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Economic Review
Federal Reserve Bank of Dallas
January 1986
1
The Case of the World's Missing Money
Leroy O. Laney
Because one country' s export is another country's
import, one would expect the summation of current
account balances around the world to net to zero.
They do not. I n fact, there has been a large and
growing total current account deficit in recent
years. This article analyzes sources of the
discrepancy, geographically and by type, and
provides some thoughts regarding its prospects.
One might extrapolate future growth in the world's
current account deficit, but such growth could be
retarded by several factors . Among these is the
possibility of a growing positive trade account
asymmetry, as well as lower oil prices and
interest rates .
10
Velocities of M1 and the Monetary Base:
A Correction of Standard Formulas
Dale K. Osborne
Government statistics on velocity are computed by
formulas that do not agree with the definitions of
velocity. The formulas treat transactions that do
not use money as if those transactions did use
money. This article presents a framework that shows
how the many types of transactions in a modern
economy may be properly accounted for and gives
corrected formulas for the main velocity concepts .
This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)
Economic Review
Federal Reserve Bank of Dallas
January 1986
President
Robert H. Boykin
First Vice President
William H. Wallace
Senior Vice President and Director of Research
Harvey Rosenblum
Vice President and Associate Director of Research
James E. Pearce
Assistant Vice President and Senior Economist
Leroy O . Laney
Eugenie D. Short
Economists
Nationall I nterna tional
W . Michael Cox
Gerald P. O' Driscoll, Jr.
Robert T. Clair
John K. Hill
Richard C. K. Burdekin
Steven L. Green
Regional/Energy
Stephen P. A. Brown
William C. Gruben
Ronald H. Schmidt
Hilary H. Smith
Roger H. Dun stan
William T. Long, III
Editorial
Virginia M . Rogers
Elizabeth R. Turpin
Graphics and Typesetting
Publications Department
The Economic Review is publish ed by the Federal
Reserve Bank of Dallas and will be issued six times
in 1986 (J anuary, March, May, July, September, and
November). The views expressed are those of the
authors and do not necessarily reflect the positions
of the Federal Reserve Bank of Dallas or the Federal
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send requests for single- and multiple-copy subscriptions, back issues, and address changes to the Public
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Articles may be reprinted on the condition that the
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is provided with a copy of the publication containing
the reprinted material.
Tbe Case of the World's
Missing Money
Leroy O. Laney
Assistant Vice President and Senior Economist
Federal Reserve Bank of Dallas
No country in today's world has an economy completely closed to international transactions, but the
world as a whole is still a closed economy. (So far
we have not opened any trading or financial relationships with other planets.) According to reported
balance of payments statistics, however, the world
runs a global deficit on the current account of its
balance of payments that recently has approached
$100 billion annually. This amount may not seem
like much compared to many contemporary global
economic magnitudes, but in recent years it has
risen to a significant percentage of total balance of
payments flows .
Some reason for concern exists in a world in
which major policy decisions are made because of
balance of payments pressures. Where can that
missing money be found? Are there any particular
accounts, countries, or groups of countries that are
responsible? Can an overstated U.S. current account
deficit explain the continued coexistence of the
record deficit and the strong dollar?
Conceptually, one nation's export should be some
other nation's import, and vice versa. Illegal international traffic goes unrecorded, of course, but the
underground economy might not bias the numbers
Economic Review I January 1986
either way unless an illegal transaction were recorded on one side but not the other. I n order for a
global asymmetry to emerge, either recorded exports must go unrecorded as imports, or recorded
imports must go unrecorded as exports. For example, an industrial country consultant to an oilprodUCing country may not report as income a
recorded payment by that country.
The current account, the most widely used
measure of the balance of payments today, includes
not only international trade in goods, but also the
so-called "invisible" items like services-such as
shipment costs, travel and tourism, investment income, royalties, advertising and professional fees,
worker remittances and pensions, and private and
official unilateral transfers . In any period, by definition, a given country' s current account is balanced
by equal capital flows in the opposite direction . In
the box, the chart of accounts illustrates the fundamentals of a typical balance of payments.
If the current and capital flows (official plus
private) do not offset each other, a statistical
discrepancy account exists to fill any gap. An individual country's statistical discrepancy may consist of either unrecorded capital or current account
Balance of Payments Structural Components
Acc ounts
Debits
Cre dits
Merchandise exports and imports . .
a
a*
Se rvices
Net inves tment in come
Shipment and other transportation
Trave l
....... . .. .
Net m il itary tra nsactions ..... . .... .
Other services, net .. . ..
b
c
d
e
f
b*
c*
d*
e*
f*
Re mitta nces, pen sions, and other transfers .
g
g*
h
h*
Current account
Capital account
Official and private short- and long-term
capita l flows, net.
. ....... .
i*
Statistica l discre pancy ...... . ....... .. .. .
Current account ba lance
(a * + b* + c * + d * + e * + f* + g*)
- (a + b + c + d + e + f + g)
Summation of balance of payments accounts
a+b+c+d+e+f+g+h+
=
a * + b* + c * + d * + e* + f* + g* + h* + i*
flows . Some of the global current account discrepancy can be traced to statistical discrepancies of individual countries, but other origins also exist.
This article identifies so me of the sou rces of the
discrepancy in the global balance of paym ents . But
it is hard to use this information to adjust existing
balance of payments numbers. Un less a marked improvement occu rs in ba lance of payments repo rting-which can take p l ace on ly at the individua l
country level- it is not like ly that this discrepancy
will disappear.
Current account balances by country group
Recent International Monetary Fund data on current
account balances for major country groupings are
shown in Tab le 1 .1 For the United States, t he impact
of the 1981-82 recession can be detected as the
shrinking domestic demand has cut back on U .S.
2
purchases of foreign goods and services . But then
an expanding economy combined wit h a strong
do ll ar drove the U.S . current account increas ingly
into deficit. Movements in oi l prices in 1979 and recent problems of the developing countries are also
discernib le in the data.
The other countr ies category in Tab le 1 includes
some of the 148 member nations in the Fund. It is
apparent, however, that this group does not contribute much to the globa l deficit sum and has even
had a net current account surp lus in recent years.
The most important of these other countries are the
Soviet Union and nonmember Eastern European
countries. The figures for other countries in Table 1
are estimates based on incomp lete information and
represent only convertible or hard-cu rrency transactions . The re lative importance of the Soviet Union is
ill ustrated by U .S. Centra l Inte lligence Agency
Federa l Rese rve Ba nk of Da ll as
Table 1
WORLD CURRENT ACCOUNT BALANCES
(In billions of U.S. dollars)1
Countries
1977
1978
1979
1980
1981
1982
1983
1984
Industrial countries ...... .. .
-2.4
31.9
-5.6
-38.8
3.1
1.2
2.2
-34.2
United States . . . . .. . .. ...
Other industrial
countries ...
Of which.
Japan . ... , .
West Germany .... . ....
-11.7
- 12 .3
2.6
6.6
10.7
-3.8
- 35.5
-93.4
9.3
44 .2
-8.2
-45.4
-7.7
5.0
37.7
59.1
11 .3
8.5
17.0
13.4
-7.9
0.1
-9.5
-8.3
6.2
0.8
8.1
10.2
22 .2
10.0
36.4
13.1
Developing countries . ..... .
-0.1
-36.2
0.2
22.6
-56.3
-99.6
-70.5
-43.9
By region
Africa ... .. ...........
Asia .... .... .. .... . . . .
Europe ........... . . . .
Middle East ........ . . .
Western Hemisphere
- 10.4
-0.9
-9.0
31 .8
-11.6
-15.4
-8.9
- 7.1
14.5
- 19.4
-6.6
- 15.2
-9.9
53.7
-21.7
-5.3
-21.8
- 12 .5
91 .6
-29.3
-25. 2
-23.4
- 10.5
45 .8
- 43 .1
- 24.4
-19.8
- 6.7
-6.5
- 42.1
-15 .5
-16.3
-5.3
- 21.7
-11.7
- 10.9
-7 .9
-3 .3
-16.3
-5.5
Fuel exporters . . . . .
Nonfuel exporters . .... .
25 .0
-25.1
- 0.7
-35.5
54.0
- 53.8
100.1
-77.5
34.7
- 91 .0
- 23.4
-76 .2
-17.0
-53.6
-5.7
-38 .2
. ........ ..
-6.9
-3.5
-2.1
-3.0
-2.8
2.6
4.9
6.7
Total' ... ....... . .. ... .. ..
-9.5
-7.8
-7.6
-19.1
-56.0
-95.8
-63.5
-71.4
By analytical criteria
Other countries'
1. On goods. se rvic es. and private transfers.
2. Covers es timated bal ances reported by the Intern ation al M onetary Fund on current transactions only in conve rtibl e currencies of the USSR
and other nonm ember countries of Eas tern Europe.
3. Refl ec ts errors. omissions. and asymmetries in reported balance of paym ents statistics on current account. plus bal ance of listed groups with
countries not in cluded.
SOURCE OF DATA : International Monetary Fund, World Economic Outlook. April 1985 (Washington. D.C., 1985), Tabl e 29, p. 23&.
estimates in Table 2. Because the Soviet Union has
run a trade and current account surplus in most recent years, the global current account deficit puzzle
cannot be solved here. The Soviet current account
surplus has been counterbalanced largely by sizable
outflows that can be recorded only on the statistical
discrepancy or errors and omissions account. This
includes an estimate of Soviet trade credit extended
to finance their exports-including arms-to nonCommunist hard-currency trade partners. 2 In any
case, given the relatively small scale of Soviet transactions with the rest of the world, any inaccuracies
in reporting are unlikely to be that important.
The most interesting aspects of Table 1, however,
are the counterintuitive total deficit, the fact that it
has increased substantially in recent years, and its
volatility .
Economic Review I January 1986
Who else is out there? Since 1982, when developing country deficits peaked, the discrepancy has
declined somewhat, but it has remained at high
levels after that. Can the origin of this total deficit
be traced?
The discrepancy in international merchandise trade
An IMF estimate of the composition of the total
deficit is shown in Table 3. One striking aspect of
this breakdown is that, despite the global current
account deficit, the world balance of merchandise
trade transactions usually has been recorded as a
surplus . Two explanations commonly are offered for
this surplus.
One explanation - purely statistical- can only be
partial and washes out in the overall current account. It has been suggested that excessively large
3
Table 2
SOVIET UNION HARD-CURRENCY BALANCE OF PAYMENTS
(In million s of U .S. dollars)
1979
1980
Trade balan ce .
1,837
1,714
Current account ba lance ...
2,177
1,904
-175
Capital account ba lance ...
340
1,630
5,840
- 2,517
-3,534
- 5,635
2,993
Ba lances
Errors and omi ss ion s
2
......
1981
200
1982
1983
1984'
4,433
4,713
4,175
4,333
4,663
4,225
-1,340
1,650
200
- 6,313
4,425
1 . Estimated .
2. In cludes Soviet hard-curre ncy aid to, and trade w ith, other CEMA coun tries; and trade credi ts exte nded to fi nance Soviet
exports- in cludi ng arm s- to non-Com munist hard-currency t rade pa rtn ers.
SOU RCES OF DATA: U.S. Ce ntra l Inte ll igence Agency, Handbook of Economic Statistics, 1980, Report no. ER 80-10452
(Was hington, D.c.: National Foreign Assess ment Center, Octobe r 1980), Tab le 49 , p. 72 ; and
Handbook of Eco nomic Sta tistics, 1985, Report no. CPAS 85-10001 (Was hin gton, D.c.: Di rec torate
of Inte llige nce, Septembe r 1985), Tab le 46, p. 72 .
adjustment factors are used for converting imports
from a cost, insu rance, and freig ht shares (c.i.f.)
basis to one which excludes these charges. 3
When customs stati stic s are co ll ected initia ll y for
imports o n a c.i.f. basis, some conversion is
necessary to make them comparab le to exports in
the overall balance of payments . But an offsetting
entry is then necessary in the services component of
the curre nt ac count. If the adjustment factor is
large, this wou ld help exp lain both the globa l trade
surp lus and the global defic it in services. But the
overa ll globa l current accou nt deficit is no closer to
being exp lain ed, because any overestimation is
ca nce ll ed within the curre nt acco un t.
The other freq uent exp lanatio n derives from the
practice of recording exports and imports at the
time t hey cross nationa l fro ntiers rather than when
owners hip actually changes . This practice leaves a
substantial portion of world trade contin uously in
transit because exports may be recorded when they
leave one country but not be recorded unti l weeks
or mo nths later as imports by the receiving country .
This discrepancy sho ul d t herefo re get large r w hen
w o rld trade is inc reasing and sma ll er w hen wo rld
Tab le 3
DECO MPOSITION O F CURRENT ACCOU NT ASYMMETRY
(In billions of U .S. do ll ars)'
Coun tries
1977
1978
1979
1980
1981
1982
1983
1984
. .... . . . ...... . . . .. .
-9.5
7.8
-7.6
-19.1
-56.0
-95.8
- 63.5
-71.4
Trade balance
Timing asymmetry 2 • . . •
Res idual asymmetry
Services and private
transfers .. . ..... . , . , .
16.0
5.6
10.4
16.1
13.9
2.2
20.8
23 .0
-2 .2
29.2
7.9
21 .3
19.6
- 1.3
20.8
-0.9
- 11.8
10.9
15.7
4.8
10.9
19.7
6.5
13.2
-25 .5
-23 .9
- 28.4
-48 .3
- 75 .6
-94.8
-79 .1
-91 .2
Tota l
1. O n goods. serv ices, and private tra nsfers.
2. In te rn ational Monetary Fund estimates of the di ffe rence between the beg inn ing-of-yea r and end-of-yea r "floa t"; that is, the value of those
exports that have no t yet bee n recorded as Imports (usuall y beca use t he goods are in trans it or beca use of delays in t he processi ng of the
doc um entation). The es timates should be v iewed onl y as rou gh orders of mag nitude.
SO URCE OF DATA : Intern ationa l Monetary Fund, World Eco nomic O utlook, April 1985 (Was hington, D.C., 1985), Tabl e 29, p. 236 .
4
Fede ra l Reserve Bank of Da llas
Chart 1
Global Timing Asymmetry and World Trade
TIMING ASYMMETRY1
(MILLIONS OF U.S. DOLLARS)
30
WORLD TRADE
(PERCENT CHANGE)
30
,
20
.................
20
\
\ WORLD TRADE
10
10
\
\
\
TIMING ASYMMETRY
o
\
o
-10
-10
-20~~--~----~----L---~----~--~----~~
1977
1978
1979
1980
1981
1982
1983
-20
1984
1. See Table 3.
SOURCE OF PRIMARY DATA: Intern ation al Monetary Fund .
trade declines .4 In Chart 1, the IMF estimate of this
timing asymmetry' in Table 3 is compared to
changes in the total exports of IMF member countries. A marked correspondence does exist between
the timing asymmetry and changes in recorded
world trade, but part of the estimation procedure
for this component is based on world trade values .
In Table 3, the trade balance asymmetry is
decomposed into the estimate of timing asymmetry
and a residual. The residual, which includes effects
of the first explanation above as well as any other
factors, has been more of a random influence. The
two years that do stand out, however-1980 and
1981-are not easily explained.
One possible explanation is an increase in oil inventories held at sea-a reduction in the average
speed of the world tanker fleet or the use of idl e
tankers for storage. But if this is in fact the source
of the 1980-81 discrepancy, then it should be
reflected more correctly in the timing asymmetry
category. The argument itself may not seem very
convincing in retrospect, because 1980 was a year in
which oil prices were rising, OPEC (Organization of
Petroleum Exporting Countries) was in full control,
and Saudi Arabia was at peak production . Incentives for the use of tankers as floating storage
Economic Review I January 1986
vehicles by oil producers did not occur very much
u nti I about 1983.
Some incentives for floating inventory buildup
from the consumer side did exist, on the other hand,
prior to the advent of the oil glut, so that this explanation is more plausibl e. Major oil importing
countries such as Japan could have then been more
responsible for the 1980-81 residual than taking
into account a view only the producer side would
accede to .
The price effect of the second oil shock could explain the 1980 ex perience partially, but not that for
1981, since pric es had leveled off. If oil price effects
dominated the residual item, moreover, the component in subsequent years would have become
negative with falling prices.
Ill ega l traffic might contribute to the residual
world trade discrepancy, but no hard evidence
exists. Smuggling in drugs, and even gold and other
commodities-which may be a significant part of
trade for some developing economies-probably is
not recorded as imports or exports. If goods are
smuggled out of an exporting country but imported
legally by another country, a negative discrepancy
would result. This would not help explain the
positive balance in the residual category . Only if
5
legally recorded exports were smuggled into the
country of destination would an explanation be
found.
Regarding gold, we do know that the world's
largest producer, South Africa, records gold in its
exports. Only part of these gold exports are recorded as corresponding imports of other countries.
Differences in valuation also occur. Under flexible exchange rates, an export may be valued at an
exchange rate different than that of its corresponding import. Foreign trade receipts or expenditures
may be underrec orded or overrecorded to avoid
taxes or exchange controls . And grants-in-aid may be
recorded differently by recipient and donor
countries .
Unfortunately, the trade balance residual cannot
be linked predominantly to any of these factors . The
residua l is likely to res ult from both these and a
combination of other factors . It is harder to explain,
however, why it run s largely in one direction . An
allocation of the residual against particular countries or zones also cannot be based on very rigorous
analysis.
The discrepancy in services
and private international transfers
From Table 3, it is also quite clear that the world
current account deficit can be traced to the deficit
in the invisibles category, which more than offsets
the usual surplus on the global trade account. This
invisib les deficit has grown significantly in recent
years .
Among the components of this category, shipment and investment income are by far the most important recent sources of the negative discrepancy.
Other service components - travel and transportation, for example-show little substantial asymmetry, tending just to fluctuate between a positive
and a negative balance.
The shipment component for IMF member countries has been a source of a large negative
discrepancy for some time . As mentioned in the
discussion of trade asymmetry, this category is
l inked to merchandise trade by its inclusion of items
such as freight and insurance. When imports are
recorded on a c.i.f. basis, however, a more reliable
source for shipment payments usually is available in
the customs records . Exports on an f.o.b. or f.a .s.
basis do not include shipment costs . Typically,
therefore, receipts from these services are
6
understated relative to payments .
In addition, world shipment payments are likely
to exceed world shipment receipts because of the
existence of ships flying "flags of convenience."
Payment for the services of these fleets likely will
be recorded accurately in a country's balance of
payments, but receipts for such services will not.
The flag state considers the shipping line to be an
extraterritorial entity not part of its own economy,
and credits also often go unrecorded in the
shipowners' country of residence . While this source
of current account discrepancy is large, it has
tended to be more or less stable over time .
The negative discrepancy on investment income,
which is less sta ble, has grown during the 1980s. The
existence of a negative global balance here probably is traceable to the fact that payers of interest
and dividend s are larger and more identifiable than
are the recipients . Those on the receiving end often
are paid through interm ediaries and may not be
reporting income in order to avoid tax or exchange
control. I n this case, some geographic identification
is plausible. A downward bias on credits is likely in
countries whose residents are net receivers of investment income-mainly industrial and oil-ex porting
countries. The growth in this category' s asymmetry
may be attributed simply to the growth in value of
transactions in the category itself.
Another source of services asymmetry that has
grown in recent years can be traced to relationships
between oil exporters and the industrial countries.
Foreign industrial-country consultants who provide a
variety of se rvices to oil-exporting countries also
have incentives to underreport. I n addition,
payments are often made to multinational entities
whose nationality is difficult to determine.
Country distribution of the global asymmetry
If it were possible to identify the global current account discrepancy relative to specific countries,
some progress could be made in more accurate accounting, economic analysis, and policy decision
making. While identification of individual countries
as the source is difficult, it is possible to generalize
to a certain extent about groups of countries . The
deficit discrepancy is likely to come more from the
industrial or oil-ex porting countries than from the
non-oil group of countries .
Part of this generalization is founded in reasoning
along the lines of the investment income discussion
Federal Reserve Bank of Dallas
Ch a rt 2
Global Trade and Current Account Imbalance 1
BILLIONS OF U.S. DOLLARS
40r-----------------------------------~
20
------- _ - - - - - - - .... ...........TRADE
,
.....
"",'"
---_ ..
o ~--------------------------'~~----------~
-20
-40
-60
-80
-100
__
__ ____ __ ____ __ ____
1977 1978 1979 1980 1981 1982 1983 1984
~~
~~
~
~
~
~
~
~_J
1. See Table 3.
SOURCE OF PRIMARY DATA: Intern ational Monetary Fund.
above. If we can identify the kinds of transactions
most likely to give rise to a discrepancy, then we
can identify the countries that more frequently conduct those kinds of transactions . Because residents
of industrial and oil-exporting countries are more
often on the receiving end of investment income
transactions, logically they would probably contribute more to the global deficit on the services
component of the current account.
It may be less likely that recorded current account deficits of the non-oil developing countries
are overstated . Most of those countries historically
have had fewer net recipients of investment income.
Moreover, they have generally run large current account deficits for some time . By accounting definition, these deficits have resulted in the growth of
foreign debts so evident in recent years . Some
analysis even indicates that the debt of these countries exceeds substantially their accumulated current account deficits. Thus, their deficits would
need to have been all the higher to account for
present debt levels. I n Mexico, over the 1978-82
period, for example, the increase in gross debt was
$58.4 billion, while the cumulated current account
deficit was only $36.4 billion. s
All this should not be taken to mean that
residents of the non-oil developing countries do not
Economic Review I January 1986
also have incentives to underreport investment income. And given the amount of capital flight from
these countries, especially recently, one cannot ignore the investment income that may be accruing to
residents of thes e countries also.
Another reason for assigning the discrepancy
more to the industrial countries, however, is simply
that this group conducts more transactions than the
developing countries do. It can be assumed that the
discrepancy is at least partially related to the
volume of transactions . In 1984, those countries
classified by the IMF as industrial economies accounted for over 70 percent of member-country
exports.
Less can be said about the quality of balance of
payments reporting across countries. It might be
assumed that because industrial countries can
devote more resources to the collection of balance
of payments statistics, their accounts are more accurate . On the other hand, this advantage could be
offset by the trade volume considerations above,
and the errors and omissions accounts of industrial
countries are frequently enormous.
As a case in point, the U.S. errors and omissions
account shows quite large net inflows in recent
years . In 1982, a record year, inflows on the U.S.
errors and omissions account were over four times
7
the recorded U.S. current account deficit. It is still
conventionally believed that the errors and omissions item derives mainly from capital flows rather
than current account transactions . The role of the
U.S. dollar as a haven currency in the recent past no
doubt has fostered an image of the U.S. as a home
for flight capital. But the sheer size of the U.S . errors and omissions account is testimony to the
fallibility of balance of payments accounting in the
world's largest industrial country.
The outlook for the discrepancy
It is not likely that improved methods for balance
of payments accounting can eliminate the
worldwide discrepancy. Concern can be evinced at
the global level, but when the deficit cannot be
assigned accurately to specific countries, little can
be done to correct it. The individual country level,
moreover, is the only place any correction can be
made . Even if discrepancy could be allocated accurately among countries, it is not clear that greater
resources devoted to the problem would solve it.
This problem is illustrated by the probable role of
the industrial countries, whose share may be greater
than developing countries even though their
methodological and 's tatistical procedures are more
sophisticated.
Moreover, regardless of the country and its
statistical sophistication, the collection of balance
of payments statistics faces at least one obstacle
not present in collecting data on domestic transactions . I n any international transaction, one party is
foreign, and less information is available. Adding to
the problems are different classifications of transactions across countries, as well as a host of other factors that make international commerce more complex than purely domestic economic activity .
Some components of the discrepancy seem to expand with international commerce in general. The
total current account deficit has declined somewhat
since 1982 but has trended upward throughout the
1970s. It might be assumed, therefore-barring any
drastic improvement in data collection-that we
must simply resign ourselves to a growing current
account deficit asymmetry as other world economic
magnitudes increase secularly over time.
This growth in the global deficit might not
necessarily come to pass, however. As demonstrated
in Chart 2, much of the fluctuation in the overall
current account deficit derives from the positive
8
trade asymmetry. To the extent that the trade asymmetry imparts volatility to the overall series-much
as the merchandise trade account often imparts
most of the volatility to a single nation's current account balance-the effect of growth in world trade
will be to make the deficit smaller. As indicated in
Chart 1, the trade asymmetry does tend to follow
changes in world trade, but the relationship is
positive. Cyclical effects may still be in evidence,
but a secular increase in world trade over time
could be at least one influence that might
counteract any increase in the services deficit.
Conclusion
The foregoing precludes any single cause for the
global current account asymmetry and leaves little
hope that it can be eliminated . Relatively little
formal analysis has been devoted to analyzing the
conundrum, but it is more than just a statistical
curiosity. If current account balances are off by
substantial amounts, entire policies and attitudes
toward international adjustment may be affected.
Although the problem likely will not disappear, it is
by no means clear, on the other hand, that the
world deficit will increase to significantly higher
than present proportions . With greater stability in
world economic activity-and especially with lower
interest rates and oil prices-the global deficit may
even decline substantially. Forces within the global
deficit also could pull in opposite directions,
especially because the different components that
contribute to the overall balance are related to different factors .
1. Frequent revisions to this IMF data contribute to problems in
analyzing the discrepancy. The data in Table 1 appeared in the
International Monetary Fund's World Economic Outlook, April
1985 (Washington, D.C., 1985), Table 29, p. 236.
2. Also included in the errors and omissions account of Table 2 is
an estimate of Soviet hard-currency aid to, and trade with,
other members of the Council for Economic Mutual Assistance
(CEMA), which includes Poland, Bulgaria, East Germany,
Czechoslovakia, Romania, and Hungary.
3. In trade terminology, here and later, c.Lt. indicates that "cost,
insurance, and freight" are included; f .o.b. means "free on
Federal Reserve Bank of Dallas
board"; and f .a. s. is "free alon gsi de ship." The value of imports frequently is quoted on a c.i.f. basis, but it may be on a
customs basi s. Both exports and imports- more frequently the
fo rm er - ca n be quoted on an f .a.s. basis.
4. One estimate indicates that the length of t he transport lag in
recorded world trade averages 0.6 of a month. With res pe ct to
trade f lows, it has been estimated that about 3 percent of exports are not received and coun ted as imports until t he fo ll owing ca lend ar year . See William L. Hemphill, Resea rch Depart-
Economic Review I January 1986
ment, Intern at ional Monetary Fu nd, "Estimation of the Tim in g
Asymmetry in Inte rn ational Trade," Staff Papers 27 (Ma rch
1980): 135-60.
5. Given a net direct and portfo lio investment inf low of $10.2
billion and a combi ned decrease in in ternational reserves plu s
extern al assets of comm ercia l ba nk s of only $0.3 billion, this
yie lds an implicit capita l outflow of $32.5 billion over t he
period .
9
Velocities of M1 and the
Monetary Base: A Correction of
Standard Formu las
Dale K. Osborne
Professor of Finance
The University of Texas at Dallas
Consultant
Federal Reserve Bank of Dallas
Kenneth Mason, while exp loring deep in the
Pamirs, ran out of money and was lent some by a
yak owner: " I w rote out o n half a sheet of notepaper to Cox' s, Karachi : ' Pl ease pay bearer on
receipt of this the sum of fifty pound ste rlin g.' It
must've been eight or nin e months later that I
heard from my bankers, Cox' s at Karachi, that a
greasy pi ece of paper had arriv ed and had been
presented in the Peshawar bazaar and was sa id to
be worth fifty pounds ste rling. That piece of paper
had gone from hand to hand allover Central Asia .
It had marks of people that couldn' t sign. It had
thumb marks w hi ch had been dipped in ink. It had
been to Samarkand an d Kiva and God knows
where, and it' d come over the Khyber Pass and
was presented in Pes hawar bazaa r and was still
said to be worth fifty pounds ste rling. "
- From "Topees Overboard, " in
Plain Tales of the Raj,
edited by Charles Allen
The purpose of this article is to explain velociti es of
circulation and equations of exchange clearly and
correctly. It is intended to help students who are
confused by the explanations in their textbooks and
empirical researchers who wish to compute velocity
correctly. The basic problem is this : the thing called
velocity in nearly all explicit definitions is not the
10
thing called velocity in further textbook discussion s,
in empirical research, or in official statistics. Alternatively, if the thing called veloc ity in official
statistics and empirical research is intended to be
the thing defined by the usual explicit definition, it
is never computed correctly.1
The article proceeds as follows. Section 1 explains
the fundamental concepts of the subject in a very
simple example. The example is intended mainly for
students, bu t it also serves as a base for fu rther
development. Section 2 explains the confusion
stated above and shows what choices we have in
clearing it up. Section 3 briefly discusses the importance of velocity in economic analysis and policy.
Section 4 presents an accounting framework useful
for deriving equations of exchange. Section 5
presents equations of exchange in M1 and formulas
for computing the velocities of M1 . Section 6 does
the sa me for the monetary base. Section 7 gives formulas relating the velocities of M1 and those of the
monetary base.
1. A very simple example
Consider a mythi ca l ec onomy with no credit, no
securities, no middlemen, and no means of payment
Federal Reserve Bank of Dallas
except gold coins . Coins change hands for goods
and services (" goods" hereafter) in every transaction . All transactions are " final" in the sense of being made by final consumers, so all transactions
count in GNP. Finally, nobody eats the beans he
grows but sells them to others and eats beans grown
by someone else, so there is no imputed income and
all of GNP is generated by monetary transactions.
There is only one kind of velocity in this mythical
economy, and its relation to certain other macroeconomic magnitudes may be shown in the
economy' s equation of exchange. Like all correct
equations of exchange, the equation for this
economy represents a double classification of all
transactions that occur during a certain arbitrary
period of time-the "period of analysis." One
classification groups transactions according to what
is paid, and the other groups them according to
what is paid for .
Let there be k coins, all existing throughout the
period, and let mi (j
1, .. .,k) be the value (e.g., $1)
of the jth one. The total value of all k coins, m 1 +
... + mk' defines the money stock, M.
=
M : = m1
(1 )
+ ... +
mk·
2
Let coin j change hands - that is, be paid - Vi
times during the period (Vi = 0 if coin j never
changes hands during the period). Changes of hands
in "making change," such as the surrender of a $1
coin for ten dimes, are called conversions, not
payments, and do not count in vi" By definition, Vi is
the velocity, or rate of turnover, of coin j during the
period . The velocity of money, V, is the weighted
average velocity of all coins, weights being the
values of the coins :
(2)
V: =
+ ... +
m1 + ... +
m 1 v1
mkvk
mk
=
Classified according to what is paid, total
payments
m 1 v1 + ... + mk vk
MV, or the stock
of money times its velocity . MV is the left-hand side
of the equation of exchange for this economy.
To get the right-hand side, we classify all the
transactions according to what is paid for . Let there
be n goods and let q j (i = 1,... ,n) be the total
amount of good i sold during the period (qj
0 if
good i is never sold during the period). Let Pj be the
average price at which good i is sold . Total
payments for good i are Pjqj, and total payments for
=
=
=
Economic Review
I January 1986
all goods are P1 q 1 + ... + Pnqn ' This sum is the
scalar product of the vectors p and q, where p =
(P1 , ... ,Pn) and q = (q1, ··· ,qn); I shall denote the sum
by G. Thus total payments, classified according to
what is paid for, are
(3)
Most economists write P1q1 + ... + pnqn as PQ
(or sometimes PT), where P is a price index intended
to represent the average price of all goods and Q
(or T) is a quantity index supposed to represent the
average quantity of goods sold . But neither index
can be defined satisfactorily except under uselessly
rare conditions, and I will not perpetuate their
formal use. 3
Clearly, MV equals G identically, no matter what
values mi' Vi' Pj, or qj take during the period. This
fact is expressed by the equation of exchange for
this economy,
(4)
MV = G.
Note carefully how velocity is defined in equation
2, as the weighted average of velocities which are
themselves defined as "number of times paid ."
Velocity is not defined by equation 4 or as the ratio
of C to M . Yet the equation
(5)
V
= CIM
always holds because equation 4 always holds .
Although equation 5 does not define velocity, it is
very useful in computing it. The individual velocities
Vi are not easily recorded, even in this simple economy, and the computation of V directly from its
definition would not be feasible . Total sales and the
money stock are somewhat more easily recorded.
In practice, therefore, V would be computed by
dividing Minto C . This does not mean that velocity
is a residual, determined by p, q, and M but not influencing these variables in any way . Velocity is
computed residually but not defined residually .
If velocity were defined residually, equation 4
would contain only three independently defined
variables and would therefore be a useless identity.
Take any three variables x, y, and z; define a fourth
variable w as the ratio yzlx; then the equation wx
yz holds identically but imparts no information not
already contained in the definition of w : it is a
useless identity. The equation of exchange is an
identity, but a very usefu lone, for it expresses a
relation between four independently defined
=
11
variables and imparts information not contained in
any of the four definitions; it follows from the conjunction of the four definitions, not from any proper
subset of them .'
Velocity is not a behavioral residual, either, taking whatever value is necessary to satisfy the equation of exchange when M, p, and q vary in whatever
manner we might imagine. Velocity is the inverse of
the average " resting period" of money; if velocity is
12 during some year, for instance, each dollar's
worth of coins is " at rest" for a month on the
average. The resting period of money depends on
the stock of money, the demand of traders to hold
money, and institutional arrangements in the
payments system-just as in the real world. s
If this mythical economy had intermediate-goods
transactions, so that not all transactions counted in
GNP, it would have two kinds of velocity- income
velocity and transaction velocity. Both velocities
would be defined as weighted-average rates of
money turnover, but only final-goods transactions
would count in the former while all transactions
would count in the latter. Let us now open this
possibil ity but, for the time being, continue to interpret C as nominal GNP and Vas income velocity .
2. Current practice
When we return to the real world, we find velocity,
either income or transaction velocity, used in two
distinct senses, often by the same writer and
sometimes on the same page . Income velocity' is
nearly always defined explicitly in terms of turnover, just as above. But fast on the heels of the
definition there usually follows a discussion of
equation 4, with the right-hand side interpreted as
nominal GNP (and, of course, with the definition of
M appropriately modified for modern conditions).
Since the writer has not expl icitly introduced a new
definition of velocity, we naturally infer that the V
of equation 4 is the one he defined earlier on his
page. But if this inference is correct, equation 4 cannot be true of any economy that, like ours, has
much consumer credit or imputed income. Nominal
GNP exceeds total spending on final goods by that
part of national income sold on credit plus the part
not sold at all but consumed directly by its producers. Therefore, if the explicit definitions of the
variables are to be taken seriously, equation 4 is
just a mistake.
12
But equation 4 is widely regarded as an identity
in the real world (just as it is correctly regarded in
the mythical economy) and an elementary one at
that. Since the possibility that economists cannot
get their elementary identities right is too gruesome
to contemplate, the V in equation 4 must not represent velocity in the sense of turnover. If equation 4
really is an identity in the real world, V cannot be
understood in the sense of turnover but only in the
sense implied by equation 4 and expressed more
directly as
(6)
V : = CIM,
that is, as a residual variable that takes on whatever
value is required for the truth of equation 4. Velocity is just along for the ride .
In its sense as a residual, velocity has no explicit
definition but is defined implicitly by the way it is
discussed . Writers who discuss the velocity of M2 or
of some larger credit aggregate such as total debt
are obviously not using the word in the sense of
turnover-even if they verbally defined it that way
a few sentences earlier-because these aggregates
contain financial instruments that cannot be spent.
Only things that can be spent-media of exchange
or means of payment- have velocity in the sense of
turnover. But anything can have a velocity in the
sense of a residual. Evidently, the behavior of such
a velocity can never be explained .
We can end this confusion in one of two ways .
Either we stop explicitly defining velocity in the
sense of turnover and start calling it the GNPmultiple, as equation 6 defines it, or we start using
it in the same sense of turnover in which we explicitly define it. The first choice would make current practice respectable; the second requires a
change in that practice. All in favor of the first
choice may stop reading.
Complaints about velocity-as-residual go back at
least to Knut Wicksel1. 6 Such complaints seem even
more pertinent today because of recent developments in monetary theory that pay attention to payment arrangements (see Kohn, for example). These
developments require the use of velocity in its
original sense of turnover and need equations of exchange that are correct when velocity is used in this
sense. Unfortunately, the derivation of such equations is much more complicated in our world than it
was in the mythical economy described in section 2.
Before embarking on this project, let us see why
Federal Reserve Bank of Dallas
1
I
velocity gets so much attention.
3. Some questions concerning velocity
and equations of exchange
Equations of exchange, such as equation 4, are
usually associated with the Quantity Theory of
Money (in fact, they are often called " quantity
equations"). There is no good rea son for this
association, for every correct equation of exchange
is an identity; as such, it is independent of all
theories and must fit into any useful theory, not just
the Quantity Theory. Neither the Quantity Theory
nor any other monetary theory has special claims on
equations of exchange, and no us ef ul theory can
contradict them . Moreover, the Quantity Theory is
not confined to an equation of exchange but consists of substantive propositions about the behavior
of M, V, p, and q . According to the simplest version,
both V and q depend on forces that are independent
of M, so that only p varies when M does: prices vary
directly with the quantity of money. More sophisticated versions do not imply this proportionality,
especially in the short run . But all versions regard
money and prices as far more changeable than real
transactions .
Today all carefurly specified monetary theories
accept that velocity depends on institutional arrangements and payment practices that evolve slowly but are subject to the influence of inflation (even
though the calculations make sense only when it is
a residual). Only the most naive versions of Keynesian theory regard velocity as a behavioral residual
that tends to vary inversely with the money stock,
leaving real macroeconomic magnitudes unchanged .
Such a theory cannot explain the data, which show
that large changes in money tend to cause fairly
large changes in velocity in the same direction. 7
Velocity, then, is by no means the exclusive concern of Quantity Theorists, and it figures prominently in current issues of monetary theory and policy.
The stability of velocity is an especially lively issue,
for it relates to the stability of money demand and
(according to some writers) to the choice among
monetary policies.
Stability- referring either to the magnitude of
velocity or, more often, to its rate of change-bears
a one-to-one relation to the resting period of money:
both velocity and the resting period are stable or
unstable together. The resting period depends on
the demand for money, among other things. If this
Economic Review
I January 1986
demand is unstable, velocity ought to be too, so
one way to evaluate the stability of money demand
is to study the stability of velocity. As money demand is widely thought to have been unstable during much of the past decade, it accounts for some
of the recent interest in velocity.8
Two things, however, should be noticed about the
relation between the stabil ities of money demand
and velocity. First, the relation is not one-to-o ne.
Although velocity and the re st ing period are related
one-to-one, the resting period and money demand
are not. The resting period also depend s on mon ey
supply. If supply is unstable, velocity can be
unstable even if demand is stable. It is the stability
of excess demand for money (demand minus supply)
that bears most directly on the stability of velocity.
If supply has been as unstabl e as some scholars
maintain,9 it might well have destabilized velocity .
Second, the velocity that reflects the resting
period is transaction velocity-the rate of money
turnover in transactions of all kinds, not just the
transactions counted in GNP. Desired holdings of
money depend on planned purchases of used cars
as well as new ones, of barber shops as well as haircuts, of securities as well as apples. An unstable excess demand for money would cause an unstable
transaction velocity but would bear no necessary
relation to income velocity . This fact is overlooked
in much of the recent literature, which tends to
dwell on income velocity .
The role of velocity in monetary policy is very
complex but can be indicated in a rough sort of way
by equation 7,
(7)
IlM
M
IlV
IlG
=-,
V
G
+-
which follows from equation 4. Equation 7 does not
apply to our economy, but it does serve to highlight
some controversies by expressing the relation between the percentage changes, or growth rates, implied by equation 4. The right-hand side represents
the growth rate of GNP,lO which, according to the
equation, always equals the sum of the growth rates
of money and velocity. (The appropriate version of
equation 7 for our economy would account for
credit sales, imputed income, and intermediate
transactions .)
If velocity is unstable, so that IlV/V fluctuates appreciably from period to period, steady growth in
13
Table 1
LIST OF TRANSACTIONS
Transac tions
Involving the publi c
The public
1.
2.
3.
4.
S.
6.
7.
8.
9.
10.
11 .
12.
13.
Between bank s
Banks
Buys goods for cash .
Buys new bank securities for cash .
Repays debt to banks in cash.
Deposits cash in banks .
Buys goods for deposits.
Lends deposits to the public .
Repays debt with deposits .
Buys securities in secondary mark ets from
the public with deposits.
Buys securities in secondary markets from
banks with deposits.
Buys new securities from banks with deposits.
Repays debt to banks with deposits.
Buys goods on credit.
Withdraws cash from deposits.
19. Buy securities from other banks in secondary
markets.
20. Lend reserve balances to other banks .
21 . Repay loans of reserve balances to other banks
22 . Transfer reserve balances to other banks in
clearing checks .
Banks
14.
1 S.
16.
17.
18.
Retire securities with ca sh.
Issue deposits for goods.
Iss ue deposits as loans to the public .
Issue deposits to retire their securities .
Issue deposits to buy securities from the
public in secondary markets.
GLOSSARY OF TERMS
Banks. All issuers of deposits.
Bank securities. All liabilities, other than deposits,
of banks to the public .
Cash. Federal Reserve notes and U.S. coins
outstanding.
Cash reserve. Cash held by banks .
Currency. Cash held by the public.
Currency issued. Cash paid to the public by banks.
Currency retired. Cash paid to or deposited in bank~
by the public .
14
Deposits. Demand liabilities used as media of
exchange.
Nonbank securities. Liabilities of the public to other
members of the public or to
banks, whether represented by
the issuance of paper securities
or entries in account books.
Reserves. Cash reserves plus banks' reserve balances
with the Federal Reserve.
Reserves issued. Currency retired.
Reserves retired. Currency issued .
Federal Reserve Bank of Dallas
r-------------
I
I
(5)
..
CURRENCY
TRANSFERRED
(-12-)
":""
I ...,.l-__-_...
_____
~~~___________ - - - - -
NONBANK SECURITIES
. . .:I~-DE-P-O-S-IT-S. . .:._IS,S:. -:-:-:-:'-:-::-RE-T-IR-E-D-(C-:~:'
.....' • • •
TRANSFERRED (DT)
':'.1
RESERVES ISSUED (RI)
(7)iI
(1 7)
BANK SECURITIES
ISSUED (BSI)
NONBANK SECURITIES
RETIRED (NBSR)
i
I
I
I
------..1I
(10)
BANK ·SECURITIES
RETIRED (BSR)
(8)
I
I
I
(13)
i
~
I
I
(9)
I
I
(14)
CURRENCY ISSuED (CI),
RESERVES RETIRED (RR)
I
I
I
I
I
~----------------
I
I
I
I
(18)
SECuRITIES TRANSFERRED (ST)
1_ _ _ _ _ _'1
I
I
--------.1
(19)
RESERVES TRANSFERRED (RT)
1------..11
1 (22)
1..-_ _ _ _--'
DEPOSIT·PAYMENT
RESERVE TRANSFERS
(DPRn
GNP requires compensating changes in the money
stock . The appropriate growth rate for money might
be 10 percent one quarter, 0 percent the next, and
- 5 percent the next, all depending on the fluctuations of velocity . One way to conclude that velocity
is unstable is to regard it as a residual and to
believe that private income-producing transactions
are unstable; a steady value of M would then cause
fluctuating values of V. Another way is to believe
that the resting period of money is unstable because
the demand for money is unstable. Either way leads
to calls for active management of the money stock
and probably for other kinds of government action
Economic Review I January 1986
as well . Unstable velocity thus seems to call for
"fine tuning."
If velocity is stable, however, fine tuning might
destabilize the economy. According to some
scholars, the appropriate policy is steady growth
(perhaps negative) of the money stock. If income
can sustain 2-percent growth and velocity grows
steadily at 3 percent, just keep money shrinking
steadily at 1 percent."
A controversial issue that cuts across the differences between the Fine Tuning and Steady
Money camps is the identification of money. If you
identify money as M1, you are not I ikely to be im15
pressed by figures purporting to show an unstable
velocity of M2-even disregarding the fact that the
only part of M2 possessing a velocity is M1 . This
controversy has called forth a third Gampsometimes called the Seekers After the Right
Aggregate-who say, almost in so many words,1 2
" Let us end this sterile controversy over the meaning of money. Let' s find the financial aggregate that
has the stabl est velocity. Then we' ll call it money
and urge the central bank to make it grow at the appropriate rate." The Seekers use " velocity" in the
sense of a residual, so that the velocity of some aggregate is just its GNP-multiple. They show no concern that the aggregate with the stabl est multiple
might consist mainly of financial instruments well
beyond the central bank's present powers.
This brief discussion has only scratched the surface of a large and complex subject, but it is
enough to show that velocity figures in large issues.
4. A framework for transaction accounting
The best way to explain velocity and equations of
exchange in intuitively satisfying detail is to see how
they depend on the many kinds of transactions that
occur in a modern economy. We need not aim at utter realism, tracking down every transaction no matter how rare or obscure, but we ought to take account of the major types . These are listed in Table 1,
diagrammed in the chart , and explained as follows.
4.1. Assumptions and conventions
1 . Gifts, taxes, theft, and transactions with the
central bank are disregarded .
2. The sum of currency and reserves-that is, the
monetary base- is constant during the period of
analysis. (This sum also equals the sum of reserve
balances and cash .) Currency, reserve balances,
reserves, and deposits may vary .
3. Banks issue securities only to the public . All interbank borrowing occurs in transaction 20. The
public issues securities to itself (as when one
member of the public borrows from another
member) and to banks . All borrowing, except between banks, falls under security issuance; it is
"gross," because gross flows are the relevant
variables in velocity analysis.
4. All repayment of debt, except between banks
(which occurs in transaction 21), falls under security
retirements . The retired securities were issued
before or during the period of analysis.
16
5. All secondary transactions in securities fall
under Securities Transferred (transactions 8, 9, 18,
and 19). The transferred securities were issued
before their transfer, possibly during the period of
analysis.
6. All security transactions-that is, BSI, BSR,
NBSI, NBSR , and ST -are by check or wire (just
" check" hereafter) except transactions 2, 3, and 14.
7. Deposits outstanding are invariant to Deposits
Transferred (just their ownership changes), but they
rise with Deposits Issued and fall with Deposits
Retired . The sum of deposits and currency-that is,
M1-may vary.
8. Reserves Transferred represents transfers of
reserve balances between banks . These transfers
occur in four kinds of transactions: (1) Banks buy
securities from each other in secondary markets, as
in transaction 19 (which does not include banks'
purchase of their own securities, because such transactions fa II under BSR). (2) Banks lend reserve
balances (Federal Funds Lent) to other banks (transaction 20). (3) Banks repay such loans (Federal Funds
Repaid , tran saction 21). (4) Banks cover their
adverse clearings . A bank has adverse clearings
when, during the clearing period (a fraction of the
period of analysis, a business day in most places),
the total value of checks written on it exceeds its
receipts of checks written on other banks . (I include
wire transfers under the heading of " checks.")
Adverse clearings cause a bank to lose reserves
through Deposit-Payment Reserve Transfers in
transaction 22 .
Every solid line in the chart represents transactions involving reserve transfers; every dashed line
represents transactions that might induce simultaneous or subsequent reserve transfers . I n transaction 15, for example, a bank issues deposits in
payment for goods. If the seller of goods is also a
depositor at the bank, the transaction remains
within the bank and has no effect on the bank's
reserve position (if the seller subsequently
withdraws the payment in cash, it is then counted in
transaction 13); if the seller holds his deposits at
another bank, the transaction potentially induces a
reserve transfer. For another example, consider
transaction 10, where bank A sells its security to
someone who pays by check . If the check is on
bank A , no reserve transfer occurs- just a change in
the composition of the bank's liabilities; but if the
check is on bank B, reserves will move from B to A
Federal Reserve Bank of Dallas
unless the check is offset in clearing. I n either case,
deposits are "retired."
9. Only one type of barter occurs-transaction 12,
the exchange of goods for securities. (A barter transaction is one that is not executed strictly by a
medium of exchange. l l ) Other types of barter occur
in practice, as when you trade your 1941 Harley 74
for a 1959 Chevrolet Apache. This type of barter
really ought to be accounted for in calculating
transaction velocity (and income velocity in some
cases, as when I paint your house in exchange for
financial advice). The virtual disregard of barter
leads to a possibly serious exaggeration of calculated velocities. The formal remedy is explained
below.
10. Credit card and travelers'-check transactions
deserve special comment. Transactions involving
cred it cards issued by the merchant for use in the
merchant's store are straightforward examples of
transaction 12 . Transactions involving third-party
cards are more complex and seem capable of two
treatments . On the one hand, the transaction slip
with your signature on it is rather like a check
drawn on a bank, ordering the issuer of your credit
card to pay the merchant the amount stated on the
slip. The merchant will deposit the slip in his credit
card account at his bank. He can write ordinary
checks on this account once the funds are collected
by the bank via the credit card clearing system, the
only difference being that he gets only about 97
percent of the amount thus deposited .14 You then
owe the bank the amount of the purchase, just as if
you had written an overdraft on your deposit account. Therefore, we could treat a $100 transaction
of this sort as if the bank had lent you $100 by increasing your deposit account and you then wrote a
$100 check on this account to the merchant. Under
this treatment, transactions 16 and 5 increase by
$100 each, but transaction 12 does not enter the
picture-that is, there is no "sale on credit." Sales
on credit occur only when the merchant grants the
credit; according to this treatment, it is not the merchant but the bank that grants the credit.
On the other hand, th.e signed transaction slip
could be regarded as your IOU to the merchant,
who then sells the IOU to the bank that maintains
his credit card account. The bank buys this transferred security by issuing deposits to the merchant,
just as if it bought a two-name bill of exchange
(your name and the merchant's). Thus interpreted,
Economic Review I January 1986
the transaction would be treated as a $100 sale on
credit and a $100 security transfer against deposits
issued, so transactions 12 and 18 would increase by
$100 each . This treatment is appropriate if the merchant remains liable to the bank in case you refuse
to pay your bill.
The merchant definitely is not liable if he phones
the issuer for an authorization before accepting
your card (for the authorization commits the issuer
to acceptance). He definitely is liable if the purchase exceeds $50 and he fails to obtain authorization . And, of course, he is liable if the card is listed
as "bad" on the weekly memo sent out by the
issuer.
I n the first case, the issuer' s authorization means
that he, not the merchant, grants credit. In the second case, the merchant's failure to obtain authorization means that he, not the issuer, grants the credit.
In the third case (fraudulent use), no one grants
credit but the merchant is defrauded .
Strictly speaking, then, some third-party credit
card sales should be entered under transactions 5
and 16, and some should be entered under transactions 12 and 18. It is clear in principle which ones
should go where, but in practice it is impossible to
tell. The lack of requisite data forces us to treat
them all the same way. All things considered, the
first treatment seems best, but the reader will have
to make the decision for himself.
11 . Travelers' checks are easier. They should be
treated as cashier' s checks (even when issued by
nonbank firms), to which they are economically
identical. Both instruments commit the issuer to pay
cash upon presentment and both disappear afterwards. Thus a purchase of goods for travelers'
checks goes under transaction 5. A purchase of
travelers' checks for cash goes under transaction 4.
A purchase for deposits is not treated as a transaction but as a conversion .
4.2. Classification of transactions
according to what is paid for
The goods transactions are 1, 5, 12, and 15 . Transactions 1, 5, and 15 are payments of M1, but only the
first of these is a payment of the monetary base.
Transaction 12 is not a payment of anything; it is included so that the total goods transactions will
equal total sales of goods.
The set of financial transactions depends on how
we identify money. On the M1 identification, the
17
financial transactions are 2 and 10 (BSJ); 14 and 17
(BSR); 6, 12, and 16 (NBSI); 3, 7, and 11 (NBSR); and
8,9,18, and 19 (ST). (Th e last one could be left off
this li st, because it is a transaction between banks
and does not involve M1. I includ e it so that ST will
includ e all secondary sec urity transactions .) Transa ct ions 4 and 13 are not financial on the M1 identification of money beca use they merely convert
on e form of M1 into another; transactions 20, 21,
and 22 are not financial beca use they ju st redistribute rese rve balan ces among banks and do not
fall und er a subhea ding (such as ST) that is
recog ni zed as financial from the M1 point of vi ew .
Every transaction m entioned in the prec eding
paragraph is financial from the standpoint of the
monetary base. Transactions 4 and 13 do not ju st
convert one form of mon ey into another but involve
the is suance or retirem ent of bank debt. Transactions 20, 21, and 22 represe nt major uses of the
monetary base in creating and settling debts; that
these debts lie wholly within the banking system is
neither here nor there . ' 5
Notice that this class ification is not a partition.
Transaction 12 is both a goods and a financial transaction; 4, 13, 20, 21, and 22 are neither goods nor
financial transactions on the M1 identification. The
classification according to what is paid is not a partition , either.
4.3. Classification of transactions
according to what is paid
Payments of M1 occur in transactions 1 -3 , 5-11,
and 15-18. Transaction s 4 and 13 are not payments
but conversion s of M1 ; transaction 14 is a cash payment, but the cash is not counted in M1 beca use it
is in banks. The M1 payments are divided into currency payments (tran sact ion s 1 -3) and deposit
payments (transactions 5-11 and 15-18).
Payments of the monetary base are payments of
c urrency' 6 (transactions 1-4) or rese rves (transactions 13, 14, and 19- 22). The total val ue of transaction 22 depend s on the flows of checks betwee n
banks caused by deposit payments . Thus deposit
payments figure implicitly in payments of the base.
5. Velocities of M1
We shall consider five velocities of M1 : transaction,
income, intermediate-goods, goods (the sum of the
preceding two), and financial velocities . Each velocity is a weighted average of the corresponding
18
velocities of currency and deposits, where the
weights are the average quantities of currency and
deposits, respectively, outstanding during the
period.
Let C1 denote average currency, 0 denote
average deposits, C1 P denote total payments of currency (from the M1 point of view), and DP denote
total payments of deposits. 17 The (transaction)
velocities of currency and deposits, Vc and Vd' are
defined by
1
Vc :
1
= C1 P/C1
Vd := DP/D .
The tran saction velocity of M1, V1 , is then defined
by
V1 : = (C1 Vc
1
(8)
+
DVd)/(C 1
+
D).
The other velocities of M1 are defined in a similar
manner (e.g., its goods velocity is defined as the
same weighted average of the goods veloc ities of
currency and deposits, where the latter velocities
are defined as ratios of total cash (or deposit)
payments for goods to C1 (or D). As it is obvious
how these definitions are expressed, I shall not write
them down .
The average quantity of M1 outstanding during
the period is denoted by M 1 ; it equals C1 + D. The
total value of all payments of M1 therefore equals
M1 V1 ·
As noted above, M1 payments occur in transactions 1-3,5- 11, and 15-18. They are shown in row s
3-6 of Table 2, where aj denotes the total value of
transaction i during the period.
Column 12 of the table shows a1 + a 2 + a 3 as
C1 P (row 3 of column 12); it shows the sums of rows
4, 5, and 6 as DT, DR, and OJ (these and oth er abbreviations are defined in the chart). Column 13
shows the sum of DT, DR, and OJ as DP, and the
sum of DP and C1 P as M1 V1 , which equals total
payments of M1 .
Columns 1-6 of the table show what M1 is paid
for. Row 8 of the table shows the sums of these columns . Row 9 shows aggregates of things paid for.
The aggregates relative to M1 are C and F1 , where
(9)
F1 :
= BSJ +
BSR
+
NBSJ
+
NBSR
+
ST,
representing total financial transactions from the
standpoint of M1 . Note that C represents total sales
Federal Reserve Bank of Dallas
".,
'"
...
'"
'"=
...
I:
:::I
.
.
-<
~
;;'
<
;J;l
II>
n'
o
3
:::I
o
I'l
G
G
(9) Aggregates
a'2
(8) Sums of columns
(7) New nonbank
securities
(6) New deposits
a,s
as
(4) Existing deposits
(5) Existi ng deposits,
retiring them
a,
--
Goods
(')
(3) Currency
(2) Cash reserves
(1) Reserve bala nces
Paid
~
TRANSACTIONS MATRIX
Table 2
(3)
Bank
-
BSI
a, o
a2
BSR
a 17
a'4
New bank secu rities
securities
retired
(2)
F,
NBS I
a 12
a'6
a6
nonbank
secu rities
(4)
New
NBSR
a"
a7
a3
F
ST
a'8
a9
a8
a' 9
(6)
(5)
Nonbank
secu rities Securities
retired
transfe rred
a4
a4
New
deposits
(7)
a '3
a 13
reti red
Deposits
(8)
a 20
a 20
-
a 2,
a 2,
repaid
fu nds
lent
fund s
(10)
Federal
(9)
Federal
rows
ment reserve
transfers
a 22
a 22
2a'2
01
DR
OT
C, P+a 4 =CP
CRP
RBP
(' 2)
Sums
of
(")
Deposit-pay·
OP
RP
I
l
C,P + OP=M,V,
RP + CP=MV
Agg regates
(13)
of goods, as in section 1, and is considerably larger
than GNP.' ·
Evidently, G + F1 exceeds M1 V1 by 2a 12 + a14 +
a19· If we take thi s discrepancy into account, we get
the Transaction Version of the equation of exchange
in M1 :
(10)
M1 V1 = G
+
F1 - 2a 12 - a14 - a19.
The goods velocity of M1, v1g, is the weighted
average of the goods velocities of currency and
deposits; it always obeys the relation
(11 )
The financial velocity of M1, V1 f, is the weighted
average of the financial velocities of currency and
deposits (definitions of which should be obvious),
and always obeys the relation
(12)
V1f = (F1 - a12 - a14 -
a19 )IM 1.
Goods and financial velocities sum to transaction velocity .' 9 These velocities are not defined by
equations 10- 12, but they satisfy those equations
identica IIy.
Goods velocity may be divided into income
velocity, V1 Y, and intermediate-goods velocity, V1 i.
For j = 1, 5, 12, 15, write
(13)
aj
=
a/ + a/.
where superscript y denotes "final " sales (sales
counted in national income) and superscript i
denotes intermediate sales. Sil)1ilariy, write
(14)
GY = a 1 Y + a sY + a12 Y + a1SY
Gi = a1i + a si + a12 i + a1
l
ror produces an artificial instability in velocity as
usually computed .
GNP does not appear in any of the preceding
equations. If we want to express income velocity in
terms of GNP, Y, we can use the identity
Y = GY
The income velocity, V1 Y, is defined as the
weighted average of the income velocities of currency and deposits (definitions obvious) and satisfies
identically the equation
(16)
Income velocity is almost universally computed as
GNP divided by M1, thus being wrong by the
amount of imputed income and credit sales relative
to M 1 . If imputed income or credit sales are less
stable than national-income sales generally, the er20
YN ,
where YN denotes nonmarket (or imputed) income,
and write
(17)
V1Y = (Y - a1/
-
YN )IM 1.
Therefore, to correct the published statistics on the
income velocity of M1, we must subtract the M1
multiples of income sales on credit and imputed income from the published figures.
We have one more M1 velocity, the intermediateThis is defined in an obvious way
goods velocity
and always obeys the equation
V/
(18)
The velocities V 1 , V1 Y, V1 i, and V/ are defined independently of each other and of the variables G,
GY, Gi, and F1; yet they always obey the relation
(19)
6. Velocities of the monetary base
The size of the monetary base, or its quantity, M, is
constant throughout the period but the quantities of
its components may vary. Let C denote the average
quantity of currency outstanding, CP denote total
payments in currency, R denote average reserves
outstanding, and RP denote the total payments of
these reserves . The (transaction) velocities of currency and reserves are Ve and V" respectively,
The Income Version of the equation of exchange in
M1 is
(15)
+
Ve : = CPIC
Vr:= RPIR.
The transaction velocity of the monetary base, V, is
defined by the weighted average
(20)
V : = (CVe
+
RV,)/(C
+
R).
All velocities of the base are defined as weighted
averages of the corresponding velocities of currency
and reserves .
As M = C + R, total payments of the base equal
MV. Column 13 of Table 2 shows MV as the sum of
rows 1-3 .
Since MV contains elements from every column
but one, the simplest way to derive an equation of
Federal Reserve Bank of Dallas
exchange in the monetary base is to use all the
transactions and then correct for double counting .
The sum of all transactions, in the sense of what is
paid for, is G + F + A 22 , where, as shown in row 9
of the table, F is the sum of the sums of columns
2-10 and represents total financial transactions from
the standpoint of the monetary base:
F : = F1
(21)
+ a4 +
a13
+
a20
+
a21 ·
(We keep a22 out of F for later convenience .) Proceeding as indicated, we get the Transaction Version
of the equation of exchange in the monetary base,
(22)
MV = G
+
F - OP - 2a12
+
a22 .
This equation holds identically for all possible
values of all transactions.
The transaction velocity of the base may be computed from the equation
(23)
V
= (G +
F - OP - 2a 12
+
a22)/M,
but a possibly more useful formula is shown in the
next section .
The transaction velocity of the base could be formally expressed as the sum of goods and financial
velocities, but the definitions of goods and financial
velocities would be artificial. It is true that by subtracting as and a1S (deposit payments for goods)
from G we could write the formal expression vg
(G - as - a12 - a1s )/M, which looks like a goods
velocity comparable to the velocity expressed in
equation 11 . But the numerator of this expression
does not really equal total base payments-for
goods, because it does not include the reserve
transfers (counted in a22 ) caused by checks written
for goods. Not only are these transfers not
distinguished from the rest of a22 in clearing, but
they cannot be distinguished in principle. Checks
offset each other in clearing according to the banks
they are written on and deposited in, not the things
they pay for. Neither the amounts offset nor the
amounts cleared by reserve transfers can be traced
to the goods or financial category . The above expression for vg thus has only a formal significance.
If the reserves transferred in clearing cannot be
segregated into goods and financial categories, they
surely cannot be classified by their effect on GNP.
This means that there is no such thing (except formally) as the income velocity of the monetary base.
There is indeed an I ncome Version of the equation in the monetary base, but it is stated in terms
=
Economic Review I January 1986
of "virtual velocity." Let us write deposit payments,
OP, as
(24)
OP = OPRT
+
OPCT,
where OPRT represents that part of deposit
payments equal to the reserves transferred in clearing (which equals a22 ) and OPCT (" Deposit Payments
Clearing Themselves" ) represents the rest of deposit
payments. We cannot associate any particular
deposit payment with either part, but we can compute both parts at least in principle. Each bank's
contribution to OPRT in any given clearing period
equals the excess (if any) of its on us checks over its
to us checks (checks written on the bank to another
depositor of the bank are both on us and to us). The
sum of these excesses, for all the banks where they
are positive, for all the clearing periods in the
period of analysis, equals OPRT (equals a22 ). The
sum of min {on us, to us} for all banks and clearing
periods equals OPCT. Now if the banks had not invented offset clearing, and if checks remaining
within banks had passed between banks but were
otherwise identical (e.g., if your landlord banked
elsewhere than at your bank), the banks could get
together each day and exchange reserves check by
check until they had cleared every check. They
would be a lot busier, but obviously they could accomplish the job with the same total quantity of
reserves that support the actual transfers made
under modern clearing arrangements. In other
words, clearing practices save potential reserve
transfers in the amount OPCT. Although this saving
economizes on time and trouble, it does not reduce
the net value of transfers . The same net transfers
would occur either with or without clearing
offsets.2 o Given the interbank distribution of checks,
reserves could be transferred back and forth in the
whole amount OP without causing any other
changes in financial or goods transactions (beyond
the additional time and trouble of the unnecessary
transfers). These are the considerations behind the
concept of virtual velocity .
Separating MV into its components, using equation 24, and recalling that OPRT
a22 , we can
write
=
(25) MV
+
OP
= CVe +
R(V,
+
OPCT/R)
+
a22.
Let us call V, + OPCT/R the virtual velocity of
reserves and denote it by W, (think of two V' s run
together).2 1 The virtual velocity is what the actual
21
velocity could be without affecting any other aspect
of economic activity (beyond those noted). Let us
call the weighted average of the velocity of currency and the virtual velocity of reserves the virtual
velocity of the monetary base, W:
(26)
W : = (CVe
+
RW,)/(C
+
R).
and all together,
(34)
MV
+
OP = MW
MW = C
+
+ a22 ,
F -
2a12"
Now the Income Version follows readily,
(29)
MWY =
cy -
a1 / ,
where WY is the virtual income velocity of the
monetary base, defined in terms of the actual
payments of the base in national-income purchases
and the payments that are saved by clearing practices. The virtual income velocity of the base
satisfies identically the equation:
(30)
WY = (CY - a1 /)/M.
The definitions of virtual intermediate-goods (Wi)
and financial (Wi) velocities ought to be obvious by
now. These velocities satisfy identically the
equations
(31)
and
(32)
The relation between all the velocities of the base
can be expressed simply once we introduce a name
and symbol for the part of virtual velocity that is
saved by clearing offsets. We can call this part the
"unrealized velocity," VU; from equations 24 and 27,
v=
+
Wi
+
Wi.
The relation between income velocities is simple.
From equations 16 and 30, MWY = M1 V1Y, that is,
WY = (M 1 /M)
and the equation of exchange can be expressed in
terms of W:
(28)
VU = WY
7. Relations between the velocities
Then equation 25 becomes
(27)
+
W = V
v1 Y.
The ratio M1/M is usually called the money
multiplier.22 I will denote it by m:
(35)
m : = M1 /M,
so that
WY = mV1 Y.
(36)
Similarly, from equations 18 and 31, it follows that
(37)
The relation between financial velocities is not so
simple. From equations 12, 21, and 32,
MW' = M1 V1 '
+
(a 4
+ a13 + a14 + a1 9 + a 20 + a 21 )·
The term in parentheses represents transactions
that are monetary from the standpoint of the base
but not from that of M1 . From the former standpoint, these transactions are payments of money to
create, transfer, or retire bank liabilities; from the
latter standpoint, they are either mere conversions
of one form of money to another (transactions 4
and 13) or uses of reserves unaccompanied by uses
of money (transactions 14, 19, 20, and 21). Indeed,
these transactions are the only ones, apart from
reserve transfers through clearing, that bear conflicting interpretations . Denoting their value by B, and
their M-multiple by b,
(38) b :
= (a 4 +
a13
+
a14
+
+
a1 9
a 20
+
a 21 )/M,
we can write the equation
+
W - (OP - a22 )/ M
(39)
W - OPCT/M
The relation between transaction velocities now
follows from equations 19, 34, 36, 37, and 39 :
= W - Vu,
Wi = mV1 '
(40)
W = mV1
where
+
b.
b.
Alternatively,
(33)
VU : = OPCT/M.
Then
W = V
22
+
Vu,
(41)
V
= mV1 +
b - VU
In this equation, the transaction velocity of the base
equals the multiplier times the transaction velocity
Federal Reserve Bank of Dallas
of M1 plus a correction factor; this factor is the
M-multiple of all transactions, other than clearings,
that are monetary from the standpoint of the base
but not of M1, minus the unrealized velocity of the
base, which is the M-multiple of all transactions that
move deposits but not reserves. Thus the correction
factor adds (the M -multiple of) purely base transactions and subtracts purely M1 transactions.
8. Summary
The velocity of money, in the sense of turnover, has
interested economists for many years . Yet conventional modern treatments make sense only if velocity is interpreted as a residual, even though it is still
conventionally defined in terms of turnover. This
paper, about velocity in the sense of turnover, has
presented an accounting framework for the derivation of equations of exchange and the computation
of transaction, goods, financial, and income
velocities of both M1 and the monetary base.
Although the framework accounts for most of the
transactions in our economy, it disregards transactions involving the central bank and the federal
government. The incorporation of such transactions
would be conceptually straightforward but computationally tedious .
In the context of current discussions of velocity,
the most important formulas are probably equations
17 and 36, which show how to compute the income
velocity of M1 and the virtual income velocity of
the monetary base in terms of GNP. Unfortunately,
the credit-sales data needed for these computations
are not regularly published. A research project
under way is attempting to estimate the required
figures . I n the meantime, it is impossible to say
whether or not the inaccurate conventional computations of velocity give a fair picture of its
stability.
1. This charge is scarcely credible in view of the long history of
the subject. Thomas M . Humphrey has traced equations of exchange involving a velocity term all the way back to 1804
("Algebraic Quantity Equations before Fisher and Pigou,"
Economic Review, Federal Reserve Bank of Richmond,
September 1984, 13-22). Arthur W . Marget wrote a whole book
about the subject and its hi story up to the middle 1930s (The
Th eory of Prices. vol. 1 [New York : Prentice-Hall, Inc., 1938)).
This encyclopedic but barely readable book addresses nea rly
every question ever raised about equations of exc hange.
Economic Review I January 1986
2. Throughout this paper, the symbol ": =" indicates that the
variable to the left of it is being defined by the expression to
the right of it. The subject of velocity calls for especia lly
careful observance of the di stinctions between definitions.
identities. and other equations. All symbolic definitions are
identities. but not all identities are definitions . All identities
are equation s. but not all eq uation s are identiti es.
3. See Irving Fisher's famous tournam ent of ind ex-number formul as in Th e Purchasing Power of Money. rev. ed. (New York :
The Macmillan Co .. 1920 [1911], 198-233.385-429). This tournament had no winners and cou ld never have any. I ts rul es
consist of a set of crite ri a that index-number formulas ought to
meet, but no formula can mee t all the criteria .
4. Unfortun ate ly. many economists regard equ ation s of exchange
as " use less tautologi es." or " trui sms." This a ttitud e shows in
the following remark by J. R. Hicks in " A Suggestion for
Simplifying th e Theory of Money," Economica (N ew Series) 2
(February 1935): 1:
To anyone who comes over from the theory of va lue to the
th eory of money. there are a number o f things whic h are rather
startling. Chief of these is the preocc upation of mon eta ry
theori sts with a ce rt ain equa tion. w hi ch states that the pri ce of
goods multiplied by th e quantity of goods eq uals the amount of
money which is spent on them. This equ ation crops up aga in
and aga in. and it has all sorts of ingenious littl e arithm eti ca l
tricks perform ed on it.
This attitude probably derives from the neoclass ica l way of
thinking. which really allows no role foi mon ey in making exchanges. For criticism, see Robert W . Clower. " A Reconsideration of the Microfoundations of Monetary Theory." Western
Economic Journal 6 (December 1967): 1- 8. and Douglas Gal e.
Money: In Equilibrium (Cambridge: Cambridge University Press,
1982). A more direct answer to snobhishn ess about equations
of excha nge was given by Marget, p. 98:
Viewed ... in th e light of th e ac tual historica l developm ent
of ... the subj ec t .... the importance of the " truisti c" character of
[usef ul equations of exc hange] ... is that the gradual attainm ent
of this " trui sti c" charac ter. instead of providing ground for
criticism ... ,becomes a record of slow ac hievement, over centuries, of prec isely the kind that is represe nted by the advance
of knowledge in any branch of sc ience. An ea rli er proposition.
rega rd ed in its own day as a " truism," is shown by later inves tiga tion to be true in fac t only und er certain speci fi c condition s of which not even the nature was at first recog nized ....
5. Howard S. Ellis gave a clear account of the rol e of convention
and institutional arrangem ents in " Some Fundam entals in the
Theory of Velocity," The Quarterly Journal of Economics 52
(May 1938]: 431 - 72, and there cited mu ch of the useful earlier
literature. Meir Kohn further advanced the subject in " In
Defense of the Finance Constraint. " Economic Inquiry 19 (April
1981): 177-95.
6. See Knut Wicksell, Lectures on Political Economy , vol. 2,
Money, published in Sweden in 1906, tran s. E. Classen. ed.
Lionel Robbin s (London: Routledge and Kegan Paul, 1935), 60,
61 .
7. This has been known at leas t since Cantil Ion. For a discussion.
see Charles Rist. History of Monetary and Credit Theory.
23
published in France in 1938, trans. j ane Degras (N ew York : The
Macmillan Co., 1940), chap. 2.
8. The conventional theory and econometrics of money demand
are in a sorry state. See Thomas F. Cooley and Stephen F.
LeRoy, " Identi fication and Estimation of Money Demand, "
American Economic Review 71 (December 1981): 825-44. The
study of demand stabi lity, via velocity, is therefore quite
natural.
9. See especia lly Milton Friedman, "Monetary Poli cy: Theory and
Practice," Journal of Money, Credit, and Banking 14 (February
1982): 98-118; "Monetary Variability: United States and
j apa n," 15 (August 1983): 339-43; and "T he Fed Hasn' t
Changed Its Ways," Wall Street Jo urnal, 20 August 1985, 24.
10. In this paper I do not distinguish between real and nominal
GNP, but the ri ght-hand side of equation 7 can be expressed
as
l!.G
G
= (q'l!.p) /(P'q)
+
(P'l!.q) /(P'q),
where dots denote sca lar products. The f irst term represents
the contribution of price changes (the inflationary component) had quantities rema ined consta nt, and the seco nd
represents the real compo nent had prices remai ned consta nt.
These terms are related to Laspeyres indexes of price and
quantity changes . Most of the interest in steady income
growth ce nters on the second term .
11 . The twentieth-ce ntury leader of the Steady Money camp is
Mi lton Friedman, whose views rest partly on the be lief that
velocity would be stab le if the money stock were stab le and
partly on the wish to reduce the rol e of centra l banks and
other government arm s in private affairs. See, for exa mpl e, A
Program for Monetary Stability (New York : Fordham University
Press, 1959), and Capitalism and Freedom (Chicago: The
University of Chi cago Press, 1962). Most of the economi sts
who are very well known to the publi c, however, are Fine
Tun ers .
12. See, for examp le, William A. Barnett, " T he Optimal Level of
Monetary Aggregation," Journal of Money, Credit, and Banking 14 (November 1982, pt. 2): 687-710. This paper, like many
others by this author, energetica lly argues the case for what is
ca lled Divisia aggregation. It se rves pretty well as a manifesto
of the Divisia brotherhood, which is a splinter group among
the Seekers. See, for example, William A. Barnett and Paul .A.
Spindt, Board of Governors of the Federal Reserve System,
Divisia Monetary Aggregates: Compilation, Data, and
Historical Behavior, Staff Studies no. 116 (Washington, D.C. :
Board of Governors, 1982).
13. Some writers define barter more broadly, as any transaction
not involving money. William Stanley j evons, in Money and
the Mechanism of Exchange (New York : D. Appleton and Co.,
1882 (1879), 189, expressed it lik e this:
No sooner have a people fu ll y experienced the usefulness of a
good system of money, than they begi n to discover that they
can dispense with it as a medium of excha nge, and return to a
method of traffic closely resembling barter. With barter they
24
begin and with barter they end; but the second form of
barter .. .is very different from the first.
jevon s' s "second form of barter" involves c ircu lating credit
(bills of exchange in ea rli er days, bank deposits today). His
usefu l book, intended for a lay audience before the days of
universa l sc hooling, received timely reviews in The Hartford
Post, Th e Boston Saturday Evening Gazette, and Popular
Science . The 1879 edition cited some of these reviews at the
back of the book .
14. About 3 percent is kept by the bank as its fee for maintaining
the account and guaranteeing payment on all credit ca rd purchases up to $50; it is as if the bank rem itted at 97 percent of
par. I have d isrega rded this comp li catio n.
15. Strictly speaking, transactions 5 and 15, too, should be regarded as financial from the standpoi nt of the monetary base.
If transaction 12 is financial because it exc hanges debt, why
are not transactions 5 and 157 I n strict logic, they are; I do
not co unt them as such in order to minimi ze the correctio ns
for double co unting.
16. Notice that currency payments are defined differently in the
M1 and the monetary-base identif icat ion s of money.
17. Using Stiel tjes integrals (because quantities change abruptly),
C, and 0 are fo und by integrating C,(t) and D(t) over the
period and dividing by the length of the period, where C,(t)
and D(t) are currency and deposits at instant 1.
18. In the mythical economy of section 2; G represented both
GNP and total sa les of goods.
19. It should be noted that the goods, but not the financial,
ve loc ity of M1 is affected by our treatment of credit card
purchases. The fi rst trea tment makes the goods ve locity- and
therefore the transaction and income velocity- greater than
does the seco nd one.
20. Here, for simpli city, I am disregarding the fact that checks remaining within the bank create no potential reserve transfers.
If such checks were randomly reassigned so that they trave led
between bank s and thus reached the clearinghouse, they
would induce a statistica ll y sma ll increment to the actual
amount of reserve transfers. Such addition al transfers might,
in turn, indu ce additional borrowing of federal funds.
21 . Or think of velocity pronounced with a Swedish accent. This
is how Knut Wicksell wou ld have pronounced it, and he introduced the term " virtual velocity" (though the co ncept had
lon g been known). See, for examp le, Wicksell's Lectures on
Political Economy: Money , 67ff. Note, howeve r, that I def ine
virtual velocity somewhat differently than Wicksell. I think
Wickse ll would have reserved the term for what I will later
call "u nreali zed ve locity. "
22. The multiplier is not co nstant. For an interesting and informative study of its determinants, see S. C. Tsiang, "T he Diffusion of Reserves and the Money Supp ly Multipl ier, " Economic
Journal 88 [June 1978): 269-84.
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