Archive for the 'Irving Fisher' 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.


The Trump Rally

David Beckworth has a recent post about the Trump stock-market rally. Just before the election I had a post in which I pointed out that the stock market seemed to be dreading the prospect of a Trump victory, based on the strong positive correlation between movements in the dollar value of the Mexican peso and the S&P 500, though, in response to a comment by one of my readers, I did partially walk back my argument. As the initial returns and exit polls briefly seemed to be pointing toward a Clinton victory, the correlation between the peso and the S&P 500 (futures) seemed to be very strong and getting stronger, and after the returns started to point increasingly toward a Trump victory, the strong correlation between the peso and the S&P 500 remained all too evident, showing a massive decline in both the peso and the S&P 500. But what seemed like a Trump panic was suddenly broken, when Mrs. Clinton phoned Trump to concede and Trump appeared to claim victory with a relatively restrained and conciliatory statement that calmed the worst fears about a messy transition and the potential for serious political instability. The survival of a Republican majority in the Senate was perhaps viewed as a further positive sign and strengthened hopes for business-friendly changes in the US corporate and personal taxes. The earlier losses in S&P 500 futures were reversed even without any recovery in the peso.

So what explains the turnaround in the reaction of the stock market to Trump’s victory? Here’s David Beckworth:

I have a new piece in The Hill where I argue markets are increasingly seeing the Trump shock as an inflection point for the U.S. economy:

It seems the U.S. economy is finally poised for robust economic growth, something that has been missing for the past eight years. Such strong economic growth is expected to cause the demand for credit to increase and the supply of savings to decline

Though this is not the main point, I will just register my disagreement with David’s version of how interest rates are determined, which essentially restates the “loanable-funds” theory of interest determination, which is often described as the orthodox alternative to the Keynesian liquidity preference theory of interest rates. I disagree that it is the alternative to the Keynesian theory. I think that is a very basic misconception perpetrated by macroeconomists with either a regrettable memory lapse or an insufficient understanding of, the Fisherian theory of interest rates. In the Fisherian theory interest rates are implicit in the intertemporal structure of all prices, they are therefore not determined in any single market, as asserted by the loanable-funds theory, any more than the price level is determined in any single market. The way to think about interest-rate determination is to ask the following question: at what structure of interest rates would holders of long-lived assets be content to continue holding the existing stock of assets? Current savings and current demand for credit are an epiphenomenon of interest-rate determination, not a determinant of interest rates — with the caveat that every factor that influences the intertemporal structure of prices is one of the myriad determinants of interest rates.

Together, these forces are naturally pushing interest rates higher. The Fed’s interest rate hike today is simply piggybacking on this new reality.

If “these forces” is interpreted in the way I have suggested in my above comment on David’s previous sentence, then I would agree with this sentence.

Here are some charts that document this upbeat economic outlook as seen from the treasury market. The first one shows the treasury market’s implicit inflation forecast (or “breakeven inflation”) and real interest rate at the 10-year horizon. These come from TIPs and have their flaws, but they provide a good first approximation to knowing what the bond market is thinking. In this case, both the real interest rate and expected inflation rate are rising. This implies the market expects both higher real economic growth and higher inflation. The two may be related–the higher expected inflation may be a reflection of higher expected nominal demand growth causing real growth. The higher real growth expectations are also probably being fueled by Trump’s supply-side reforms.


I agree that the rise in real interest rates may reflect improved prospects for economic growth, and that the rising TIPS spread may reflect expectations of at least a small rise in inflation towards the Fed’s largely rhetorical 2-percent target. And I concur that a higher inflation rate could be one of the causes of improving implicit forecasts of economic growth. However, I am not so sure that expectations of rising inflation and supply-side reforms are the only explanations for rising real interest rates.

What “reforms” is Trump promising? I’m not sure actually, but here is a list of possibilities: 1) reducing and simplifying corporate tax rates, 2) reducing and simplifying personal tax rates, 3) deregulation, 4) tougher enforcement of immigration laws, 5) deportation of an undetermined number of illegal immigrants, 6) aggressively protectionist international trade policies.

I think that there is a broad consensus in favor of reducing corporate tax rates. Not only is the 35% marginal rate on corporate profits very high compared to the top corporate set by other countries, the interest deduction is a perverse incentive favoring debt rather than equity financing. As I pointed out in a post five years ago, Hyman Minsky, one of the favorite economists of the left, was an outspoken opponent of corporate income taxation in general, precisely because it encourages debt rather than equity financing. I think that the Obama administration would have been happy to propose reducing the corporate tax rate as part of a broader budget deal, but no broader deal with the Republican majority in Congress was possible, and a simple reduction of the corporate tax rate would have been difficult for Obama to sell to his own political base without offering them something that could be described as reducing inequality. So cutting the top corporate tax rate would almost certainly be a good thing (but subject to qualification by the arguments in the next paragraph), and expectations of a reduction in the top corporate rate would tend to raise stock prices, though the effect on stock prices would be moderated by increased issues of new corporate stock.

Reducing and simplifying corporate and personal tax rates seems like a good thing, but there’s at least one problem. Not all earnings of taxable income is socially productive. Lots of earned income is generated by completely, or partially, unproductive activities associated with private gains that exceed social gains. I have written in the past about how unproductive many types of information gathering and knowledge production is (e.g., here, here, here, and here). Much of this activity enables the person who acquires knowledge or information to gain an information advantage over people with whom he transacts, so the private return to the acquisition of such knowledge is greater than the social gain, because the gain to one party to the trade comes not from an increase in output but by way of a transfer from the other less-informed party to the transaction.

The same is true — to a somewhat lesser extent, but the basic tendency is the same – of activity aimed at the discovery of knew knowledge over which an intellectual property right can be exercised for a substantial length of time. The ability to extract monopoly rents over newly discovered knowledge is likely to confer a private gain on the discoverer greater than the social gain accruing from the discovery, because the first discoverer to acquire exclusive rights can extract the full value of the discovery even though the marginal benefit accruing to the discovery is only the value of the new knowledge over the elapsed time between the moment of the discovery and the moment when the discovery would have been made, perhaps soon afterwards, by someone else. In general, there is a whole range of income accruing to a variety of winner-takes-all activities in which the private gain to the winner greatly exceeds the social gain. A low marginal rate of income taxation increases the incentive to engage in such socially wasteful winner-takes-all activities.

Deregulation can be a good thing when it undermines monopolistic price-fixing and legally imposed entry barriers entrenching incumbent suppliers. A lot of regulation has historically been of this type. But although it is convenient for libertarian ideologues to claim that monopoly enhancement or entrenchment characterizes all government regulation, I doubt that most current regulations are for this purpose. A lot of regulation is aimed at preventing dishonest or misleading business practices or environmental pollution or damage to third-parties. So as an empirical matter, I don’t think we can say whether a reduction in regulation will have a net positive or a net negative effect on society. Nevertheless, regulation probably does reduce the overall earnings of corporations, so that a reduction in regulation will tend to raise stock prices. If it becomes easier for corporations to emit harmful pollution into the atmosphere and into our rivers, lakes and oceans, the reductions in private costs enjoyed by the corporations will be capitalized into their stock prices while the increase in social costs will be borne in a variety of ways by all individuals in the country or the world. Insofar as stock prices have risen since Trump’s election because of expectations of a roll back in regulation, it is not clear to me at least whether that reflects an increase in net social welfare or a capitalization of the value of enhanced rights to engage in socially harmful conduct.

The possible effects of changes in immigration laws, in the enforcement of immigration laws and in trade policies seem to me far too murky at this point even to speculate upon. I would just observe that insofar as the stock market has capitalized the effects of Trump’s supposed supply-side reforms, those reforms would have tended to reduce, not increase, inflation expectations. So it does not seem likely to me that whatever increase in stock prices we have seen so far reflects a pure supply-side effect.

I am more inclined to believe that the recent increases in stock prices and inflation expectations reflect expectations that Trump will fulfill his commitments to conduct irresponsible fiscal policies generating increased budget deficits, which the Republican majorities in Congress will now meekly accept and dutifully applaud, and that Trump will be able either to cajole or intimidate enough officials at the Federal Reserve to accommodate those policies or will appoint enough willing accomplices to the Fed to overcome the opposition of the current FOMC.

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.

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.

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, 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.

The Great, but Misguided, Benjamin Strong Goes Astray in 1928

In making yet further revisions to our paper on Hawtrey and Cassel, Ron Batchelder and I keep finding interesting new material that sheds new light on the thinking behind the policies that led to the Great Depression. Recently I have been looking at the digital archive of Benjamin Strong’s papers held at the Federal Reserve Bank. Benjamin Strong was perhaps the greatest central banker who ever lived. Milton Friedman, Charles Kindleberger, Irving Fisher, and Ralph Hawtrey – and probably others as well — all believed that if Strong, Governor of the New York Federal Reserve Bank from 1914 to 1928 and effectively the sole policy maker for the entire system, had not died in 1928, the Great Depression would have been avoided entirely or, at least, would have been far less severe and long-lasting. My own view had been that Strong had generally understood the argument of Hawtrey and Cassel about the importance of economizing on gold, and, faced with the insane policy of the Bank of France, would have accommodated that policy by allowing an outflow of gold from the immense US holdings, rather than raise interest rates and induce an inflow of gold into the US in 1929, as happened under his successor, George Harrison.

Having spent some time browsing through the papers, I am sorry — because Strong’s truly remarkable qualities are evident in his papers — to say that the papers also show to my surprise and disappointment that Strong was very far from being a disciple of Hawtrey or Cassel or of any economist, and he seems to have been entirely unconcerned in 1928 about the policy of the Bank of France or the prospect of a deflationary run-up in the value of gold even though his friend Montague Norman, Governor of the Bank of England, was beginning to show some nervousness about “a scramble for gold,” while other observers were warning of a deflationary collapse. I must admit that, at least one reason for my surprise is that I had naively accepted the charges made by various Austrians – most notably Murray Rothbard – that Strong was a money manager who had bought into the dangerous theories of people like Irving Fisher, Ralph Hawtrey and J. M. Keynes that central bankers should manipulate their currencies to stabilize the price level. The papers I have seen show that, far from being a money manager and a price-level stabilizer, Strong expressed strong reservations about policies for stabilizing the price level, and was more in sympathy with the old-fashioned gold standard than with the gold-exchange standard — the paradigm promoted by Hawtrey and Cassel and endorsed at the Genoa Conference of 1922. Rothbard’s selective quotation from the memorandum summarizing Strong’s 1928 conversation with Sir Arthur Salter, which I will discuss below, gives a very inaccurate impression of Strong’s position on money management.

Here are a few of the documents that caught my eye.

On November 28 1927, Montague Norman wrote Strong about their planned meeting in January at Algeciras, Spain. Norman makes the following suggestion:

Perhaps the chief uncertainty or danger which confronts Central Bankers on this side of the Atlantic over the next half dozen years is the purchasing power of gold and the general price level. If not an immediate, it is a very serious question and has been too little considered up to the present. Cassel, as you will remember, has held up his warning finger on many occasions against the dangers of a continuing fall in the price level and the Conference at Genoa as you will remember, suggested that the danger could be met or prevented, by a more general use of the “Gold Exchange Standard”.

This is a very abstruse and complicated problem which personally I do not pretend to understand, the more so as it is based on somewhat uncertain statistics. But I rely for information from the outside about such a subject as this not, as you might suppose, on McKenna or Keynes, but on Sir Henry Strakosch. I am not sure if you know him: Austrian origin: many years in Johannesburg: 20 years in this country: a student of economics: a gold producer with general financial interests: perhaps the main stay in setting up the South African Reserve Bank: a member of the Financial Committee of the League and of the Indian Currency Commission: full of public spirit, genial and helpful . . . and so forth. I have probably told you that if I had been a Dictator he would have been a Director here years ago.

This is a problem to which Strackosch has given much study and it alarms him. He would say that none of us are paying sufficient attention to the possibility of a future fall in prices or are taking precautions to prepare any remedy such as was suggested at Genoa, namely smaller gold reserves through the Gold Exchange Standard, and that you, in the long run, will feel any trouble just as much as the rest of the Central Bankers will feel it.

My suggestion therefore is that it might be helpful if I could persuade Strakoosch too to come to Algeciras for a week: his visit could be quite casual and you would not be committed to any intrigue with him.

I gather from the tone of this letter and from other indications that the demands by the French to convert their foreign exchange to gold were already being made on the Bank of England and were causing some degree of consternation in London, which is why Norman was hoping that Strakosch might persuade Strong that something ought to be done to get the French to moderate their demands on the Bank of England to convert claims on sterling into gold. In the event, Strong met with Strakosch in December (probably in New York, not in Algeciras, without the presence of Norman). Not long thereafter Strong’s health deteriorated, and he took an extended leave from his duties at the bank. On March 27, 1928 Strong sent a letter to Norman outlining the main points of his conversation with Strakosch:

What [Strakosch] told me leads me to believe that he holds the following views:

  • That there is an impending shortage of monetary gold.
  • That there is certain to be a decline in the production by the South African mines.
  • That in consequence there will be a competition for gold between banks of issue which will lead to high discount rates, contracting credit and falling world commodity prices.
  • That Europe is so burdened with debt as to make such a development calamitous, possibly bankrupting some nations.
  • That the remedy is an extensive and formal development of the gold exchange standard.

From the above you will doubtless agree with me that Strakosch is a 100% “quantity” theory man, that he holds Cassel’s views in regard to the world’s gold position, and that he is alarmed at the outlook, just as most of the strict quantity theory men are, and rather expects that the banks of issue can do something about it.

Just as an aside, I will note that Strong is here displaying a rather common confusion, mixing up the quantity theory with a theory about the value of money under a gold standard. It’s a confusion that not only laymen, but also economists such as (to pick out a name almost at random) Milton Friedman, are very prone to fall into.

What he tells me is proposed consists of:

  • A study by the Financial Section of the League [of Nations] of the progress of economic recovery in Europe, which, he asserts, has closely followed progress in the resumption of gold payment or its equivalent.
  • A study of the gold problem, apparently in the perspective of the views of Cassel and others.
  • The submission of the results, with possibly some suggestions of a constructive nature, to a meeting of the heads of the banks of issue. He did not disclose whether the meeting would be a belated “Genoa resolution” meeting or something different.

What I told him appeared to shock him, and it was in brief:

  • That I did not share the fears of Cassel and others as to a gold shortage.
  • That I did not think that the quantity theory of prices, such for instance as Fisher has elaborate, “reduction ad absurdum,” was always dependable if unadulterated!
  • That I thought the gold exchange standard as now developing was hazardous in the extreme if allowed to proceed very much further, because of the duplication of bank liabilities upon the same gold.
  • That I much preferred to see the central banks build up their actual gold metal reserves in their own hands to something like orthodox proportions, and adopt their own monetary and credit policy and execute it themselves.
  • That I thought a meeting of the banks of issue in the immediate future to discuss the particular matter would be inappropriate and premature, until the vicissitudes of the Dawes Plan had developed further.
  • That any formal meeting of the banks of issue, if and when called, should originate among themselves rather than through the League, that the Genoa resolution was certainly no longer operative, and that such formal meeting should confine itself very specifically at the outset first to developing a sound basis of information, and second, to devising improvement in technique in gold practice

I am not at all sure that any formal meeting should be held before another year has elapsed. If it is held within a year or after a year, I am quite certain that it I attended it I could not do so helpfully if it tacitly implied acceptance of the principles set out in the Genoa resolution.

Stratosch is a fine fellow: I like him immensely, but I would feel reluctant to join in discussions where there was likelihood that the views so strongly advocated by Fisher, Cassel, Keynes, Commons, and others would seem likely to prevail. I would be willing at the proper time, if objection were not raised at home, to attend a conference of the banks of issue, if we could agree at the outset upon a simple platform, i.e., that gold is an effective measure of value and medium of exchange. If these two principles are extended, as seems to be in Stratosch’s mind, to mean that a manipulation of gold and credit can be employed as a regulator of prices at all times and under all circumstances, then I fear fundamental differences are inescapable.

And here is a third document in a similar vein that is also worth looking at. It is a memorandum written by O. E. Moore (a member of Strong’s staff at the New York Fed) providing a detailed account of the May 25, 1928 conversation between Strong and Sir Arthur Salter, then head of the economic and financial section of the League of Nations, who came to New York to ask for Strong’s cooperation in calling a new conference (already hinted at by Strakosch in his December conversation with Strong) with a view toward limiting the international demand for gold. Salter handed Strong a copy of a report by a committee of the League of Nations warning of the dangers of a steep increase in the value of gold because of increasing demand and a declining production.

Strong responded with a historical rendition of international monetary developments since the end of World War I, pointing out that even before the war was over he had been convinced of the need for cooperation among the world’s central banks, but then adding that he had been opposed to the recommendation of the 1922 Genoa Conference (largely drafted by Hawtrey and Cassel).

Governor Strong had been opposed from the start to the conclusions reached at the Genoa Conference. So far as he was aware, no one had ever been able to show any proof that there was a world shortage of gold or that there was likely to be any such shortage in the near future. . . . He was also opposed to the permanent operation of the gold exchange standard as outlined by the Genoa Conference, because it would mean by virtue of the extensive credits which the exchange standard countries would be holding in the gold centers, that they would be taking away from each of those two centers the control of their own money markets. This was an impossible thing for the Federal Reserve System to accept, so far as the American market was concerned, and in fact it was out of the question for any important country, it seemed to him, to give up entirely the direction of its own market. . . .

As a further aside, I will just observe that Strong’s objection to the gold exchange standard, namely that it permits an indefinite expansion of the money supply, a given base of gold reserves being able to support an unlimited expansion of the quantity of money, is simply wrong as a matter of theory. A country running a balance-of-payments deficit under a gold-exchange standard would be no less subject to the constraint of an external drain, even if it is holding reserves only in the form of instruments convertible into gold rather than actual gold, than it would be if it were operating under a gold standard holding reserves in gold.

Although Strong was emphatic that he could not agree to participate in any conference in which the policies and actions of the US could be determined by the views of other countries, he was open to a purely fact-finding commission to ascertain what the total world gold reserves were and how those were distributed among the different official reserve holding institutions. He also added this interesting caveat:

Governor Strong added that, in his estimation, it was very important that the men who undertook to find the answers to these questions should not be mere theorists who would take issue on controversial points, and that it would be most unfortunate if the report of such a commission should result in giving color to the views of men like Keynes, Cassel, and Fisher regarding an impending world shortage of gold and the necessity of stabilizing the price level. . . .

Governor Strong mentioned that one thing which had made him more wary than ever of the policies advocated by these men was that when Professor Fisher wrote his book on “Stabilizing the Dollar”, he had first submitted the manuscript to him (Governor Strong) and that the proposal made in that original manuscript was to adjust the gold content of the dollar as often as once a week, which in his opinion showed just how theoretical this group of economists were.

Here Strong was displaying the condescending attitude toward academic theorizing characteristic of men of affairs, especially characteristic of brilliant and self-taught men of affairs. Whether such condescension is justified is a question for which there is no general answer. However, it is clear to me that Strong did not have an accurate picture of what was happening in 1928 and what dangers were lying ahead of him and the world in the last few months of his life. So the confidence of Friedman, Kindelberger, Fisher, and Hawtrey in Strong’s surpassing judgment does not seem to me to rest on any evidence that Strong actually understood the situation in 1928 and certainly not that he knew what to do about it. On the contrary he was committed to a policy that was leading to disaster, or at least, was not going to avoid disaster. The most that can be said is that he was at least informed about the dangers, and if he had lived long enough to observe that the dangers about which he had been warned were coming to pass, he would have had the wit and the good sense and the courage to change his mind and take the actions that might have avoided catastrophe. But that possibility is just a possibility, and we can hardly be sure that, in the counterfactual universe in which Strong does not die in 1928, the Great Depression never happened.

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.

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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