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Irving Fisher and His
Compensated Dollar Plan
Don Patinkin

T

his is a story that illustrates the interrelationship between economic history and economic thought: more precisely, between monetary history
and monetary thought. So let me begin with a very brief discussion of
the relevant history.
In 1879, the United States returned to the gold standard from which it had
departed at the time of the Civil War. This took place in a period in which
“a combination of events, including a slowing of the rate of increase of the
world’s stock of gold, the adoption of the gold standard by a widening circle
of countries, and a rapid increase in aggregate economic output, produced a
secular decline ˙ in the world price level measured in gold˙ (Friedman and
..
...”
Schwartz 1963, p. 91; for further details, see Friedman 1990, and Laidler 1991,
pp. 49–50). The specific situation thus generated in the United States was described by Irving Fisher (1913c, p. 27) in the following words: “For a quarter of
a century—from 1873 to 1896—the dollar increased in purchasing power and
caused a prolonged depression of trade, culminating in the political upheaval
which led to the free silver campaign of 1896, when the remedy proposed was
worse than the disease.” This was, of course, the campaign which climaxed with
William J. Bryan’s famous “cross of gold” speech in the presidential election
of 1896. Fisher’s view of this campaign reflected the fact that it called for the
unlimited coinage of silver at a mint price far higher than its market value, a
policy that would have led to a tremendous increase in the quantity of money
and the consequent generation of strong inflationary pressures.

The author is Professor of Economics Emeritus at the Hebrew University of Jerusalem.
The views expressed herein do not necessarily reflect those of the Federal Reserve Bank of
Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/3 Summer 1993

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Federal Reserve Bank of Richmond Economic Quarterly

Though Bryan was defeated in the subsequent election, his objective was
nevertheless accomplished by the unprecedented increase in the output of gold
that began in the 1890s as a result of the discovery of new gold deposits in
South Africa and Alaska, as well as the development of more efficient processes
for the extraction of gold from the ore. Thus the world output of gold in 1899
was nearly three times the average annual output during the 1880s, and in 1905
it was nearly four times as large (Wright 1941, pp. 825–26). As a result, the
U.S. price level increased from 1896 to 1913 by almost 50 percent—a fact
duly noted and emphasized by Fisher (1913b, p. 217).1 It was this 40-year
experience of serious economic, political, and social problems generated by
significant changes in the price level—in either direction—that led Fisher to
formulate his compensated dollar plan for stabilizing it.
Another important fact is that “guilt by association” with the declared
objective of the silver campaign to generate a great increase in the quantity of
money and hence in prices had caused the quantity theory itself to fall into disrepute. This situation was clearly reflected in Fisher’s statement in the preface
to his 1911 Purchasing Power of Money that “it would seem that even the theorems of Euclid would be challenged and doubted if they should be appealed
to by one political party as against another˙ The attempts by promoters of
...
unsound money to make an improper use of the quantity theory—as in the first
Bryan campaign—led many sound money men to the utter repudiation of the
quantity theory.” In fact, that situation was the immediate reason for Fisher’s
writing the book; namely, that “the quantity theory needs to be reintroduced
into general knowledge” (ibid., p. viii).
Note finally that when in 1913 Fisher proposed his compensated dollar
plan, the Federal Reserve System had not yet come into existence. Though the
Act establishing it was approved toward the end of that year, the role that it
might play in stabilizing the price level did not become part of general thinking
about monetary policy until the 1920s. This delay was due in part to the fact
that in the first years of the Federal Reserve System, its policy was more or
less dictated by the exigencies of World War I and, in part, to the time that
was naturally needed for the System to gain experience in the workings of
monetary policy (see Barger 1964, Chap. 3; Wicker 1966, pp. 57–58).

1 Fisher’s 50 percent figure was based on the wholesale price index which the Bureau of
Labor Statistics had begun to publish only in 1890. Consequently, for the period before that,
Fisher (in the statement cited in the preceding paragraph) had to suffice with a general statement
about the increased purchasing power of the dollar. This is a minor illustration of another important interrelationship: that between economic thought and economic measurement. For a much
more significant illustration, see Patinkin (1976) for the interrelationship between macroeconomic
theory and measurement in the 1930s.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

3

1. THE PLAN: RATIONALE AND DETAILS
With that as background, let me begin the story with Fisher’s already-mentioned
classic exposition of the quantity theory in his The Purchasing Power of Money.
That—or rather its inverse, the price level—is indeed the major concern of the
book. The book, however, also has a subtitle—Its Determination and Relation
to Credit Interest and Crises—and that is an almost equally important concern.
Though most of The Purchasing Power of Money (henceforth, PPM) is
devoted to the long-run proportionality between the quantity of money and
the price level, Fisher attached great importance to Chapter 4 of the book on
“transition periods,” in which this proportionality did not obtain. And lest the
term “transition” mislead, let me point out that Fisher emphasizes that “periods
of transition are the rule and those of equilibrium the exception, [so that] the
mechanism of exchange is almost always in a dynamic rather than a static
condition” (ibid., p. 71).
It is accordingly in this chapter that Fisher develops his theory of “crises,”
or what we now call “cycles.” This was based on the fundamental distinction
that (with due acknowledgment to Alfred Marshall and even earlier writers)
he had already made in his 1896 Appreciation and Interest (Chaps. 1–3 and
12), and again in his 1907 Rate of Interest (Chap. 5 and its appendix), between
nominal and real rates of interest. Fisher begins his analysis of the period of
transition by assuming that the economy is in a state of equilibrium which is
disturbed, and adds that “any cause which disturbs equilibrium will suffice to
set up oscillations. One of the most common of such causes is an increase in
the quantity of money” (PPM, p. 70). Accordingly, the “chief factor” that he
studies for this purpose is a change in the quantity of money (ibid., p. 55).
As a result of, say, an increase in this quantity, there follows an initial
increase in the price level, which in turn causes an increase in the velocity of
circulation, for “we all hasten to get rid of any commodity which, like ripe fruit,
is spoiling on our hands. Money is no exception; when it is depreciating, holders
will get rid of it as fast as possible” (ibid., p. 63). This causes a further increase
in the price level. As a result of the increasing price level, the nominal rate of
interest also increases. But—because of the failure of people to realize “that
they are daily gambling in changes in the value of money” (what in later writings Fisher denoted as “money illusion”), as well as of inadequate “knowledge
as to prospective price levels” on the part of lenders—“not sufficiently”; that is,
the nominal rate does not increase sufficiently to leave the real rate unchanged
(PPM, pp. 346, 321, and 63, respectively; see also Rate of Interest, p. 86).2

2 In his Theory of Interest (1930) many years later, Fisher attributed this insufficiency of
adjustment to the “almost universal lack of foresight” (ibid., pp. 43–44).

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Federal Reserve Bank of Richmond Economic Quarterly

Because of the consequent decline in the real rate of interest, businessmen’s
“profits increase, loans expand, and the Q’s [i.e., outputs] increase” (PPM,
p. 63). This expansionary process continues until ultimately lending rates of
interest rise to correspond to the rate of inflation, which then causes difficulties for the business-borrowers “who have counted on renewing their loans at
the former rates,” hence to some bankruptcies, hence to “runs on the banks”
and a consequent decrease in bank credit and deposits, and hence in the
money supply—as a result of which pressure prices begin to decline (ibid.,
pp. 65–66).
The decline creates the opposite relationship between the nominal and real
rates of interest, this time as a result of the lack of knowledge on the part of
the borrowers. This increase in the real rate of interest generates a contractional process—which Fisher pedantically describes in the same step-by-step
sequence (with the signs reversed) that he had described in the expansionary
one (ibid., p. 69). Indeed, Fisher based his whole theory of the business cycle
on the miscalculations of the real rate of interest caused by a fluctuating price
level: in the picturesque words with which he entitled one of his later articles
on the subject, “The Business Cycle Largely a ‘Dance of the Dollar’ ” (1923b).
(In a subsequent article on “Our Unstable Dollar and the So-Called Business
Cycle” [1925], Fisher also provided what he regarded as statistical verification
of his theory.)3
From this analysis of the cycle there immediately followed Fisher’s prescription for eliminating, or at least greatly mitigating, it: if the source of the
problem is the instability of the price level, then the solution to it is to stabilize
this level.4 Accordingly, Fisher devotes the concluding chapter of Purchasing
Power to a description and criticism of various proposals to accomplish this
purpose, and to the presentation of his own proposal. The following year,
he expanded on his proposal in an article in the December 1912 issue of
the Economic Journal. Shortly afterwards, in the February 1913 issue of the
Quarterly Journal of Economics, he presented a more detailed description in
an article entitled “A Compensated Dollar,” under which name his proposal
has since been known. And the only significant difference between the “new
and revised” 1913 edition of Purchasing Power (henceforth, PPM–2) and the
original one is the addition of the appendix “Standardizing the Dollar,” in

3 In

the history of econometrics, this article is notable for Fisher’s having introduced and
applied for this purpose the technique of the distributed lag, the term for which he then also
coined (see Alt 1942, p. 114, n. 4; see also Koyck 1954, pp. 30–32).
4 It is interesting to note that stabilization of the price level was the policy advocated by
many quantity theorists at the time (including Keynes of his quantity-theory period), though not
all for the same reason and/or by the same means. See Patinkin (1972) and Laidler (1991, Chaps.
3 and 5). See also the brief discussion of Wicksell on pp. 10–11 below.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

5

which Fisher refers to his QJE article and spells out his proposal in greater
detail than in the original edition.5,6
In the appendix, Fisher considers it “easier to explain the principle of the
proposal” by considering the case in which all gold coin has been withdrawn
from circulation and replaced by gold certificates which can be redeemed upon
demand from the government for a certain quantity of gold bullion (PPM–2, p.
495). As an example of this aspect of his proposal, as well as to reassure his
reader that its like already existed in the world, Fisher referred to the similar
situation that existed under the gold exchange standard that was in operation
in India, the Philippines and in other countries (PPM and PPM–2, pp. 337–40;
1913b, pp. 226–27). Another way in which Fisher tried to present his plan in
familiar clothing was by relating it to “the ancient custom of seigniorage” and
to refer to it alternatively as “the adjustable seigniorage plan” (1913b, pp. 224,
395–96; see also PPM and PPM–2, pp. 330–1; PPM–2, pp. 498–99), in the
sense that his plan called for making adjustments in the amount of dollars that
one would receive for a given quantity of gold. In an accompanying footnote
(1913b, p. 224, n. 1), however, he admitted that for several reasons (including
the fact that it would not provide the government with revenue, which was of
course the historical purpose of seigniorage) it was a “peculiar sort of seigniorage.” (A similar observation was subsequently made by B.M. Anderson [1913,
p. 42; see Section 3 below].)
Fisher then proceeds to explain that if an index of the price level should
increase by, say, 1 percent, then the purchasing power of a dollar gold-certificate
would be restored by increasing the “gold content” of a dollar by 1 percent;
and if during the following quarter that should not succeed in restoring the
original price level, the gold content would be further increased—and so forth.
Here, then, was a rule in the modern sense of the term (Fischer 1990, p. 1168).
Now, to increase the gold content of the dollar means to decrease the dollar
price of a given quantity of gold, and vice versa. Thus in the back of Fisher’s
mind when he formulated his proposal (and more or less explicitly in some of
his later discussions of it) there may have been the relation:
dollar price of basket of goods and services =
gold price of basket times dollar price of gold.

5 See

the list of differences between the two editions on p. xii of the 1913 edition.
other discussions of Fisher’s proposal, see Lawrence (1928, Chap. 7), Reeve (1943,
Chap. 11 et passim), and Dorfman (1959, vol. 4, pp. 288–93). It is also briefly discussed in the
respective encyclopedia articles on Fisher by Allais (1968, p. 480) and Tobin (1987, p. 373b).
See also Fisher’s autobiographical account in his Stable Money (1934b, pp. 374–89), as well as
the chapters on “The Commodity Dollar” and “Money Illusion” in Irving N. Fisher’s biography
of his father (1956). See also the discussion in the recent biography by R.L. Allen (1993, pp.
162–67 et passim).
6 For

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Federal Reserve Bank of Richmond Economic Quarterly

It would thus seem that any change in the gold price of the basket can be
offset by an appropriate change by the mint in the dollar price of gold, thereby
leaving the dollar price of the basket unchanged.
This relation, however, holds only in an economy in which not only dollars,
but physical quantities of gold (in, say, the form of blank gold slugs of a fixed
weight, the dollar value of which is determined by the mint price of gold)
are part of the circulating medium of exchange, so that the gold price of a
basket accordingly means the number of gold slugs that have to be paid for
a basket. For then a, say, decrease in the mint price of gold, in order to offset
an increase in the dollar price of a basket, will in the first instance (i.e., before
any subsequent change in that dollar price) decrease the dollar value of a gold
slug and hence (by “instant arbitrage” between paying in dollars and paying
in slugs) cause a proportionate increase in the slug price (i.e., the number of
slugs that have to be paid for a basket). But the decrease in the mint price
will also decrease the total quantity of money in the economy to an extent
determined by the proportion of this quantity that individuals choose to hold in
the form of slugs. And after the “first instance,” this decrease will ultimately
(on crude-quantity-theory assumptions) generate an equiproportionate decline
in both the dollar and slug prices of a basket.7
On the other hand, the foregoing relation is obviously not relevant for the
pure form of Fisher’s plan in which only gold certificates are in circulation,
the dollar value of which is not affected by the change in the mint price of
gold. Nor would the situation be different if gold coins (the dollar value of
7 The following example illustrates this process. Assume for simplicity that individuals always hold half of their money balances in the form of dollars and half in the form of gold slugs
(evaluated at the mint price). Assume further that initially all prices in the foregoing relation are
unity. Denote this as Situation I. Let there now be an increase in the output of gold, hence a 10
percent increase in the money supply (which again is equally divided between dollars and slugs),
and hence a 10 percent increase in the price level (Situation II). In accordance with Fisher’s plan,
let the mint price be reduced by 9 percent so as to offset this price increase, but assume that in the
first instance the dollar price of a basket remains unchanged; on the other hand, since the dollar
value of a slug has decreased, this means that the slug price has increased (Situation III). Since
gold slugs (evaluated at the mint price) constitute only half of the money supply, this 9 percent
reduction in their mint price causes a reduction of only 4.5 percent in the total money supply, and
hence ultimately a 4.5 percent reduction in both the dollar and slug prices of the basket (Situation
IV). These developments are described in the following table:

dollar price of basket = gold-slug price of basket times dollar price of gold
I
1.00 = 1.00
II 1.10 = 1.10
III 1.10 = 1.21
IV 1.05 = 1.155

x
x
x
x

1.00
1.00
0.91
0.91

Note that the 9 percent reduction in the mint price does not suffice to restore the original dollar
price of a basket, but see next section on subsequent changes.
I am indebted to my colleague Tsvi Ophir for the construction of this example.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

7

which would also not be affected) continued to circulate as well. For as Fisher
emphasized, the value of the gold actually contained in such coins generally
would be less than the nominal value of the coin itself, so that an anticipated,
say, decrease in the price index and hence increase in the mint price of gold
would not lead to the melting down of coins in order to obtain gold to sell to
the mint. In brief, “Gold dollars would, in such a system, be mere tokens—like
brass checks—entitling the holder to gold bullion” (1913b, p. 222).8

2. THE PLAN: CRITIQUE
Having briefly indicated the nature of Fisher’s compensated-dollar proposal, let
me go on to say that it is a most puzzling one to have been advanced by the author of The Purchasing Power of Money. First of all, this book (as noted above)
regards changes in the quantity of money to be the major cause of changes in
the price level. We should accordingly expect that in any stabilization proposal
that Fisher would present, he would assign a primary role to the quantity of
money. I do not mean that we should expect him to have advocated the policy
of, say, the Chicago School 20 years later to stabilize the price level by making
offsetting changes in this quantity (see Patinkin 1969, pp. 245-46), for there
was as yet no institutional framework in the United States that would have
enabled using the quantity of money as a policy variable. In particular, there
was as yet no central bank; nor was it part of generally accepted thinking at
that time to generate peacetime changes in the quantity of money by having the
government deliberately incur budgetary deficits or surpluses. But we should at
least have expected Fisher to have emphasized and clearly explained the way
in which his proposal would generate the necessary offsetting changes in the
quantity of money and hence in the price level. Of this, there are only passing
remarks in the appendix that Fisher added to the second edition of his book
and in his 1913 QJE article.
Second, not only did Fisher not associate his plan with the quantity theory
of money, but his presentation of it smacks of the commodity theory of money:
the theory that claims that the value of money is determined by the value of the
gold which it contains or for which it can be redeemed, and accordingly the
theory which is the antithesis of the quantity theory that Fisher was forcefully
advocating. In the words of B.M. Anderson, one of its leading advocates at the
8 Fisher was fully aware of the danger that anticipated changes in the price of gold in
accordance with his plan could encourage speculative purchases or sales of gold to the mint that
would generate losses for the government. In order to prevent such speculation, he stipulated that
there be a difference between the mint buying and selling price (which difference he denoted as
a “brassage” charge) and that any change in the mint price of gold as a result of a change in the
price index be less than this difference (1913b, pp. 227, 385–88).

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Federal Reserve Bank of Richmond Economic Quarterly

time, the commodity theory contends “that by putting more bullion behind the
coin you can ipso facto raise the value of the dollar” (1913, p. 42).9
Third, even Fisher’s aforementioned passing remarks on the quantity of
money refer only to the changing amounts of money (i.e., gold certificates)
that miners would receive when they sold new gold to the mint, and that
“jewelers and others who desire gold bullion” would have to pay when they
bought gold from it (1913b, pp. 222–23; see also PPM and PPM–2, p. 343).
But Fisher’s argument in Purchasing Power is that it is the stock of monetary
gold that influences the price level, not the flows into or out of it. In fact,
he distinguishes sharply between these two concepts, and even illustrates this
distinction with one of his ingenious and complicated diagrams (PPM and
PPM–2, p. 105). These flows are, to begin with, small relative to the stock.
Furthermore, even they would be affected only to a minor extent; namely, to
an extent determined by the elasticity of supply of the gold mines, and the
elasticity of demand of the arts, with respect to small percentage changes in
the price of gold. Thus changes in that price cannot be expected to exert any
significant short-run influence on the price level.
Fourth, in his exposition of the quantity theory in terms of his famous
equation of exchange
MV + M V = PT,
it is the total quantity of money, currency (M) plus demand deposits (M ) —
what we today denote as M1—that matters. But the compensated dollar plan
directly affects only M. Now, it is true that in his Purchasing Power, Fisher
assumed that “deposits are normally a more or less definite multiple” of M
(PPM and PPM–2, p. 50, italics added; see also pp. 53–54). But in periods
of transition—which, as we recall, “are the rule,” and which surely are the
periods for which his plan was designed—the ratio of M to M changes (ibid.,
p. 61). It is, however, also true that Fisher assumed that this change reinforces
the effect of the change in M: that, say, a price rise generated by an increase
in the quantity of money also “increases the ratio of M to M” (ibid.). Still, it
is puzzling that he completely disregarded the role of demand deposits.
Fifth, Fisher does not indicate that, under the gold standard that then
prevailed, changing the dollar price of gold in accordance with his proposal
meant changing the foreign exchange rate. At the same time, he was in favor
of fixed exchange rates in order to avoid “again restoring the uncertainties
9 Anderson’s full statement is cited below. In order to avoid possible misunderstanding, let
me emphasize that the long-run implications of the quantity theory, on the one hand, and of the
commodity theory, on the other, are the same in the sense that both imply that the marginal cost
of producing gold equals its mint price. But whereas the quantity theory explains that this equality
is achieved over a period of time during which, say, an increase in the quantity of money raises
prices and hence this marginal cost until it equals the mint price of gold (i.e., until equilibrium
is achieved), the commodity theory contends that this equality always obtains.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

9

of international exchange” (PPM and PPM–2, p. 340). And in an amazing
statement, he declared in his 1913 QJE article that his plan did not involve
“abandoning the gold standard” (ibid., p. 221), for “it is the possibility of turning
gold dollars or gold certificates into commercial bullion which is the essence
of the gold standard” (ibid., p. 223, n. 1)—as if the price at which this was
done, and hence the exchange rate thereby determined, was of no consequence.
In all fairness, however, I must note that there is one discussion in Purchasing
Power (pp. 341–43) which might be interpreted as advocating the adoption of
the compensated dollar proposal by all gold-standard countries of the world in
a way which would leave their exchange rates unchanged. On the other hand,
though the numerical illustration of the operation of the plan in Appendix II
of the 1913 QJE article (here described as “the adjustable seigniorage plan”)
is based on the assumption that it is adopted only in the United States (ibid.,
p. 394), there is no indication in it of the consequent effect on the exchange
rate. In Appendix III to the article, however, there is a brief consideration of
the case in which all countries adopt the proposal (ibid., p. 396).10
There is, however, a simple answer to most of the above puzzles; namely,
that the person who is our present concern is not Irving Fisher the author of
the scientific work on The Purchasing Power of Money, but Irving Fisher the
deviser of a plan to be “sold” to the economics profession as well as to the
business community and government—and to be “packaged” accordingly. The
quantity theory of money was out of favor in some circles, so the plan should
not be explicitly associated with it. The commodity theory of money had influential supporters, so the plan should be presented in language that had the
sounds of that theory. The gold standard was sacred, so it should be emphasized
that the plan did not involve its abandonment.

3. THE RECEPTION BY THE PROFESSION
The foregoing criticisms of Fisher’s plan are not new. Indeed, most of them
were raised immediately after its publication, though they did not deter Fisher
from persisting in advocating the plan for many years to come. Thus in the issue
of the QJE following the one with Fisher’s article, Frank Taussig (1913)—the
doyen of American economists—published a critique of Fisher’s plan in which
he said:
More stress should be laid, however, than Professor Fisher does, on
the fact that the plan can work out its results only through its effects on
10 I should note that Allais (1968, p. 480) presents a more favorable view of Fisher’s plan
in a long-run context. He claims that if it had been in operation during the nineteenth century,
then “the long-run increases and declines in the price level, which actually occurred and whose
drawbacks are evident, could have been avoided.” Fisher, however, regarded his plan as one that
would deal with short-run problems as well.

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Federal Reserve Bank of Richmond Economic Quarterly
the quantity of coined gold ˙ The consequences on prices [of an increase
...
in the gold content of the dollar] will be precisely the same as those of diminished production or limited coinage. Professor Fisher seems to expect a
closer connection. His analysis implies, almost states in terms, that prices will
accommodate themselves at once or very promptly to the bullion equivalent
of the coined dollar; that as the bullion required for the dollar increases, prices
will fall quasi-automatically in proportion; and that as the bullion equivalent
lessens, prices will be correspondingly affected at once. Now, no one has stated
more clearly and explicitly than Professor Fisher himself, in his Purchasing
Power of Money, the grounds for maintaining that the connection between the
bullion equivalent in the coined dollar and prices will work out its effects
solely through changes in quantity. He has shown that the connection between
the quantity of coined money and general prices is by no means a close one.
It is not only loose and uncertain, but we are much in the dark concerning
the degree of looseness and uncertainty. Economists should be very chary of
prediction in such matters, and Professor Fisher makes predictions which the
event might greatly falsify. (1913, pp. 402–3; italics in original)

As might be expected from an economist with a primary interest in international trade theory and policy, Taussig (1913, pp. 410–11) also pointed out the
effect of Fisher’s plan on the exchange rate. He stressed that while that effect
would be immediate, the effect on domestic prices would at best take place
with a lag. Thus if in the face of an inflationary process the gold content of the
dollar were increased—which would mean that the dollar appreciated in the
foreign exchanges—the receipts of exporters would immediately be affected
adversely, while their domestic costs of production would decline only after
a lag. Exporters would then put pressure on Congress and the government to
abandon the policy. Furthermore, Taussig left no doubt about his opinion that
an “international agreement” for the adoption of the compensated dollar plan–
which would have the benefit of obviating the need for changes in the exchange
rate–seemed to him “in the highest degree unlikely” (ibid., p. 407).
In light of these as well as other objections, Taussig concluded, “On the
whole, I conclude that this proposal for radical change gives better opportunity
for ingenious intellectual exercise than for practical efficacy” (ibid., p. 416).
Interestingly enough, Fisher’s Quarterly Journal of Economics article also
evoked a critical reaction from Knut Wicksell. In a note entitled “Another
Method of Regulating the Value of Money” which he submitted in 1913 to that
journal, Wicksell began with a criticism of Fisher’s plan on the grounds that
although of course the method proposed by professor Fisher always must be
regarded as a step in the right direction, it will generally prove to be too small
a step to have immediately any practical bearing at all on the level of prices.
Fisher forgets, it seems to me, that an alteration of the mint price will directly
influence only the new gold, and as the gold produced every year is only a
small fraction of the whole amount of gold and hence of the volume of money,

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

11

the possible alteration of the value of money and of the level of prices will at
first only be a fraction of a fraction or practically nil. (emphasis in original)

As an alternative to Fisher’s plan, Wicksell then went on to spell out the details
of the policy that he had advocated in his 1898 Geldzins und G¨ terpreise11 and
u
in his 1907 Economic Journal article on “The Influence of the Rate of Interest
on Prices” to stabilize the price level by means of central-bank interest-rate
policy. In a very polite and respectful letter of rejection to Wicksell dated
January 7, 1914, however, Taussig (then editor of the QJE) did not refer to
Wicksell’s criticism of the plan, but simply explained that since Wicksell’s policy proposal was familiar to American economists from his two aforementioned
publications, he (Taussig) had reluctantly concluded that the journal could not
publish the note.12
Fisher also presented his plan at the 1912 Meetings of the American Economic Association. And here the sounds of the commodity theory of money
are unmistakable:
Both on the basis of theory and of facts, we may accept as sound the
principle that the lighter the gold dollar the less its purchasing power and the
more magnified the scale of prices; and that the heavier the dollar the greater
its purchasing power and the more contracted the scale of prices. Evidently
if we can find some way to increase the weight of the dollar just fast enough
to compensate for the loss in the purchasing power of each grain of gold, we
shall have a fully “compensated dollar,” that is, a dollar which has constantly
restored to it any purchasing power it may lose by gold depreciation. (1913c,
pp. 20–21)

Again, the value of a gold coin “would be determined just as the value of a
gold certificate or any other paper money is today determined, by the ultimate
bullion with which it would be interconvertible” (1913c, p. 24).
In any event, one Albert C. Whitaker (1913, pp. 31–32) began his discussion of the paper with the statement that “at one place in his paper Professor
Fisher has followed the instincts of a good propagandist and has invited even
11 See

pp. 189–92 of the 1936 translation of this book under the title Interest and Prices.
am indebted to Lars Jonung for providing me with a copy of Wicksell’s note, as well
as of Taussig’s reply, and granting me permission to cite from them here.
In a comment on this paragraph, David Laidler has pointed out to me that the English
version of Wicksell’s Lectures on Political Economy, Vol. II: Money (which was translated from
the third [1929] edition of the Swedish original) contains a “Note on Irving Fisher’s Proposal
for the Regulation of the Purchasing Power of Money” (ibid., pp. 225–28). An attached editorial
footnote explains that this “Note” was added by Wicksell to the second (1915) Swedish edition,
and that Wicksell had indicated in the preface to that edition that it constituted a brief resume of
a 1913 paper which he had published in Ekonomisk Tidskrift. The title of that paper was similar
to the one he submitted to the QJE, and so I presume that its contents were also similar. In any
event, the “Note” in the English translation contains the same criticism of Fisher’s plan cited
here–including the same emphasis on “fraction of a fraction.”
12 I

12

Federal Reserve Bank of Richmond Economic Quarterly

those who repudiate the quantity theory to join with him in support of the
adjustable seigniorage plan”13 and then went on to emphasize that “it is clear
the author of the plan himself conceives it simply as one which will provide for
an approximate stability in the purchasing power of the money unit merely by
way of and through its effects upon the quantity of standard coin in circulation”
(italics in original).
At the same time, Whitaker questioned the practicality of the plan because
he
[did] not at all follow Professor Fisher in his assumption that the amount of
change of seigniorage [i.e., in the gold content of the dollar] required to correct
a given change in the price level can be clerically or ministerially determined,
or even approximately so determined. (ibid., p. 32; italics in original)

And again:
I may be wrong, but I think the assumed substantial proportionality between
seigniorage change and consequent price level change (or correction), would
be likely to prove so far away from what we should actually experience as to
suggest strongly the abandonment of the ministerial or clerical determination
of the seigniorage. (ibid., p. 34)

With these last two comments, another discussant, O.M.W. Sprague (1913, p.
40), who played an important role in the discussions that led up to the Federal
Reserve Act (Warburg 1930, vol. 1, pp. 35–6; Friedman and Schwartz 1963,
pp. 410–11), expressed his agreement.
Whitaker also pointed out that, in order to avoid fluctuations in the exchange rate,
the only method to be recommended for putting Professor Fisher’s general
plan for an adjustable seigniorage into effect, would be to have an international
agreement between the leading nations providing for equal and simultaneous
alterations of the seigniorage charge in all, determined upon the basis of a
world’s index number. (ibid., p. 35)

Of particular interest is the comment of a then leading exponent of the
commodity theory of money, B.M. Anderson (1913, p. 42), part of which I
have cited above:
Because I am not a quantity theorist, I am disposed to believe that Professor Irving Fisher’s plan of stabilizing the dollar might be feasible. If he
put it on a quantity theory basis, and tried to raise the value of the dollar
by charging a real seigniorage, and so checking the increase in the number
of dollars, I should be very skeptical. But his plan is not a real seigniorage
13 No such statement appears in the published version of Fisher’s paper. Presumably, however, he did make it in his oral presentation. In any event, he did make it in some of his later
writings (see below).

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

13

plan. The coined dollar is interconvertible with the gold bullion, and you can
always get your bullion back. I believe that by putting more bullion behind
the coin you can ipso facto raise the value of the dollar, and consequently
lower the level of prices. But I do not see how, on the basis of the quantity
theory, you could be sure of getting any definite result by Professor Fisher’s
plan. (ibid., italics in original)

Another discussant was E.W. Kemmerer (1913, p. 45), a staunch advocate
of the gold standard, who accordingly opposed the plan on the grounds that “its
adoption would demoralize the international exchanges.” He also described as
“visionary” the “hope of securing a comprehensive international agreement on
this scheme” and thereby enabling the plan to operate without causing changes
in exchange rates.
In his reply to his critics, Fisher (1913d) agreed with Kemmerer’s statement
about the effect on the exchange rates, and said that “for this reason I should
not advocate the plan for one nation alone, but should advocate it only under
international agreement” (ibid., p. 48). But in the paragraph following that statement, Fisher explained to another of his critics that one of the ways in which
a reduction in the price of gold would “tend to contract the currency” would
be by “diverting gold ˙ to countries where the price had not been changed”—a
..
diversion which would take place only with respect to countries that were not
part of an “international agreement” and with respect to which the dollar would
accordingly appreciate.14 Nor did he address the basic question that had been
raised by both Whitaker and Anderson as to the questionable quantitative effect
that changing the gold content of the dollar would have on the total stock of
money, as distinct from its effect on the inflow and outflow of gold into this
stock.
During 1913 there appeared many other articles on Fisher’s plan by both
American and European economists. In one of them, David Kinley (1913, pp.
9–10, 16–17), an influential monetary economist of the period (see Dorfman
1959, vol. 4, p. 313 n.) in effect pointed out that Fisher’s proposal would change
only the quantity of currency in circulation, whereas the price level also depended on the quantity of demand deposits as determined by the volume of
bank credit—and in this context rejected Fisher’s assumption of a constant ratio
14 Further evidence on Fisher’s ambivalent treatment of this issue is provided by the following footnote in a 1913 article objecting to his plan by one E.M. Patterson:

[Fisher’s] ready admission of the serious effect on foreign trade is surprising. In
reply to the question, “Would not the adoption of the plan by the United States alone
play havoc with our foreign trade?” he answers “Yes, most certainly. Foreign exchange
would become uncertain and variable. While the plan could be worked if adopted by
one nation without the concurrence of others, its benefits would be best secured through
its adoption by a number of nations.” The New York Times, December 22, 1912. (ibid.,
p. 869, n. 14)

14

Federal Reserve Bank of Richmond Economic Quarterly

between the two.15 J.M. Clark (1913) wrote that the plan was an improvement
over the gold standard, but pointed out possible complications.
Fisher’s reaction to these articles was presented in his “Objections to a
Compensated Dollar Answered” (1914), which included a selected bibliography of the literature that had grown up about his plan. In his article Fisher
intensified his effort to sell his plan by means of arguments which made it all
things to all men (ibid., pp. 820–22).
Thus it was not true that “the plan assumes the truth of the quantity theory
of money. . . . On the contrary, the plan will seem simpler, I think, to those
who believe a direct relationship exists between the purchasing power of the
dollar and the bullion from which it is made—without any intermediation of the
quantity of money—than it will seem to quantity theorists”—and here Fisher
cites B.M. Anderson’s aforementioned statement at the 1912 meetings of the
American Economic Association. On the other hand, it was not true that “it
contradicts the quantity theory” for, say, “an increase in the weight of the virtual
dollar, i.e., a reduction in the price of gold bullion, would tend to contract the
currency, by diverting gold from the mint into the arts ˙ A decrease, of course,
...
would have the opposite effect.”
There was no reason to fear that “the correction of the price level would
be too sudden,” for
all adjustments require time. Changes of the flow of gold into or out of circulation are like changes in a mill pond from the sluice gates. The pond
does not jump its level down or up every time the gate is opened or closed.
The change of level begins immediately but it is not completed immediately.
(italics in original)

On the other hand, there was no reason to fear that “the correction of the price
level would be too slow”:
How prompt the effect would actually be, we have no exact means of knowing.
I should expect an appreciable effect within a week. One can scarcely deny
that the effect would begin at once, for the instant that the price of gold is
decreased, even a little, there would be at least some tendency to increase the
use of gold in the arts and, consequently, an immediate reduction in the amount
of gold taken to the government for money. If this be conceded, the plan would
surely, under any conceivable circumstances, have a great and quick influence
toward stability. (first and last set of italics in this passage added)

Fisher then proceeded to support his plan with misleading examples. “The
closure of the Indian mints in 189316 had an almost immediate influence in
raising the value of the rupee”—as if a valid inference could be drawn from
15 Actually, as noted above, Fisher did not maintain this assumption for “periods of transition”
(PPM and PPM–2, p. 55).
16 For details, see Nambudiripad (1955), pp. 57 ff.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

15

a situation in which there was a complete stoppage of the sales of bullion to
the mint in exchange for new coinage, to a situation in which net sales to the
mint were slightly reduced as a result of the decrease in the output of gold
and increased diversion into the arts caused by a decline of 1 percent in the
mint price. “The rate of exchange on London in New York has often changed
from the maximum to the minimum inside of a fortnight”—as if the arbitrage
that rapidly adjusted exchange rates between those two gold-standard countries
by shifting amounts of gold from an existing monetary stock of gold from the
market for dollars to that for sterling (or vice versa) is of any relevance for
the speed of adjustment of the price level involved in the compensated dollar
plan—which depends on a change in the level of the stock (see p. 8 above).

4. THE HIGH POINT OF THE COMPENSATED DOLLAR
In his 1914 article (p. 818), as well as in the appendix that he had added
to the revised edition of Purchasing Power of Money (1913a, p. 494), Fisher
referred to a book that he hoped shortly to publish about his plan. So let me
skip the many additional discussions of his plan in the immediately following
years and turn to the book in question. This finally appeared in 1920 under the
title Stabilizing the Dollar and is the most systematic and detailed presentation
of the compensated dollar proposal. Here again we find statements that sound
more like those of a commodity theorist than a quantity theorist, such as the
following example:
I do not think that any sane man, whether or not he accepts the theory of
money which I accept,* will deny that the weight of gold in a dollar has a
great deal to do with its purchasing power. More gold will buy more goods.
Therefore, more gold than 23.22 grains will, barring counteracting causes,
buy more goods than 23.22 grains will buy. Therefore if the dollar, instead
of being 23.22 grains, or about one-twentieth of an ounce of gold, were an
ounce or a pound or a ton of gold, it would, other things equal, surely buy
more than it does now, which is the same thing as saying that the price level
would be lower than it is now.
A Mexican gold dollar weighs about half as much as ours and therefore
has less purchasing power. If Mexico should adopt the same dollar that we
have, no one could doubt that its purchasing power would rise about twofold,
that is, the price level in Mexico would fall about half. Likewise, if we should
adopt the Mexican dollar, our prices would about double.
* Thus B.M. Anderson, Jr., probably the ablest writer among the few who still
dissent from the “quantity theory” in any form, nevertheless approves of the
proposal to stabilize the value of a dollar by adjusting its weight.
(ibid., p. 90)

Note, too, the misleading nature of the argument in the second paragraph: for
the changes in the price level there described are not the short-run ones that

16

Federal Reserve Bank of Richmond Economic Quarterly

Fisher claimed for his plan, but the long-run changes associated with the new
equilibrium that would be established after the monetary stock of gold (and
hence the quantity of money) had been slowly and fully adjusted to the change
in the gold content of the dollar in question—including the adjustment generated
by the specie-flow mechanism activated by the change in the exchange rate.
In this book, Fisher (ibid., pp. 87–96) again emphasized that his plan did
not involve the abandonment of the gold standard. Under the heading “The
Essentials of a Gold Standard,” he justified this statement on the grounds that
the mint would continue to buy and sell gold in exchange for gold certificates,
which he termed “yellowbacks”—presumably to distinguish them from the
famous greenbacks, which could not be redeemed for gold. In this context, he
also mentioned importers and exporters as buyers and sellers, respectively, of
gold. But he did not point out that his plan, based as it was on a varying price
of gold, meant (in basic contrast with the gold standard as it then operated)
that the exchange rates at which they carried out their international transactions
would also vary. This fact was, however, pointed out in an appendix to the book
on “Technical Details,” but with practically no indication of the difficulties for
international trade that this would generate, and only with the expression of
the hope and anticipation that the plan would be adopted by other countries as
well (ibid., pp. 172–82; see also p. 235, sec. D).
In another appendix to the book (ibid., pp. 214–51), Fisher repeated his
presentation of the plan as one that could be supported whether or not one
believed in the quantity theory, and also discussed criticisms that had been
levied against the plan. Though he did not explicitly refer to the one about
the slowness with which the plan would affect prices, he did make a major
modification in it which could increase this speed. In particular, Fisher added
the possibility of adopting a “definite–reserve system” in which any change
in the price of gold also revalued the existing monetary stock of gold with a
consequent change in the quantity of gold certificates that could be issued. This
was contrasted with the “indefinite-reserve system,” which is how he termed
the system he had until then advocated. In Fisher’s words:
Under the “indefinite-reserve” system the only inflow and outflow of
[gold] certificates would be through the deposit and withdrawal of gold, just
as at present; whereas under the “definite-reserve” system there would be,
in addition, an inflow and outflow of certificates through special issues or
cancellations to keep the total outstanding volume of certificates in tune with
the gold reserve ˙
...
The “definite” system would act more promptly to stabilize the price
level than would the “indefinite,” because, for one reason, the change in the
circulation would be more prompt. The instant any change in the dollar’s
weight is made there is a change in the number of dollars of the reserve, and
the volume of certificates is readjusted to this changed reserve immediately.
Under the “indefinite” system, on the other hand, the circulation would be
affected somewhat more slowly and only as the flow of gold deposits and
withdrawals became changed. (ibid., pp. 129–31)

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

17

Significantly enough, however, Fisher does not explain the mechanism by which
“the volume of certificates [in circulation] is readjusted.” Furthermore, in view
of the smallness of the flows relative to the stock of gold, surely the term “more
slowly” grossly understates the difference in speed at which these two systems
would operate.
There are also three minor and somewhat piquant points about the book
that I would like to mention. First, Fisher rhetorically asked, “Why did not
our civilization improve [i.e., standardize] its monetary units years ago, as it
improved all other units? Why was so simple an idea overlooked or ignored?”
To this he replied, “because until recently it lacked the necessary instrument,
the index number” (ibid ., p.113, italics in original)—an allusion (inter alia)
to the fact that the United States began publishing such numbers only in 1890
(see n. 1 above), and a nice example of Fisher’s concern with the relation
between theory and measurement. Correspondingly, he attributed the continued
resistance to his plan even after such numbers were available to conservatism,
to “resistance to change” (ibid., p. 237). In this context he added:
And now this obstacle of conservatism—the one great obstacle—has been
considerably lessened by the Great War, which has shaken the whole world out
of old ruts. Even Great Britain is considering giving up her ancient monetary
system—of pounds, shillings, and pence—in favor of a decimal coinage. (ibid.,
p. 239)

He was one “Great War” too early.
Second, in this book Fisher coined the term “money illusion” to denote
“the illusion that money is always fixed in value,” and that it is only the prices
of goods that change (ibid., pp. 35–39; see also pp. xxxii–xxxiii). (Several years
later, he published a book with this title; see below.)
The third point is the dedication of Stabilizing the Dollar to “John Rooke,
Simon Newcomb, and Alfred Russel Wallace.” In another of its appendixes entitled “Precedents,” under the rubric “Direct Anticipations,” Fisher lists Rooke as
the one who (in 1824) had first published a proposal “substantially like that proposed in this book,” and after him under that rubric lists Simon Newcomb (ibid.,
p. 293).17 What intrigues me, however, is the dedication to Wallace, by many
considered the joint discoverer with Charles Darwin of the theory of evolution.
17 Under this rubric, Fisher also lists Alfred Marshall, as well as three obscure American
and English writers of the 1890s. It was, of course, to Newcomb as an anticipator of the equation
of exchange that Fisher had also dedicated his Purchasing Power of Money (see p. 25, n. 2). In
his later book on Stable Money (1934b, pp. 26–28), Fisher presents a more detailed account of
Rooke’s proposal. Fisher lists Marshall on the basis of the second of two plans described in a
footnote in the latter’s 1887 article on “Remedies for Fluctuations of General Prices” (p. 206,
n. 2), which Fisher (1920, p. 294) describes as “in principle, virtually that of this book.” Note,
however, that as Fisher (ibid, p. 293) himself points out, Marshall states in that footnote that he
does not advocate either of the two plans. Note, too, the excerpt from an October 1912 letter
which Marshall wrote Fisher in which he expresses some reservations about the plan (reproduced
in Pigou, ed. 1925, pp. 477–78).

18

Federal Reserve Bank of Richmond Economic Quarterly

Wallace is listed in the aforementioned appendix under the rubric “Remote
Anticipations of the Plan to Stabilize the Dollar,” in the category of those who
advocated doing so by printing irredeemable paper money “regulated by an
index number of prices” (ibid., pp. 290–91). Thus in the 1898 paper to which
Fisher refers, Wallace explains that if the index should show a decline in prices,
the “Mint” would “issue fresh money,” and that
This money is sent to the Treasury and is at once brought into circulation by
being paid away in salaries, wages, purchase of materials, &c., in the various
Government departments ˙ On the other hand, when prices are rising, owing
...
to there being rather more money in circulation than is necessary, instructions
are sent to the Treasury to cancel a certain amount of the money paid in for
taxes, stamps, &c., till the balance is restored. (Wallace, 1898, p. 148).

In this appendix, Fisher (1920, p. 291) explains that the “essential difference”
between plans such as those of Wallace and his own “is that between redeemability and irredeemability.” But is there really an essential difference
between always being able to “redeem” a gold certificate for a possibly varying quantity of gold, on the one hand, and always being able to purchase with
irredeemable money a given quantity of gold at a possibly varying market price,
on the other?
So as an outsider to economics, Wallace was free from the attachment to
gold and thus advocated a stabilization policy that was more in the spirit of
the quantity theory. He was also explicit about what Fisher (in his definitereserve system) left unspecified; namely, the role of the Treasury in injecting or
withdrawing quantities of money from circulation. Here was a true anticipator
of the Chicago School of the 1930s. But what remains a puzzle for me is why
Fisher chose to dedicate the book to Wallace in preference to the well-known
economists he cited in the same category with him—among them Carl Menger
and Charles Gide (Fisher 1920, p. 291).18
Let me finally turn to that part of the book which in effect constituted a
most significant turning point in Fisher’s campaign for the compensated dollar,
even if he did not at the time recognize it as such. I am referring to the last
clause in Fisher’s “Tentative Draft of an Act to Stabilize the Dollar” that also
appears in the book’s appendix on “Technical Details.” It reads:
The Federal Reserve Board could assist in the prompt and efficient operation of the new system by having due regard to the rise and fall of the Index
Number, as suggested by Mr. Paul Warburg. This would help [by] its adjustment of the rate of discount and its general loan policy to be such as to keep
the volume of individual deposits subject to check approximately proportional
both to bank reserves and to the Government gold reserve against gold bullion
dollar certificates. (ibid., p. 213)
18 It

is interesting to note that Fisher had already referred to Wallace in his 1914 article (p.
818, n. 1).

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

19

Presumably, this clause represented Fisher’s response to those who criticized
his plan (including Warburg19 ) on the grounds that it dealt only with the currency component of the money supply. But Fisher failed to recognize that far
from strengthening the case for the compensated dollar, this clause actually
undermines it. For if success of the plan is dependent on the ability of the
Federal Reserve to control the volume of demand deposits, then one might as
well dispense with the plan and depend solely upon the Federal Reserve to
stabilize the price level directly by controlling the total money supply!
The high point in Irving Fisher’s protracted campaign for the compensated
dollar was reached when two years later the House Committee on Banking
and Currency held hearings on such an act (subsequently described by Fisher
[1934b, p. 152] as “practically in the form” of his aforementioned “Tentative
Draft”) which had been submitted by Congressman T. Alan Goldsborough
(the “First Goldsborough Bill”). Interestingly enough, this bill provided for a
modified version of Fisher’s definite-reserve system. In particular, it called for
maintaining a 50 percent gold reserve against gold certificates and stated that:
If on any date the reserve falls short of 50 per centum [as it would if the
price of gold were reduced—i.e., the gold content of the dollar increased—in
order to offset an increase in the price level] it is to be restored by withdrawing
from circulation and canceling gold bullion dollar certificates.
If on any date the reserve exceeds said 50 per centum it is to be restored
by issuing and putting into circulation the requisite number of new gold bullion
dollar certificates.
The Secretary of the Treasury is authorized to make said withdrawals of
certificates from circulation by withdrawing from the Government deposits in
national banks and to issue certificates and place them in circulation by adding
to those deposits. (H.R. 11788, 1922, p. 3)

So the bill was more specific than Fisher had been in Stabilizing the Dollar
(see above) about the role of the Treasury in the case of the definite-reserve
system. But it too did not make explicit the implications of this system for
the Treasury’s budgetary deficit or surplus. It should also be emphasized that
neither the bill nor Fisher’s “Tentative Draft” stipulated that the plan should
only be adopted as part of an international agreement.
Needless to say, the first witness in the hearings on the bill was Fisher himself (1922, 1923a), who in his book-length testimony (which at times clearly
tried the patience of the committee) repeated much of what he had written on
the evils of an unstable dollar, the workings of the compensated dollar proposal, and his arguments in favor of it—including (in a more egregious form)
his aforementioned misleading argument about Mexico.20 In his testimony, he
19 See Warburg (1920, pp. 702–3). Warburg was one of the five members of the original
(1914–18) Federal Reserve Board; see Barger (1964, pp. 50–51).
20 “The Mexican dollar now is half the value of ours. On the other side of us, across the

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Federal Reserve Bank of Richmond Economic Quarterly

also stressed the importance of the cooperation of the Federal Reserve for the
success of the proposal, and explicitly referred in this context to the aforementioned last clause of the “Tentative Draft” of the bill that he had presented in
his Stabilizing the Dollar (Fisher 1922, p. 27; see also pp. 46–47).
Kemmerer (who as a result of his having repeatedly preached the virtues of
the gold exchange standard to the new countries that had been established after
World War I had become known as “the international money doctor”21 ) also
presented a statement to the Committee. Though agreeing with the importance
of stabilizing the price level, he pointed out that “how long a time would be
required for such changes in the size of the bullion dollar, working through the
money and deposit currency supply, to reduce the price level, say, 1 percent,
is a debatable question” (Kemmerer 1923, p. 158). And in the concluding
paragraphs of his statement he stated:
In the judgment of the writer any plan for stabilizing the monetary unit
to be successful should be international in its scope, including at least three or
four of the leading commercial nations and more if possible. For one country
to adopt the plan alone would throw its exchanges entirely out of adjustment
with those of gold-standard countries (and also of silver-standard countries),
and would give rise to all the evils of widely fluctuating exchange rates. (ibid.,
p. 160)

Significantly enough, in his summary many years later of the hearings on the
bill, Fisher (1934b, p. 155) said that Kemmerer “wrote (among other things) a
strong endorsement of the ‘Compensated Dollar’ plan,” and made no mention
whatsoever of the serious reservations that Kemmerer had expressed, which—in
view of the absence of any reference in the bill to an international agreement—
were tantamount to a recommendation to reject it.

5. THE DECLINE OF THE COMPENSATED DOLLAR
Neither the First Goldsborough Bill, nor the second (1924) slightly revised
version,22 was reported out of Committee. And with the increasing importance
of Federal Reserve monetary policy in the years which followed, Fisher slowly
came around to accepting the view that the objective of stabilizing the price
Canadian border, they have the same dollar as we have. Suppose Mexico ˙ would say ˙ ‘we are
..
..
going to have on this continent just one dollar of equal value in Canada, Mexico, and the United
States.’ Immediately prices in Mexico would be cut in two ˙ Is there any doubt about that?”
...
(Fisher 1922, pp. 23–24, italics added)
21 See Groseclose (1965), p. 141. See also Barber (1985), pp. 59–60, and his reference (ibid.,
p. 209, n. 48) to Kemmerer’s presidential address to the American Economic Association (1927),
in which the latter described the advice that he had given to many countries in connection with
the “establishment of the gold standard” (ibid., p. 4).
22 The revision consisted of the deletion of the clause that required a 50 percent reserve
against gold certificates. See H.R. 494, 68 Cong. 1 Sess., December 5, 1923.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

21

level could be achieved by this policy alone, without the need for a compensated
dollar. Thus his 1928 The Money Illusion includes a discussion of the Federal
Reserve’s “duty to control or influence credit” by means of its open market
operations, as well as by the fixing of its rediscount rates (ibid., pp. 131–35).
Though in this book Fisher again presented his compensated dollar proposal
(in its definite-reserve version), he concluded this presentation by saying:
When my Stabilizing the Dollar was written, I relegated credit control to
the Appendix, assuming that all banking, even central banking,23 would still
be conducted purely for private profit. My aim was to make the whole plan
of stabilization—both gold control and credit control—as “automatic,” that is
as free from discretion, as possible.24
Since that time, however, as has been shown in this book, discretionary
credit control has actually come into existence. This, when duly perfected
and duly safeguarded, will greatly simplify and improve the technique of
stabilization and will make gold control secondary to credit control. (Money
Illusion, pp. 192–93)

Even though it includes The Money Illusion in its list of references, there
is no mention of “credit control,” and accordingly no indication of this shift
in emphasis, in the entry “Compensated Dollar” that Fisher wrote for the 1930
Encyclopaedia of the Social Sciences. On the other hand, this shift is expressed
in an even more marked way in Fisher’s 1932 Booms and Depressions. The
roughly 20 percent decline in prices that had taken place in the preceding
two years had greatly increased the real burden of debt with a resulting wave
of bankruptcies, and had led Fisher to assign great importance to this factor
as a generator of depressions.25 Correspondingly, he stressed the desirability of “reflating” the price level to its original level—and then stabilizing it
there. Chapter 10 of the 1932 book is accordingly devoted to a description of
“Remedies” to accomplish this subsequent stabilization. Most of this chapter
is devoted to the role that can be fulfilled by Federal Reserve monetary policy
in accomplishing this objective by effecting changes in the quantity of money
and hence on the price level. There is only a brief mention of the compensated
23 This

is a most disingenuous statement for Fisher to have made: it is certainly not the view
that he expressed in the 1913 Hearings before the Senate Committee on Banking and Currency
on the Federal Reserve Act (Fisher 1913e, pp. 1129–59). Nor does it accord with his description
of this act in his Stable Money (1934b, p. 148).
24 Another questionable aspect of Fisher’s discussion on these pages is his presentation of the
compensated dollar plan as being necessarily more “automatic” than a Federal Reserve monetary
policy that would also be based on the price index.
25 See also his “Debt-Deflation Theory of Great Depressions” (1933a). Note that in contrast
with his Purchasing Power of Money (1911, 1913)—in which a depression was explained as the
result of the fact that the price level was decreasing (see p. 4 above)—Fisher now emphasized
the role played by the fact that it was low. That is, his emphasis shifted from the rate of change
of prices to their absolute level. See Patinkin (1972, pp. 5–10). This aspect of Fisher’s analysis
of the depression has been much emphasized by Tobin (1985, p. 36b; 1987, p. 375b).

22

Federal Reserve Bank of Richmond Economic Quarterly

dollar plan, and even then not as the first choice. In Fisher’s words:
A simple application of the compensated dollar plan would be to rely
principally upon credit control, and only at long intervals regulate the weight
of the dollar when other means proved inadequate. (ibid., p.139)

But Fisher does not explain why the compensated dollar plan would help in
cases where “credit control” proved “inadequate.”
Another significant aspect of this chapter is that in it Fisher comes full
circle in the sense that (to the best of my knowledge) it is the first time he
explicitly discussed stabilization policies within the analytical framework of
the equation of exchange that he had developed in his 1911 Purchasing Power
of Money. Similarly, he does so more explicitly than before in terms of the
quantity theory. And since (T given), the equation implies that P is affected by
V as well as by M, he also proposed a policy of influencing the price level by
what he called “velocity control” (Booms and Depression, pp. 140–1). This was
to be based on Silvio Gesell’s plan of issuing “stamped money,” which (Fisher
said) “would operate as a stamp tax on hoarding—increasing the velocity as
well as the quantity of money” (ibid., pp. 226–28). Fisher’s subsequent book
on After Reflation, What? (1933b) again assigns the major responsibility for
stabilizing the price level to Federal Reserve monetary policy, and again does
so within the analytical framework of the equation of exchange (ibid., Chap. 7;
Chap. 8 of the 1934 edition). Velocity control also earns brief mention (1933b,
pp. 95–98; 1934a, pp. 106–9). Fisher spelled out this last proposal in greater
detail in a book on Stamp Scrip that he also published in 1933.
So that is the anticlimactic denouement of the story of the compensated
dollar plan. I should however note that in After Reflation, What?, Fisher again
mentioned the compensated dollar plan as one that could be brought into operation if a “reasonable credit” policy would not be able to deal adequately with
great inflows or outflows of gold (1933b, pp. 93–95; 1934a, pp. 104–5). But
Fisher’s reference to this as a serious possibility was at variance with the enthusiastic description he had presented in his 1928 Money Illusion (pp. 131–35)
of how the open market sales of the Federal Reserve in 1922 had prevented the
monetary expansion and consequent inflation that otherwise would have taken
place as a result of its “huge gold reserves.” Furthermore, even if a central
bank in a gold-standard country should have to take additional steps in order to
deal with undesired gold movements, those steps are usually described as the
appreciation or depreciation of the exchange rate, and surely it is misleading
to describe them in terms of the compensated dollar plan.
In a section entitled “My Personal Views” in his book Stable Money
(1934b)—which in many ways can be regarded as Fisher’s concluding work
on the subject—he wrote:
As to the problem of stable money in the United States, while a rough
stabilization could be obtained by sole reliance on adjusting the price of gold

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

23

according to the compensated dollar plan, I do not think a really accurate
stabilization is feasible without also a direct control of the total volume of
checking deposits or what may be called checkbook money ˙ I would de...
pend for a stable dollar mainly on open market operations and occasional
adjustments of rediscount rates ˙ (ibid., pp. 396–97)
...

So even at the end Fisher could not bring himself to giving up his compensated dollar plan entirely. Indeed, only in his 1935 100% Money—a book
which (as Fisher indicates in its preface [p. ix]) was much influenced by the
memoranda on this subject prepared by Henry Simons and his colleagues at
the University of Chicago—is there no mention whatsoever of the compensated
dollar plan. Here (once the 100 percent system was installed) stabilization of
the price level was to be achieved by open market operations and velocity
control alone (ibid., pp. 89–91). Fisher, however, might have felt that since
100 percent money would prevent sharp fluctuations in the volume of demand
deposits and hence of the quantity of money, there would be no need for any
further action.
“On January 15, 1934, President Roosevelt sent a special message to
Congress, which was again a confirmation of his intention of ‘˙ restoring the
..
price level, and, ˙ arriving eventually at a less variable purchasing power for
..
the dollar˙ ” (Stable Money, 1934b, p. 369, ellipses in original). That was
...’
Fisher’s description of Roosevelt’s decision to devalue the dollar, a decision
that was put into effect at the end of that month, when Roosevelt raised the
price of gold from $20.67 to $35.00 an ounce. So the question naturally arises
as to the role that Fisher and his compensated dollar plan played in this decision
to (in his terms) decrease the gold content of the dollar. In his fascinating paper
on “Irving Fisher, F.D.R., and the Great Depression” (1977), William R. Allen
cites a letter that Fisher wrote Roosevelt in April 1933 in which he referred to
“the compensated dollar plan to which devaluation is the natural introduction”
(ibid., p. 570, n. 44). Allen also refers to letters that Fisher subsequently wrote
Roosevelt suggesting various levels to which the price of gold should be raised,
as well as a letter that Fisher wrote his wife in August 1933 reporting on a conversation that he had had with Roosevelt on the subject. Allen, however, adds
that “apparently, Fisher gave the President no hint of what ‘the compensated
dollar plan’ was” (ibid.).26
26 In

this footnote, Allen also cites a letter that Fisher had written to President Hoover in
July 1931, in which Fisher had disingenuously written:
On thinking over our talk of Wednesday, I wonder if, when you expressed the fear that
stabilizing the purchasing power of money would change the basis of contracts, you
thought I was pleading for support by you of my old “Compensated Dollar Plan.” I
was not. It became evident long ago that immediate, practical progress lay along other
lines.

24

Federal Reserve Bank of Richmond Economic Quarterly

It would, however, appear that Fisher’s main influence on Roosevelt was
exerted at one remove by people who had accepted his policy view. This was
particularly true of George F. Warren, who was one of Roosevelt’s chief monetary advisers in the last half of 1933 (Dorfman 1959, vol. 5, p. 581 n.). In
particular, Warren’s book with Frank A. Pearson on Prices (1933, pp. 163–
66, 168) provides a sympathetic account of the compensated dollar plan. This
situation was also reflected in the following passage from a letter that Fisher
wrote his son in February 1934:
..
˙ it was a “proud moment” when the President signed the devaluation bill.
I often wonder how much he realizes that his monetary policy goes back to
me in large part—through Warren and Rogers and Rand, as well as directly.
And the public doesn’t know it except here and there. But I take a lot of
satisfaction in the mere adoption of the policy of course. (emphasis in original
letter; cited by W.R. Allen 1977, p. 576, n. 67)

6. CONCLUDING OBSERVATIONS
In his posthumously published History of Economic Analysis (1954), Schumpeter wrote that “some future historian may well consider Fisher as the greatest
of America’s scientific economists up to our own day” (ibid., p. 872). Similarly, Samuelson (1967, p. 17) wrote that from the viewpoint of analytical
contributions, “Irving Fisher would emerge as perhaps the greatest single name
in the history of American economics.” I would, however, associate the compensated dollar plan less with Fisher the scientific and analytical economist
(with his notable contributions to capital theory as well as monetary theory)
than with Fisher the possessor of two other character traits. The first is Fisher
the gadgeteer. This trait manifested itself early in the form of the gadget that
he invented in 1884 at the age of 17 to improve the internal mechanism of the
piano—what was subsequently described in his son’s biography as “the first of
a long line of brain-waves with which he bombarded the patent office” (I.N.
Fisher 1956, p. 13).27 In his scientific writings, Fisher also made use of pedagogical gadgets: like the hydraulic mechanism which he depicted on p. 38 of
his 1892 doctoral dissertation on Mathematical Investigations in the Theory of
Value and Prices (and of which he actually constructed a model a year later28 )
to illustrate the utility-maximizing conditions of general-equilibrium analysis.
Similarly, there were the diagrams in The Purchasing Power of Money (pp. 21,
27 For details of other inventions, see the page references listed under the entry “inventions”
in the index to this biography. See also the references listed under the entry “as inventor” on p.
317 of the index to R.L. Allen’s recent biography of Fisher (1993).
28 See its photograph, as well as that of the second model which he constructed in 1925, at
the beginning of the reprint of this dissertation as listed in the References below.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

25

23) which explain the equation of exchange in terms of weights on the two
sides of a fulcrum; and the diagrams (on pp. 116–19 and 128) of the flows of
gold into, between, and out of interconnected vessels which explain the relation
between these flows, on the one hand, and the level of the monetary stock of
gold, on the other. Then, of course, there was the gadget which he invented
that in the 1920s made him a multi-millionaire; namely, the “visible card index
system” (I.N. Fisher 1956, pp. 160–3 et passim; R.L. Allen 1993, pp. 109–10,
136, 185–86). The compensated dollar plan was also in the nature of a gadget:
for in the eyes of its deviser, here was an automatic device which, by simply
changing one price in the economy, achieved the stabilization of the price level
in general.
The second of Fisher’s character traits with which I would associate his
plan was Fisher the inveterate crusader for different causes during his long life;
e.g., healthy living, world peace, and prohibition.29 In the zeal to advance his
cause, a crusader is less concerned than the scientist with the requirements of
objectivity, consistency, careful analysis of causal relations, and strict adherence
to rules of evidence. Fisher was no exception. Indeed, his recent biographer
has observed that
[Fisher’s] devotion to his multiple crusades was so complete that on occasion
he used all the tools of science he could muster to support them. He occasionally bent a few facts and twisted logic slightly to make his case. When
this occurred, which was not common, it was rhetoric and likely entirely
unconscious on Fisher’s part. He was incapable of intended dishonesty or
deliberate deceit, but he was capable and occasionally guilty of self-delusion.
The conflict between his two roles, besides competition for time and energy,
was apparent only to others, not to Fisher. (R.L. Allen 1993, p. 6)

And on the basis of the foregoing account of the way in which Fisher repeatedly
evaded criticisms of his plan (particularly in its original form) and continued
over the years to support it by sometimes questionable arguments, I would cite
Fisher’s crusade for his compensated dollar plan as an example par excellence
of Allen’s general observation. At the same time, we should not overlook the
fact that Fisher’s persistent advocacy of this plan played a major role in placing
the problem of stabilizing the price level on the agenda of U.S. monetary policy
in the interwar period.
POSTSCRIPT
In the extensive literature on price stabilization that has developed since the
early 1980s, there are frequent references to Fisher’s compensated dollar plan,
29 See

the biographies by I.N. Fisher (1956) and R.L. Allen (1993). It is also instructive
to see the large number of items dealing with these and similar subjects among the 2,500-odd
entries in the Bibliography of the Writings of Irving Fisher that was compiled by I.N. Fisher
(1961, 1972).

26

Federal Reserve Bank of Richmond Economic Quarterly

and to his 1920 Stabilizing the Dollar in particular. But sometimes this name
is taken in vain. Thus Philip Cagan’s 1987 paper on “A Compensated Dollar:
Better or More Likely than Gold” suggests (inter alia) preserving the purchasing power of money, not by stabilizing the price level, but by issuing indexed
money (i.e., money whose nominal value changes equiproportionately with the
price index), which would become “the primary medium of exchange” (ibid.,
p. 272). As I have, however, shown elsewhere (Patinkin 1993, pp. 122–24),
and as illustrated by the Israeli experience of the early 1980s, an economy
whose money supply is mostly indexed will generate a frictionless inflationary
process, which will accordingly continue indefinitely at indeterminate rates.
In his article on “Explorations in the Gold Standard and Related Policies
for Stabilizing the Dollar,” Robert Hall (1982) has suggested stabilizing the
price level by modifying Fisher’s rule for achieving this objective by making
offsetting changes in the price of gold to making such changes in the price of
a fixed basket of commodities, and thus (presumably by the operation of substitution effects) generating similar changes in the prices of other commodities.
The efficacy of such effects for this purpose is itself doubtful. But quite apart
from that is the basic problem that arises from the fact that, in contrast with
Fisher’s proposal that the government buy and sell gold at the price that it
fixes in order to make it effective, Hall emphasizes that the government should
not make purchases or sales of the basket of commodities used to define the
value of the dollar (ibid., pp. 120–21). But how else can the government make
effective its announced price for the basket? Surely, the announcement per se
will not do so. And surely we have had enough experience to demonstrate that
administrative price controls break down in the face of pressures created by
inflationary policies that generate increases in the money supply.30
On the other hand, Fischer Black’s proposal in his “A Gold Standard with
Double Feedback and Near Zero Reserves” (1981) can rightly be regarded as
a generalization of the modified version of Irving Fisher’s compensated dollar
proposal in its definite-reserve form that was incorporated in the First Goldsborough Bill (see above, p. 19). In particular, whereas that bill required the
Secretary of the Treasury to take action after an offsetting change in the price
of gold in order to maintain a 50 percent gold reserve against gold certificates
in circulation, Fischer Black’s plan is a bit different. It leaves the monetary
authority free to fix the reserve ratio between gold reserves and the quantity of
money in circulation at a level that it chooses and places the responsibility for
establishing and maintaining this ratio on open market operations that change
the quantity of money. (It also advocates fixing this ratio as close as possible
to zero.) I should, however, point out that this affinity with Fisher’s plan leaves
Fischer Black’s plan open to the same criticism leveled above (pp. 8–9 and
16) about the misleading nature of associating with the gold standard (whose

30 For

a detailed critique of Hall’s proposal, see McCallum (1985, pp. 26–32).

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

27

hallmark is the fixed exchange rate) a plan based on changes in the price of
gold and hence in the exchange rate.
I hope on some future occasion to deal at greater length with the issues
raised in the aforementioned literature.
A PERSONAL NOTE
In a paper some years ago, I expressed puzzlement that “in its policy discussions, the Chicago school of the 1930s and 1940s did not do justice to
Irving Fisher—despite the fact that long before the Chicago school, Fisher had
advocated the policy of stabilizing the price level as a means of mitigating—if
not avoiding—cyclical fluctuations” (Patinkin 1973, p. 280).31 My work on the
present paper has suggested an answer to that puzzle. Because of his many
persistent crusades, as well as his also having persisted in losing a fortune in
the 1929 crash and its aftermath, Fisher had by the 1930s come to be regarded
as a crank, with his reputation as a scientist suffering accordingly (see Tobin
1987, pp. 370a and 371a–b, and Schumpeter 1954, p. 873; on his persistent
losses, see I.N. Fisher 1956, pp. 262–67). Furthermore, his name was still
associated with the outmoded compensated dollar plan, which for the Chicago
school (with its policy of stabilizing the price level by directly changing the
quantity of money through open market operations as well as by the generation
of budget deficits) was simply an encumbrance. So in addition to the natural
process of the succession of generations, of the young taking over leadership
from the old, there was no reason for the Chicago school to have invoked
Fisher’s name in support of its program. Indeed, in view of his reputation at
the time, it would have been counterproductive for it to have done so. In brief,
by that time the Chicago school had become a leader on questions of monetary
policy, and Fisher a follower—as exemplified by his acknowledgment to Henry
Simons and his colleagues in his 1935 book 100% Money. And perhaps that
too was a reason that in this book Fisher did not mention his compensated
dollar plan (see p. 23, above).
On one occasion in my life I had the privilege of meeting Irving Fisher
personally. It was at the January 1947 meetings of the Econometric Society in
Atlantic City, the first scientific conference that I ever attended, at which I also
presented a paper. Fisher was chairman of my session, and I remember him as
a short, bearded, and wizened old man. Three months later he died at the age
of 80.

31 The emphasis is on “policy discussions”: for in both the undergraduate and graduate
courses on monetary theory that I attended at the University of Chicago in the early 1940s, Lloyd
Mints devoted much attention to Fisher’s transactions approach to the quantity theory. To the
best of my memory, he also had us read chapters from The Purchasing Power of Money. Fisher’s
equation of exchange also provided the theoretical framework for the policy proposals of the
Chicago school. On all this, see Patinkin (1969).

28

Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES*
Works of Irving Fisher
(1892). Mathematical Investigations in the Theory of Value and Prices. Transactions of the Connecticut Academy, vol. 9 (July), reprinted, New Haven:
Augustus M. Kelley, 1961, together with Fisher’s (1896) Appreciation and
Interest.
(1896). Appreciation and Interest. Publications of the American Economic
Association, Third Series, XI (August). New York: Macmillan, for the
American Economic Association. Reprinted, New Haven: Augustus M.
Kelley, 1961, together with Fisher’s preceding work.
(1907). The Rate of Interest. New York: Macmillan.
(1911). The Purchasing Power of Money: Its Determination and Relation to
Credit, Interest, and Crises. New York: Macmillan.
(1912). “A More Stable Gold Standard,” Economic Journal, vol. 22 (December), pp. 570–76.
(1913a). The Purchasing Power of Money: Its Determination and Relation to
Credit, Interest, and Crises, rev. ed., New York: Macmillan. Reprinted,
New York: Augustus M. Kelley, 1963. (Date of revised edition as given
in some copies of the reprint [viz., 1922] is incorrect.)
(1913b). “A Compensated Dollar,” Quarterly Journal of Economics, vol. 27
(February), pp. 213–35. Appendixes I, II and III: pp. 385–97.
(1913c). “A Remedy for the Rising Cost of Living: Standardizing the Dollar,”
American Economic Review, Supplement, vol. 3 (March), pp. 20–28.
(1913d). [“Standardizing the Dollar—Discussion.”] American Economic
Review, Supplement, vol. 3 (March), pp. 46–51.
(1913e). Testimony before the U.S. Congress, Senate Committee on Banking
and Currency. Banking and Currency, vol. 2. Hearings on S. 2639,
H.R. 7837, 63 Cong. 1 Sess. Washington: Government Printing Office.
(Hearings on the Federal Reserve Act.)
(1914). “Objections to a Compensated Dollar Answered,” American Economic
Review, vol. 4 (December), pp. 818–39.
(1920). Stabilizing the Dollar. New York: Macmillan.
(1922). Testimony before the U.S. Congress, House of Representatives,
Committee on Banking and Currency. Stabilization of the Purchasing

* Reprinted and translated works are cited in the text by year of original publication; the
page references to such works in the text are, however, to the pages of the reprint or translation
in question.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

29

Power of Money. Hearings on H.R. 11788, 67 Cong. 4 Sess. Washington:
Government Printing Office. (Hearings on the First Goldsborough Bill.)
(1923a). Testimony before the U.S. Congress, House of Representatives,
Committee on Banking and Currency. Stabilization of the Purchasing
Power of Money, Part 2: Opposition and Rebuttal. Hearings on H.R.
11788, 67 Cong. 4 Sess. Washington: Government Printing Office.
(1923b). “The Business Cycle Largely a ‘Dance of the Dollar,’ ” Journal of
the American Statistical Association, vol. 18 (December), pp. 1024–28.
(1925). “Our Unstable Dollar and the So-Called Business Cycle,” Journal of
the American Statistical Association, vol. 20 (June), pp. 179–202.
(1928). The Money Illusion. New York: Adelphi.
(1930a). “Compensated Dollar,” in Edwin R.A. Seligman, ed., Encyclopaedia
of the Social Sciences, New York: Macmillan, vol. 4, pp. 134–35.
(1930b). The Theory of Interest. New York: Macmillan. Reprinted, New York:
Kelley and Millman, 1954.
(1932). Booms and Depressions. New York: Adelphi.
(1933a). “The Debt-Deflation Theory of Great Depressions,” Econometrica,
vol. 1 (October), pp. 337–57.
(1933b). After Reflation, What? New York: Adelphi.
(1933c). Stamp Scrip. New York: Adelphi.
(1934a). After Reflation, What?, [2d edition.] New York: Adelphi.
(1934b). Stable Money. New York: Adelphi.
(1935). 100% Money. New York: Adelphi.
Other Works Cited
Allais, Maurice. “Irving Fisher,” in David L. Sills, ed., International Encyclopedia of the Social Sciences. New York: Macmillan and The Free Press,
vol. 5 (1968), pp. 475–85.
Allen, Robert Loring. Irving Fisher: A Biography. Cambridge, Mass.: Blackwell, 1993.
Allen, William R. “Irving Fisher, F.D.R., and the Great Depression,” History
of Political Economy, vol. 9 (1977), pp. 561–87.
Alt, Franz L. “Distributed Lags,” Econometrica, vol. 10 (April 1942), pp.
113–28.
Anderson, B. M., Jr. [“Standardizing the Dollar—Discussion,”] American
Economic Review, Supplement, vol. 3 (March 1913), pp. 41–43.
Barber, William J. From New Era to New Deal: Herbert Hoover, the
Economists, and American Economic Policy, 1921–1933. Cambridge,
England: Cambridge University Press, 1985.
Barger, Harold. The Management of Money. Chicago: Rand McNally, 1964.

30

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Black, Fischer. “A Gold Standard with Double Feedback and Near Zero
Reserves” (manuscript) 1981, reproduced with some revisions in Black,
Business Cycles and Equilibrium. Oxford: Basil Blackwell, 1987, pp.
115–20.
Cagan, Phillip. “A Compensated Dollar: Better or More Likely Than Gold?” in
James A. Dorn and Anna J. Schwartz, eds., The Search for Stable Money:
Essays on Monetary Reform. Chicago: University of Chicago Press, 1987,
pp. 261–77.
Clark, J. M. “Possible Complications of the Compensated Dollar,” American
Economic Review, vol. 3 (September 1913), pp. 576–88.
Dorfman, Joseph. The Economic Mind in American Civilization, vols. 4 and 5,
1918–1933. New York: Viking Press, 1959.
Fischer, Stanley. “Rules Versus Discretion in Monetary Policy,” in Benjamin
M. Friedman and Frank H. Hahn, eds., Handbook of Monetary Economics,
vol. 2. Amsterdam: North Holland, 1990, pp. 1155–84.
Fisher, Irving Norton, comp. A Bibliography of the Writings of Irving Fisher:
Supplement. New Haven: Yale University Press, 1972.
, comp. A Bibliography of the Writings of Irving Fisher. New
Haven: Yale University Press, 1961.
. My Father, Irving Fisher. New York: Comet, 1956.
Friedman, Milton. “The Crime of 1873,” Journal of Political Economy, vol.
98 (December 1990), pp. 1159–94.
, and Anna Jacobson Schwartz. A Monetary History of the United
States, 1867–1960. Princeton: Princeton University Press, for the National
Bureau of Economic Research, 1963.
Groseclose, Elgin. Fifty Years of Managed Money: The Story of the Federal
Reserve, 1913–1963. London: Macmillan, 1965.
Hall, Robert E. “Explorations in the Gold Standard and Related Policies for
Stabilizing the Dollar,” in Robert E. Hall, ed., Inflation: Causes and
Effects. Chicago: University of Chicago Press, for the National Bureau of
Economic Research, 1982, pp. 111–22.
Kemmerer, E. W. “Economic Advisory Work for Governments,” American
Economic Review, vol. 17 (March 1927), pp. 1–12.
. Statement presented to the U.S. Congress, House of Representatives, Committee on Banking and Currency. Stabilization of the
Purchasing Power of Money, Part 2, Opposition and Rebuttal. Hearings on
H.R. 11788, 67 Cong. 4 Sess. Washington: Government Printing Office.
1923. (Hearings on the first Goldsborough bill.)
. [“Standardizing the Dollar—Discussion,”] American Economic
Review, Supplement, vol. 3 (March 1913), pp. 44–46.

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Kinley, David. “Objections to a Monetary Standard Based on Index Numbers,”
American Economic Review, vol. 3 (March 1913), pp. 1–19.
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Princeton University Press, 1991.
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Review, March 1887, reprinted in A.C. Pigou, ed., 1925, pp. 188–211.
McCallum, Bennett T. “Bank Deregulation, Accounting Systems of Exchange,
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. Essays On and In the Chicago Tradition. Durham, N.C.: Duke
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. “Keynes and Econometrics: On the Interaction between the
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reprinted, New York: Kelley & Millman, 1956.

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Reeve, Joseph E. Monetary Reform Movements. Washington: American
Council on Public Affairs, 1943.
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Fellner and others, eds., Ten Economic Studies in the Tradition of Irving
Fisher. New York: John Wiley, 1967, pp. 17–37.
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Unpublished speech, 1920, in Warburg, vol. 2 (1930), pp. 695–714.
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Journal, vol. 17 (June 1907), pp. 213–20.

D. Patinkin: Irving Fisher and His Compensated Dollar Plan

33

. F¨ rel¨ sningar i nationalekonomi, h¨ ft II, Om penningar och
o a
a
kredit, (1906). Stockholm and Lund: Fritzes, Berlingska. 2d ed. 1915; 3d
(posthumous) ed. 1929, ed. by E. Sommarin. As translated from the 1929
ed. by E. Classen under the title Lectures on Political Economy, vol. 2,
Money, ed. by Lionel Robbins. London: George Routledge and Sons, 1935.
. Geldzins und G¨ terpreise: Eine Studie uber die den Tauschwert
u
¨
des Geldes bestimmenden Ursachen. Jena: Gustav Fischer, 1898. Translated
by R. F. Kahn under the title Interest and Prices: A Study of the Causes
Regulating the Value of Money. London: Macmillan, 1936.
Wright, Chester W. Economic History of the United States. New York and
London: McGraw-Hill, 1941.

ACKNOWLEDGMENTS
This is a much extended and revised version of a paper presented in November
1991 at a seminar of the Federal Reserve Bank of Richmond when I was
a visiting scholar there. I am greatly indebted to Robert Graboyes, Robert
Hetzel, and Thomas Humphrey of the Research Department of the Bank for
their contributions to the discussion at the seminar itself and for the informal
discussions with them afterwards during my visit, as well as for their valuable
comments and suggestions on an earlier draft of this paper. I owe a special
thanks to Hetzel and his assistant Max Reid for providing me with photocopies
of the various congressional hearings at which Fisher testified. As usual, I
have benefited greatly from David Laidler’s comments on an earlier draft. My
thanks for their valuable comments and suggestions on that draft are also due
to William R. Allen, Stanley Fischer, Zvi Griliches, Herschel Grossman, Tsvi
Ophir, and Nathan Sussman.
I am grateful to J.S. Cramer, Jean-Paul Fitoussi, Harry Flam, Lars Jonung,
and Thomas Rymes for providing me with material not available in Jerusalem,
as well as to Dan Gelvan and Fred Simons for translating some of this material.
In the writing of this paper, I have made much use of the excellent library of
the Bank of Israel, in which connection I repeatedly benefited from the help of
its head, Uzi Pumpian, and his staff. I would also like to thank my secretary
Vivian Nadir for her usual most efficient assistance, particularly in connection
with the preparation of the bibliography and the checking of the references
to it.
I would like finally to express my appreciation to the Latsis Foundation
for financial support.

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Federal Reserve Bank of Richmond Economic Quarterly

A Quantity Theory
Framework for
Monetary Policy
Robert L. Hetzel

O

ne of the oldest and most useful ideas in economics is the quantity
theory of money. The quantity theory explains the determination of
variables measured in dollars such as the price level. Modern expositions of the quantity theory assume that the monetary authority controls directly
a reserve aggregate like the monetary base (currency plus bank deposits with
the monetary authority). In actual practice, however, monetary authorities use
an interest rate rather than a reserve aggregate as their policy variable. This fact
poses a challenge to the quantity theorist. How does he reconcile his theory
with actual policy procedures? There are no modern expositions of the quantity
theory that assume interest rate targeting by the monetary authority.
This article provides such an exposition. The exposition brings out the
standard quantity theory distinction between the determination of the real and
nominal quantity of money and explains changes in the price level as equating
the nominal demand with the nominal supply of money.
Modern expositions of the quantity theory assume reserve control in part
because reserve control constitutes a major item on the reform agenda of quantity theorists. Control of reserves and, at one remove, a monetary aggregate
constitutes control of a nominal variable and, therefore, draws attention to the
responsibility of the monetary authority to control the price level, also a nominal variable. Quantity theorists dislike the interest rate as a policy variable.
Interest rate control suggests that the monetary authority is controlling the

The views expressed in this article are those of the author and do not necessarily reflect those
of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/3 Summer 1993

35

36

Federal Reserve Bank of Richmond Economic Quarterly

price of resources made available to investors. The analysis here retains these
concerns. In particular, the article explains how rate targeting encourages the
public to confuse the monetary authority’s control over nominal variables with
control over real variables. These concerns motivate a proposal for a change in
monetary policy procedures designed to help the Fed achieve its goal of price
stability.

1. AN EXAMPLE AND SOME BASIC PRINCIPLES
An Example of Money Creation
Suppose the monetary authority sets a target for the interest rate and follows a
“lean-against-the-wind” policy of raising its rate target when economic activity
strengthens and lowering it when economic activity weakens. Because information on the economy becomes available with a lag, the monetary authority
would then supply reserves when economic activity strengthens and withdraw
them when economic activity weakens. Furthermore, it would not necessarily
offset these changes in reserves later. As a result, random disturbances would be
permanently incorporated into future levels of reserves and money. By following a “let bygones-be-bygones” policy of base drift in reserves, the monetary
authority causes the price level to wander randomly.1
Suppose also that introduction of a new technology raises the rate of return
on capital and, therefore, investment demand. When the market rate, reflecting
this higher return, begins to rise above its targeted level, the monetary authority
buys securities. As a result, the monetary base and the money stock increase.2
The individuals who sold securities to the monetary authority did so because they were offered a good price, not because they wanted to reduce their
holdings of assets. After selling securities, they allocate their additional money
among different assets to replace the securities sold. Temporarily, the increased
demand for financial assets depresses the interest rate. Consequently, real expenditure rises until the price level increases sufficiently to return real money
balances to their original level. Real money balances return to their original
level through a rise in the price level, not through a fall in the nominal quantity
of money.

1 The idea that rate pegging by the monetary authority makes nominal variables into a random
walk is mentioned in Friedman’s (1969, p. 104) “The Role of Monetary Policy” and is developed
systematically in Goodfriend (1987).
2 This exposition can be compared to Friedman (1969), who uses the notion of a helicopter
drop of money. The counterpart here to the helicopter is rate smoothing in the presence of a
positive real sector disturbance.

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

37

Real Versus Nominal and the Natural Rate Assumption
An understanding of the consequences of the monetary authority’s reserve injection begins with the distinction between real and nominal variables. Real
variables are real quantities or relative prices. A real quantity is usually measured in physical units. The real quantity of money is a measure of the purchasing power or command over goods represented by the nominal quantity
of money. A relative price is the price of a commodity expressed in terms
of another commodity. The real rate of interest is a relative price measuring
the price of commodities today in terms of commodities in the future. It is the
market interest rate adjusted for expected inflation. In contrast to real variables,
nominal variables are dollar amounts or dollar prices. Thus the nominal quantity
of money is the number of dollars the public holds. A special case of a nominal
variable is the market interest rate, which is the price of a dollar today in dollars
tomorrow.
An individual’s welfare depends upon his real income (the purchasing
power of income measured in terms of goods) and the relative prices of the
goods he consumes (the scarcity of those goods in terms of other goods). An
individual is better off if his real income increases so he can consume more
of all goods. He is no better off if his dollar income (and cash balances)
increases, but at the same time all dollar prices increase by the same amount
so his real income is unchanged. The idea that people care about real, not
nominal, variables is called the natural rate assumption (hypothesis).3
The monetary authority controls a nominal variable—the monetary base. It
follows from the natural rate assumption that the rise in the real rate of interest,
which is governed by real factors like investment opportunities and the public’s
thrift, can only be restrained temporarily by changes in money creation. Similarly, the real quantity of money desired by the public is not changed by an
injection of reserves. After the reserve injection, at the original price level, the
public holds a larger quantity of real money balances than desired. The price
level must rise to return real money balances to their desired, lower value.
The natural rate assumption thus implies that the monetary authority cannot
maintain an arbitrary target for the interest rate. Although the interest rate is
a nominal variable, its equilibrium value is the sum of the real rate consistent
with equilibrium in the economy (the natural rate) and an inflation premium
equal to the inflation expected by the public. If the monetary authority sets a

3 Alternatively, one can say that individual choice is not affected by money illusion. Different
economists, of course, give empirical content to the natural rate assumption in different ways.
Most monetarists, for example, assign considerable importance to temporary effects of money on
real variables because of transitory confusion between changes in the price level and changes in
relative prices and because of the existence of contracts in nominal terms. The key assumption
is that these monetary nonneutralities are transitory so that the monetary authority has no ability
to affect real variables in a sustained or systematic way.

38

Federal Reserve Bank of Richmond Economic Quarterly

rate target below the equilibrium market rate (the nominal natural rate), banks
have an incentive to acquire assets and their deposits and the money stock
increase.4 The public’s money balances then rise above their desired level. The
public responds by spending at a faster rate and the inflation rate rises.
Nominal Determinacy
A corollary to the natural rate assumption that the public cares only about real
variables is the proposition that only the monetary authority can give nominal variables well-defined (determinate) equilibrium values. Patinkin (1965)
showed that when the monetary authority targets the monetary base, the price
level is made determinate through a real balance effect. A rise in the price
level above its equilibrium value reduces the real value of the base and nominal money. This fall in real balances restrains the public’s real expenditure until
the price level falls back to its equilibrium value.
When the monetary authority targets an interest rate, however, the monetary
base varies endogenously, that is, with the demand for it by the public. If the
monetary authority does no more than specify an interest rate target, even one
equal to the economy’s nominal natural rate, a random movement in the price
level will induce a corresponding change in the demand for nominal bank credit
and, consequently, in the supply of nominal bank deposits and money. Changes
in the money supply then validate the changes in money demand produced
by changes in the price level, and the price level possesses no equilibrium
value.
If the monetary authority targets an interest rate, it must provide a nominal
reference point that gives nominal variables well-defined values. It does so by
giving the expected future price level a well-defined value. Although with a
rate target the monetary base is determined endogenously, the monetary authority limits the public’s demand for it indirectly by giving the future price level
expected by the public a well-defined value (Dotsey and King 1983; McCallum
1986). One way to understand nominal determinacy with rate targeting is to
compare it to the way a monetary authority achieves nominal determinacy by
exchange rate targeting. Assume the Fed targets the Deutsche mark price of a
dollar. As shown in equation (1), the DM/$ exchange rate equals the product of
the ratio of the German price level (DM/German good) to the U.S. price level
($/U.S. good) and the real terms of trade (German good/U.S. good). The nominal reference point or benchmark for the dollar is the German price level. If the
U.S. price level rises above its equilibrium level, the foreign exchange value of
the dollar falls, and the Fed buys dollars with Deutsche marks. The monetary
4 The terminology “nominal natural rate” and “natural rate” is in Friedman’s (1969, p. 101)
“The Role of Monetary Policy.”

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

39

base and the money stock fall and the price level returns to its equilibrium
level.
DM
DM
German good German good
·
=
(1)
$
$
US good
US good
With a rate target, the nominal benchmark is the expected future price
level. In the case of a rate target, the Fed targets the price of today’s dollars
($t ) in terms of tomorrow’s dollars ($t+1 ), or one plus the interest rate (1 + rt ).
As shown in equation (2), this price equals the product of the ratio of the
future price level expected by the public to the contemporaneous price level
and the real terms of trade with the future. If the price level were to rise
above its equilibrium value, the ratio of the expected future price level to the
contemporaneous price level would fall, that is, expected inflation would fall.
Consequently, the inflation premium in the interest rate would decline. The
resulting decline in the interest rate would increase the demand for money. It
would also prompt the monetary authority to sell securities and decrease the
monetary base. Because the demand for money would increase, while the supply would decrease, an excess demand for money would return the price level
to its equilibrium value. If the price level were to deviate from its equilibrium
value, a relative price effect would be created, analogous to a real balance
effect, that would return the price level to its equilibrium value.5

1 + rt =

$t+1
=
$t

Et

$
good
$
good

t+1

·

(good)t+1
(good)t

(2)

t

A Graphical Presentation of the Quantity Theory
The quantity theory can be summarized with the money demand and supply
schedules of Figure 1, which determine the nominal money stock and the goods
price of money (the inverse of the price level). For the reasons explained in
5 In practice, the monetary authority does not tie down the expected future price level by
targeting a fixed value of the price level. Instead, it allows the price level to vary in response
to shocks. It must, however, impart inertia to changes in the public’s expectation of the future
price level relative to changes in its contemporaneous value. It does so through its dislike for
large jumps in nominal prices. Goodfriend (1987) defines jumps relative to expected values. He
assumes that the monetary authority dislikes both discrepancies between the contemporaneous
price level and the prior period’s expectation of the contemporaneous price level and between
the contemporaneous price level and the expected future price level. In this way, the monetary
authority imposes a level and a change constraint on prices that make the public’s expectation of
the future price level well defined, while still allowing it to vary.

40

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 The Supply of and Demand for Money
Ms
t

Md
t

( M s )’
t

1
Pt
1
Pt

Mt

M d, M s

+

the preceding section, the schedules are well defined because the monetary
authority behaves in a way that allows the public to form an expectation of the
future price level. (See also Hetzel [1988].)
The nominal money demand schedule (Mtd ) is the product of the price level
and the demand for real money. Because increases in the price level (reductions
in the inverse of the price level) cause proportional increases in the demand for
nominal money, the demand schedule is negatively sloped. The schedules in
Figure 1 are drawn for a given expectation of the future price level. A rise in
the price level above its equilibrium value, given the public’s expectation of the
future price level, causes a reduction in expected inflation. As a consequence,
the market rate of interest falls through a reduction in the inflation premium.
The reduction in the market rate generates an increase in the quantity of money
demanded, which adds to the curvature of the money demand schedule.
Under the assumption that the central bank smooths the market rate, the
fall in the market rate due to the rise in the price level just described causes
the monetary authority to reduce the monetary base and the money supply. The
nominal money supply schedule (Mts ), therefore, is positively sloped. In contrast to the money demand schedule, which depends primarily on the behavior
of the public, the money supply schedule depends upon the reserve-supplying
behavior of the monetary authority. Shifts in the money supply schedule depend
upon the extent to which the monetary authority smooths the interest rate, that

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

41

is, the extent to which it varies reserves when the interest rate changes. Shifts
in the money supply schedule also depend upon the extent of base drift, that
is, the extent to which, if at all, the monetary authority subsequently offsets
changes in reserves induced by changes in the interest rate. Finally, shifts in
the money supply schedule depend upon the trend rate of growth of reserves,
money, and prices the monetary authority allows.6
These schedules are summarized in the quantity equation (3):
Ms = (k · y) · P, where (k · y) · P = Md .

(3)

The fraction of real output (y) the public wants to hold as money is k, which
is a function of variables like the interest rate. The public’s demand for real
money then is (k · y), and its demand for nominal money is (k · y) times the
price level P. The price level varies to make the nominal value of real money
desired by the public (Md ) equal to the nominal supply (Ms ).
The schedule (Mts ) shows the rightward shift in the money supply schedule
discussed in Section 2, where the monetary authority smooths the interest rate
during a positive real sector disturbance to aggregate demand. The graphical
illustration of this example highlights the key ideas of the quantity theory.
First, it is useful to organize an understanding of the price level by classifying
variables according to the way in which they affect money demand and supply
schedules. Second, the money supply schedule, whose behavior is dominated
by the monetary authority, shifts independently of the money demand schedule. Third, because the equilibrium values of real variables are ultimately tied
down by real factors, shifts in the money supply schedule eventually appear as
changes in the price level.
Over periods of time too short for the price level to vary sufficiently to
equate the nominal quantity of money supplied and demanded, it is useful to
view nominal output, rather than the price level, as the equilibrating variable,
as in equation (4).
Ms = k · ( y · P) = k · Y, where k · Y = Md

(4)

Nominal output (Y) is the product of real output (y) and the price level (P).
Figure 2 illustrates equation (4). If at the actual level of nominal output
money supply Ms exceeds money demand Md , 1/Yt exceeds its equilibrium
6 The money supply schedule depends upon the behavior of the monetary authority summarized in its reserves-supply function and the behavior of commercial banks and the public
summarized in the reserves-money multiplier. With rate targeting, the key behavioral relationships
of the money supply function concern the former rather than the latter relationship. Fluctuations
in the reserves-currency and reserves-deposits ratios of the reserves-money multiplier are automatically offset at the prevailing funds rate target. For example, if currency flows out of banks
or if banks increase the desired level of excess reserves, the funds rate rises. In order to maintain
its funds rate target, the monetary authority supplies reserves, thereby accommodating changes in
these ratios and avoiding a change in deposits.

42

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 The Supply of and Demand for Money
Ms
t

Md
t

( M s )’
t

1
Yt
1
Yt

Mt

d
s
M , M

+

value, and the public will increase its expenditure in an attempt to reduce its
money holdings. The result will be to raise nominal expenditure until nominal
output rises (1/Y falls) to its equilibrium value.7
Quantity Theory and Monetarist Hypotheses
Milton Friedman and Anna Schwartz (1963) have given the quantity theory a
specific form, often referred to as monetarism, through their hypothesis that
shifts in the money supply schedule have been large relative to shifts in the
money demand schedule.8 Their hypothesis possesses two distinct parts. The
first is that large shifts in the money supply schedule have destabilized the
7 Figure 2 is drawn assuming a given expectation of the future level of nominal output. Because nominal output is the product of the price level and real output, the slopes of its schedules are
determined by the relationship of the contemporaneous price level relative to the expected future
price level, as explained for Figure 1. The relationship of contemporaneous real output relative to
expected future real output reinforces these price relationships. A level of real output that is high
relative to expected future real output causes the public to save a relatively large fraction of its
income and depresses the real rate. The resulting decline in the market rate increases the demand
for money by lowering money’s opportunity cost. Also, the supply of money falls because of rate
smoothing by the monetary authority.
8 Friedman prefers the term quantity theory to monetarism, which was coined by the staff of
the Federal Reserve Bank of St. Louis for an article in their Review by Karl Brunner (1968). A
number of economists helped revive the quantity theory in the United States, for example, Karl
Brunner and Allan Meltzer, Phillip Cagan, Thomas Mayer, William Poole, and Clark Warburton.

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

43

behavior of nominal and real income. Their empirical evidence for this part is
twofold. They show that turning points in the rate of growth of the money stock
have preceded turning points in the business cycle. They also argue that shifts
in the money supply schedule can often be attributed to specific historical circumstances rather than to contemporaneous changes in economic activity. The
second part of their general hypothesis is that much of the observed variability
in real money demand has resulted from prior actions of the monetary authority.
Specifically, destabilizing shifts in the money supply schedule have produced
destabilizing shifts in the money demand schedule. These empirical generalizations lead Friedman (1959) to recommend moderate, stable money growth.
There is now a consensus that the quantity theory is the only useful framework for explaining the long-run behavior of prices. The monetary authority can
shift the money supply schedule independently of the money demand schedule
so that it can control the long-run behavior of the price level. The magnitude
of secular shifts in the money demand function is limited by real factors like
growth in real income and payments technology. There is no such limitation
on the behavior of the money supply. Over long periods of time, inflation
has reflected the behavior of the money supply. There is less consensus over
Friedman and Schwartz’s hypotheses about the monetary causes of the business
cycle and the stability of money demand. The basic quantity theory assumption
that the price level is a monetary phenomenon does not require acceptance of
these latter two hypotheses, however.

2. THE QUANTITY THEORY AS A GUIDE FOR POLICY
Interest rate targeting encourages the public to confuse the role of the monetary
authority, which is to control the nominal quantity of money and the price level,
with the role of commercial banks, which is to set a real rate of interest that
rations available resources to investors. The quantity theory counters this confusion through its distinction between money and credit and between nominal
and real variables.
The monetary authority is responsible for the money creation of commercial banks. In addition to creating deposits, commercial banks ration credit by
setting its price, the real interest rate. When the monetary authority targets an
interest rate, the public is encouraged to assume that the monetary authority
can control the credit rationing of commercial banks. The public then assumes
that the monetary authority can ensure a steady flow of credit to the economy
and can avoid “large” changes in the price of credit. When the monetary authority tries to manage the extension of credit, the money supply becomes a
function of credit demand. The resulting changes in money require changes
in the price level. The view of monetary policy as the management of credit
has at times produced large deflations as in the Depression and, at other times,
large inflations as in wartime.

44

Federal Reserve Bank of Richmond Economic Quarterly

When the commercial banking system extends credit by adding to the assets it holds, it must persuade the public to hold a larger real value of deposits.
If this intermediation does not simply draw funds away from other forms of
intermediation, the increase in bank deposits must correspond to a reduction
in consumption by the public. When the monetary authority extends credit by
acquiring an asset, however, it does no more than create through a bookkeeping
operation the corresponding liabilities (the monetary base). Because monetary
base creation requires no one to refrain from consumption, it does not increase
the resources available to investors. A “central bank” does not intermediate
between savers and investors. It is not a bank, and it cannot increase the
resources commercial banks make available to investors.
The belief that the monetary authority regulates the flow of credit entails the
implicit assumption that the quantity of money is self-regulating. The fallacy in
this assumption is the failure to distinguish between the mechanism for limiting
real credit extension and that for limiting money creation. As explained below,
the real interest rate limits the quantity of real credit demanded, but not the
nominal quantity of money demanded.
If money were a commodity, its equilibrium quantity would depend upon
its real resource costs of production. The market mechanism that limits the
supply of a commodity through the real costs of production, however, does not
limit the quantity of bank deposits. It is true that banks incur resource costs
in providing deposits. The resources that can be obtained in exchange for a
dollar of deposits, however, greatly exceed the bookkeeping cost of creating
that dollar. Because the resources obtained from creating an additional dollar
exceed the cost of creating that dollar, the monetary authority must limit the
nominal quantity of deposits and money.
The way market forces limit the availability of real credit differs from the
way the monetary authority limits the nominal quantity of money. When a bank
extends credit, it credits the deposits of the borrower. The borrower then draws
down those deposits in order to purchase goods and services. The bank loses
reserves when it loses the deposits. When the bank goes into the market for
reserves (issues CDs or borrows federal funds) to replace the lost reserves, it
must pay the market rate of interest. The real rate implicit in the market rate
limits the real amount of credit banks extend because it conveys information
about the scarcity of resources. The interest rate does not, however, convey
information about the “scarcity” of nominal money.

3. FOMC PROCEDURES IN A QUANTITY THEORY
PERSPECTIVE: A PROPOSED CHANGE
How can the natural rate assumption that the monetary authority cannot control
the real rate in a sustained way be reconciled with the fact that the Federal Open

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

45

Market Committee (FOMC) uses the funds rate as its policy instrument?9 The
FOMC can use the funds rate to target a nominal variable. The simplest case
would be to set the funds rate to achieve a target for money (McCallum 1981).
As part of such targeting procedures, the Fed shapes the way the public forms
its predictions of the future values of nominal variables. Those predictions, in
particular the expected future value of the price level, make the contemporaneous price level well defined. With a target for the rate of growth of nominal
output, for example, the expected inflation rate would equal the targeted growth
in nominal output minus the expected growth in real output.
An implication of the quantity theory is that, to stabilize the price level,
the monetary authority must set its interest rate target equal to the economy’s
equilibrium rate. Because an interest rate consists of two parts, a real rate
and an inflation premium, it follows that the monetary authority must perform
two tasks in setting its rate instrument. First, it must change its instrument in
line with changes in the economy’s equilibrium real rate. Second, as explained
above, it must set the interest rate in a way that allows the public to predict
the future price level.
This section suggests two changes designed to help the monetary authority achieve these two tasks. The first requires an explicit target for inflation.
The second involves the use of indexed bonds to measure the correspondence
between the monetary authority’s implicit target for inflation and the public’s
expectation for inflation.10
Milton Friedman (1959) for one has argued that targeting inflation or the
price level directly would be destabilizing. For this reason, it would be useful
to use nominal output as an intermediate target. With the suggested changes,
for example, at its December meeting, the FOMC would vote on an explicit
multi-year target path for inflation. At the February meeting, FOMC members would submit their predictions for real output growth for the current year

9 At

times, the FOMC has targeted the funds rate directly. Other times it has targeted the
funds rate indirectly by setting the discount rate and a target for the level of borrowed reserves.
Given the positive relationship between borrowed reserves and the difference between the funds
rate and the discount rate, the latter procedure amounts to an indirect funds rate target.
10 Implementation of the proposal advanced here would require creation of a measure of
expected inflation through the issue of Treasury zero-coupon bonds with different maturities.
Half the bonds would be indexed to the price level and half would be conventional, nonindexed
bonds. Unlike holders of the nonindexed bonds, holders of the indexed bonds would not have to
worry about the depreciation due to inflation of the dollar payment they receive when their bonds
mature. For this reason, the difference in yield between the nonindexed and indexed bonds would
provide a measure of expected inflation. Moreover, the existence of bonds of different maturities
would provide a term structure of expected inflation. Given the current value of the price level,
this term structure would yield estimates of the price level expected in future years.
The Fed could issue the indexed bonds. (It would buy short-term securities to offset the resulting decline in the monetary base.) It would be better for the Treasury to issue the bonds, however,
because it could issue them in sufficient quantities to ensure a liquid market. For more discussion,
see Hetzel (1992), U.S. Congress (1992a), and the testimony by Michael Boskin, Alan Greenspan,
Representative Stephen Neal, William Poole, and Alan Walters in U.S. Congress (1992b).

46

Federal Reserve Bank of Richmond Economic Quarterly

consistent with the long-run inflation target. When combined with the currentyear inflation target, the median value of FOMC members’ predictions for real
output growth would yield an intermediate target for nominal output growth.
The Board staff would convert the target for nominal output growth into an
intra-yearly target path in level form. At subsequent FOMC meetings, the Board
staff would display its predictions of nominal output relative to this target path.
Also at the February meeting, the Board staff would continue to make
predictions for money growth for the current year consistent with the inflation target. Subsequent observations of money and nominal output relative to
their intra-yearly paths would offer information useful in assessing whether the
FOMC was achieving its inflation target.
Assuming the existence of indexed bonds with varying maturities, the
FOMC would have available a measure of the price level expected by the public
in succeeding years. These observations on the expected price level would be
displayed relative to the multi-year target path for the price level consistent
with the FOMC’s inflation targets. In setting the funds rate, the FOMC would
take account of the gap between the targeted path for the price level and the
path expected by the public.
These procedures would keep the funds rate equal to the economy’s equilibrium rate. They would also make the inflation premium in the equilibrium
rate, that is, the inflation expected by the public, consistent with the Fed’s
objective for inflation. Responding to the measure of expected inflation made
available by indexed bonds, the Fed would keep expected inflation on target.

4. CONCLUDING COMMENT
With the suggested policy procedures, the FOMC could still use the funds rate
as its policy variable. Changes in the funds rate would appear reasonable in
that they would respond to changes in the real rate as reflected in the yield
on the indexed bond. However, changes in the funds rate would be explicitly
directed toward achieving an inflation target.
These procedures possess a quantity theory spirit in that they keep the
monetary authority’s attention focused on nominal variables under its control—
the rate of growth of nominal output and the price level. Despite their quantity
theory spirit, the suggested procedures do not depend on stability of the public’s
demand function for money. Money, nevertheless, would play an important role.
The money targets advertise to the public that the price level is a monetary
phenomenon and that monetary authority alone has the responsibility for control of the price level. Public discussion by the FOMC of its targets for money
would constitute an important way of influencing the public’s expectation of
the future price level and of keeping that expectation in line with the FOMC’s
target.

R. L. Hetzel: A Quantity Theory Framework for Monetary Policy

47

REFERENCES
Brunner, Karl. “The Role of Money and Monetary Policy,” Federal Reserve
Bank of St. Louis Review, vol. 50 (July 1968), pp. 9–24.
Dotsey, Michael, and Robert G. King. “Monetary Instruments and Policy Rules
in a Rational Expectations Environment,” Journal of Monetary Economics,
vol. 12 (September 1983), pp. 357–82.
Friedman, Milton. The Optimium Quantity of Money. Chicago: Aldine, 1969.
. A Program for Monetary Stability. New York: Fordham University
Press, 1959.
, and Anna J. Schwartz. A Monetary History of the United States,
1867–1960. Princeton: Princeton University Press, 1963.
Goodfriend, Marvin. “Interest Rate Smoothing and Price Level TrendStationarity,” Journal of Monetary Economics, vol. 19 (May 1987), pp.
335–48.
Hetzel, Robert L. “Indexed Bonds as an Aid to Monetary Policy,” Federal
Reserve Bank of Richmond Economic Review, vol. 78 (September/October
1992), pp. 13–23.
. “The Monetary Responsibilities of a Central Bank,” Federal
Reserve Bank of Richmond Economic Review, vol. 74 (September/October
1988), pp. 19–31.
McCallum, Bennett T. “Some Issues Concerning Interest Rate Pegging, Price
Level Determinacy, and the Real Bills Doctrine,” Journal of Monetary
Economics, vol. 17 (January 1986), pp. 135–60.
. “Price Level Determinacy with an Interest Rate Policy Rule and
Rational Expectations,” Journal of Monetary Economics, vol. 8 (November
1981), pp. 319–29.
Patinkin, Don. Money, Interest, and Prices. New York: Harper & Row, 1965.
U.S. Congress. “Fighting Inflation and Reducing the Deficit: The Role of
Inflation-Indexed Treasury Bonds,” Thirty-Third Report by the Committee
on Government Operations. 102 Cong. 2 Sess., October 29, 1992a.
. “Inflation-Indexed Treasury Debt as an Aid to Monetary Policy.”
Hearings before the House Commerce, Consumer, and Monetary Affairs
Subcommittee of the Committee on Government Operations. 102 Cong. 2
Sess., June 16 and 25, 1992b.

Credit Aggregates from the
Flow of Funds Accounts
Milton P. Reid, III and Stacey L. Schreft

O

ne reason analysts study financial variables is to determine how activity in financial markets affects the macroeconomy. For example,
there is evidence that reduced credit flows contributed to the Great
Depression (Bernanke 1983). Likewise, the Federal Reserve’s Credit Restraint
Program of 1980 magnified the 1980 recession by increasing uncertainty about
credit availability (Schreft 1990). More recently, analysts have debated the implications of rapid credit growth for financial stability (Federal Reserve Bank of
Kansas City 1986) and argued that debt repayment by consumers and businesses
contributed significantly to the 1990–91 recession and the unusually weak recovery that followed (1992 Economic Report of the President, p. 27). The link
between financial intermediation and economic growth and development is an
ongoing area of study (e.g., McKinnon 1973; Greenwood and Smith 1993).
Analysts use both broad and narrow measures of credit in macroeconomic
research. Support for using broad measures of credit comes from the ease
with which different forms of credit substitute for one another. Because of this
substitutability, broad measures reflect more accurately, for example, the extent
to which credit availability is reduced during a credit crunch. Moreover, broad
measures complement the monetary aggregates. In fact, since 1983, the Federal
Open Market Committee, the Federal Reserve System’s monetary policymaking
arm, has set monitoring ranges for domestic nonfinancial debt.
In contrast, narrow measures focus only on specific types of credit. Some
researchers focus on bank credit, for example, because they argue that it plays

The authors thank Dan Bechter, Tom Humphrey, Dawn Spinozza, Roy Webb, and John
Weinberg for helpful comments. The views expressed in this article are those of the authors
and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal
Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/3 Summer 1993

49

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Federal Reserve Bank of Richmond Economic Quarterly

a crucial role in the mechanism by which monetary policy is transmitted to
the real economy (see Morgan [1992] for a summary of this position). These
researchers justify the use of the narrow measure by arguing that for some borrowers bank credit is the only form of credit available to finance spending plans;
substitutability of bank and nonbank credit is not possible for these borrowers.
The leading source of data on credit aggregates is the Flow of Funds Accounts (FOFA). This article provides an introduction to the accounts. The first
section describes the nature, history, and availability of the accounts. Section 2
explains the accounts’ organization by sector and transaction. The third section
traces the behavior over time of various credit measures from the FOFA. Section
4 highlights features of the accounts that warrant caution, and finally Section
5 provides suggestions for additional readings that provide a more thorough
discussion of the accounts.

1. AN INTRODUCTION TO THE FLOW OF FUNDS
Nature of the Accounts
The FOFA are designed to measure the financial and nonfinancial transactions
associated with sectoral and aggregate investment activity. By cataloging the
financial flows associated with current income and production, the FOFA complement the National Income and Product Accounts (NIPA). While the NIPA
measure total saving and investment in a particular sector, the FOFA reveal
how a sector finances investment in excess of its saving. That is, according to
economist James Tobin (1962, p. 190), the FOFA are an
ex post record of the processes by which supplies and demands for various
financial assets are balanced. . . . The basic behavior behind the flow of funds
is the adjustment of the balance sheets, or portfolios, of individuals, business
firms, and financial enterprises toward a desired allocation of wealth among
holdings of various assets and debts. In this adjustment, the basic decision
variables are stocks; and flows will be dominated by attempts to adjust stocks
to changes in total wealth, interest rates, and other determinants.

The information in the FOFA is potentially of great use to economists, policymakers, and financial market participants. Surprisingly, however, knowledge
and use of these accounts for economic analysis has been limited. This reserved
reaction to the FOFA data is similar to that initially given to the NIPA data that
were first developed in the early 1930s. Economist James Duesenberry (1962,
p. 173) has noted that national income analysis was not embraced until John
Maynard Keynes’ work in The General Theory of Employment, Interest, and
Money (1936) created interest in the interaction of macroeconomic aggregates.
However, according to Duesenberry, “the Keynes of flow of funds analysis
has not yet revealed himself.” Perhaps the wait is over. The past decade has

Reid and Schreft: Credit Aggregates

51

witnessed renewed interest and advances in studying the interaction of the real
and financial sectors of the economy. Moreover, the increasingly rapid pace of
financial innovation will surely add to this interest.
History
The FOFA are based on research by Morris A. Copeland (1952), who had been
studying financial flows when the NIPA became available in the early 1930s.
With his training in accounting and with the NIPA in mind, Copeland began to
calculate financial flow measures for the banking sector, and then, over a decade
later, he compiled aggregate data for all sectors. In 1944, the National Bureau
of Economic Research invited Copeland to develop a more complete system
to account for financial flows. Copeland accepted the invitation, and in 1952,
the Bureau published the results: U.S. financial flows and related balances for
1936 through 1942.
The Board of Governors of the Federal Reserve System continued the
project and presented the result of its efforts in late 1955 in Flow of Funds
in the United States, 1939–1953. The data, however, were on an annual basis
and available only with a substantial time lag. In 1959, the Federal Reserve
published a revised presentation with quarterly data. Since then the Federal
Reserve has published regularly quarterly FOFA data.
Availability
Quarterly estimates are available for most series dating back to 1952, and
annual estimates exist as far back as 1946. In general, FOFA data for a given
quarter are first released about two months after the quarter ends. These data
are only preliminary estimates because some of the source data needed to more
accurately represent flows of funds are not yet available. Thus, with each new
release of FOFA data, estimates for previous quarters may be revised. Generally, data for only the five most recent quarters are revised. Annually, however,
the Federal Reserve revises the entire FOFA to incorporate methodological
and definitional changes and new source data. These adjustments are usually
released with the second-quarter estimates. While these revisions often are not
large, in some instances they can be substantial. The 1992 annual revision, for
example, caused the estimate of home mortgage debt for the nonfarm noncorporate business sector to more than triple, from $42.5 billion to $151.1 billion
for 1991:1.

2. STRUCTURE OF THE ACCOUNTS
The FOFA are organized along two dimensions: by economic sector and by
transaction type. The FOFA partition the economy into financial and nonfinancial

52

Federal Reserve Bank of Richmond Economic Quarterly

sectors. The nonfinancial sector is then divided further into three categories:
Private Domestic Nonfinancial, U.S. Government, and Foreign. Thus, the FOFA
split the economy into four broad sectors: Financial, Private Domestic Nonfinancial, U.S. Government, and Foreign. In contrast, the NIPA traditionally
break down the economy into four different sectors: Consumer, Business, Government, and Foreign.
The FOFA also are organized by the types of transactions among these
sectors. Financial claims, such as demand deposits, bonds, corporate equities,
and mortgages, represent different financial transaction categories. Nonfinancial
capital transactions, which consist of saving and investment flows, constitute
another transaction category. Estimates of the nonfinancial capital flows come
directly from the NIPA. Data on income, transfer payments, and expenditures
on goods and services, are not included in the FOFA, except to the extent that
saving is the balance of current receipts less current outlays.
In addition to being organized along those two dimensions, the FOFA also
report data in two different but related ways: for stocks of financial assets and
liabilities and for financial and nonfinancial capital flows. For each sector, the
reported stocks provide a balance sheet of the financial assets and liabilities of
that sector. The reported flows record the change in balance sheet holdings of
financial assets and liabilities between the current period and the previous one.
The flow data also report nonfinancial capital transactions from the NIPA.
Sectors
Figure 1 shows the level of credit market debt owed by each sector from 1952:1
to 1993:1. Descriptions of each sector follow.
Private Domestic Nonfinancial Sector
Households. The household sector is composed primarily of individuals, but
also includes personal trusts and nonprofit organizations that serve individuals.
Unlike its treatment in some other accounts, the household sector does not
include directly any data on business activities.
Nonfinancial Business. The nonfinancial business sector includes farm business, nonfarm noncorporate business, and corporate nonfinancial business. Estimates of all farming activity in the United States, including corporate farm
activity, are counted in the farm business sector. Unincorporated business enterprises, such as partnerships and proprietorships, engaged in nonfinancial,
nonagricultural activities comprise the nonfarm noncorporate business subsector. Finally, the corporate nonfinancial business subsector is the same as the
nonfinancial corporate group of the NIPA with the exception that farm corporations are omitted. This subsector, therefore, includes all private corporations
not included in the farming or financial sectors. Since the FOFA include a

Reid and Schreft: Credit Aggregates

53

Figure 1 Credit Market Debt by Sector

8000

Billions of Dollars

Private Domestic
Nonfinancial
800
U.S. Government
Financial
80
Foreign
8
1952 55

58

61 64

67

70

73

76

79

82

85

88

91

Source: Federal Reserve Board, FOFA.

+

foreign sector, only the domestic activities of these corporations are included
in the private domestic nonfinancial business sector.
State and Local Governments. The state and local government sector embodies the governments of all 50 states, their localities, United States territories, and
the District of Columbia, as well as the economic institutions (e.g., debt-issuing
authorities and trust funds) operated by these governments. Only retirement
funds for employees of state and local governments are excluded; they are
considered part of the financial sector.
Foreign
Only data on capital transactions between the United States (including its territories) and foreign economic entities are included in the foreign sector. Flows
of funds between two foreign economic agents are excluded entirely from the
FOFA. In general, the location of an economic entity is the basis for determining whether its activities are foreign or domestic. Thus, the activities of a
subsidiary of a U.S. corporation located in a foreign nation are included in the
foreign sector. Likewise, the activities of a subsidiary of a foreign corporation
located in the United States are considered domestic activities in the FOFA.

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Federal Reserve Bank of Richmond Economic Quarterly

U.S. Government
The U.S. government sector includes the activities of all agencies that are
part of the budget of the United States and all off-budget activities, with the
exception of certain financial activities. The Federal Reserve System is not
included in this sector, nor are certain Treasury accounts related to monetary
policy. Also, some federally sponsored credit agencies are not considered part
of the United States government sector. Specifically, the financial sector includes the activities of the Federal Home Loan Banks, Federal Home Loan
Mortgage Corporation, Federal National Mortgage Association, Federal Land
Banks, Federal Intermediate Credit Banks, and Banks for Cooperatives.
Financial Sector
Federally Sponsored Credit Agencies and Federally Sponsored Mortgage Pools.
Federally sponsored credit agencies are considered private financial institutions
despite their close legal association with the federal government. These institutions typically engage in very specific lending activities (e.g., the making of
residential mortgages and farm loans). Federally sponsored mortgage pools include the Government National Mortgage Corporation, the Federal Home Loan
Mortgage Corporation, and the Farmers Home Administration. These agencies
raise funds by issuing securities that are backed by a pool of mortgages.
Monetary Authority. This sector includes the Federal Reserve System and
certain Treasury accounts related to the conduct of monetary policy.
Commercial Banking. The commercial banking sector includes all banks that
have head offices in the 50 states, U.S. branches of foreign banks, Edge Act
and agreement corporations, U.S. agencies of foreign banks, bank holding companies, and banks in U.S. territories and possessions.
Private Nonbank Finance. Private nonbank finance includes all private financial institutions that are not part of the commercial banking sector. Included in
this sector are deposit-taking firms such as savings and loan associations, mutual savings banks, and credit unions. In addition, insurance companies, private
pension funds, state and local government employee retirement funds, finance
companies, real estate investment trusts, money market and other mutual funds,
and securities brokers and dealers are among those counted in this sector.
Transaction Categories
The FOFA are also organized by transaction categories. Transaction categories
are broadly divided into two subcategories: nonfinancial and financial. The
nonfinancial subcategory includes current transactions and capital transactions.

Reid and Schreft: Credit Aggregates

55

Figure 2 Financial Liabilities by Transaction Category

8000

Billions of Dollars

Deposit Claims at
Financial Institutions
Credit Market
Instruments
800
Corporate
Equities
Insurance and
Pension Fund Reserves
80
1952 55

58

61 64

67

70

73

76

79

82

85

88

91

Source: Federal Reserve Board, FOFA.

+

In the FOFA, current transactions are summarized by total saving for each
sector as in the NIPA, where saving is defined as the excess of current receipts
over current outlays. Saving then enters as a source of funds for each sector
in the capital account. Investment expenditures are the other half of the capital
account. Financial transactions account for the remainder of the transactions
in the FOFA. Figure 2 shows the level of financial liabilities for the major
financial transaction categories.
Financial Transaction Categories
Monetary Reserves. Monetary reserves are financial assets that can be used
for intervention in foreign exchange markets by monetary authorities and for
settlement of international transactions. The primary financial instruments included in this transactions category are gold, foreign currencies, and special
drawing rights (SDRs). Transactions in these instruments occur among the
U.S. government, monetary authorities, and the foreign sector.
Insurance and Pension Fund Reserves. Financial assets held by insurance
companies and pension plans for payment of claims to household beneficiaries
are included in this category.

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Federal Reserve Bank of Richmond Economic Quarterly

Net Interbank Claims. Interbank claims involve transactions occurring between depository institutions and either the Federal Reserve or the foreign
sector. Loans by the Federal Reserve to member banks, as well as depository
institution reserves and vault cash held at the Federal Reserve, are included in
this category. Federal funds and security repurchase agreements, however, are
not included.
Deposit Claims on Financial Institutions. Deposit claims can be held in a
number of different forms, including demand deposits, time deposits, federal
funds, and money market fund shares. In all instances, the deposit claim is
a liability of the financial institution receiving the funds and an asset of the
individual or institution that lends or deposits the money.
Credit Market Instruments. Credit market instruments represent the primary
source of funds to the nonfinancial sector. Instances of both direct and indirect
finance are included in this category. One example of direct finance occurs when
corporations issue bonds directly to the nonfinancial sector. The auctioning of
U.S. government securities to private firms is another example of direct finance.
Home mortgages, on the other hand, are an example of indirect finance where
funds flow through the financial sector; mortgages are typically issued by a
financial company using money that has been deposited with the institution by
the nonfinancial sector.
Corporate Equities. Corporate equities are not debt. Instead, equities represent claims of ownership on a corporation. Unlike the treatment of most other
financial instruments in the FOFA, equity issues are considered an asset of the
holder, but not a liability of the issuer.
Other Claims. Any financial transaction that is not included in any transaction
category described above is included in the “other claims” category. Security
credit, trade credit, and equity in noncorporate business are among the items
included in this category.

3. MOVEMENTS OVER TIME
The FOFA data include narrowly defined measures of credit, such as bank credit
or trade credit, and broader aggregations of these more narrow measures. At
times the Federal Reserve System has monitored various measures of credit—
both narrow and broad—in attending to the financial problems affecting credit
markets. The broad credit aggregate most commonly used in policymaking
and economic research is domestic nonfinancial debt. As Figure 3 indicates,
in real terms this credit aggregate exhibited steady growth of 3.75 percent per

Reid and Schreft: Credit Aggregates

57

Figure 3 Real Domestic Nonfinancial Debt
10000

Billions of 1987 Dollars

8000
6000

4000

2000
1952 55

58

61

64

67 70

73

76

79

82

85

88

91

Source: Federal Reserve Board, FOFA.

+

year from 1952:1 through 1993:1. In 1993:1, it made up 78.5 percent of total
debt owed by all sectors. Table 1 shows that between 1980:4 and 1993:1 the
U.S. government’s debt outstanding grew by more than 400 percent, thereby
increasing its share of total debt relative to the debt of the private and foreign
sectors. As Table 2 indicates, however, the U.S. government’s share of the
financial assets of the nonfinancial sector actually fell from 2.6 percent to 2.0
percent over the same time period.

4. CAUTIONS
No data source is perfect, and the FOFA are no exception. The following are
some potential shortcomings of the FOFA of which the user must be aware.
Double Counting
The FOFA data are supposed to measure borrowing to finance purchases of real
goods. Some borrowing, however, may finance purchases of financial assets.
This results in a “double counting” of debt. Although this double counting rarely
inflates debt above its underlying trend (Wilson et al. 1986, p. 519), caution

58

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Credit Market Debt Owed by All Sectors
1980:4

1993:1

Billions
of
Dollars
Total
Private Domestic Nonfinancial
Household
Nonfinancial Business
State & Local Governments
U.S. Government
Foreign
Financial

Percent
of
Total

Billions
of
Dollars

Percent
of
Total

4,731.0
3,200.5
1,405.8
1,484.3
310.4
735.0
191.7
603.8

100.0
67.6
29.7
31.4
6.6
15.5
4.1
12.8

15,163.3
8,756.9
4,191.5
3,603.8
961.6
3,140.2
319.5
2,946.6

100.0
57.8
27.6
23.8
6.3
20.7
2.1
19.4

Source: Federal Reserve Board, FOFA.

Table 2 Total Financial Assets of Nonfinancial Sectors
1980:4

1993:1

Billions
of
Dollars
Total
Private Domestic Nonfinancial
Households
Business
State & Local Governments
U.S. Government
Foreign

Percent
of
Total

Billions
of
Dollars

Percent
of
Total

8,688.2
8,000.6
6,390.5
1,363.2
246.9
228.7
458.8

100.0
92.1
73.6
15.7
2.8
2.6
5.3

22,308.9
19,860.3
16,147.1
2,973.2
740.0
455.8
1,992.8

100.0
89.0
72.4
13.3
3.3
2.0
8.9

Source: Federal Reserve Board, FOFA.

should nevertheless be used in interpreting higher debt levels reported in the
FOFA data. Such debt levels may appear to reflect an overleveraged financial
position, when in reality they only indicate greater financial intermediation in
the economy.
Flows, Not Transactions Volumes
The flows reported in the FOFA do not necessarily indicate the total volume
of transactions in a period. For instance, a flow of $200 would be recorded in
the FOFA in both of the following hypothetical examples, although the total
volume of transactions is different. Both cases assume that the commercial
banking sector has $1,000 of home mortgages as assets on its balance sheet,

Reid and Schreft: Credit Aggregates

59

and that this $1,000 is a financial liability of the household sector. An additional
assumption is that the household sector is comprised of five individuals each
owing $200 to the banking sector. In the first case, one individual repays his
mortgage, thereby lowering the assets of the banking sector and the liabilities
of the household sector by $200. In the second case, the same individual and
two other individuals repay their mortgages. This action decreases the assets of
the banking sector and liabilities of the household sector by $600. Meanwhile,
the remaining two individuals borrow an additional $200 each in mortgage
debt. Because of these actions, the assets of the banking sector and liabilities
of the household sector are increased by $400. On net, the second case leads to
a decrease of $200 in the assets of the banking sector and in the liabilities of
the household sector. In both cases, the reported flows are equal, but the gross
volume of transaction activity is much greater in the second example.
Comparisons with Other Data Sources
Estimates in the FOFA can differ significantly from data in other sources. In
most instances, these differences can be reconciled. For instance, private domestic nonfinancial debt measures in the FOFA are reported on a quarter-end
basis. Furthermore, unlike data on flows, the data on levels are not adjusted to
remove discontinuities in the series caused by definitional changes, loss of the
underlying data source, valuation adjustments, or other statistical problems. The
debt measures reported with the monetary aggregate data, however, have been
adjusted to eliminate these problems and are reported as a monthly average
obtained by computing the mean of consecutive month-end levels.
In addition, personal saving, as estimated by the FOFA, differs significantly from the corresponding figure reported in the NIPA. One reason for this
difference is the treatment of consumer expenditures for durable goods. The
FOFA consider consumer durable expenditures to be investment; therefore,
these expenditures are included in personal saving. In the NIPA, durable goods
purchases are part of the current account. Additionally, saving by farm corporations and government insurance and pension fund reserves are contained in the
personal saving measure of the FOFA. The remaining difference between the
NIPA and FOFA measures of personal saving equals the statistical discrepancy
of the household sector.
Estimates of international capital flows also can differ significantly depending on the source of the data. Hooker and Wilson (1989) document these
differences between international transactions estimates in the FOFA and balance of payments statistics.
Zero Government Investment
Another shortcoming, one shared by the NIPA, is the treatment of government
expenditures. All government expenditures are considered current consumption, not saving or investment. Some government expenditures, however, such

60

Federal Reserve Bank of Richmond Economic Quarterly

as spending for the construction of highways and new buildings, are similar to
private spending that is included in the capital account. Additionally, treatment
of the social security program is not consistent with the treatment of private
pension programs. Payments by individuals to private pension programs are a
form of saving in the FOFA, but social security payments are not. As a result,
many analysts would question the FOFA estimate of saving and investment by
the government sector.
Valuation
For corporate equities and mutual fund shares, levels are reported at market
values, but flows are not. Instead, flows are net purchases plus reinvested dividends. Debt instruments, however, are not adjusted for fluctuations in their
market prices (i.e., “marked to market”). In general, financial instruments are
valued at acquisition cost.
Sectoring
When using FOFA data, one should give careful consideration to the exact
definition of the sectors of the economy because the sector names can be misleading. Two instances of this deserve special attention. First, the household
sector includes nonprofit organizations and trusts. Second, the private sector
includes state and local governments.
Statistical Discrepancies
The user of FOFA data should be aware of the statistical discrepancies that
balance the system. The FOFA contain discrepancies for every sector and every
transaction category in the economy. As seen in Figure 4, the magnitude of the
FOFA household discrepancy can be quite large relative to personal saving.
On average, the household discrepancy was 21.3 percent of personal saving in
absolute terms for the 1952:1 to 1993:1 period.
Residual Estimation of the Household Sector
Many transactions categories of the household sector are measured as residuals.
That is, estimates for holdings of the household sector are determined by subtracting estimates for all other sectors from the estimate of the total holdings
for the entire economy. Therefore, errors in estimates for other sectors of the
economy lead to inaccurate calculation of the household sector’s holdings. In
recent years, several authors have cited this method as the explanation for the
widening household discrepancy and consequently for the divergent measures
of personal saving by the FOFA and NIPA (see, for example, Wilson et al.
1989).

Reid and Schreft: Credit Aggregates

61

Figure 4 Ratio of Household Discrepancy to Personal Saving
200

150

Percent

100

50

0

-50
1952 55

58

61

64

67

70

73

76

79

82

85

88

91

Note: The figure shows two large spikes in the periods of 1970:4 and 1971:4. These spikes
represent periods of low saving, not extremely large discrepancies. The estimated savings for
+
the periods were $31.1 and $34.7 billion, respectively, while the discrepancies were $55.9 and
$64.2 billion. In fact, the discrepancy/saving ratio was −50.5 in 1991:1 when the discrepancy
reached its largest absolute value of $316.5 billion and personal saving measured $626.3 billion.
Source: Federal Reserve Board, FOFA.

5. SUGGESTIONS FOR FURTHER READING
Much has been written about the FOFA. The following articles and publications
provide additional guidance in understanding the FOFA. The Federal Reserve
Board’s Guide to the Flow of Funds Accounts provides a complete overview of
the accounts. Particularly important is its discussion of the various sectors and
transaction categories. This publication also provides, in line-by-line detail, a
description of the source and/or construction of each data series. Additionally, it
presents the accounting identities that constrain the FOFA using a matrix representation of the FOFA system. It also analyzes the movement of the data over
time. Wilson, Freund, Yohn, and Lederer in “Measuring Household Saving:
Recent Experience from the Flow-of-Funds Perspective” furnish an excellent
analysis of the gap between the NIPA and FOFA measures of personal saving
in their discussion of the growing household sector discrepancy. Hooker and
Wilson in “A Reconciliation of Flow of Funds and Commerce Department

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Federal Reserve Bank of Richmond Economic Quarterly

Statistics on U.S. International Transactions and Foreign Investment Position”
explain the differences between the international transactions statistics reported
in the FOFA and the Commerce Department’s Balance of Payments Statistics.
Finally, Ritter’s “The Flow of Funds Accounts: A Framework for Financial
Analysis” and Van Horne’s “Flow-of-Funds Analysis” detail the theoretical
background for the accounts’ construction.

REFERENCES
Bernanke, Ben S. “Nonmonetary Effects of the Financial Crisis in the
Propagation of the Great Depression,” American Economic Review, vol.
73 (June 1983), pp. 257–76.
Copeland, Morris A. A Study of Moneyflows in the United States. New York:
National Bureau of Economic Research, 1952.
Duesenberry, James S. “A Process Approach to Flow-of-Funds Analysis,” in
National Bureau of Economic Research, ed., The Flow of Funds Approach
to Social Accounting. Princeton: Princeton University Press, 1962.
Economic Report of the President. Washington: United States Government
Printing Office, 1992.
Federal Reserve Bank of Kansas City. Debt, Financial Stability, and Public
Policy, Proceedings of a Symposium sponsored by the Federal Reserve
Bank of Kansas City, 1986.
Greenwood, Jeremy, and Bruce D. Smith. “Financial Markets in Development
and the Development of Financial Markets,” Working Paper 93–07. Center
for Analytic Economics, Cornell University, March 1993.
Hooker, Sarah A., and John F. Wilson. “A Reconciliation of Flow of Funds
and Commerce Department Statistics on U.S. International Transactions
and Foreign Investment Position,” Finance and Economics Discussion
Series, no. 84. Washington: Board of Governors of the Federal Reserve
System, 1989.
McKinnon, Ronald I. Money and Capital in Economic Development. Washington: Brookings Institution, 1973.
Morgan, Donald P. “Are Bank Loans a Force in Monetary Policy?” Federal
Reserve Bank of Kansas City Economic Review, vol. 77 (1992), pp. 31–41.
Ritter, Lawrence S. “The Flow of Funds Accounts: A Framework for Financial
Analysis,” The Bulletin of the C. J. Devine Institute of Finance, no. 52,
August 1968, pp. 4–31.
Schreft, Stacey. “Credit Controls: 1980,” Federal Reserve Bank of Richmond
Economic Review, vol. 76 (November/December 1990), pp. 25–55.

Reid and Schreft: Credit Aggregates

63

Tobin, James. “Comment” [on “A Process Approach to Flow-of-Funds
Analysis”], in National Bureau of Economic Research, ed., The Flow of
Funds Approach to Social Accounting. Princeton: Princeton University
Press, 1962.
Van Horne, James C. “Flow-of-Funds Analysis,” in The Function and Analysis
of Capital Market Rates, 2d ed. Englewood Cliffs, N.J.: Prentice-Hall,
Inc., 1984.
Wilson, John F., Elizabeth M. Fogler, James L. Freund, and Guido E. van
der Ven. “Major Borrowing and Lending Trends in the U.S. Economy,
1981–85,” Federal Reserve Bulletin, vol. 72 (August 1986), pp. 511–24.
Wilson, John F., James L. Freund, Frederick O. Yohn, Jr., and Walther Lederer.
“Measuring Household Saving: Recent Experience from the Flow-ofFunds Perspective,” in Robert E. Lipsey and Helen Stone Tice, eds., The
Measurement of Saving, Investment, and Wealth. Chicago: The University
of Chicago Press, 1989.

Over-the-Counter
Interest Rate Derivatives
Anatoli Kuprianov

O

ver-the-counter (OTC) interest rate derivatives include instruments
such as forward rate agreements (FRAs), interest rate swaps, caps,
floors, and collars. Broadly defined, a derivative instrument is a formal agreement between two parties specifying the exchange of cash payments
based on changes in the price of a specified underlying item or differences in
the returns to different securities. Like exchange-traded interest rate derivatives
such as interest rate futures and futures options, OTC interest rate derivatives
set terms for the exchange of cash payments based on changes in market interest rates. An FRA is a forward contract that sets terms for the exchange
of cash payments based on changes in the London Interbank Offered Rate
(LIBOR); interest rate swaps provide for the exchange of payments based on
differences between two different interest rates; and interest rate caps, floors,
and collars are option-like agreements that require one party to make payments
to the other when a stipulated interest rate, most often a specified maturity of
LIBOR, moves outside of some predetermined range.
The over-the-counter market differs from futures markets in a number
of important respects. Whereas futures and futures options are standardized

The author benefited from conversations with the following individuals: Keith Amburgey of
the International Swap Dealers Association, Inc., Albert Bashawaty of Morgan Guarantee
Trust Company, Richard Cohen of Chase Manhattan Bank, N.A., Steen Parsholt of Citibank,
N.A., David E. Schwartz and Robert J. Schwartz of Mitsubishi Capital Market Services,
Inc., and Robert M. Spielman of Chase Manhattan Bank. Timothy Cook, Bob LaRoche, John
Walter, and John Weinberg read earlier drafts of this article and made many helpful editorial
suggestions. Any remaining errors or omissions are the sole responsibility of the author.
Opinions expressed herein are those of the author and do not necessarily reflect those of the
Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 79/3 Summer 1993

65

66

Federal Reserve Bank of Richmond Economic Quarterly

agreements that trade on organized exchanges, the over-the-counter market is
an informal market consisting of dealers, or market makers, who trade price information and negotiate transactions over electronic communications networks.
Although a great deal of contract standardization exists in the over-the-counter
market, dealers active in this market custom-tailor agreements to meet the
specific needs of their customers. And unlike futures markets, where futures exchange clearinghouses guarantee contract performance through a system of margin requirements combined with the daily settlement of gains or losses, counterparties to OTC derivative agreements must bear some default or credit risk.
The rapid growth and energized pace of innovation in the market for interest rate derivatives since 1981, the date of the first widely publicized swap
agreement, has proven truly phenomenal. The advent of trading in interest
rate swaps was soon followed by FRAs, caps, floors, collars, as well as other
hybrid instruments such as forward swaps, options on swaps (swaptions), and
even options on options (captions).
This article offers an introduction to OTC interest rate derivatives. The first
five sections describe some of the most common types of OTC derivatives:
FRAs, interest rate swaps, caps, floors, and collars. The final section discusses
policy and regulatory concerns prompted by the growth of the OTC derivatives
market.

1. FORWARD RATE AGREEMENTS
FRAs are cash-settled forward contracts on interest rates traded among major
international banks active in the Eurodollar market. An FRA can be viewed as
the OTC equivalent of a Eurodollar futures contract. Most FRAs trade for maturities corresponding to standard Eurodollar time deposit maturities, although
nonstandard maturities are sometimes traded (Grabbe 1991, Chap. 13). Trading
in FRAs began in 1983 (Norfield 1992).
Banks use FRAs to fix interest costs on anticipated future deposits or interest revenues on variable-rate loans indexed to LIBOR. A bank that sells an FRA
agrees to pay the buyer the increased interest cost on some “notional” principal
amount if some specified maturity of LIBOR is above a stipulated “forward
rate” on the contract maturity or settlement date. The principal amount of the
agreement is termed “notional” because, while it determines the amount of the
payment, actual exchange of the principal never takes place. Conversely, the
buyer agrees to pay the seller any decrease in interest cost if market interest
rates fall below the forward rate. Thus, buying an FRA is comparable to selling,
or going short, a Eurodollar or LIBOR futures contract.
The following example illustrates the mechanics of a transaction involving
an FRA. Suppose two banks enter into an agreement specifying:
– a forward rate of 5 percent on a Eurodollar deposit with a three-month
maturity;

A. Kuprianov: OTC Interest

67

– a $1 million notional principal; and
– settlement in one month.
Such an agreement is termed a 1 × 4 FRA because it fixes the interest rate
for a deposit to be placed after one month and maturing four months after the
date the contract is negotiated. If the three-month LIBOR is 6 percent on the
contract settlement date, the seller would owe the buyer the difference between
6 and 5 percent interest on $1 million for a period of 90 days. Every 1 basis
point change in the interest rate payable on a principal of $1 million for a 90day maturity changes interest cost by $25, so that the increase in the interest
cost on a three-month Eurodollar deposit over the specified forward rate in
this case is $25 × 100 basis points = $2,500. But the interest on a Eurodollar
deposit is paid upon maturity (at the end of the term of the deposit), whereas
FRAs are settled on the contract maturity date (which would correspond to the
date the underlying hypothetical deposit would be placed). Therefore, to make
the cash payment on the FRA equivalent to the extra interest that would have
been earned on a Eurodollar deposit paying 6 percent, the $2,500 difference in
interest costs calculated above is discounted back three months using the actual
three-month LIBOR prevailing on the settlement date. Thus, if 90-day LIBOR
turns out to be 6 percent on the contract maturity date the buyer would receive
$2,463.05 = $2,500/[1 + 0.06(90/360)].
More generally, final settlement of the amounts owed by the parties to an
FRA is determined by the formula
Payment =

(N)(LIBOR − FR)(dtm/360)
,
1 + LIBOR(dtm/360)

where
N = the notional principal amount of the agreement;
LIBOR = the value of LIBOR for the maturity specified by the contract
prevailing on the contract settlement date;
FR = the agreed-upon forward rate; and
dtm = maturity of the forward rate, specified in days.
If LIBOR > FR the seller owes the payment to the buyer, and if LIBOR < FR
the buyer owes the seller the absolute value of the payment amount determined
by the above formula.

2. INTEREST RATE SWAPS
A swap is a contractual agreement between two parties to exchange, or “swap,”
future payment streams based on differences in the returns to different securities
or changes in the price of some underlying item. Interest rate swaps constitute
the most common type of swap agreement. In an interest rate swap, the parties
to the agreement, termed the swap counterparties, agree to exchange payments

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 U.S. Dollar Interest Rate Swaps

2000
1400

Billions of Dollars

1200
1000
800
600
400
200
0
Year-End 1985

1986

1987

1988

1989

1990

1991

Source: Market Survey Highlights, Year End 1991, International Swap Dealers Association, Inc.

indexed to two different interest rates. Total payments are determined by the
specified notional principal amount of the swap, which is never actually exchanged. Financial intermediaries, such as banks, pension funds, and insurance
companies, as well as nonfinancial firms use interest rate swaps to effectively
change the maturity of outstanding debt or that of an interest-bearing asset.1
Swaps grew out of parallel loan agreements in which firms exchanged
loans denominated in different currencies. Although some swaps were arranged
in the late 1970s, the first widely publicized swap took place in 1981 when
IBM and the World Bank agreed to exchange interest payments on debt denominated in different currencies, an arrangement known as a currency swap.
The first interest rate swap was a 1982 agreement in which the Student Loan
Marketing Association (Sallie Mae) swapped the interest payments on an issue
of intermediate-term, fixed-rate debt for floating-rate payments indexed to the
three-month Treasury bill yield. The interest rate swap market has grown rapidly
since then. Figure 1 displays the year-end total notional principal of U.S. dollar
1 See

Wall and Pringle (1988) for a more comprehensive survey of market participants.

A. Kuprianov: OTC Interest

69

interest rate swaps outstanding from 1985 to 1991. Based on market survey data
published by the International Swap Dealers Association (ISDA), U.S. dollar interest rate swaps comprise about one-half of all interest rate swaps outstanding:
the notional principal amount of U.S. dollar interest rate swaps outstanding as
of the end of 1991 was just over $1.5 trillion, compared to almost $3.1 trillion
for all interest rate swaps.
Swap Dealers
Early interest rate swaps were brokered transactions in which financial intermediaries with customers interested in entering into a swap would seek
counterparties for the transaction among their other customers. The intermediary collected a brokerage fee as compensation, but did not maintain a continuing
role once the transaction was completed. The contract was between the two
ultimate swap users, who exchanged payments directly.
Today the market has evolved into more of a dealer market dominated
by large international commercial and investment banks. Dealers act as market
makers that stand ready to become a counterparty to different swap transactions
before a customer for the other side of the transaction is located. A swap dealer
intermediates cash flows between different customers, or “end users,” becoming
a middleman to each transaction. The dealer market structure relieves end users
from the need to monitor the financial condition of many different swap counterparties. Because dealers act as middlemen, end users need only be concerned
with the financial condition of the dealer, and not with the creditworthiness of
the other ultimate end user of the instrument (Brown and Smith 1990).
Figure 2 illustrates the flow of payments between two swap end users
through a swap dealer. Unlike brokers, dealers in the over-the-counter market
do not charge a commission. Instead, they quote two-way “bid” and “asked”
prices at which they stand ready to act as counterparty to their customers in a
derivative instrument. The quoted spread between bid and asked prices allows
an intermediary to receive a higher payment from one counterparty than is paid
to the other.

Figure 2 The Dealer Market for Interest Rate Swaps

FIXED PAYMENTS

FIXED-RATE
PAYER

FIXED PAYMENTS

(ask rate)

(bid rate)

DEALER
FLOATING
PAYMENTS

FLOATING
PAYMENTS

FLOATINGRATE
PAYER

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Federal Reserve Bank of Richmond Economic Quarterly

Swap Market Conventions
There are many different variants of interest rate swaps. The most common is
the fixed/floating swap in which a fixed-rate payer makes payments based on a
long-term interest rate to a floating-rate payer, who, in turn, makes payments indexed to a short-term money market rate to the fixed-rate payer. A fixed/floating
swap is characterized by:
– a fixed interest rate;
– a variable or floating interest rate which is periodically reset;
– a notional principal amount upon which total interest payments are based;
and
– the term of the agreement, including a schedule of interest rate reset dates
(that is, dates when the value of the interest rate used to determine
floating-rate payments is determined) and payment dates.
The fixed interest rate typically is based on the prevailing market interest rate
for Treasury securities with a maturity corresponding to the term of the swap
agreement. The floating rate is most often indexed to three- or six-month LIBOR, in which case the swap is termed a “generic” or “plain vanilla” swap,
but can be indexed to almost any money market rate such as the Treasury
bill, commercial paper, federal funds, or prime interest rate. The maturity, or
“tenor,” of a fixed/floating interest rate swap can vary between 1 and 15 years.
By convention, a fixed-rate payer is designated as the buyer and is said to be
long the swap, while the floating-rate payer is the seller and is characterized
as short the swap.
Timing of Payments
A swap is negotiated on its “trade date” and takes effect two days later on its
initial “settlement date.” If the agreement requires the exchange of cash at the
outset, as in the case of a “nonpar” swap, the transaction takes place on the
initial settlement date. Interest begins accruing on the “effective date” of the
swap, which usually coincides with the initial settlement date. (Forward swaps,
in which the effective date of the swap is deferred, are an exception to this
rule.) Floating-rate payments are adjusted on periodic “reset dates” based on the
prevailing market-determined value of the floating-rate index, with subsequent
payments made on a sequence of payment dates (also known as settlement
dates) specified by the agreement. Typically, the reset frequency for the floatingrate index is the term of the interest rate index itself. For example, the floating
rate on a generic swap indexed to the six-month LIBOR would, in most cases,
be reset every six months with payment dates following six months later. The
floating rate can be reset more frequently, however, as in the case of swaps
indexed to Treasury bill rates, which are reset weekly.

A. Kuprianov: OTC Interest

71

Fixed interest payment intervals can be three months, six months, or one
year. Semiannual payment intervals are most common because they coincide
with the intervals between interest payments on Treasury bonds. Floating-rate
payment intervals need not coincide with fixed-rate payment intervals, although
they often do. When payment intervals coincide, it is common practice to exchange only the net difference between the fixed and floating payments.
Price Quotation
The price of a fixed/floating swap is quoted in two parts: a fixed interest rate
and an index upon which the floating interest rate is based. The floating rate
can be based on an index of short-term market rates (such as a given maturity
of LIBOR) plus or minus a given margin, or set to the index “flat”—that is, the
floating interest rate index itself with no margin added. The convention in the
swap market is to quote the fixed interest rate as an All-In-Cost (AIC), which
means that the fixed interest rate is quoted relative to a flat floating-rate index.
The AIC typically is quoted as a spread over U.S. Treasury securities with
a maturity corresponding to the term of the swap. For example, a swap dealer
might quote a price on a three-year generic swap at an All-In-Cost of “72–76
flat,” which means the dealer stands ready to “buy” the swap (that is, enter into
the swap as a fixed-rate payer) at 72 basis points over the prevailing three-year
interest rate on U.S. Treasuries while receiving floating-rate payments indexed
to a specified maturity of LIBOR with no margin, and “sell” (receive fixed and
pay floating) if the other party to the swap agrees to pay 76 basis points over
Treasury securities.
Bid-asked spreads in the swap market vary greatly depending on the type
of agreement. The spread can be as low as 3 to 4 basis points for a two- or
three-year generic swap, while spreads for nonstandard, custom-tailored swaps
tend to be much higher.
The Generic Swap
As an illustration of the mechanics of a simple interest rate swap, consider
the example of a generic swap. Fixed interest payments on a generic swap
typically are based on a 30/360 day-count convention, meaning that they are
calculated assuming each month has 30 days and the quoted interest rate is
based on a 360-day year. Given an All-In-Cost of the swap, the semiannual
fixed-rate payment would be
(N)(AIC)(180/360),
where N denotes the notional principal amount of the agreement.
Floating-rate payments are based on an actual/360-day count, meaning
that interest payments are calculated using the actual number of days elapsed

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Federal Reserve Bank of Richmond Economic Quarterly

since the previous payment date, based on a 360-day year. Let dt denote the
number of days since the last settlement date. Then, the floating-rate payment
is determined by the formula
(N)(LIBOR)(dt /360).
To illustrate, suppose a dealer quotes an All-In-Cost for a generic swap at
10 percent against six-month LIBOR flat. If the notional principal amount of
the swap is $1 million, then the semiannual fixed payment would be
$50,000 = ($1,000,000)(0.10)(180/360).
Suppose that the six-month period from the effective date of the swap to the
first payment date (sometimes also termed a settlement date) comprises 181
days and that the corresponding LIBOR was 8 percent on the swap’s effective
date. Then, the first floating-rate payment would be
$40,222.22 = ($1,000,000)(0.08)(181/360).
Often a swap agreement will call for only the net amount of the promised
payments to be exchanged. In this example, the fixed-rate payer would pay the
floating-rate payer a net amount of
$9,777.78 = $50,000.00 − $40,222.22.
A payment frequency “mismatch” occurs when the floating-rate payment
frequency does not match the scheduled frequency of the fixed-rate payment.
Mismatches typically arise in the case of swaps that base floating-rate payments
on maturities shorter than the six-month payment frequency common for fixedrate payments. Macfarlane, Ross, and Showers (1990) discuss swap mismatches
in some detail.
Day-Count Conventions
A wide variety of day-count conventions are used in the swap market. Fixed
payments can be quoted either on an actual/365 (bond equivalent) basis or on
an actual/360 basis. Floating-rate payments indexed to private-sector interest
rates typically follow an actual/360 day-count convention commonly used in the
money market. Floating-rate payments tied to Treasury bill rates are calculated
on an actual/365 basis, however.
Nongeneric Swaps
An interest rate swap that specifies an exchange of payments based on the
difference between two different variable rates is known as a “basis swap.”
For example, a basis swap might specify the exchange of payments based on
the difference between LIBOR and the prime rate. Other interest rate swaps
include the forward swap, in which the effective date of the swap is deferred;

A. Kuprianov: OTC Interest

73

the swaption, which is an option on an interest rate swap; and puttable and
callable swaps, in which one party has the right to cancel the swap at certain
times. This list is far from exhaustive—many other types of interest rate swaps
are currently traded, and the number grows with each year. Abken (1991b)
describes a variety of different swap agreements.
Swap Valuation
Interest rate swaps can be viewed as implicit mutual lending arrangements. A
party to an interest rate swap implicitly holds a long position in one type of
interest-bearing security and a short position in another. Swap valuation techniques utilize this fact to reduce the problem of pricing an interest rate swap
to a straightforward problem of pricing two underlying hypothetical securities
having a redemption or face value equal to the notional principal amount of
the swap. The method used to value a fixed/floating swap is outlined below.
Partitioning a Swap
A fixed/floating swap can be partitioned into (1) a bond paying a fixed coupon
and (2) a variable-rate note with payments tied to the variable-rate index. Let
S(0, T) denote the value of a T-period swap on its initial settlement date (date
0), B(0, T) the value of a hypothetical T-period fixed-rate bond paying a coupon
equal to the fixed-rate payments specified by the agreement, and V(0, T) the
value of a variable-rate note maturing at date T. Assuming that the face or
redemption value of both hypothetical securities is equal to the notional principal amount of the swap, the value of the swap to a fixed-rate payer can be
expressed as
S(0, T) = V(0, T) − B(0, T).
Pricing the Variable-Rate Note
A variable-rate note whose payments are indexed to market interest rates is
valued at par upon issuance and just after each interest payment is made. Thus,
assuming that payment dates coincide with interest rate reset dates, the value of
the hypothetical variable-rate note V(0, T) will just equal the notional principal
amount of the swap on every reset date. On any other date the value of a
variable-rate note—exclusive of accrued interest—is just the present value of
the next known interest payment plus the present value of the face value of the
note, the latter amount representing the value of all remaining payments on the
note as of the next settlement date.
Pricing the Fixed-Rate Note
The hypothetical fixed-rate note B(0, T) can be priced using standard bond
valuation techniques. The convention in swap markets is to quote the AIC

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Federal Reserve Bank of Richmond Economic Quarterly

as a semiannual bond-equivalent rate. The formula for valuing a bond paying
semiannual fixed coupon payments is
2T

[(C/2)/(1 + y/2)t ] + [N/(1 + y)T ],

B(0, T) =
t=0

where C is the annual coupon payment, T the number of years to maturity, N
the principal or face value, and y the yield-to-maturity of the bond.
By definition, the All-In-Cost of a fixed/floating swap is the yield to maturity that just makes the value of the hypothetical fixed-rate bond equal to the
notional principal amount of the swap. The annual coupon payment for this
hypothetical bond is determined by the AIC and the notional principal amount
of the agreement:
C = (AIC/100)(N),
where AIC is expressed as a percentage rate. It is easy to see that the value
of the hypothetical bond implicit in this fixed/floating swap will be par (the
notional principal amount of the swap) when
y = AIC/100.
Nonpar Swaps
In most cases swaps are priced so that the initial value of the agreement is zero
to both counterparties; that is, so that the value of both hypothetical component
securities is just equal to the notional principal amount of the swap. Occasionally, however, a swap may be priced such that one party owes money to the other
at initial settlement, resulting in a “nonpar” swap. Nonpar swaps are used to
offset existing positions in swaps entered into in previous periods where interest
rates have changed since the original swap was negotiated, or in cases where
a given cash flow needs to be matched exactly (Dattatreya 1992). Valuation
methods for nonpar swaps are somewhat more involved than the simple case
discussed above. Interested readers can find more comprehensive discussions
of swap valuation in Beckstrom (1990), Iben (1990), and Macfarlane, Ross,
and Showers (1990).
The Effect of Changes in Market Interest Rates on Swap Values
A change in market interest rates affects the value of a fixed/floating swap
in much the same way that it affects the value of a corporate bond with a
comparable maturity. To see why, note that a change in market interest rates
will have no effect on the value of the hypothetical variable-rate note implicit
in a fixed/floating swap on interest rate reset dates. Therefore, on reset dates a
change in market interest rates will affect the value of the swap only through
its effect on the value of the hypothetical fixed-rate bond. Since an increase in

A. Kuprianov: OTC Interest

75

interest rates lowers the value of the bond, it increases the value of the swap
position for a fixed-rate payer to the same degree it would increase the value
of a short position in a fixed-rate bond.
Between interest rate reset dates the amount of the next payment due on
the variable-rate note is predetermined. Thus, a change in market interest rates
affects the values of both the hypothetical variable-rate note and the hypothetical fixed-rate bond. The change in the value of the variable-rate note partially
offsets the change in the value of the fixed-rate note in this case. As a general
rule the price behavior of a fixed/floating interest rate swap will approximate
the price behavior of a fixed-rate note with a maturity equal to the term of the
swap less the maturity of the variable interest rate. For example, a two-year
generic swap indexed to six-month LIBOR will approximate the behavior of a
fixed-rate bond with a term to maturity of between 18 and 24 months, depending
on the amount of time since the last interest rate reset date (Burghardt et al.
1991, p. 86).
The value of a fixed/floating swap generally changes over time when the
term structure of interest rates is upward-sloping. Only when the term structure
is flat and market interest rates remain unchanged will the value of an interest
rate swap remain unchanged over the life of the agreement (Smith, Smithson,
and Wakeman 1988).

3. INTEREST RATE CAPS
The buyer of an interest rate cap pays the seller a premium in return for the right
to receive the difference in the interest cost on some notional principal amount
any time a specified index of market interest rates rises above a stipulated “cap
rate.” The buyer bears no obligation or liability if interest rates fall below the
cap rate, however. Thus, a cap resembles an option in that it represents a right
rather than an obligation to the buyer.
Caps evolved from interest rate guarantees that fixed a maximum level
of interest payable on floating-rate loans. The advent of trading in over-thecounter interest rate caps dates back to 1985, when banks began to strip such
guarantees from floating-rate notes to sell to the market (Kahle 1992). The
leveraged buyout boom of the 1980s spurred the evolution of the market for
interest rate caps. Firms engaged in leveraged buyouts typically took on large
quantities of short-term debt, which made them vulnerable to financial distress
in the event of a rise in interest rates. As a result, lenders began requiring
such borrowers to buy interest rate caps to reduce the risk of financial distress
(Burghardt et al. 1991). More recently, trading activity in interest rate caps has
declined as the number of new leveraged buyouts has fallen. Figure 3 shows
that the total notional principal amount of caps, floors, and collars outstanding
at the end of 1991 actually fell to $311 billion from $360 billion at the end of

76

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 U.S. Dollar Caps, Collars, and Floors

400

Billions of Dollars

300

200

100

0
Year-End 1990

Year-End 1991

Source: Market Survey Highlights, Year End 1991, International Swap Dealers Association, Inc.

1990 (floors and collars are discussed below).
Market Conventions
An interest rate cap is characterized by:
– a notional principal amount upon which interest payments are based;
– an interest rate index, typically some specified maturity of LIBOR;
– a cap rate, which is equivalent to a strike or exercise price on an option;
and
– the period of the agreement, including payment dates and interest rate
reset dates.
Payment schedules for interest rate caps follow conventions in the interest
rate swap market. Payment amounts are determined by the value of the index
rate on a series of interest rate reset dates. Intervals between interest rate reset
dates and scheduled payment dates typically coincide with the term of the
interest rate index. Thus, interest rate reset dates for a cap indexed to sixmonth LIBOR would occur every six months with payments due six months

A. Kuprianov: OTC Interest

77

Figure 4 The Payoff to Buying a One-Period Interest Rate Cap
Profit

rc

Interest
Rate

later. Cap buyers typically schedule interest rate reset and payment intervals to
coincide with interest payments on outstanding variable-rate debt. Interest rate
caps cover periods ranging from one to ten years with interest rate reset and
payment dates most commonly set either three or six months apart.
If the specified market index is above the cap rate, the seller pays the buyer
the difference in interest cost on the next payment date. The amount of the
payment is determined by the formula
(N) max(0, r − rc )(dt /360),
where N is the notional principal amount of the agreement, rc is the cap rate
(expressed as a decimal), and dt is the number of days from the interest rate
reset date to the payment date. Interest rates quoted in cap agreements follow
money market day-count conventions, so that payment calculations assume a
360-day year.
Figure 4 depicts the payoff to the buyer of a one-period interest rate cap.
If the index rate is above the cap rate, the buyer receives a payment of (N)(r −
rc )(dt /360), which is equivalent to the payoff from buying an FRA.2 Otherwise,
the buyer receives no payment and loses the premium paid for the cap. Thus, a
cap effectively gives its buyer the right, but not the obligation, to buy an FRA
2 One difference between the payoff to an FRA and the payoff to an in-the-money cap is
that an FRA pays the present value of the change in interest payable on the notional principal at
settlement (which corresponds to the reset date of a cap), while payments on caps are deferred. The
value of the payment has the same present value in both cases, however, so that the comparison
between the payoff to a cap and a call option on an FRA remains accurate.

78

Federal Reserve Bank of Richmond Economic Quarterly

with a forward rate equal to the cap rate. Such an agreement is known as a call
option. A one-period cap can be viewed as a European call option on an FRA
with a strike price equal to the cap rate rc .3 More generally, multi-period caps,
which specify a series of future interest rate reset and payment dates, can be
viewed as a bundle of European call options on a sequence of FRAs.
Example of an Interest Rate Cap
Consider the example of a one-year interest rate cap that specifies a notional
principal amount of $1 million and a six-month LIBOR cap rate of 5 percent.
Assume the agreement covers a period starting January 15 through the following
January 15 with the interest rate to be reset on July 15. The first period of a cap
agreement typically is excluded from the agreement, so the cap buyer in this
example will be entitled to a payment only if the six-month LIBOR exceeds 5
percent on the July 15 interest rate reset date. Suppose that six-month LIBOR
is 5.5 percent on July 15. Then, on the following January 15 (184 days after
the July 15 reset date) the seller will owe the buyer
$2,555.56 = ($1,000,000)(0.055 − 0.050)(184/360).
Comparison of Caps and Futures Options
A one-period cap can be compared to a put option on a Eurodollar futures
contract. To see why, note that the payoff at expiration to a put option on
Eurodollar futures is
(N) max(0, K − F)(90/360),
where N is the notional principal amount of the agreement ($1 million for a
Eurodollar futures option), K is the strike price and F is the price of the
underlying futures contract. The price index used for Eurodollar futures can
be written as F = 100 − r, where r is the three-month LIBOR implied by the
futures price. Now, write K = 100 − rk , where rk is the futures interest rate
implied by the strike price K. Then, the payoff at expiration to a Eurodollar
futures option can be expressed as
(N) max[0, 100 − rk − (100 − r)](90/360) = (N) max(0, r − rk )(90/360).
The right-hand side of this expression is just the payoff to a one-period interest
rate cap indexed to three-month LIBOR with a cap of rk .
Despite the similarities between the caps and Eurodollar futures options,
the two instruments differ in a number of noteworthy respects. First, futures
3 A European option can be exercised only on its expiration date. Similarly, a cap buyer can
only “exercise” his option if the index rate is above the cap rate on the interest rate reset date,
so that the interest rate reset date corresponds to the expiration date on a European-style option.

A. Kuprianov: OTC Interest

79

Figure 5 The Effect of Buying a Cap on Interest Expense
Interest Expense

+

=

rc
a. Unhedged
Exposure

b. Cap
Payment

rc

Interest
Rate

c. Hedged
Exposure

options are standardized, exchange-traded instruments, whereas caps are overthe-counter instruments whose payments can be tailored to match the payment
schedule of any variable-rate loan. Eurodollar futures options are based on
three-month LIBOR, whereas caps can be bought over the counter to match
virtually any maturity interest rate up to one year. Second, futures options are
American-style options that can be exercised at any time before the expiration
date. In contrast, caps resemble a strip of European options—a cap can be
“exercised” only if the specified index rate is above the cap rate on a given
reset date. Third, Eurodollar futures options are cash settled on the option
expiration date, while a cap is settled in arrears—that is, the payment period
falls some time after the interest rate reset date.

Hedging Uses of Caps
Figure 5 illustrates the effect that buying a cap has on the interest expense
associated with a floating-rate loan. The first panel depicts the unhedged or
inherent exposure of a firm with a loan tied to six-month LIBOR. The firm is
exposed to the risk that market interest rates will rise before the next interest
rate reset date on the loan and drive up its interest costs. The second panel
illustrates the effect that buying a cap has on interest expense. If interest rates
rise above the 5 percent cap rate, the payment received from the cap seller
offsets the firm’s increased interest expense. The hedged position, illustrated in
the third panel, shows how buying a cap limits the firm’s interest expense to a
maximum amount determined by the cost of servicing the debt at the cap rate
plus the premium paid for the instrument.

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Figure 6 The Payoff to Buying a One-Period Interest Rate Floor
Profit

rf

Interest
Rate

4. INTEREST RATE FLOORS
The buyer of an interest rate floor pays the seller a premium in return for
the right to receive the difference in interest payable on a notional principal
amount when a specified index interest rate falls below a stipulated minimum,
or “floor rate.” Buyers use floors to fix a minimum interest rate on an asset
paying a variable interest rate indexed to some maturity of LIBOR. Like an
interest rate cap, a floor is an option-like agreement in that it represents a right
rather than an obligation to the buyer. The buyer of an interest rate floor incurs
no obligation if the index interest rate rises above the floor rate, so the most a
buyer can lose is the premium paid to the seller at the outset of the agreement.
The payment received by the buyer of an interest rate floor is determined
by the formula
(N) max(0, rf − r)(dt /360),
where N is the notional principal amount of the agreement, rf is the floor rate
or strike price, and dt is the number of days from the last interest rate reset
date to the payment date. Figure 6 depicts the payoff to a one-period floor as
a function of the value of the underlying index rate. If the index rate is below
the floor rate on the interest rate reset date the buyer receives a payment of
(N)(rf − r)(dt /360), which is equivalent to the payoff from selling an FRA at a
forward rate of rf . On the other hand, if the index rate is above the floor rate
the buyer receives no payment and loses the premium paid to the seller. Thus,
a floor effectively gives the buyer the right, but not the obligation, to sell an
FRA, which makes it equivalent to a European put option on an FRA. More

A. Kuprianov: OTC Interest

81

generally, a multi-period floor can be viewed as a bundle of European-style put
options on a sequence of FRAs maturing on a succession of future maturity
dates.
Comparison of Floors and Futures Options
Purchasing a one-period interest rate floor yields a payoff closely resembling
that of a long Eurodollar futures call option. The payoff to a call option on a
Eurodollar futures contract is
(N) max(0, F − K)(90/360),
where F = 100−r is the index price of the underlying futures contract and K is
the strike price. As before, write K = 100−rk . Then, the payoff to a Eurodollar
futures call option can be expressed in terms of the underlying interest rate as
(N) max(0, rk − r)(90/360),
which is the same as the payoff to a one-period interest rate floor indexed to
90-day LIBOR with a floor rate equal to rk . The one noteworthy difference
between the two instruments is that a Eurodollar futures option can be exercised at any time, while a floor resembles a European option that can only be
exercised on its expiration date. Like caps, interest rate floors settle in arrears,
whereas a futures option settles on its expiration date.

5. INTEREST RATE COLLARS
The buyer of an interest rate collar purchases an interest rate cap while selling a
floor indexed to the same interest rate. Borrowers with variable-rate loans buy
collars to limit effective borrowing rates to a range of interest rates between
some maximum, determined by the cap rate, and a minimum, which is fixed by
the floor strike price; hence, the term “collar.” Although buying a collar limits a
borrower’s ability to benefit from a significant decline in market interest rates,
it has the advantage of being less expensive than buying a cap alone because
the borrower earns premium income from the sale of the floor that offsets the
cost of the cap. A zero-cost collar results when the premium earned by selling
a floor exactly offsets the cap premium.
The amount of the payment due to or owed by a buyer of an interest rate
collar is determined by the expression
(N)[max(0, r − rc ) − max(0, rf − r)](dt /360),
where, as before, N is the notional principal amount of the agreement, rc is
the cap rate, rf is the floor rate, and dt is the term of the index in days. Figure

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 The Payoff to Buying a One-Period, Zero-Cost Collar

Profit

rc

+

a. Buy Cap

rf

=

b. Sell Floor

rf
rc

Interest
Rate

c. Buy Collar

Figure 8 Put-Call Parity

Profit

+

a. Buy Cap

Interest
Rate

=

b. Sell Floor

c. Buy FRA

7 illustrates the payoff to buying a one-period zero-cost interest rate collar. If
the index interest rate r is less than the floor rate rf on the interest rate reset
date, the floor is in-the-money and the collar buyer (who has sold a floor) must
pay the collar counterparty an amount equal to (N)(rf − r)(dt /360). When r is
greater than rf but less than the cap rate rc , both the floor and the cap are outof-the-money and no payments are exchanged. Finally, when the index is above
the cap rate the cap is in-the-money and the buyer receives (N)(r − rc )(dt /360).
Figure 8 illustrates a special case of a zero-cost collar that results from the
simultaneous purchase of a one-period cap and sale of a one-period floor when
the cap and floor rates are equal. In this case the combined transaction replicates

A. Kuprianov: OTC Interest

83

Figure 9 The Effect of Buying an Interest Rate Collar on
Interest Expense
Interest Expense

+

a. Unhedged
Exposure

rf

rc

b. Collar
Payment

=

rf

rc

Interest
Rate

c. Hedged
Exposure

the payoff of an FRA with a forward interest rate equal to the cap/floor rate.
This result is a consequence of a property of option prices known as put-call
parity.
More generally, the purchase of a cap and sale of a floor with the same
notional principle, index rate, strike price, and reset dates produces the same
payout stream as an interest rate swap with an All-In-Cost equal to the cap or
floor rate. Since caps and floors can be viewed as a sequence of European call
and put options on FRAs, buying a cap and selling a floor with the same strike
price and interest rate reset and payment dates effectively creates a sequence
of FRAs, all with the same forward rate. But note that an interest rate swap
can be viewed as a sequence of FRAs, each with a forward rate equal to the
All-In-Cost of the swap. Therefore, put-call parity implies that buying a cap
and selling a floor with the same contract specifications results in the same
payment stream that would be obtained by buying an interest rate swap.
In recent years dealers in the OTC derivatives market have shown a great
deal of ingenuity in devising new hybrid instruments yielding an almost endless
variety of payout patterns. Interested readers can find descriptions of other types
of derivatives in Abken (1989), Burghardt et al. (1991), Smith and Smithson
(1990), and Smith, Smithson, and Wilford (1989).
Hedging Uses of Interest Rate Collars
Figure 9 illustrates the effect that buying a one-period, zero-cost collar has on
the exposure to changes in market interest rates faced by a firm with outstanding variable-rate debt. The first panel depicts the firm’s inherent or unhedged
interest exposure, while the second panel illustrates the effect that buying a

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Federal Reserve Bank of Richmond Economic Quarterly

collar has on interest expense. Finally, the third panel combines the borrower’s
inherent exposure with the payoff to buying a collar to display the effect of a
change in market interest rates on a hedged borrower’s interest expense. Note
that changes in market interest rates can only affect the hedged borrower’s
interest expense when the index rate varies between the floor and cap rates.
Outside this range, the borrower’s interest expense is completely hedged.

6. RISK AND REGULATION IN THE
OVER-THE-COUNTER DERIVATIVES MARKET
Regulatory Concerns
The OTC derivatives market is often characterized as unregulated because no
federal regulatory agency oversees trading activity in this market, as the Commodity Futures Trading Commission (CFTC) does with futures markets or the
Securities and Exchange Commission (SEC) does with securities markets.4
Yet it would be misleading to characterize the OTC derivatives market as
completely unregulated. Many of the largest derivatives dealers are affiliates
of commercial banks, which rank among the most heavily regulated of all
firms. Bank regulatory agencies routinely conduct on-site examinations to review procedures in place for controlling risks at the institutions they supervise.
Additionally, regulations imposed by the federal banking agencies include minimum capital requirements designed to take account of credit risk exposure
arising in connection with derivative instruments.5 While not subject to the
comprehensive regulatory oversight applied to commercial banks, investment
banks dealing in OTC derivatives are subject to SEC scrutiny. And the International Swap Dealers Association (ISDA)—an industry association organized
by the major OTC derivatives dealers—sets standards for market practices and
addresses the legal and public policy issues affecting the market.
Nonetheless, the rapid growth and sheer size of the OTC derivatives market
has sparked debate over the risks posed by the growth of trading in derivative
instruments and the appropriate scope of market regulation.6 When all types of
derivative agreements are taken into account, including currency swaps, caps,
floors, collars, and swaptions, the total notional principal amount of outstanding
agreements exceeded $4 trillion at the end of 1991, with derivatives dealers
acting as middlemen to most transactions. Much of the trading activity in
this market takes place between a relatively small number of large dealers,
resulting in an interdependent web of obligations among those dealers.7 Unlike
4 See

Abken (1991a) for a description of these other markets.
(1990) discusses capital requirements for OTC derivatives.
6 For example, see Corrigan (1992), Bank for International Settlements (1992), and Hansell
and Muehring (1992).
7 Data in ISDA’s Market Survey Highlights, Second Half 1991, indicates that 47 percent of
all new interest rate swaps arranged in 1991 were between ISDA member organizations.
5 Rogers

A. Kuprianov: OTC Interest

85

exchange-traded derivatives such as futures contracts and futures options, where
the exchange clearinghouses guarantee contract performance through a system
of margin requirements, daily settlement of gains and losses, and the backing of
the capital of clearing member firms, OTC derivative instruments are bilateral
arrangements that carry no independent third-party guarantee. As a result, counterparties to OTC instruments face the risk of default, known as counterparty
credit risk. Moreover, the absence of contract standardization means that OTC
derivatives tend to be less liquid than exchange-traded derivatives, which can
make it difficult to execute transactions in periods of extreme price volatility
or when a counterparty’s credit standing is questioned.
A recent joint study by the three federal banking agencies examined the
risks posed by the growth of trading in OTC derivatives (Board of Governors
of the Federal Reserve System, Federal Deposit Insurance Corporation, and
Office of the Comptroller of the Currency 1993). The study found that risks
associated with OTC derivatives differed little from the risks traditionally borne
by financial intermediaries. Although it did identify a number of concerns, the
study concluded that trading in derivative instruments has not contributed to
the overall fragility of the financial system and does not pose undue risks
for organizations active in this market. To the contrary, it cited at least one
instance—namely, the period of exchange rate turbulence in European currencies in September of 1992—where it concluded that foreign currency markets
were not likely to have performed as well as they did during the crisis without
the existence of foreign currency derivatives that enabled financial institutions
to manage their currency positions.
The joint study identified six different types of risks in connection with
derivative instruments: credit risk, market risk, liquidity risk, settlement risk,
operating risk, and aggregation risk. As noted earlier, much of the concern over
the growth of the market has centered around the issue of counterparty credit
risk because of the sheer size of the market and the size of credit exposures
borne by dealers. Because derivative instruments tie together so many different
markets around the world, regulators have expressed concerns that aggregation,
or interconnection risk, might make it difficult to contain a financial crisis to
keep it from spreading to other markets. The remainder of this article discusses
some of the risks associated with OTC derivatives and the legal, regulatory,
and market arrangements that have developed to deal with such risks.
Counterparty Credit Risk
Measuring the Credit Risk Exposure of an FRA
The credit risk exposure associated with an FRA, or any other derivative instrument for that matter, differs from that of a debt instrument because an FRA
is not a funding transaction and therefore involves no exchange of principal.
At its inception the value of an FRA is zero to both parties, so there is no
initial credit risk. Potential credit risk is bilateral: a party to an FRA is exposed

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Federal Reserve Bank of Richmond Economic Quarterly

to credit risk when the value of the agreement becomes positive to him or
her, and the value of an FRA can change so as to gain value to either party.
Unlike a loan agreement, where financial distress on the part of a borrower
always exposes the lender to default risk, financial distress on the part of an
FRA counterparty does not necessarily expose the other counterparty to the
risk of default. A financially distressed firm has no incentive to default on an
agreement that has positive value to it—and even if such a counterparty were
to default, the nondefaulting party would suffer no loss.
Since an FRA involves no exchange of principal, potential credit risk exposure is a small fraction of the notional principal amount of the agreement.
Credit risk exposure is determined by the value of the FRA, which corresponds
to the cost of replacing the FRA. To illustrate, recall the earlier example of
a 1 × 4 FRA with a notional principal of $1 million and a forward rate of 5
percent. If market interest rates rise by 50 basis points immediately after the
agreement is negotiated, the value of the FRA to the buyer is just the current
present value of $1,250 (50 basis points × $25 per basis point), or
$1,229.51 = $1,250/[1 + 0.050(120/360)].
This calculation determines the value of the agreement exactly 30 days before
its scheduled settlement, or maturity date. The credit risk exposure borne by
the FRA buyer in this example is just over 1/10 of 1 percent of the notional
principal amount of the agreement.
Measuring the Credit Risk Exposure of an Interest Rate Swap
A swap counterparty’s credit risk exposure is determined by the cost of replacing the agreement in the event of a default. The cost of obtaining a replacement
swap is determined by the difference between the All-In-Cost of the old swap
and the AIC on a replacement swap. As an illustration, consider the case of a
fixed-rate payer in a swap with one year left to maturity and a 7 percent AIC. If
the floating-rate payer defaults when the prevailing market rate on a one-year
replacement swap is 8 percent, the nondefaulting party will be required to pay
an extra 1 percent per year on the notional principal to replace the swap. The
replacement value of the swap is just the net present value of the difference in
interest payments.
In discussing swap valuation methods it was useful to view a swap as
an implicit mutual lending arrangement in which the counterparties exchanged
loans indexed to two different interest rates. In looking at credit risk exposure,
however, it can be useful to view a swap as a bundle of FRAs, all with forward
rates equal to the All-In-Cost of the swap. Thus, the swap in the above example
can be viewed as a combination of a 0 × 6 FRA and a 6 × 12 FRA, each with a
forward rate of 7 percent. The replacement cost of the swap is just equal to the
value of the two component FRAs when the underlying index rate is 8 percent.

A. Kuprianov: OTC Interest

87

As with FRAs, the potential credit risk exposure of an interest rate swap
typically is a small fraction of the notional principal amount of the agreement.
By one estimate, the expected lifetime credit exposure associated with an interest rate swap varies from 0.002 percent of the notional principal for a swap
with a one-year maturity to 4.5 percent for a swap with a ten-year maturity
(Simons 1989).
Credit Risk Exposure of Caps, Floors, and Collars
Sellers of caps and floors face no credit risk, since neither type of agreement
requires the buyer to make any payments other than the initial premium. But
cap and floor buyers face the risk of nonperformance on the part of the seller
any time a cap or floor goes “in-the-money”—that is, any time the seller is
required to make payments to the buyer. Since a collar involves a short position
in a floor and a long position in a cap, it can expose both the buyer and seller
to counterparty credit risk.
The credit risk exposure faced by the buyer of an interest rate cap can be
compared to the risk exposure of a fixed-rate payer in an interest rate swap. In
both cases, the buyers face the risk that the seller will default when interest rates
rise. Similarly, the buyer of an interest rate floor faces a credit risk exposure
analogous to that of a floating-rate payer, or seller, of an interest rate swap.
The total credit risk exposure in each case is determined by the cost of buying
a replacement cap or floor.
Netting Arrangements
When dealers first began acting as intermediaries in swap agreements the risk
associated with each swap was accounted for separately. As the market grew,
swap dealers found themselves parties to multiple agreements with the same
counterparty. Concern over their growing aggregate exposure led many dealers
to adopt “master” agreements that treated all their transactions with a given
counterparty as supplements to a single consolidated agreement. These master
agreements gave swap counterparties the right to terminate all supplemental
swap agreements in the event of default on any one of the swaps. The advent
of the master agreement represented an attempt by swap dealers to limit the
credit risk exposure with any single counterparty to the net value of all swaps
with that counterparty. Today virtually all OTC derivatives utilize a standardized master agreement designed by the International Swap Dealers Association
(Gooch and Pergam 1990).
The Status of OTC Derivatives Under Bankruptcy Law
Before the enactment of recent amendments to the Bankruptcy Code, there was
some question as to whether master swap agreement netting provisions would

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Federal Reserve Bank of Richmond Economic Quarterly

be legally enforceable in the event of bankruptcy. The U.S. Bankruptcy Code
grants a firm in bankruptcy proceedings an “automatic stay” from the claims of
its creditors. The automatic stay allows a bankrupt firm to postpone scheduled
debt payments and overrides most other contractual obligations pending the
resolution of all claims against the firm. Thus, although virtually all lending
agreements give creditors the right to demand accelerated repayment of a loan
in the event of a default on a scheduled payment, default inevitably delays
repayment in practice. Often, creditors of the bankrupt firm receive only a
fraction of the amounts owed them even if the firm ultimately emerges from
bankruptcy proceedings as a reorganized entity. Swap market participants faced
the risk that the Bankruptcy Courts might enforce the automatic stay against
swap agreements, making the netting provisions of the ISDA master swap
agreement unenforceable. Nondefaulting counterparties would then face the
risk that a bankruptcy trustee might selectively default only on swaps having a
negative value to a bankrupt counterparty, a practice known as “cherry picking.”
Public Law 101–311, enacted on June 25, 1990, amended the Bankruptcy
Code to exempt swap agreements executed under a single master agreement
such as the ISDA master agreement from the automatic stay normally applicable to creditors of a bankrupt firm. The amendments were enacted to make the
netting provisions of the ISDA master swap agreement enforceable in the event
of bankruptcy. The Bankruptcy Code amendments also authorize nondefaulting
swap counterparties to utilize any collateral posted in connection with a swap
agreement to offset the net amount owed by a bankrupt counterparty (Rogers
1990). In this respect, the law treats OTC derivatives analogously to exchangetraded futures contracts.8 These provisions greatly mitigate the potential loss
faced by swap counterparties when the parties involved have multiple agreements with one another.
The Status of Swap Agreements Under Banking Law
Commercial banks and thrift institutions are not subject to the provisions of
the Bankruptcy Code. Instead, bank failure resolution is governed by federal
and state banking laws, which gives the Federal Deposit Insurance Corporation
(FDIC) and the Resolution Trust Corporation (RTC) (in the case of certain
savings and loan institutions) considerable discretion in dealing with failing
federally insured depository institutions. The FDIC and RTC may act in the
capacity of either a conservator or a receiver. An institution placed in conservatorship is not declared legally insolvent. It continues its normal business
operations under the close scrutiny of federal regulators pending resolution of
8 Williams (1986) stresses the importance of the exemption of futures margin requirements
from the automatic stay as a prime reason for the existence of futures markets.

A. Kuprianov: OTC Interest

89

its financial difficulties. Institutions in conservatorship are either returned to
private sector control, through a sale or merger, or they are eventually declared
insolvent. When a federally insured depository institution is declared legally
insolvent either the FDIC or RTC becomes the receiver for the institution. Regulators may resolve bank failures either through a “purchase and assumption”
transaction in which the failed institution is taken over by another bank or thrift
or, less often, through liquidation.9
The Financial Institutions Reform, Recovery, and Enforcement Act of
1989 (FIRREA) contains provisions similar to the netting provisions of the
Bankruptcy Code requiring the receiver of a failed bank or conservator of
a failing bank to treat all supplemental swap agreements executed under a
single master agreement as a single contract. In the event of a default or
liquidation of a bank or thrift, the institution’s counterparties maintain the
right to accelerate repayment of all swap agreements made under a single
master agreement. Counterparties do not have an automatic right to terminate
existing swap agreements when an institution is placed into conservatorship,
however, because an institution in conservatorship has not legally failed (although they do retain the right to demand accelerated repayment in the event
of a default or breach of another covenant). FIRREA gives bank regulators
the express right to transfer all derivative instruments covered by a single
master agreement, along with other bank assets, to another institution, either
when the institution is in conservatorship or in the case of a purchase and
assumption transaction. But in this latter case the master agreement and all
its supplements must be treated as a single agreement and transferred together
with all applicable collateral. Thus, the law discourages federal regulators from
cherry picking among individual OTC agreements that are part of a larger
master agreement.10 Nondefaulting counterparties still face the risk that their
agreements might be assigned to a counterparty with a relatively weak credit
standing, however.
Although recent legislation has reduced the legal risks faced by domestic
counterparties, derivatives dealers with exposures to counterparties outside of
the United States still face risks arising from the uncertain legal status of
netting arrangements under foreign laws. At present, ISDA is working with
authorities in other countries to enact bankruptcy legislation resembling the
recent Bankruptcy Code amendments enacted in the United States. Until such
legislation is enacted, however, internationally active OTC derivatives dealers
face considerable legal risk.

9 Dotsey

and Kuprianov (1990) describe bank failure resolution policies in more detail.
Gooch and Pergam (1990) and Rogers (1990) for more details on banking law and
netting arrangements.
10 See

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Aggregation or Interconnection Risk
Aggregation or interconnection risk refers to the risk that a disruption in one
market, caused by the default of a major institution or some other event, might
cause widespread difficulties throughout the OTC derivatives market or even
spread to other financial markets. Market liquidity risk is one source of interconnection risk. OTC derivatives dealers operate in many different markets
at once. They must often execute complex, multi-legged transactions to create
custom-tailored instruments for their customers while attempting to hedge the
resulting exposure to market risk. The successful execution of such operations
depends on the ability to complete a number of transactions in different markets almost simultaneously. But experience shows that market liquidity can
evaporate quickly, especially in times of financial stress when market participants have reason to question the creditworthiness of potential counterparties.
Reduced liquidity can make it difficult for a dealer to hedge its exposure to
market price risk or, in the event of a default by a counterparty, make obtaining
a replacement swap a costly proposition.
Counterparty credit risk can also be a source of aggregation risk because
such a large fraction of trading in OTC derivatives takes place between the dealers themselves. The default of a single major dealer could have a significant effect on the outstanding positions of other major dealers. In addition to potential
losses from credit risk exposures, a default by a major derivatives dealer would
leave other dealers exposed to considerable price risk. Dealers use derivatives
both to hedge their outstanding commitments to other OTC counterparties as
well as other asset holdings. These dealers would need to rebalance their portfolios, either by buying or selling new derivative instruments or by quickly
selling existing asset holdings. The resulting flurry of activity might conceivably disrupt not only the OTC derivatives market, but other markets as well.
To date, losses incurred by counterparties to OTC derivatives have yet to
even approach the magnitude of losses incurred in the course of more traditional lending and investment activities. Worth noting in this regard is that
financial markets have survived at least one default by a major derivatives
dealer—that of Drexel Burnham Lambert in 1990—without serious disruption,
although it has certainly provided headaches for Drexel’s former counterparties.
Recent legislation recognizing netting arrangements was designed to help contain the consequences of a default by a major derivatives dealer in the United
States, although, as noted earlier, other countries have been slow to enact such
legislation.
Market Arrangements for Controlling Risks
Managing the credit risk associated with a position in an instrument such as
an interest rate swap requires credit evaluation skills of the type commonly
associated with bank lending. Thus, as the swaps market evolved into a dealer

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91

market where financial intermediaries assumed the role of counterparty to the
end users of swap agreements, commercial banks, which have traditionally
specialized in credit risk evaluation and have the capital reserves necessary
to support credit risk management, came to dominate the market for swaps
and other OTC derivatives. Only in cases where a counterparty is deemed a
poor credit risk are performance bonds, such as margin requirements of the
type employed by futures exchanges, used to substitute for credit evaluation.
When performance bonds are used, the agreement often provides for the periodic settlement of changes in the value of a derivative instrument using a
process resembling the daily marking-to-market of futures contracts, although
settlement generally takes place at less frequent intervals with OTC derivatives
(Smith, Smithson, and Wakeman 1986).
The widely publicized financial difficulties of many firms and banks in
recent years has made market participants sensitive to the issue of counterparty
credit risk. As a result, dealers with less than AA credit ratings have found it
increasingly difficult to trade in OTC derivatives. The heavy loan losses and
resulting financial difficulty experienced by many commercial banks in recent
years has hampered the ability of such institutions to compete in this market. At
the same time, a number of investment banks have formed separately capitalized subsidiaries so as to enhance their credit standing and remain competitive
in the derivatives market.11 Thus, market discipline has had the salutary effect
of restricting the activities of less creditworthy counterparties.

7. CONCLUDING COMMENTS
The evolution of the over-the-counter derivatives market has revolutionized
the nature of financial intermediation in money markets in a span covering
a little more than a decade. Along with the benefits derivatives offer firms
in managing cash flows, however, the rapid growth of the market has raised
new concerns for regulators and policymakers. Industry spokesmen argue that
existing market arrangements are adequate to address such concerns, a view
increasingly shared by regulators and policymakers.12 The development of the
ISDA master agreement in recent years, along with recent changes in banking
laws and in the U.S. Bankruptcy Code, has gone far to minimize the potential
for widespread market disruption that could result from a default on the part
of a major dealer in the swaps market. And concerns about counterparty credit
risk have led market participants themselves to limit the activities of dealers
with less than outstanding credit ratings.
11 Federal regulators have yet to grant commercial banks approval to form separately capitalized subsidiaries of the type investment banks have begun to use. See Chew (1992, 1993) and
Peltz (1993) for a more detailed discussion of this trend.
12 For example, see Hansell and Muehring (1992), Phillips (1992), and Shale (1993).

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Abken, Peter A. “Globalization of Stock, Futures, and Options Markets,”
Federal Reserve Bank of Atlanta Economic Review, vol. 76 (July/August
1991), pp. 1–22.
. “Beyond Plain Vanilla: A Taxonomy of Swaps,” Federal Reserve
Bank of Atlanta Economic Review, vol. 76 (March/April 1991), pp. 12–29.
. “Interest-Rate Caps, Collars, and Floors,” Federal Reserve Bank
of Atlanta Economic Review, vol. 74 (November/December 1989), pp.
2–24.
Bank for International Settlements. Recent Developments in International Interbank Relations. Basle, Switzerland: Bank for International Settlements,
1992.
Beckstrom, Rod A. “Fundamental Models for Pricing Swaps,” in Robert J.
Schwartz and Clifford W. Smith, Jr., eds., The Handbook of Currency
and Interest Rate Risk Management. New York: New York Institute of
Finance, 1990.
Board of Governors of the Federal Reserve System, Federal Deposit Insurance
Corporation, and Office of Comptroller of the Currency. “Derivative
Product Activities of Commercial Banks,” Joint study conducted in
response to questions posed by Senator Riegle on derivative products.
January 27, 1993.
Brown, Keith C., and Donald J. Smith. “Plain Vanilla Swaps: Market Structures,
Applications, and Credit Risk,” in Carl R. Beidleman, ed., Interest Rate
Swaps. Homewood, Ill.: Business One Irwin, 1990.
Burghardt, Galen, Belton, Lane, Luce, and McVey. Eurodollar Futures and
Options. Chicago: Probus Publishing Company, 1991.
Chew, Lillian. “Judgement of Salomon,” Risk, vol. 6 (March 1993), pp. 8–9.
. “Kings of the Road,” Risk, vol. 5 (September 1992), pp. 94–98.
Corrigan, E. Gerald. “Painful Period Has Set Stage for Banking Rebound,”
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