ways that together could resolve the capital account imbalance. First, Germany could draw down against its gold supply, liquidate its foreign assets, and sell domestic assets to foreigners, including art, real estate, and factories. The problem here was that Germany simply did not have anywhere near enough gold or transferable assets left after it had paid for the war, and it was hard to imagine any sustainable way of liquidating real estate. This option was always a non-starter.

Second, Germany could run massive current account surpluses to match the reparations payments. The obvious problem here, of course, was that this was unacceptable to the belligerents, especially France, because it meant that German manufacturing would displace their own, both at home and among their export clients. Finally, Germany could borrow every year an amount equal to its annual capital and current account deficits. For a few years during the heyday of the 1920s bubble, Germany was able to do just this, borrowing more than half of its reparation payments from the US markets, but much of this borrowing occurred because the great hyperinflation of the early 1920s had wiped out the country’s debt burden. But as German debt grew once again after the hyperinflation, so did the reluctance to continue to fund reparations payments. It should have been obvious anyway that American banks would never accept funding the full amount of the reparations bill.

What the Entente wanted, in other words, required an unrealistic resolution of the need to balance inflows and outflows. Keynes resorted to accounting identities not to generate a model of reparations, but rather to show that the existing model implicit in the negotiations was contradictory. The identity should have made it clear that because of assumptions about what Germany could and couldn’t do, the global economy in the 1920s was being built around a set of imbalances whose smooth resolution required a set of circumstances that were either logically inconsistent or unsustainable. For that reason they would necessarily be resolved in a very disruptive way, one that required out of arithmetical necessity a substantial number of sovereign defaults. Of course this is what happened.

Actually, if it had not been for the insane Bank of France and the misguided attempt by the Fed to burst the supposed stock-market bubble, the international system could have continued for a long time, perhaps indefinitely, with US banks lending enough to Germany to prevent default until rapid economic growth in the US and western Europe enabled the Germans to service their debt and persuaded the French to allow the Germans to do so via an export surplus. Instead, the insane Bank of France, with the unwitting cooperation of the clueless (following Benjamin Strong’s untimely demise) Federal Reserve precipitated a worldwide deflation that triggered that debt-deflationary downward spiral that we call the Great Depression.

About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. 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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