Full text of Review (Federal Reserve Bank of St. Louis) : September/October 1988

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Vol. 70, No. 5




September/October 1988

3 Have Li.S. Exports Been Larger Than
Reported?
24 W hy Have State Per Capita Incom es
Diverged Recently?
37 Ttesting the Expectations M odel o f the
Term Structure: Som e Conjectures
on the Effects o f Institutional
Changes
4G The Puzzling Growth o f the M onetary
Aggregates in the 1980s

THE
FEDERAL
ARESERVE
RANK of
rtf ST. LOUIS

1

Federal Reserve Bank of Si. Louis

Review
Septem ber/O ctober 1988

In This Issue . . .




In the first article o f this Review, M ack Ott investigates the relation b e ­
tw een the in creasin gly large U.S. m erch andise trade deficits occu rrin g
since the mid-1970s and a lesser-known, p u zzlin g attribute o f the U.S. bal­
ance o f paym ents du rin g this era — the in creasin gly large statistical d is­
crepancy. Starting from the accou n tin g relation betw een export reportin g
errors and the disagreem en t b etw een the current and capital sides o f the
balance o f paym ents, Ott builds the case for the discrepan cy b ein g evi­
d en ce o f a persistent u n d errep ortin g o f U.S. m erch andise exports. In direct
evid en ce consistent w ith this v ie w from studies o f u n d errep ortin g in in ter­
national services trade and from U.S. d om estic studies o f understated tax­
able in com e are discussed to m otivate the statistical tests w h ic h follow .
T h e test results are consistent w ith an affirm ative an sw er to the a rticle’s
question: U.S. m erch andise exports have been u n d errep o rted since the
mid-1970s.
*

*

*

From the early 1930s through the late 1970s, p er capita in com es rose
faster in lo w -in co m e states than in h igh -in co m e states, resulting in a sub­
stantial red u ction in state p e r capita in com e inequality. This long-stan din g
tren d has since reversed: since 1978, the interstate in eq u a lity o f p e r capita
in com es has risen in all but o n e year.
In this issu e’s secon d article, “W h y Have State Per Capita In com es D i­
verged R ecently?” Cletus C. C ou gh lin and T h om as B. M an delbau m fin d
that the recen t increase in in com e in equ ality stem s from the rapid g row th
in 10 h igh -in com e A tlantic Coast states alon g w ith relatively s lo w grow th
in 10 lo w -in co m e states scattered throu ghou t the n a tio n ’s interior. A fter
con siderin g several explanations o f regional grow th, in clu d in g the m o ve­
m ent o f industrial activity from the Frost Belt to the Sun Belt and the “ farm
crisis,” the authors co n clu d e that d eclin in g en ergy prices du rin g the 1980s
w as the p rim a iy con tribu tor to the rising in equ ality o f state p er capita
in com e.
*

*

*

Explaining the beh avior o f interest rates has been a long-stan din g p r e o c ­
cu pation fo r m an y econom ists. A lthou gh eco n o m ic th eory suggests that
the relationship betw een short- and lon g-term interest rates is sim ple,
em pirical research, alm ost u niform ly, has rejected it. In the third article o f
this issue, M ich ael T. B elongia and K ees G. K oedijk re-exam ine a basic
m o d el o f interest rate determ in ation b y co n sid erin g the effects o f several
w ell-k n ow n p o lic y changes.
In th eir “ T estin g the Expectations M o d e l o f the T erm Structure: Som e
C on jectu res o n the Effects o f Institu tional Changes," B elongia and K oedijk
co n sid er h o w changes in the Federal R eserve’s im p lem en ta tio n o f m o n e ­
tary p o lic y and the op era tion o f the Eu ropean M on eta ry System m a y have
affected interest rate behavior. U sing data fo r five countries, the authors

SEPTEMBER/OCTOBER 1988

2

fin d that forw ard rates are not related o n e-to-on e w ith changes in actual
three-m on th interest rates in the U nited States, G erm any and Switzerland.
Even though con sid erin g the operatin g p roced u res o f the Fed and the
EMS led to som e im p rovem en t in the results, the persistent m o d el re jec­
tions leave beh in d m an y u nsolved pu zzles.
*

*

*

In the 1980s, the relationships b etw een the g ro w th o f the m on etary base
and the grow th o f the m ajor m on etary aggregates, M l, M2 and M3, has
ch anged dram atically. Historically, M l had gro w n m o re s lo w ly than the
m o n eta iy base, w h ile M2 and M3 had grow th about 2 to 3 percen tage
points faster. Beginning in early 1984, how ever, M l began to g ro w m uch
faster than the m o n eta iy base, w h ile M2 and M3 g re w m ore slo w ly than
the base. In the final article in this Review, “T h e P u zzlin g G row th o f the
M o n e ta iy A ggregates in the 1980s,” Albert E. Burger presents a fram ew ork
o f analysis that h elps unravel this mystery.
Burger derives m u ltipliers that link the m o n e ta iy base to M l, M2 and
M3. T h e co m p o n en t ratios o f these m u ltipliers su m m arize the key asset
po rtfo lio decision s m ade by the pu blic that affect the grow th o f the aggre­
gates. Th e author presents the recen t beh avior o f these ratios in a h istori­
cal context to em p h a size the dram atic nature o f the changes that occu rred
in the 1980s. He traces the acceleration in M l relative to base grow th to the
sharp rise in the p u b lic’s h oldin gs o f checkable dep osits relative to its
h oldin gs o f currency, an unusual historical d evelop m en t. Burger also
show s that M2 and M3, in addition to bein g affected by this developm en t,
also have been affected b y a rise in the p u b lic’s h oldin gs o f checkable d e ­
posits relative to the oth er financial assets that co m p o se these aggregates.
T h e key develop m en ts associated w ith this ch an ged beh avior o f the
co m p o n en t ratios — the financial innovations in the 1970s and 1980s, and
the sh aip red u ction o f inflation and interest rates in the 1980s — are also
discussed. T h e au thor show s that, although the relationships b etw een the
grow th o f the m o n e ta iy base and the M l, M2 and M3 aggregates ch anged
significantly in the 1980s, the grow th o f these m on etary aggregates rem ains
tied to the grow th o f the m o n eta iy base.


FEDERAL RESERVE BANK OF ST. LOUIS


3

Mack Ott
Mack Ott is a senior economist at the Federal Reserve Bank of St.
Louis. The author acknowledges the helpful suggestions and
criticisms of Andrew Kamarck, Tom Mayer, Guy Meredith, Gordon
Midgely, Marius van Nieuwkerk, Lois Stekler, A.C.J. Stokman, Bill
Witte, Geoffrey Wood, Stephen Wright and seminar participants at
Notre Dame and Appalachian State Universities. Nancy D. Juen
and Rosemarie V. Mueller provided research assistance.

Have U.S. Exports Been Larger
Than Reported?

J . N LATE 1987, Ihe U.S. C o m m erce D ep a rlm en l
a n n ou n ced that in its m o n th ly trade reports, ex ­
ports to Canada w o u ld h en ceforth use Canadian
custom s data on im ports from the U nited States
rather than U.S. export data. T h e rationale fo r this
proced u re is the d o cu m en ted in accu racy since
1970 o f U.S. cu stom s data fo r exports to Canada.
T h e discrepan cies betw een the U.S. and Canadian
data have b ecom e substantial both in absolute
term s — n early $11 billion in 1986 — and in term s
o f th eir effect on the U.S. trade balance — a 42
p ercen t red u ction in the 1986 U.S. trade deficit
w ith Canada. W hite these errors are co rrected in
the annuai recon cilia tion o f U.S-Canadian trade
data, th eir persisten ce raises a b roa d er question:
A re U.S. exports to o th er cou ntries sim ilarly
u nderstated?
This possibility raises som e im portan t political
and eco n o m ic issues. In recen t years, the trade
balance has been the focus o f m u ch eco n o m ic
p o lic y debate, rivaling o r co m p le m en tin g such
traditional d om estic issues as em ploym en t, in ­
flation and grow th . In this context, isolatin g large
understatem ents in U.S. m erch an dise export data
is clearly a top ic w ith im portan t p o licy
im plications.
In this article, the relationship b etw een export
u n d errep ortin g and the statistical d iscrep a n cy in



the balance o f paym ents, w h ic h also rose from
in sign ifican ce to p ro m in en ce du rin g the 1970s, is
d evelo p ed and is used to assess the validity o f
estim ated U.S. export u n d errep ortin g in the 1970s
and 1980s.

BALANCE OF PAYMENTS
ACCOUNTING, REPORTING ERRORS
AND THE STATISTICAL
DISCREPANCY
T h e first p ostw ar U.S. trade deficit d id not occu r
until 1971, a qu arter o f a cen tu ry a fte rW o rld W ar
II. D uring the early 1970s, the U.S. m erch andise
trade account alternated b etw een deficits and
surpluses; despite the com paratively w eak grow th
o f U.S. m erch andise exports relative to im ports,
h ow ever, the d eclin in g U.S. current accou nt b al­
ance rem ain ed in surplus du rin g m ost years until
1982, prim arily becau se o f strong in com e from U.S.
foreign investm ents.
A lo n g w ith the d eclin in g current accou nt bal­
ance, a p ersisten tly large d iscrep a n cy arose b e ­
tw een the current a n d capital accou nt balances.
Since the first OPEC em bargo in 1973-74, this dis-

SEPTEMBER/OCTOBER 1988

4

crepan cy has averaged nearly $22 billion.' Before
1975, it h ad been g en erally small and negative,
averaging —$1.1 billion from 1960 to 1974. T h e
relation b etw een the current accou nt balance,
errors in exports and the statistical d iscrepan cy
can be illustrated by review in g balance o f p a y­
m ents accou nting.2

The Rudiments o f Balance o f
Payments Accounting
Balance o f paym en ts accou n tin g is structured
by tw o basic prin cip les: dou ble-en try accou ntin g
and equ ality b etw een net sales m inus gifts and the
change in financial claim s. Balance o f paym ents
accounts record a cou ntry's sales (exports) and
purchases (im ports) o f go o d s and services plus
transfers to foreign ers as w e ll as its len d in g to
(capital exports) and b o rrow in g from (capital im ­
ports) o th er countries. T h e sum o f go o d s and ser­
vices pu rchased and sold to foreigners, minus
transfers, in a given p erio d is called the current
account balance; the con com itan t ch ange during
the sam e p erio d in the co u n try’s financial position
du e to capital ou tflow s and in flow s is ca lled its
capital account balance. Oftentim es, discussion
focu ses on bilateral balances — fo r exam ple, b e ­
tw een the U nited States and Japan; h ow ever,
cou ntries gen era lly have surpluses w ith som e
countries and deficits w ith others, and the overall
balance w ith all cou ntries is the m ost inform ative
m easure o f a cou ntry's international eco n om ic
con d ition . A n illustration o f these p rin cip les in a
three-cou n try exa m p le w ill high ligh t the offsetting
equ ality o f the current and capital accou nt bal­
ances assuming they are completely and accurately
measured.

An Illustration o f Balance o f
Payments Accounting
Suppose that total w o r ld m erch an dise trade
du rin g a qu arter con sisted o f a $1 m illio n c o m ­
p u ter s old b y the U nited States to Japan and
$300,000 w o rth o f crystal im p o rte d by the U nited
States from Ireland, each paid fo r w ith short-term

'Throughout this article, the statistical discrepancy reported will
be the “total discrepancy” — that is, the statistical discrepancy
as it would be without the reconciliation adjustment for unre­
ported trade with Canada.
2For a more detailed discussion of balance of payments account­
ing, see chapter 15, “The Balance of Payments and Foreign
Exchange Rate," in Caves and Jones (1981). For an application
of these principles to the U.S. trade deficit, see Chrystal and
Wood (1988).


FEDERAL RESERVE BANK OF ST. LOUIS


notes. T h ese IOUs are capital im ports (inflow s) o f
the borrow ers and capital exports (outflow s) o f the
lenders. Suppose also that a corp ora tion in Ire­
land, o w n e d b y U.S. residents, h ad profits du rin g
the p erio d o f $80,000, $50,000 o f w h ic h rem ained
w ith the subsidiary as retain ed earnings and
$30,000 o f w h ic h w ere paid to the U.S. ow n ers out
o f the firm ’s dep osits in a U.S. bank. T h e profits o f
the Irish firm, in effect, are the paym ent fo r the
use o f m achines, bu ildin gs an d financial resources
that the U.S. o w n ers have sent to Irelan d — capital
services ex p o rted b y the U n ited States to Ireland.
T h e balance o f paym en ts fo r each o f the three
countries du rin g the qu arter is sh ow n in figure 1.
Som e Accounting Principles. T h e figure d is­
plays the transactions b etw een the three countries
in the T-accou nts in the u p p e r panel. Every trans­
action is en tered tw ice, u sually as a debit and a
credit but also in a variety o f o th er ways, d e p e n d ­
ing on the transaction. For exam ple, fo r the U.S.
o w n e d Irish firm ’s transactions, an $80,000 debit
fo r capital services im p orted, a m inus $30,000
debit fo r U.S. bank deposits draw n dow n, and a
plus $50,000 credit fo r the reinvested retained
earnings are the entries in the Irish accounts,
w h ile the opposite, b alancing entries a p p ea r in
the U.S. accounts. N ote that debits (left-hand side
o f T-accou nt) are en tered w ith negative signs in
the balance o f paym ents (lo w e r panel), w h ile
credits (right-hand side o f T-accou nts) are en tered
w ith positive signs. For exam ple, the co m p u ter
ex p o rted b y the U nited States to Japan appears as
a credit (export) in the U.S. current accou nt and a
debit (im port) in the Japanese current account. In
contrast, in the capital account, capital ou tflow s
(exports) a p p ea r w ith a negative sign w h ile capital
in flow s (im ports) a ppear w ith a p ositive sign.
Thus, the Japanese n ote payin g fo r the co m p u ter
appears as a deb it (capital export) in the U.S. ca p i­
tal accou nt and a credit (capital im port) in the
Japanese capital account.
The Balance o f Payments Identity. W h en the
transactions fo r each cou n try are su m m ed up, the
resulting statem ent is the balance o f paym ents

SEPTEMBER/OCTOBER 1988

Figure 1
The Relation Between International Transactions and the Balance of Payments
Transactions T-Accounts
(-)

United States

$1,000,000 note
300,000 crystal
50,000 foreign
investment

(+ )

(-)

$1,000,000 computer
exported
300,000 note
80,000 services
-3 0 ,0 0 0 U.S.
deposits

Ireland

$300,000 note
80,000 capital
services
-3 0 ,0 0 0

(-)

(+ )
$300,000 crystal
exported
50,000 Corporate
retained earnings
of U.S. subsidiary

$1,000,000 computer
imported

Japan

(+ )
$1,000,000 note

U.S.
deposits
Balance of Payments Accounts
Irish balance of payments

U.S. balance of payments

Balance on
current account

-

$1,080,000
300,000

$780,000

Balance on capital
account

Statistical discrepancy




Exports
Imports

-

Balance on
current account

$300,000
80,000

Exports
Imports

$220,000

Balance on
current account

-$1,050,000
270,000

-$7 80 ,0 00

$0

Increase
assets
Increase
assets

( - ) in Irish
abroad
( + ) in foreign
in Ireland

Balance on capital
account

Statistical discrepancy

$0
- 1,000,000

-$1,000,000

Capital Account:

Capital Account:

Capital Account:
Increase ( - ) in U.S.
assets abroad
Increase ( + ) in foreign
assets in U.S.

Current Account:

Current Account:

Current Account:
Exports
Imports

Japanese balance of payments

-$2 70 ,0 00
50,000

-$2 20 ,0 00

$0

Increase ( - ) in Japanese
assets abroad
Increase ( + ) in foreign
assets in Japan
Balance on capital
account

Statistical discrepancy

$0
1,000,000

$1,000,000

$0

6

sh ow n in the lo w e r pan el o f figure 1. Since g o o d s
and services exports (im ports) have positive (nega­
tive) signs in the current accou nt balance w h ile
capital exports (im ports) have negative (positive)
signs, the current accou nt balance (CAB) is equal
and o p p o site in sign to the capital accou nt bal­
ance (KAB) fo r each country. Th is essential id e n ­
tity o f balance o f paym ents accounting,
(1) CAB + KAB = 0,
m ust h o ld as lo n g as the international transac­
tions are p ro p e rly and c o m p le te ly recorded, as
th ey are in figure 1. In o th er w ords, if there is a
trade surplus, CAB > 0, there m ust b e a capital
deficit (net capital outflow ) o f an equal absolute
am ount, KAB = - CAB < 0, and vice versa.
T h e co m m on sense o f this fu ndam ental iden tity
is that if a cou n try sells m ore go o d s and services
to foreigners than it buys from them , foreigners
m ust balance this shortfall w ith real assets and
financial claim s on them selves — equities, real
property, bon d s and m on ey.3 C onsequently, the
balance o f paym en ts statistical discrep a n cy for
each cou n try in figure 1, a correction equal to the
sum o f CAB and KAB w ith the o p p o site sign, is
zero.
In the exam ple in figure 1, the U nited States has
an overall current accou nt surplus ($780,000), but
it has a trade deficit w ith Ireland ($220,000) and a
trade surplus w ith Japan ($1,000,000). If reportin g
errors or o m ission s are m ade w ith any country,
they w ill sh o w u p in eith er the statistical d isc rep ­
ancy, the w o r ld current accou nt balance or both.
T o see w hy, co n sid er w h at happen s w h e n re p o rt­
ing errors are m ade.

crepan cy equal to the export u nderreporting,
$100,000. Such errors can be la b eled relative er­
rors: th ey affect the current accou nt balance (e) or
capital accou nt balance (k) relative to each o th er
causing a statistical d iscrep a n cy o f equal m agn i­
tu de and o p p o site sign.
Alternatively, som e errors affect b oth current
and capital accounts. F or exam ple, su ppose the $1
m illion co m p u ter export w as co rrectly reported,
but the $80,000 earnings o f the U.S. o w n e d firm in
Ireland w e re not reported. As a result, the rise in
U.S. claim s on Ireland ($50,000) also w o u ld be unrep orted in the U nited States as sh ow n in pan el b
o f figure 2. In this case, the U.S. statistical d isc rep ­
ancy w o u ld be $30,000 becau se o f the d o cu m en ted
(bank reports) d eclin e in Irish -ow n ed U.S. assets;
h ow ever, the o th er $50,000 o f the U.S. export u n ­
derstatem ent w o u ld be offset so that the levels o f
both current and capital balances are u nderstated
b y the absolute am ou nt o f this error, $50,000. That
is, the u n rep o rted $50,000 in retain ed earnings —
u n rep o rted service in com e o n current accou nt —
is m atch ed b y the u n rep o rted $50,000 reinvested
in the firm — u n rep o rted capital o u tflo w o n ca p i­
tal account. T h ese offsetting errors, d en o te d b y a,
can be called absolute errors since th ey change
the absolute level o f both current and capital ac­
counts. T h e y d o not affect the relative levels o f the
tw o accounts; thus, th ey have n o effect on the
statistical discrepancy.
T h e general relation o f the re p o rted balance o f
paym ents data w ith the actual trade and financial
transactions can then b e su m m a rized as follow s:

(2)

cAb

= CAB + e + a

(3) KAB = KAB +
The Effects o f Errors in R ep orted Exports. In
practice, the statistical discrepan cy typically is not
zero; errors or o m ission s in the data result in a
n o n zero discrepan cy. For exam ple, su ppose the
U.S. ex p o rter h ad filed export d ocu m en ts listing
the co m p u ter sale in correctly as $900,000 w h ile
the earnings o f the Irish firm are correctly given as
$80,000. If n o offsetting errors w ere m ade, the U.S.
balance o f paym ents w o u ld be as sh ow n in figure
2, pan el a. In this case, there is a statistical d is­

3This is, of course, the same rule which describes any voluntary
exchange between two people. Any imbalance in the value of
goods and services received over time is equal and opposite in
sign to the net value of financial flows between them. Each
person gives to the other a collection of goods, money and
assets equal in value to what he receives.


FEDERAL RESERVE BANK OF ST. LOUIS


k

- a

w h ere the “ ” in dicates the re p orted data, e and
k are relative errors in the re p o rted CAB and KAB,
respectively, and a is an absolute error. T h e logic
o f the accou n tin g con ven tion s requires that

cAb + kAb + SD = 0,
so the statistical d iscrep a n cy (SD) is d efin ed as the
negative o f the sum o f the re p o rted balances,

(4) SD = -[CAB + KAB],

7

Figure 2
Source of Statistical Discrepancy
(a)
Statistical Discrepancy: Underreported Exports without
Offsetting Errors ( e = -$100,000)
U.S. Balance of Payments
Current account
Exports
Imports

-

$980,000
300,000

Balance on current account

$680,000

Capital account
Change in U.S. assets abroad
Change in foreign assets in U.S.

-$1,040,000
260,000

Balance on capital account

-7 8 0,00 0

Statistical discrepancy

$100,000

(b)
Statistical Discrepancy: Underreported Exports with partly
Offsetting Errors (a = - $50,000, e. = - $30,000)
U.S. Balance of Payments
Current account
Exports
Imports

-

$1,000,000
300,000

Balance on current account

$700,000

Capital account
Change in U.S. assets abroad
Change in foreign assets in U.S.
Balance on capital account

-7 3 0,00 0

Statistical discrepancy

$30,000

From (2), (3) and (4),
SD = - [CAB + e + a + KAB +

k

-

a],

so that, b y (1), SD is sim p ly the negative o f the sum
o f the relative errors, e and k ; that is,
(5) SD = - [

e

+

-$1,000,000
270,000

k ].

W h ile absolute errors (a) d o not affect any c o u n ­
try's balance o f paym en ts discrepancy, such errors

do sh o w up in the w o r ld balance o f paym ents
totals. Panel a o f figure 3 sh ow s that, w ith n o re­
p o rtin g errors, the current accou nt balance o f the
w o r ld is zero. T h e co m m on sense o f this is that fo r
the total tradin g system, the surpluses o f the na­
tions w ith m o re exports than im p orts m ust b al­
ance the deficits o f the nations w ith less exports
than im ports.4 Panel b o f figure 3 show s that w ith
relative current accou nt errors (e), the U.S. export

4ln macroeconomic theory, this is referred to as Walras’ Law of
Markets — the sum of trades (planned or actual) must be zero
— with excess demands ( + ) and supplies ( - ) cancelling. See
Patinkin, (1965) pp. 34-36.




SEPTEMBER/OCTOBER 1988

8

Figure 3
The World Current Account and the World Current Account
Discrepancy
(a)
No Reporting Errors
U.S. current account
Exports
Imports

-

$1,080,000
300,000

U.S. CAB

$780,000

Irish current account
Exports
Imports

-

$300,000
80,000

Irish CAB

220,000

Japanese current account

$0
-1,000,000

Exports
Imports
Japanese CAB

-1,000,000

World CAB

$0
(b)
Underreported Exports With Relative Errors (e = - $100,000)

U.S. current account
Exports
Imports

$980,000
-300,000

U.S. CAB

$680,000

Irish current account
Exports
Imports

-

$300,000
80,000

Irish CAB

220,000

Japanese current account
Exports
Imports
Japanese CAB
World CAB


FEDERAL RESERVE BANK OF ST. LOUIS


$0
-1,000,000
-1,000,000
-$100,000

9

Figure 3 cont’d.
(c)
Underreported Exports with Absolute Errors (a = - $50,000) and Relative Errors (e = - $30,000)
U.S. current account
Exports
Imports

-

$1,000,000
300,000
$700,000

U.S. CAB
Irish current account
Exports
Imports

-

$300,000
80,000

Irish CAB

220,000

Japanese current account
Exports
Imports
Japanese CAB
World CAB

-

$0
1,000,000
-1,000,000
-$ 8 0,00 0

u n d errep o rtin g results in figure 2, pan el a in an
equivalent deviation from the logica l w o r ld zero
current accou nt balance. Finally, pan el c show s
that both the absolute (a) and relative (e) errors —
the u n rep o rted U.S.-owned Irish firm ’s $50,000
retain ed earnings in figure 2, pan el b and the
$30,000 o f u n rep orted dividends — are reflected in
the w o rld CAB even thou gh the U.S. SD show s on ly
the relative ($30,000) error.

Som e in d irect evid en ce on the w o r ld current
accou nt d iscrep a n cy (see sh aded insert) im p lies
that the U.S. current accou n t reflects b oth absolute
(a) and relative (e) errors, a m ix illustrated in the
distribution o f the profits o f the U.S.-owned Irish
corp ora tion in figures 2 and 3.5 By its defin ition in
id en tity 5, the U.S. balance o f paym ents statistical
discrep a n cy reflects o n ly relative errors. Still, the
in direct im p lica tion o f u n rep o rted U.S. investm ent

5ln testimony before the Joint Economic Committee, Heller
(1984), p. 67, argued that such unreported investment earnings
might be large enough to offset the reported CAB deficit:

foreign source interest income. Her estimates suggest that
unreported interest income was substantial during the early
1980s:

There is some reason to believe that the bulk of the unrecorded
transactions is due to an underrecording of receipts of service
items such as reinvested earnings abroad, investment income
and fees. Consequently, the U.S. current account deficit, if
measured properly, is likely to have been substantially smaller
than indicated by the officially reported data. Thus it is entirely
possible that the U.S. was in substantial current account surplus
in 1983.

Stekler provides evidence that U.S. service exports are under­
stated because of unreported interest; she uses differences
between the data on U.S. claims on foreigners from three nonTreasury sources and the U.S. Treasury International Capital
Reporting System (TIC) to generate estimates of unreported




In summary, in the three cases where data on U.S. claims on
foreigners from the TIC reports can be compared with data from
other sources it appears that the TIC data seriously understate
U.S. claims. The size of the discrepancy between the data
sources can only be roughly measured, but for example, a total
on the order of $ 100 billion would not seem impossible. This
would imply that U .S. interest receipts are underestimated by
about $12 billion a year currently (assuming an average return of
12 percent). Stekler (1984), p. 7.

SEPTEMBER/OCTOBER 1988

10

The W orld’s Current Account Discrepancy
A n v e x p o rted go o d from the e o u n tiy o f origin
is an im p orted go o d fo r the cou n try o f destin a­
tion. As a consequ ence, if the data are co m p lete
and accurate, the w o rld can have n eith er a
trade deficit n or surplus; it must have a balance
(see figure 3). Yet, as sh ow n in the a cco m p a n y­
ing table, the w o rld trade data d o not y ie ld a
balance on current account.

discrepan cies is that substantial export in com e
is not bein g reported; that is, exports o f services
are understated.
T h e data in the table d ocu m en t a w o rld cu r­
rent account deficit averaging $70.9 billion du r­
ing the early 1980s. T h is w o rld CAB discrepan cy
can be accou n ted fo r by a negative service a c­
count balance, w ith u n rep o rted sh ip p in g in ­
com e, u n reported direct investm ent in com e
and u n reported p o rtfolio investm ent in com e
the largest contributors. S hipp ing in com e is
irrelevant for the U nited States; the IM F w ork in g
party fou nd it attributable to "several e c o n o ­
m ies w ith large m aritim e interests (notably
those o f Greece, H ong K on g and Eastern Eu­
ro p e)."' T h e o th er tw o d iscrep a n cy items, direct

T h rou gh ou t the first h alf o f the 1980s, w orld
m erch andise trade w as in “ surplus,” substan­
tially so in 1980 and 1981, and n egligibly so
since then. M ore b roadly throu ghou t the 1980s,
the current account — the sum o f m erch andise
and seivice trade m inus transfers — has been
in substantial deficit w ith no clear trend tow ard
balance. T h e im p lication o f these statistical

Selected Balances of World Current Account Transactions
(billions of U.S. dollars)
1980

1981

1982

1983

1984

1985

$31.1
-4 6 .8
-3 1 .9
- 2 .9
- 0 .5

$25.5
-7 5 .7
-3 5 .3
- 5 .3
0.8

-$ 0 .9
-8 8 .5
-3 4 .5
-3 .8
1.6

$3.0
-7 3 .4
-3 3 .2
- 2 .8
4.1

$9.7
-8 5 .1
-3 3 .3
- 2 .3
4.7

$7.8
-6 0 .6
-2 7 .4
0.2
5.3

13.0

11.0

2.0

8.4

10.0

21.0

- 9 .9

-1 3 .1

- 9 .0

-1 1 .6

-1 4 .9

-1 2 .5

- 7 .9

-1 8 .6

-3 1 .1

-2 8 .8

-3 8 .9

-4 6 .6

-1 1 .6

-1 5 .2

-1 2 .2

-1 4 .0

-1 2 .1

- 4 .5

4.9
6.5

0.1
5.2

- 1 .5
3.6

4.6
6.3

1.6
6.6

4.0
2.7

Current account (excluding
official transfers)
Official transfers

- 9 .2
-1 9 .6

-4 5 .0
-1 7 .6

-8 5 .8
-1 7 .5

-6 4 .1
-1 5 .3

-6 8 .8
-1 6 .9

-5 0 .1
-1 5 .5

Current account (including
official transfers)

-2 8 .8

-6 2 .6

-1 0 3 .4

-7 9 .4

-8 5 .7

-6 5 .6

Merchandise trade balance
Service balance
Shipment
Other transportation
Travel
Reinvested earnings on direct
investment
Other direct
investment income
Other (portfolio)
investment income
Other official
transactions
Other private
transactions
Private transfers

SOURCE: International Monetary Fund, Report on the World Current Account Discrepancy, table 6.

'International Monetary Fund (1987), p. 3.


FEDERAL RESERVE BANK OF ST. LOUIS


11

and p o rtfo lio investm ent in com e, w e re fo u n d to
be attributable in large part to U.S. in vestors’
u n rep orted o r m isrep orted foreign in com e.T h ere are several co m m on elem en ts in these
m a jor u n rep o rted service exports com p risin g
the w o r ld CAB discrepancy. First, in each case,
the im p o rte r has rep orted receivin g a service
and payin g fo r it, but the cred ito r has not ac­
k n ow led ged the in com e receipt o r financial
arrangem ent. Second, U.S. investm ents are e i­
ther d irectly im p lica ted by the evid en ce (direct
investm ent) o r in d irectly im p lica ted by the size

2For a discussion of direct investment adjustments attributed
to U.S. nonreported or misreported income, see pp. 35-39
of International Monetary Fund (1987). For portfolio invest­
ment adjustments, the U.S. role is more conjectural in that
the working party was able only to pin down adjustments to
industrial countries and others. Yet, it is plausible that the
United States, as the largest holder of foreign securities in
the year (1983) analyzed in detail — 27.8 percent of world

earnings is that U.S. exports have b een u n d er­
stated du rin g the 1980s and that this u nderstate­
m ent is reflected partly (e) in the U.S. statistical
discrepan cy. It is esp ecially n otew o rth y h o w large
and persistent both the statistical d iscrep a n cy and
the w o rld current account balance have b een
since the mid-1970s.

The U.S. Balance o f Payments
Statistical Discrepancy: 1960—86
As chart 1 shows, the statistical d iscrep a n cy has
b ec o m e quite large since the mid-1970s. T w o ve r­
sions o f the d iscrep a n cy are sh ow n in chart 1: the
rep orted SD (SDHAT) and the total SD (SDTOT).
SD TO T in clu des the discrep a n cy du e to U.S.
u n d errep ortin g o f U.S. exports to Canada. SDHAT
has been p u rged o f this error b y the annual re c o n ­
ciliation agreed u p o n betw een the U.S. Census
Bureau o f the C o m m erce D epartm en t and its Ca­
nadian counterpart, Statistics Canada.

o f po rtfo lio earnings (seivice exports). Th ird, fo r
both direct and po rtfo lio u n rep orted earnings,
there w ill be both absolute (a) and relative er­
rors ( e ) in the U.S. balance o f paym ents: an un­
rep orted credit fo r service export and an u n re­
ported debit fo r the capital o u tflo w represen ted
b y the u nrepatriated earnings (see figure 3,
panel c). Thus, these u n rep o rted exports d o not
affect the U.S. SD, but they illustrate that the
w o rld current accou nt statistical discrep a n cy is
prim arily the result o f u n d errep o rted exports
and that U.S. firm s and individu als are in volved
in u n d errep ortin g exports.

cross-border bond holdings and 44 percent of cross-border
equities (p. 68) — is a substantial nonreporter. See pp.
45-80, in particular tables 29 and 30 where unreported U.S.
nonbank deposit interest is estimated at $7.7 billion; see
also Stekler (1984).

statistical d iscrep a n cy in id en tity 5, the exp ected
value o f this su m m ation o f errors and om ission s in
each y e a r w o u ld be zero, if such errors and om is­
sions were not systematic. Thus, o ver several years'
observations, the m ean o f the statistical d isc rep ­
ancy w o u ld ten d to be close to zero. A bsent sys­
tem atic errors, a d eclin e in the data’s reliability
m ight cause w id e r fluctuations in the SD; persist­
ent positive SDs since the mid-1970s, how ever,
suggest system atic errors.

The Source o f the Statistical
Discrepancy: Capital or Current
A ccou n t E rrors?
By its defin ition in id en tity 5, the statistical dis­
crepan cy must be du e to eith er relative overstate­
m ent (e) o f the current accou nt deficit o r relative

T h e p ersisten ce o f large positive values o f the
statistical d iscrep a n cy from 1975 on w a rd suggests
that there are n on -ra n d om errors in the U.S. bal­

u n derstatem ent ( k ) o f the capital accou nt surplus.
If capital accou nt errors are responsib le fo r the SD,
capital in flow s m ust have b een persisten tly u n d er­
stated: as equ ation 4 shows, the capital surplus
w o u ld have to be in creased in o rd e r to drive SD to

ance o f paym ents data. From the defin ition o f the

zero .6

6From a strictly logical point of view, there is also the possibility of
overstatement of U.S. gross capital outflows — that is, an exag­
geration of U.S. investment abroad; however, there is neither
empirical evidence nor a priori behavioral foundation for its
occurrence.




SEPTEMBER/OCTOBER 1988

12

Chart 1
U.S. Balance of Payments Statistical Discrepancies,
Unreconciled and Adjusted
Billions of dollars
40

Billions of dollars
40

Annual Data

-2 0

-2 0
1960

62

64

82

84

1986

NOTE: The reported statistical discrepancy, SDHAT, reflects the U.S.-Canadian m erchandise trade
reconciliation; the unreconciled statistical discrepancy, SDTOT, is the statistical discrep ancy as it would
be w ithout the U.S.-Canadian reconciliation.

A lthou gh m ost observers argue that capital ac­
count understatem ents are to blam e fo r the SD’s
large deviations, this h ypoth esis is im plausible
from a behavioral standpoint.7 Capital in flow s
prim arily represent increases in debt fo r U.S. firms

and individuals, and th ey have strong incentives
to report them since the interest paym en ts to ser­
vice these debts are tax-dedu ctible. This su p p osi­
tion has b een su p p o rted b y the IM F W orking
G rou p’s study, The World Current Account Dis-

7The Department of Commerce intimates that the statistical
discrepancy is likely to be relative capital account errors («): “ If
one assumes that a large part of cumulative net unrecorded
inflows of about $140 billion from 1979 through 1984 was
accounted for by capital inflows, foreign assets would have
been understated by that am ount. . . ” Jack Bame, quoted in
Scholl (1984), p. 26. Stekler (1983), p. 3, observes that “When
the Interagency Work Group on the Statistical Discrepancy was
set up in mid-1980, it was assumed that the bulk of the huge
positive statistical discrepancy in 1979 and 1980 was ac­
counted for by unrecorded capital inflows.” Amuzegar (1988),
p. 18, a former IMF Executive Director, reinforces this: “ . . .
capital inflows into the United States are probably under­

recorded.” Pluckhahn (1988) reports that Commerce officials
still downplay the notion of current account errors explaining
the discrepancy: “ More likely, they say, capital flow statistics —
measuring international financial transactions — have not kept
up with the ongoing deregulation of financial markets.” That SD
has been KAB error is also assumed in textbook discussions,
such as Krugman and Obstfeld (1988), p. 299, and empirical
applications of the balance of payments data; for example, see
Hooper and Morton (1982), p. 45: “The sum of the current
account plus official intervention purchases of domestic cur­
rency (I) define net private capital flow s. . . ” [italics added]


FEDERAL RESERVE BANK OF ST. LOUIS


13

crepancy, and b y the Internal Revenue Service
(1979) stu dy o f U.S. d om estic u n rep o rted in com e.
T h e W orking Group fou n d that borrow ers w o r ld ­
w id e d o consistently report international capital
inflow s, w h ile len ders have been fou nd consist­
en tly to u n d erreport th eir capital exports:
The main result o f analyzing the gaps in portfolio
investment income reporting is that the discrep­
ancy results mainly from the understatement of
receipts by the private nonbank sector and that
this deficiency is widespread across countries."
U n rep orted capital in flow s are the requisite
explan ation if the U.S. SD is du e to capital account
relative errors (K);yet, debt in crem en ts have b een
fou n d to be d ep en d a b ly reported. U nreported
capital in flow s w o u ld be inconsistent w ith both
w o r ld w id e findings and the debtors' taxm in im izin g incentives to report such debt in cre­
ments. If anything, the IM F fin d in g suggests that
the capital accou nt m a y be overstated because
som e capital ou tflow s associated w ith reinvested
earnings m a y be u n reported.9
Conversely, if U.S. m erch andise exports can be
sh ow n to be u n derstated g en erally — as th ey have
been in the specific case o f Canada — then u n d er­
statem ent o f the CAB is a plausible culprit. T h ere
are three behavioral fou ndations fo r U.S. export
understatem ent. First, is sim ple n egligen ce o r the

8lnternational Monetary Fund (1987), p. 78. Consistent with
these IMF findings indirectly implicating U.S. investors, Stekler
(1984), p. 3, observes that:
Some have argued that since the United States accounts for
about 20 percent of world services exports, that the United
States probably accounts for the sam e share of the global
services discrepancy ($15 billion in 1982).

9Note that in the 1980s, while the world current account discrep­
ancy has been a substantial deficit, the world merchandise
discrepancy has been slightly in surplus; see table a in the
shaded insert. The world current account discrepancy and the
large U.S. holding of foreign assets creates a presumption that
U.S. service exports are understated. By itself, this provides a
counter argument to the claim that unreported capital inflows
are the explanation for the statistical discrepancy. In contrast,
the absence of a worldwide merchandise export understate­
ment does not in and of itself imply anything about errors in
U.S. merchandise exports data.
10The first explanation is documented by the Commerce Depart­
ment and is one of the reasons implied for the late 1960s
episode of export underreporting in the United Kingdom. See
“ Under-recording of exports” (1969). The second has been
substantiated by the IMF Working Party Report on the World
Current Account Discrepancy, by the IRS (1979) study of unre­
ported U.S. income, in the OECD study by Veil (1982) and in
Stekler (1983). The third conjecture receives a variety of sup­
porting argument in terms of costs and competitive disadvan­
tage imposed on U.S. producers in the National Academy of
Sciences (1987) study of U.S. export controls.
"F or example, the cover page of the U.S. Department of Com­
merce release, “ Summary of U.S. Export and Import Merchan­
dise Trade” for March 1987 described the discrepancy in




costs o f reporting, esp ecia lly if the pen alties for
n on rep ortin g are small. Second, sellers have an
in cen tive to u n d errep o rt sales because, if u n d e­
tected, it redu ces th eir taxable in com e. Th ird, the
U nited States im p oses restrictions on about 40
percen t o f U.S.-manufactured m erch andise ex­
ports; to avoid outright export proh ibition s or
red u ce the h igh er costs im p o se d on foreign bu y­
ers o f U.S. m ach in ery b y such restrictions, som e
u n rep orted sales are likely.10

U.S. MERCHANDISE EXPORTS: THE
COMPARATIVE RELIABILITY OF U.S.
EXPORT DATA VS.
COUNTRY-OF-DE STIXATION
IM PO R T DATA
In principle, as illustrated in the balance o f p a y­
m ents figures 1-3, U.S. exports co u ld be m easured
b y U.S. data o r cou n tiy-of-d estin a tion im p ort data.
Yet, begin n in g in 1970, the U.S. C o m m erce D epart­
m en t has d o cu m en ted a p ersisten t u nd erstate­
m en t o f U.S. exports to Canada. R eferred to as
“ u n d ocu m en ted exports,” the extent o f this p ro b ­
lem is revealed in the annual recon ciliation o f U.S.
and Canadian trade data throu gh com parison s o f
U.S. export and Canadian im p ort data."

export reporting as follows:
The annual trade data reconciliation study with Canada (sched­
uled for release in June) indicates a substantial and growing
undercount of exports from the United States to C anada in 1986,
amounting to approximately 20 percent. This is due primarily to
the non-filing of export documents with the U.S. Customs Ser­
vice. A number of joint U .S./Canadian efforts are underway to
address this issue (informational mailings, bilateral collection of
export documents, data exchange, etc.). The annual reconcilia­
tion studies also confirm that import data are more accurate than
export data.

See also Daily Report for Executives for August 5,1987. Such
discrepancies are not unprecedented — see below, table 2 and
footnotes 21, 22, 24 and 25. More generally, smuggling is a
topic of longstanding interest to economists, both theoretically
and empirically — see Bhagwati (1974). In industrial countries,
the United Kingdom documented a pervasive period of export
understatement in the late 1960s, amounting to about 3 per­
cent of exports and, more significantly, as high as 58.2 percent
of the reported trade balance in 1966. See “ Underrecording of
Exports" (1969), p. 667. While greatly reduced from the trou­
blesome levels of the late 1960s, export underreporting in the
United Kingdom continues and is accommodated in the na­
tional income accounts by a 1 percent allowance in exports in
the CIF/FAS conversion procedure (private correspondence,
Stephen Wright, Bank of England). There is also evidence that
the Canadian export data are subject to similar lapses: During
1978-79, a refinery in New Brunswick did not file customs
reports on exports to the United States; this resulted in a $700
million understatement in petroleum products exported by ship
to the United States. See Rose (1979).

SEPTEMBER/OCTOBER 1988

14

Table 1
U.S.-Canadian Merchandise Trade, 1980-86 (billions of dollars)
Northbound Trade’
U.S.
exports
1980
1981
1982
1983
1984
1985
1986

$35.4
39.6
33.7
38.2
46.5
47.3
45.3

Southbound Trade’

U.S.-Canadian Trade Balances2

Undocumented3

Canadian
imports
(FAS)

U.S.
imports4
(FAS)

Canadian
exports

U.S.
compiled

Canadian
compiled

Reconciled

$4.9
5.0
4.2
5.1
5.3
6.0
10.2

$41.2
45.2
38.5
44.2
53.0
54.6
56.1

$41.2
45.9
45.9
51.5
65.6
68.1
67.3

$41.1
46.5
46.5
53.8
66.3
68.3
67.2

-$ 6 .1
- 6 .9
-1 2 .8
-1 3 .9
-2 0 .0
-2 1 .7
-2 2 .9

$0.2
- 1 .2
- 7 .9
- 9 .9
-1 2 .4
-1 3 .6
-1 1 .4

-$ 1 .4
-2 .8
- 9 .7
-1 1 .7
-1 5 .4
-1 5 .7
-1 3 .3

'Reported exports and imports from IMF Directions of Trade Statistics Yearbook, 1987.
2U.S.-Canadian trade balances from U.S. Bureau of Census, Department of Commerce, "Reconciliation of Canada-United States
Merchandise Trade, 1986."
Undocumented exports from U.S. Department of Commerce (1987b), table 14.
“U.S. FAS imports estimated from CIF data, adjusted using 2.0 percent CIF/FAS margin; this choice is based on a comparison of
FAS and CIF Canadian import data in the 1980s; see footnote 14.

T h e persisten t u n derstatem ent o f U.S. exports to
Canada and the resulting overstatem ent o f the U.S.
bilateral trade deficit w ith Canada in the 1980s is
sh ow n in table 1. T h e first five colu m n s in the
b o d y o f the table sh ow the n orth bou n d trade (U.S.
exports/Canadian im ports) and sou th bou nd trade
(U.S. im ports/Canadian exports) as re co rd ed by
each o f the co u n tries’ cu stom s authorities, and
th eir re co n ciled estim ate o f u n d ocu m en ted U.S.
exports. W h ile the sou th bou nd trade evinces no
substantive disparities b etw een the U.S. and Cana­
dian data, the n orth b ou n d trade data exhibit d if­
feren ces ranging from 14 p ercen t to 24 p ercen t o f
the U.S. export figures. As the u n d ocu m en ted ex­
ports colu m n shows, m ost o f this d iscrep a n cy has
been ack n ow led ged b y the U.S. authorities as an
u nderstatem ent o f exports. T h e sum o f the c o m ­
p iled and u n d ocu m en ted U.S. exports a p p ro x i­
m ate the Canadian im p ort data, in dicating that

ports results in an u nderestim ate o f the U.S. trade
balance — that is, an overstatem ent o f the trade
deficit. T h e ack n ow led ged U.S. errors — U.S. ex ­
ports — ran ged from 2 7 p ercen t to 80 percen t o f
the U .S.-com piled bilateral deficit w ith Canada
and from 4 p ercen t to 19 p ercen t o f the U.S.c o m p ile d total trade deficit w ith the w o r ld in the
1980s.12
In summary, the Canadian data are substan­
tially m ore accurate than the U.S. data as the re c­
o n ciled bilateral balance is far clo ser to the initial
Canadian balance. M o re generally, these d o cu ­
m en ted errors suggest that o th er country-ofdestin ation im p ort data m a y also offer a su perior
alternative to U.S. export data.

o f U.S. exports.

Two Problems with Using
Country-of-Destination Import Data
to Estimate U.S. Exports

T h e last three colu m n s o f the table sh o w the
bilateral trade balances du rin g the 1980s as c o m ­

T h ere are tw o basic p rob lem s w ith using
cou ntry-of-destin ation im p ort data. First, m ost

p iled b y each cou ntry a nd as re co n ciled during
conferen ces b etw een th eir respective custom s
authorities. O f course, the u nderstatem ent o f ex ­

im p ort data are re p o rted CIF (Cost + Insurance

the Canadian im p ort data are a far su perior gauge

12Computed from data in U.S. Department of Commerce
(1987b), Table 14.


FEDERAL RESERVE BANK OF ST. LOUIS


+ Freight), w h ile export data are rep orted FAS
(Free A lon gsid e Ship) — that is, not in clu d in g in-

15

surance and freight charges.11T h ese CIF im p ort
data m ust b e adju sted to approxim ate the FAS
export data.14This adjustm ent has been the sub­
ject o f som e research w ith in con clu sive results.15
Second, there is the issue o f sm uggling, esp ecially
in less-d evelo p ed o r nonindustrial countries, in
w h ic h the o m itted im ports in the cou n tiy-ofdestin ation data cou ld w e ll ex ceed the om itted
exports in the export data.16
Ch oosin g the CIF/FAS Margin. One solu tion to
the first p rob lem is sim ply to ch oose a reasonable
CIF/FAS m argin to convert CIF data to FAS data.
That is, the adjustm ent sh ou ld make sense in light
o f w h at is know n, at least anecdotally, about
freigh t and insurance charges, but sh ou ld not bias
statistical tests o f the export understatem ent
hypothesis.
T h e evid en ce suggests a true m argin fo r the
industrial countries w e ll b e lo w the 10 p ercen t
traditionally u sed b y the IM F in its Directions o f
Trade Statistics (DOTS) data on bilateral m erch a n ­
dise trade. For exam ple, the U.S. C om m erce D e­
partm ent reports that, fo r U.S. im ports, the average
CIF-FAS m argin is 5.2 percen t; the Bank o f England
estim ates 5.0 p ercen t fo r U.K. im ports; the Bank o f
N eth erlan ds estim ates a 5.6 p ercen t CIF/FAS m ar­
gin fo r D utch im ports du rin g 1980-87; and Geraci

"Another reporting valuation, FOB (Free On Board) is frequently
used as a synonym for FAS as it will be here. Strictly, FAS and
FOB differ by the amount of loading and cargo handling
charges included in the latter.
14Of the 151 IMF member countries whose bilateral trading
volumes are covered in the Directions of Trade Statistics, 15
countries report imports FAS: Australia, Bermuda, Canada,
Dominican Republic, Mexico, Papua New Guinea, Paraguay,
Peru, Poland, Romania, Solomon Islands, South Africa, Vene­
zuela, Zambia, Zimbabwe. Moreover, the IMF’s annual IFS
Yearbook reports CIF/FAS margins for each of the member
countries; however, these margins are multilateral and cannot
be used to isolate the appropriate margin on imports from the
United States.
15Since insurance and freight are services, they should not
appear in the merchandise trade account; moreover, these
services may be rendered by a domestic or a foreign seller.
Thus, they must be removed from the import data in order to
make valid comparisons. See Geraci and Prewo (1977) and
Yeats (1978).
16For an important collection of theoretical and empirical papers
on this issue, see Bhagwati (1974).
17The U.S. CIF/FAS margin was published in Daily Report for
Executives, No. 159, August 19, 1987, p.2. The U.K. margin
was obtained by telephone from Gordon Midgely of the Bank of
England and the Dutch estimate was supplied by M. van
Nieuwkerk and A.C.J. Stokman of De Nederlandsche Bank in
private correspondence.

and P rew o (1977) fou n d a 5.2 p ercen t transport
m argin fo r intra-European trade in 1970.17For the
15 cou ntries in DOTS (see fo otn ote 14) w h ic h re ­
port both FAS and CIF im p ort data, the co m p u ted
m argins fo r the 1980s range from 2.4 percen t for
Canada to 20 p ercen t fo r Peru, S olom on Islands
and Zambia.
In general, these co m p u ted CIF/FAS margins
w ere lo w e r fo r industrial than fo r n onindustrial
cou ntries and fo r cou ntries w h o se trade is p re ­
d om in a n tly w ith nearby tradin g p artners.18For
exam ple, M exico, a non indu strial country, has a
relatively lo w 4.6 p ercen t margin, w h ile Australia,
an industrial country, has a m oderate, but h igh er
10.0 p ercen t m argin. M e x ic o ’s m argin is kept lo w
by short transport lines w ith the U nited States
from w h ich it obtains nearly tw o-th irds o f its re­
po rted im ports; Au stralia’s m argin is raised b y its
relatively lo n g transport lines w ith N orth A m erica
and E u rope from w h ich it obtains m ore than h alf
its im ports.
In light o f the re p o rted estim ates and the c o m ­
pu ted CIF-FAS ratios, the em pirical tests in this
article assume that the CIF/FAS m argin fo r in du s­
trial countries is 5.2 percent, the sam e as the aver­
age co m p u ted b y the C o m m erce D epartm ent for
all U.S. im p orts.19

imports, 22.9 percent for Canadian imports and 18.3 percent
for U.S. imports; however, their estimates were obtained from
the ratio of CIF imports in country of destination to FAS exports
in country of origin. If, as we argue here, exports are under­
stated, their approximation to the CIF/FAS margin will be
biased upward. See Yeats (1978).
,9This margin also conforms with anecdotal evidence on current
U.S. shipping charges and insurance rates for both transAtlantic and trans-Pacific routes. In fact, it is actually somewhat
high relative to examples of transport and insurance rates for
ocean-shipped containers quoted in the St. Louis area in April
1988: $1400-$1600 pier-to-pier, for a 40-foot container (2680
cubic feet) Los Angeles to Yokohama, Japan. Examples of
products a 40-foot container could transport include $1 million
worth of small sporting firearms or $80,000 worth of liqueurs.
With insurance at $4 per $1000 of declared value, these exam­
ples would have CIF/FAS margins of 0.6 percent and 2.4
percent, respectively. (I am indebted to Jerry Kausch, Interna­
tional Import-Export Services, St. Louis, for these examples).
Bulk grain shipping rates, conversely, bracket the traditional 10
percent margin. From U.S. Gulf of Mexico ports to Rotterdam,
the Netherlands, large deep draft bulk carriers of up to 110,000
tons displacement charge $15/metric ton (April 1988) and
insurance of 0.15 percent of value. This implies a 4.95 percent
CIF/FAS margin for soybeans, 16.3 percent for corn and 12.2
percent for hard red winter wheat given their April 1988 prices
per metric ton, $248, $92 and $123, respectively. (I am in­
debted to John Muller of Bunge Grain Co., St. Louis, for these
examples).

18Both of these tendencies concur with the findings of Geraci and
Prewo (1977); however, their point estimates (based on 1970
OECD data) are much higher: for example, 13.8 percent for UK




SEPTEMBER/OCTOBER 1988

16

Table 2
Trade Discrepancies — Selected Areas and Country Imports from the World
Compared with World Exports to Those Areas and Countries, 1980-86
(annual averages, billions of dollars)_______________________________________
World
exports to

Imports
from the
world by1

Discrepancy

$522.4

$492.1

$30.3

95.5
11.8
12.0
7.4
18.6
6.4
7.4
27.0
11.5

80.9
8.6
9.1
9.1
13.3
1.7
6.5
24.5
16.7

14.6
3.2
2.9
- 1 .7
5.3
4.7
0.9
2.5
- 5 .2

15.3
27.1
24.2
-2 3 .0
28.5
73.4
12.2
9.3
-4 5 .2

Industrial - 202

1,240.9

1,260.6

-2 0 .7

-1 .7

Netherlands
Switzerland
Industrial-183
Industrial-174
United States

80.1
36.0
1,124.8
843.1
281.7

64.1
31.8
1,166.6
873.8
292.8

16.0
4.2
-4 1 .8
-3 0 .7
-11 .1

20.0
11.7
-3 .7
-3 .6
-3 .9

Nonindustrial-131
Western Hemisphere
Egypt
Greece
Israel
Mexico
Panama
Phillipines
Singapore
South Africa

Discrepancy as
percentage of
world exports to
5.8%

SOURCE: Data from Directions of Trade Statistics, Yearbook 1987, World exports and imports table.
'FAS imports estimated from CIF data using 10 percent CIF/FAS margin for nonindustrial countries and the IFS Yearbook CIF/FAS
margin for industrial countries (see footnote 14).
2The 20 countries classified as industrial are Australia, Austria, Belgium-Luxembourg, Canada, Denmark, Finland, France,
Germany, Iceland, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, the United Kingdom
and the United States. (Note that Belgium and Luxembourg are counted as one country.)
industrial countries less the Netherlands and Switzerland.
4lndustrial-18 less United States.

Screening f o r Valid Im p o rt Data. T h e oth er
em pirical p rob lem w ith using country-ofdestin ation im p ort data to estim ate U.S. exports is
that the im p ort data m ay not b e valid. If all co u n ­
tries' im p ort data w e re equ ally valid, then an esti­

Table 2 provid es a com parative assessm ent o f the
validity or com p leten ess o f the im p ort data o f the
nonindu strial and industrial countries.
An im partial basis fo r evaluating the validity o f a

m ate o f the w o r ld w id e U.S. export u nderstatem ent

co u n try’s im p ort data is to com pare its o w n data

cou ld be obtain ed easily from data on im ports

co m p ilin g total im p orts from all o f the cou ntries in
the w o rld w ith the sum o f the data c o m p ile d by

from the U nited States fo r all 151 cou ntries in
DOTS. T h e IM F classifies 20 o f these countries as
“ in du strial” and the others as “ non indu strial.” 20

“ The 20 countries classified as industrial by the IMF in its DOTS
are Australia, Austria, Belgium-Luxembourg, Canada, Denmark,
Finland, France, Germany, Iceland, Ireland, Italy, Japan, the
Netherlands, New Zealand, Norway, Spain, Sweden, Switzer­
land, the United Kingdom and the United States. (Note that
Belgium and Luxembourg are counted as one country.)


FEDERAL RESERVE BANK OF ST. LOUIS


the IM F o f all the in dividu al cou n tries’ exports to
that country. Since cou ntries obtain revenues from

17

tariffs and p o lice quotas on politically sensitive
im ports, a strong presu m ption exists that im port
data shou ld be m ore co m p le te — as in the U.S.Canadian case — than export data. By this postu ­
late, a country's trade data can be ju dged invalid if
its rep orted FAS im ports are less than the sum o f
w o rld exports to it. For exam ple, du rin g the 1980s,
as sh ow n in table 2, the rep orted level o f w o rld
exports to M exico ex ceed ed by 28.5 percen t the
level o f FAS im ports from the w o rld rep orted by
M exico.-' For G reece and the Phillipines, the c o r­
resp o n d in g shortfalls w ere 24.2 percen t and 12.2
percent, respectively, w h ile for Panam a it w as a
w h o p p in g 73.4 percent. For n onindustrial co u n ­
tries in the W estern H em isphere, the u nderstate­
m ent w as 15.3 percent, w h ile for all 131 n on in d u s­
trial countries, it averaged 5.8 percent. Such
u n d errep ortin g o f im ports in d evelop in g nations
has been w id e ly d o cu m en ted in the trade litera­
ture and often used as a m easure o f sm uggling
in d u ced b y tariff a vo id a n ce.-Th ese illustrations are not isolated; they reflect
gen erally the characteristics o f the nonindustrial
co u n tries’ data. A m ore system atic analysis re­
jected all but 6 o f the 131 nonindustrial cou n tries’
im p ort data.-1Given these problem s, such data are
not useful in testing the relationship b etw een U.S.
export u nderstatem ent and the U.S. SD.
A p p ly in g the same criterion to the industrial
cou n try data results in a general accep tan ce o f the
validity o f the im p ort data fo r 18 o f the 20 co u n ­

2,The full discrepancy between the U.S. and Mexican data is
further complicated by the U.S. Commerce Department’s rough
estimate that exports to Mexico are underreported by about 10
percent. (I am indebted to Gerald Kotwas, Assistant Chief
Foreign Trade Division of Census Bureau, U.S. Department of
Commerce, for this estimate.)
“ See Bhagwati (1974), especially Part III — “ Partner-Country
Data Comparisons and Faked Invoicing.” Sometimes, the
errors are positive: Probably resulting from ineffective embar­
goes, the level of imports from the world by South Africa has
exceeded acknowledged world exports by an average of 33.7
percent during the 1980s. Similarly, the level of Israeli imports
has exceeded acknowledged world exports to Israel by 22.6
percent during the 1980s.
23The general testing of the nonindustrial countries was accom­
plished using a three-part screen:

tries. O nly the data o f the N eth erlan ds and S w itz­
erland are rejected (discrepan cies statistically
significant at 1 percen t level). Excluding these tw o
cou ntries m ore than dou bles the average p ercen t­
age discrep a n cy b etw een im p orts from the w o rld
and w o rld exports to the industrial countries from
— 1.7 percen t to — 3.7 percent. T h ese tw o co u n ­
tries have a lon g tradition o f re-exp ortin g im p orted
goods, referred to as “ m erch an tin g” in the Dutch
data; re-exp orted go o d s are o m itted from their
im por t data. Consequently, w o rld exports to them
exceed their re co rd ed net im p orts by substantial
amounts, as the table shows.-4
Th e exclu sion o f re-exp orted g o o d s suggests
that som e U.S. exports m ay sim ply be u n record ed
anyw here. That is, if a U.S. sh ipm ent to the N eth er­
lands that is re-exp orted by a D utch m erchant to
France is not rep orted as a N e th erlan d s’ im port
from the U nited States, but is m easured solely as a
D utch export to France, foreign im p ort data u n ­
derstate U.S. exports. T h e om ission o f the re­
exp orted go o d s w o u ld cause the im port-based
estim ate o f U.S. exports to be understated; h o w ­
ever, it w o u ld not cause errors in the tw o co u n ­
tries’ o w n international data.2’
Given the evid en ce o f inaccurate im p ort data
illustrated in table 2, the estim ates o f the U.S. ex­
port u nderstatem ent and tests o f its h yp o th esized
relationship to the U.S. balance o f paym ents d is­
crepan cy em p lo y a data set that in clu des 17 o f the
industrial countries: o n ly the Netherlands, Switz-

24Net imports are imports less re-exported goods. The Nether­
lands, for example, does not count a landed shipment of mer­
chandise as a Dutch import if it neither a) changes title to a
Dutch resident, nor b) crosses the border (i.e. — passes
through customs). Hence, goods landed in the Netherlands
and reexported apparently have been counted by exporting
countries as an export to the Netherlands; however, according
to the Bank of the Netherlands, which compiles the Dutch trade
data, the Netherlands has not counted them as an import.
25ln principle, since the Netherlands and Switzerland report net
exports as well as net imports, the omission of U.S. exports to
any of them should be captured in their exports to other coun­
tries being similarly understated relative to the importing coun­
try’s data; that is, the sum of the two discrepancies should be
approximately zero. This offsetting does occur in the data for
Switzerland but not for the Netherlands trade data (billions of
dollars) 1980-86 averages:

(1) Availability of data on imports from the United States in each
year, 1 9 6 0 -8 6 ; (2) Substantial trade volume with the United
States (annual imports from the U.S. of at least $400 million
1 9 8 0 -8 6 ); and (3) Imports (FAS) reported from the world at least
as large as reported world exports to the country.

Only 6 of the IMF 131 nonindustrial countries passed this
screen: Indonesia, Israel, Korea, South Africa, TrinidadTobago and Venezuela. These countries accounted for only
about 20 percent of U.S. exports to nonjndustrial countries and
about 7 percent of total U.S. exports in 1986.




Discrepancy
Discrepancy
between world between world
exports and
imports and
country imports country exports
Netherlands
Switzerland

16.00
4.20

1.55
-5.05

Sum
17.55
-0.85

SEPTEMBER/OCTOBER 1988

18

Table 3
U.S. Balance of Payments Statistical Discrepancies, Observed and Adjusted,
1960-86 (billions of dollars)
1960-86
Data

Mean

Standard
error

SDHAT
SDTOT
SDAI2
SDAINC3

$7.11
9.03
3.24
5.67

$2.32
2.69
1.80
2.28

1960-74
t-test'

Mean

3.07**
3.36**
1,80
2.28*

-$ 1 .4 3
-1 .0 7
-2 .8 4
-2 .5 0

1975-86

Standard
error

t-test1

Mean

$0.64
0.58
0.75
0.69

2.25*
1.83
3.76**
3.64**

$17.78
21.64
10.85
15.88

Standard
error

t-test1

$3.05
3.44
2.63
3.13

5.82**
6.28**
4.12**
5.08**

'Test of statistical significance of mean SD; ** indicates significance at 1 percent level and * indicates significance at 5 percent level.
JSDT0T adjusted by U.S. export discrepancy with industrial countries other than the Netherlands and Switzerland.
3SDTOT adjusted by U.S. export discrepancy with industrial countries other than Canada, the Netherlands, and Switzerland.

erland and, o f course, the U nited States are o m it­
ted. A d eta iled descrip tion and listing o f the data
are con tain ed in the appen dix.

TESTS OF THE UNDERSTATED U.S.
EXPORT HYPOTHESIS
Testin g the p rop o sitio n that U.S. m erch andise
exports have been understated em ploys the d is­
crepan cy b etw een cou n tiy-of-destin ation im p ort
data and U.S. export data to determ in e h o w much,
if any, o f SDTOT can be accou n ted for by u n d er­
reportin g o f U.S. m erch an dise exports.211First, the
cou ntrv-of-destination im p ort data are used (anal­
o gou sly to the C om m erce D epartm en t’s use o f
Canadian im p ort data) to revise the U.S. balance o f
paym ents statistical discrep a n cy data; the m ean o f
the revised SD series is then tested fo r statistical
significance. Second, regression analysis is u sed to
test w h e th er the export adjustm ent variable signi­
ficantly explains the U.S. statistical discrepancy.
“ Since underreported service exports, conjectured in Heller
(1984) and documented in Stekler (1984), also form part of e in
identity 5, a portion of SDs should depend on non-merchandise
export errors.
27See the data appendix for a more detailed explanation of
SDTOT. It may appear to be possible to test the relationship
between the data on the U.S. statistical discrepancy either with
or without the Canadian errors — SDTOT and SDHAT, respec­
tively — against corresponding data on the U.S. export under­
reporting (compiled from the IMF DOTS) with or without the
Canadian component — XDI17 and XDINC, respectively. Yet,
this cannot be accomplished consistently because the corres­
ponding data are not available. SDTOT contains the U.S.
errors as compiled and, likewise, XDI17 contains the U.S.country-of-destination discrepancies as compiled; however, the
adjustment RAUSCA to obtain SDHAT from SDTOT in identity
6 removes less than the total U.S.-Canadian export discrep­
ancy but also deletes some import discrepancies. This distinc­
tion can be seen in table 1 by comparing the column of undoc­
umented U.S. exports against the difference between the U.S.


FEDERAL RESERVE BANK OF ST. LOUIS


The Adjusted U.S. Balance o f
Payments Statistical Discrepancy
T h e U.S. balance o f paym en ts statistical d isc rep ­
ancy, as re p orted in the U.S. balance o f paym ents
data, SD, is net o f the U.S.-Canadian trade d iscrep ­
ancy. T h e inclusive m easure o f the d iscrepan cy is
the a ppropriate form to test its relationship to
export u nderreporting, since n eith er U.S. data
are adju sted n o r is any cou n try e x clu d ed a p r i o r i
on the basis o f an assum ed relationship.
Therefore, w e use SDTOT, the inclusive m easure
as in chart 1,
(6) SDTOT, = SDHAT, - RAUSCA,,
w h e re RAUSCA, is the re co n ciled adju stm ent to
the U.S.-Canadian m erch an dise trade balance.27 In
o th er w ords, SDTOT, is the statistical d iscrepan cy
that w o u ld exist if U.S. m erch an dise trade w ith
Canada had b een co m p iled , unadjusted, in the

and the reconciled bilateral trade balance. In each year,
RAUSCA, the difference between the U.S. compiled and the
reconciled trade balance, is a smaller adjustment than the
undocumented exports. Moreover, as can also be seen in the
table, the undocumented exports agreed upon between the two
countries’ customs authorities do not incorporate the year’s full
difference between the U.S. and the Canadian measures of
northbound trade as obtained from the IMF DOTS. Conse­
quently, RAUSCA adjusts the statistical discrepancy in a fash­
ion that does not correspond with deleting the DOTS Canadian
export discrepancy from the total 17-country DOTS U.S. export
discrepancy. While the agreed-upon changes predominantly
reflect northbound trade statistics, southbound trade (U.S.
imports) data are also affected. Data separating RAUSCA into
northbound and southbound changes are not available. None­
theless, there is a high correlation between RAUSCA and the
bilateral U.S.-Canadian export discrepancy from DOTS during
1970-86; .943; moreover, a regression of SDTOT on XDINC,
reported in table 4, has results similar to the regressions based
on equation 7.

19

Chart 2
U.S. Balance of Payments Statistical Discrepancies,
Total and Adjusted

1960

62

64

66

68

70

72

74

76

78

80

82

84

1986

NOTE: The adjusted statistical descrepancies are SDTOT less the estimated U.S. export discrepancy:
SDAI is adjusted by the 17-country discrepancy; SDAINC is equal to SDAI with Canada omitted.

sam e fashion as m erch an dise trade w ith o th er
countries.
Using the d iscrep a n cy in the U.S. exports to the
industrial co u n tries’ (less the N eth erlan ds and
Sw itzerland) XDI17,, an adju sted statistical dis­
crepancy, SDAI,, w as com p u ted :

SDAI, = SDTOT, - XDI17,.

SDAI and SDAINC are d isp layed in table 3 fo r the
full p eriod 1960-86 and fo r the tw o subperiods,
before and after 1975.
T h e re p o rted d iscrep a n cy in the balance o f p a y­
ments, SDHAT, averaged about $7 b illion w h ile
SD TO T averaged about $9 billion du rin g the 196086 period, both statistically significant; h ow ever,
each w as com paratively sm all and negative du rin g
1960-74 and large and positive du rin g 1975-86.
T h e industrial cou n try a dju sted SDs, SDAI and

See the a p p en d ix fo r details. T o assess the p ossi­
bility that o n ly the U.S.-Canadian export d isc rep ­
ancy is m ean in gfu l in the analysis o f SDTOT, a d ­
ju sted SDs both w ith and w ith ou t the Canadian

SDAINC, are sm aller but still substantial and sta­
tistically significant in both subperiods. As chart 2
shows, the industrial cou n try d iscrep a n cy (XDI17)

d iscrep a n cy — SDAI and SDAINC, respectively, —

accounts fo r about h a lf o f the total discrepan cy
since 1975. Chart 2 also show s that the non-

are co m p u ted and rep orted in table 3. T h e m ean
and standard errors o f m eans fo r SDHAT, SDTOT,

Canadian co m p o n en t o f the exp ort d iscrep a n cy is
large and persistent.




SEPTEMBER/OCTOBER 1988

20

Table 4
Regression Analyses of Total Statistical Discrepancy’s Relation to Industrial
Countries Export Discrepancy
Estimated Coefficients1

Specification
i
ii
iii
iv

V5

vi6

Intercept
(a)
-4 .7 8
(2.85)**
-4 .6 8
(2.78)**
-1 .4 1
(0.74)
-0 .6 2
(0.30)

Dummy
(b)

4.32
(0.98)

-4 .6 1
(0.91)

-1 .3 2
(1.13)
0.20
(0.07)

Export
discrepancy
slope
(c)

Summary Statistics
Export
discrepancy
dummy
(d)

2.39
(11.10)**
2.04
(4.88)**
0.01
(0.02)
-0 .2 5
(0.27)

2.16
(2.83)**
2.74
(2.74)*

-0 .0 7
(0.13)
-0 .7 7
(0.46)

2.24
(4.62)**
4.45
(3.18)**

Hypotheses Tests2

R2

DW

P

Specification
F-test

Slope
coefficients
«1.0*
t-test

.82

2.42

- .2 2

N/A

6.46**

.82

2.41

- .2 2

ii vs. i:

0.96

2.48*

.86

3.05

-.5 3

iii vs. i:

7.99**

5.72**

.86

3.18

- .5 9

.91

—

iv vs. i: 4.38*
iv vs. ii: 7.52*
iv vs. iii: 0.82
N/A

.77

2.13

—

- .1 9

N/A

3.67**

9.36**
5.01**

'The letters under the coefficient-column headings refer to the coefficients in equation 6; absolute value of t-statistics appear in
parentheses beneath estimated coefficients; * indicates significance at 5 percent level and ** indicates significance at 1 percent
level.
^Indicates rejection at 5 percent level; ** indicates rejection at 1 percent level.
3Test of null hypothesis that added variables in unrestricted specification are zero.
“One-tail test of null hypothesis that slope coefficient is less than or equal to 1.0. In i and ii, the test reported is for full period; in iii-vi,
the test reported is for slope coefficient (c + d) for period 1975-86.
Specification v is specification iii with corrected for serial correlated residuals, AUTOREG procedure in SAS.
Specification vi is specification iii with the U.S.-Canadian export discrepancy removed from the independent variable; see footnote
25.

Regression Analysis o f the Relation
Between SD and XD
T h e m ean SDs re p o rted in table 3 fo r each subp e rio d are each statistically significant, and the
industrial country-based adjustm ent fails to
redu ce SDTOT to a level in sign ifican tly different
from zero. Consequently, the n on -zero m eans o f
the adju sted SDs im p ly that o th er errors remain,
in clu d in g u n d errep o rted service exports not in ­
clu d ed in the DOTS m erch andise trade data as
w e ll as u n rep o rted m erch andise exports to co u n ­
tries not in clu d ed in XDU7. Thus, it is still u nclear
that the U.S. m erch an dise export discrep a n cy is
substantively related to the SDTOT. A direct w a y to
test this hypothesis can be in ferred from iden tity 5.

coefficien t if each o f three con d ition s are met:
1. the discrepancy is due entirely to CAB errors, e;
2. these errors arise totally from merchandise
trade export omissions; and
3. U.S. errors in reported exports to nonindustrial
and the three omitted industrial countries are
negligible.
A llo w in g fo r shifts in this relationship b etw een the
tw o subperiods, 1960-74 and 1975-86, w e have
(7) SDTOT, =

a + bX, + c XDI17, + d\, XDI17, +
in,*

0, t < 1975

1

1, t 5* 1975.

Equation 7 provid es three tests o f the relation o f
Id en tity 5 im p lies that a regression o f SD TO T on
XDI17 sh ou ld have an in tercept not significantly

SD TO T to XD. First, it perm its tests o f the re le­
vance o f the U.S.-industrial cou n try export d is­

differen t from z e ro and a positive, unitary slope

crepan cy in the significance o f the coefficien ts c


FEDERAL RESERVE BANK OF ST. LOUIS


21

and d oil XDI17: If u n reported LJ.S. exports o f m er­
ch andise to industrial countries have been the sole
source o f SDTOT, c shou ld be statistically signi­
ficant and not significantly d ifferent from unity. On
the o th er hand, if eith er u n reported LJ.S. service
exports o r m erch andise exports to cou ntries not
in clu ded in XDI17 also matter, then c (or c + d)
shou ld be significantly larger than unitv. If XIJ117 is
irrelevant to SDTOT, n either c n or d w ill be signi­
ficantly differen t from zero. Second, equ ation 7 p er­
mits testing fo r the differen ces in the tw o su b p e­
riods by m eans o f the du m m y variable \. Third, it
p erm its a test o f om itted variables’ relevance in the
significance test o f the intercept: If the in tercep t is
not significantly different from zero, then eith er
o m itted variables are h igh ly correlated w ith XDU7
o r they have zero means. Th e results o f the regres­
sion estim ates and these specification tests are
rep orted in table 4.
T h e estim ates o f specification s (i) — (iv) test the
relevance o f the su bperiod du m m y A.. T h e F-tests
fo r the three specifications w ith in tercep t o r slope
du m m ies (ii, iii, iv) against the null h ypothesis o f no
du m m ies (i) indicate that (iii), the specification w ith
the slope dum m y, rejects the null h ypothesis and is
n ot rejected b y the specification w ith both slope
and in tercep t du m m ies (iv). Uniform ly, how ever,
the strong form o f the h ypothesis — that is, o n ly the
17 industrial cou ntry m erch andise exports are re le­
vant and, consequently, that the coefficien t on
XDI17 is 1.0 — is rejected by the t-test in the last
colu m n o f the table.
T w o additional specifications, v and vi, are also
rep orted in table 4. Th e specification tests require
the use o f the sam e data in the alternative specifica­
tions i, ii, iii, iv. Yet, th eir D urbin-W atson statistics
in dicate that specifications iii and iv have negatively
serially correlated residuals. Since this biases the
estim ated standard errors o f their coefficients, a
c o rrected estim ate o f the preferred specification iii,
d esign ated as specification v, is also rep orted in
table 4. A com parison o f v w ith iii show s only
n egligible differences. Finally, specification vi is a
regression o f SDTO T on the non-C anadian export
discrepancy, XDI17NC. Th e significance o f the esti­
m ated coefficien t d refutes

“ Regression tests parallel to those reported in table 4 were also
run on a sample including the selected nonindustrial countries
described in footnote 23. Tests of the explanatory power of the
nonindustrial countries against the null specifications omitting
them established that the sample of nonindustrial countries did
not add explanatory power to specifications restricted to indus­
trial countries.




the con ten tion that on ly the Canadian export d is­
crepan cy is related to SDTOT.
T h ese test results dem on strate that the U.S. ex ­
port d iscrep a n cy w ith the industrial cou ntries has
a statistically significant relation w ith the balance o f
paym ents discrepan cy; that is, the claim that U.S.
m erch andise export u n d errep o rtin g is a cause o f
the statistical d iscrep a n cy is not rejected. T h e in ­
dustrial cou ntry m erch andise export d iscrepan cy
is not the w h o le s to iy since the c oefficien t is greater
than unity; how ever, the DOTS nonindu strial data
are o f no avail in explain in g it.28 C onsistent w ith the
IM F study fin din gs (see pp. 10-11), the leadin g
can didate fo r addition to the m o d el seem s to be U.S.
service exports.2'1
Finally, the coefficien ts on n eith er the intercept
n or its du m m y variable are significantly different
from zero in the preferred specification s (iii, v, vi).
This suggests that if any variables have been o m it­
ted — for exam ple, service exports — th ey are
eith er h igh ly correlated w ith the U.S.-industrial
countries' m erch an dise export discrep a n cy or have
a m ean o f zero.

CONCLUSION
U.S. m erch an dise exports have been u n d er­
rep orted d u rin g 1960-86, p rim arily du rin g 1975-86.
This u n d erreportin g, m easu red by cou ntry-ofdestination m erch an dise im ports from the U nited
States, parallels the export d iscrep a n cy d o c u ­
m en ted by the U.S. C om m erce D epartm en t fo r U.S.
exports to Canada since 1970. A n estim ated export
correction based on industrial co u n tries’ im ports
from the U nited States re d u ced the statistically
significant U.S. balance o f paym en ts d iscrepan cy
from $9 billion to $3.2 billion fo r 1960-86 and from
$21.6 billion to $10.9 billion fo r the 1975-86 su bpe­
riod. M oreover, regression tests o f the industrialcou n try im p ort-b ased adjustm ent explain m ost o f
the variation in SD TO T du rin g the last 12 years.
Th ese results in dicate that U.S. exports o f m erch an ­
dise and services have been larger than rep orted
and, consequently, that U.S. m erch an dise and cu r­
rent accou nt deficits have been sm aller than re­
p o rted since the mid-1970s.

^See also Heller (1984) and Stekler (1984).

SEPTEMBER/OCTOBER 1988

22

REFERENCES
Amuzegar, Jahangir. “The U.S. External Debt in Perspective,’’
Finance and Development (June 1988), pp. 18-19.
Bhagwati, Jagdish N., ed. Illegal Transactions in International
Trade, Theory and Measurement, (North-Holland Publishing
Company, 1974).
Caves, Richard E., and Ronald W. Jones. World Trade and
Payments, An Introduction, 3d ed. (Little, Brown and Com­
pany, 1981).
Chrystal, K. Alec, and Geoffrey E. Wood. “Are Trade Deficits a
Problem?” this Review (January/February 1988), pp. 3-11.
Daily Report for Executives. “ Trade Balance: FAS/Customs
Monthly Trade Gap Widened to $14.1 billion in June, Com­
merce Says,” No. 159, August 19, 1987, pp. N5-N7.
Daily Report for Executives. “ Trade Balance: Commerce De­
partment Ready to Upgrade Monthly Reports on U.S. Trade
Deficit, Official Says,” No. 149, August 5, 1987, pp. L2-L3.
Geraci, Vincent J., and Wilfried Prewo. “ Bilateral Trade Flows
and Transport Costs," Review of Economics and Statistics
(February 1977), pp. 67-74.
Heller, H. Robert. Statement of H. Robert Heller, Vice Presi­
dent for International Economics, Bank of America N.T. &
S.A., in The Foreign Trade Dilemma: Fact and Fiction, Hearing
before the Joint Economic Committee, 98 Cong. Sess. (GPO,
1984), pp. 48-70.

Laney, Leroy O. “The Case of the World’s Missing Money,"
Economic Review, Federal Reserve Bank of Dallas, (January
1986), pp. 1-9.
National Academy of Sciences. Balancing the National Interest,
U.S. National Security Export Controls and Global Economic
Competition, (National Academy Press, 1987).
Patinkin, Don. Money, Interest and Prices, 2d ed.
Row, 1965).

(Harper &

Pluckhahn, Charles W. “ Measurement Errors Could Distort
Trade Gap Figures, Economist Says,” Investor's Daily Janu­
ary 18, 1988.
Rose, Frederick. "Error in Canada Report of Trade Surplus
Draws Fire From Economists, Politicians,” Wall Street Journal,
November 26, 1979.
Stekler, Lois. “The Statistical Discrepancy in the U.S. Interna­
tional Transactions Accounts,” Board of Governors of the
Federal Reserve System, Mimeo, October 17, 1983.
----------------“The Statistical Discrepancy in the U.S. Interna­
tional Accounts: Are We Missing Interest Income Receipts?’’
Board of Governors of the Federal Reserve System, Mimeo,
1984.
“ Under-recording of Exports,” Board of Trade Journal [United
Kingdom] September 10, 1969, pp. 665-67.

Hooper, Peter and John Morton. “ Fluctuations in the Dollar: A
Model of Nominal and Real Exchange Rate Determination,”
Journal of International Money and Finance, (April 1982), pp.
39-56.

U.S. Department of Commerce, “ United States Foreign Trade:
Summary of U.S. Exports and Import Merchandise Trade,”
Release No. FT900-87-03, March, 1987a.

International Monetary Fund, Report on the World Current
Account Discrepancy, September 1987.

“ United States Foreign Trade: Summary of U.S. Exports and
Import Merchandise Trade,” Release No. FT900-87-09,
September 1987b.

Internal Revenue Service. “ Estimates of Income Unreported
on Individual Income Tax Returns,” Department of the Trea­
sury, Publication 1104, September, 1979.

Veil, Erwin. “The World Current Account Discrepancy,” OECD
Occasional Studies (June 1982), pp. 46-63.

Krugman, Paul R., and Maurice Obstfeld. International Eco­
nomics, Theory and Policy, (Scott, Foresman/Little, Brown
College Division, 1988).

Yeats, Alexander J. “ On the Accuracy of Partner Country
Trade Statistics,” Oxford Bulletin of Economics and Statistics
(November 1978), pp. 341-61.

Appendix
Data Sources for the U.S. Export Discrepancy and the
U.S. Balance of Payments Statistical Discrepancy

p iled from the IM F D irection s o f Trad e Statistics

States. T h e estim ated U.S. export discrep a n cy for
the 17-country sam ple o f industrial countries,

tape and the U.S. balance o f paym en ts statistical

XDI17, w as obtain ed as follow s:

T h e bilateral im p ort and export data w ere c o m ­

discrep a n cy w as obtain ed from International Fi­
nancial Statistics tape.
T h e U.S. export d iscrepan cy w as estim ated us­
ing 17 industrial countries — the 20 countries
classified as industrial by the IM F less the N eth er­
lands, S w itzerlan d and, o f course, the U nited

http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis

17
XDI17, =

2 (MUSt)/1.052) -X U S tj,
j= l

23

w h ere
MUSti = CIF im p orts o f cou n try j from the
U nited States in y e a r t.
XUSt| = FAS exports o f the U nited States to
cou n try j in y e a r t.
T h e in clu d ed countries in XDI17 are: Australia,
Austria, Belgium -Luxem bourg, Canada, Denmark,
Finland, France, Germany, Iceland, Ireland, Italy,
Japan, N e w Zealand, Norw ay, Spain, Sw eden and
the U nited K in gdom .
T h e U.S. balance o f paym ents statistical d isc rep ­
ancy, SD,, w as obtain ed from the IFS tape o f the
IM F. Since the re co n ciled adjustm ent to the bilat­
eral U.S.-Canadian m erch andise trade balance is
rem oved from the data (1970-86), the annual U.S.Canadian recon ciliation , RAUSCA,, is subtracted
from the rep orted SD, SDHAT,, to get SDTOT,. That
is, from id en tity 4,
SDHAT, = - [CAB, + k A b ,] + RAUSCA,,
so that
SDTOT, = SDHAT, - RAUSCA,.
RAUSCA, w as obtain ed from U.S. D epartm ent o f
C om m erce (1987b), table 14. P rior to 1970, RAUSCA,
is zero, so SDHAT, and SDTOT, are equal.




Source Data and Constructs
(billions of dollars)
Year

USCAB

SDHAT

SDTOT

XDI17

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986

$2.82
3.82
3.38
4.40
6.82
5.41
3.03
2.59
0.59
0.42
2.33
-1 .4 5
-5 .7 8
7.07
1.92
18.13
4.17
-1 4 .4 9
-1 5 .4 5
-0 .9 7
1.84
6.87
-8 .6 4
-4 6 .2 8
-1 0 7 .0 9
-1 1 6 .4 3
-1 4 1 .4 6

-$ 1 .0 2
-1 .0 0
-1 .1 1
-0 .3 6
-0 .9 1
-0 .4 2
0.63
-0 .2 2
0.46
-1 .4 6
-0 .1 7
-9 .7 6
-1 .9 5
-2 .6 0
-1 .5 2
5.88
10.53
-2 .0 5
12.59
25.45
25.01
19.96
36.12
11.18
26.81
17.87
24.06

-$ 1 .0 2
-1 .0 0
-1 .1 1
-0 .3 6
-0 .9 1
-0 .4 2
0.63
-0 .2 2
0.46
-1 .4 6
0.43
-8 .8 6
-0 .9 5
-1 .2 0
- 0 .0 2
7.58
11.93
- 0 .0 5
15.09
29.85
29.71
24.06
39.22
13.38
31.41
23.87
33.66

$0.5422
1.0101
1.3890
0.1014
0.2590
0.5876
0.5828
0.7807
1.7465
2.0261
2.3949
2.7078
2.8999
4.1984
5.3438
4.9660
5.6111
5.8041
7.9439
11.5811
16.5480
12.2240
12.9268
12.0168
11.1532
13.3568
15.4334

XDI17NC'
$0.5851
0.9723
1.4175
0.2399
0.3888
0.6523
0.6600
0.5358
1.4384
1.6202
2.0144
2.2254
2.2613
2.7936
3.6280
3.6362
3.5931
5.5742
3.4205
6.0699
10.7420
6.5639
8.1274
6.0545
4.6521
5.9909
4.6719

1XDI17-XDCANADA

SEPTEMBER/OCTOBER 1988

24

Cletus C. Coughlin and Thomas B. Mandelbaum
Cletus C. Coughlin is a senior economist and Thomas B. Mandel­
baum is an economist at the Federal Reserve Bank of St. Louis.
Thomas A. Pollmann provided research assistance.

Why Have State Per Capita
Incomes Diverged Recently?
J . ROM the early 1930s to the late 1970s, differences in p er capita in com e across states n arrow ed
substantially. By 1978, for exam ple, on e m easure o f
state p e r capita in com e in equality h ad fallen to
less than o n e-th ird o f its 1932 value. Since 1978,
h ow ever, this tren d tow a rd greater in com e equ al­
ity across states has been sharply reversed; by
1987, state p e r capita in com e in equ ality h ad risen
back to its 1966 level.
Historically, disparate regional in com e grow th
has g en erated political pressures to alter federal
policies. For exam ple, faster in com e grow th in the
South and W est relative to the Northeast and M id ­
w est in the 1970s led to charges that these differ­
ential grow th rates w ere due, in part, to the distri­
bu tion o f federal govern m en t exp en d itu res.1Yet,
the Sun Belt-Frost Belt controversy arose du rin g a
p erio d in w h ic h state p er capita in com e grow th
w as converging. Pressures fo r in creased federal
action in the realm s o f farm policy, trade p o licy
and industrial targeting are even m o re likely to

1For example, see “The Second War Between the States”
(1977) and “ Federal Spending: The Northeast's Loss is the
Sunbelt’s Gain” (1976).
d iffe re n t views of the appropriate federal role can be found in
Reich (1988) and Weinstein and Gross (1988).
3The reversal of the income inequality trend was confirmed
statistically by regressing state per capita income inequality on
time. To allow for the possibility of a structural break in 1978, a
piecewise linear regression model was estimated. The results,
based on conventional hypotheses tests, indicated a negative
relationship between inequality and time until 1978 and a
positive relationship thereafter.


FEDERAL RESERVE BANK OF ST. LOUIS


appear because o f the in creasin g in com e diver­
gen ce across states in the 1980s.This study pursues tw o objectives. First, it id e n ­
tifies the specific states responsib le fo r the in ­
creasing in equality o f state p e r capita incom e.
Second, it exam ines w h e th er w ell-k n ow n d es crip ­
tions o f regional g row th and m a jor eco n om ic
changes can explain this n e w p h en om en on .

INCREASING INEQUALITY — WHICH
STATES ARE DIVERGING?
T h e recen t sharp reversal o f the 45-year trend
tow ard lesser state p e r capita in com e in equ ality is
sh ow n in chart l . 3 T h e m easure o f in com e in eq u a l­
ity across states used in the chart is the annual
coefficient o f variation o f state p er capita in com e;
its p recise calcu lation is d eta iled o n page 28. In ­
co m e in equality across states gen erally d eclin ed
from 1932 to 1978; since then, it has risen g ra d u ­

25

Chart 1
Inequality of State Per Capita Income
Percent

ally, but consistently. By 1987, it had clim b ed back
to its mid-1960s levels.4
Differential in com e g row th across states has tw o
o p p o sin g effects on state p er capita in com e in ­
equ ality m easures. In co m e in equ ality is red u ced
w h e n states w h o se p e r capita in com es e x ceed (are
less than) the average fo r all states exp erien ce
s lo w er (faster) than average grow th in in com e.
S im ilarly in com e in equ ality rises w h e n states
w h o se p er capita in com es ex ceed (are less than)
the average fo r all states ex p erien ce faster (slow er)
than average in com e grow th . T h e net effect on
in com e in equality d ep en d s on w h ic h o f these tw o

Percent

possible gro w th patterns p redom in ate. As chart 1
indicates, the fo rm er pattern p red o m in a ted until
the en d o f the 1970s, but the latter result has o c ­
cu rred since then.
Table 1 iden tifies the im pact o f each state on
in com e in equ ality since 1978. T h e analysis in this
table, and throu ghou t the article, focuses o n the
state’s relative p e r capita in com e — the state’s p er
capita in com e expressed as a p ercen t o f the p er
capita in com e o f all (continental) states. For exam ­
ple, if M ississippi's p e r capita in com e in 1978 w as
three-fourths o f the average p e r capita in com e o f
all states fo r that year, its relative p e r capita in ­

"Personal income consists of labor and proprietor income,
dividends, interest, rent and transfer payments. Transfer pay­
ments differ from the other components in that they are not
derived from current economic activity. The interstate inequality
of per capita income minus transfers followed similar trends as
the inequality of total per capita income; the coefficient of
variation of non-transfer per capita income for the 48 states
trended downward from 23.3 percent in 1946 to a minimum of
13.8 percent in 1976, then rose to 19.1 percent by 1987.




SEPTEMBER/OCTOBER 1988

26

Table 1
Classification of States Based on Per Capita Income Levels and
Changes
State Per Capita
Income as a Percent
of State Average

Upwardly Divergent1
Connecticut
Massachusetts
New Jersey
New Hampshire
New York
Virginia
Maryland
Rhode Island
Delaware
Florida
Downwardly Divergent2
Idaho
Montana
Louisiana
Utah
North Dakota
West Virginia
Oklahoma
Indiana
New Mexico
Texas
Upwardly Convergent3
Georgia
Maine
Vermont
North Carolina
Downwardly Convergent4
Wyoming
Nevada
Oregon
Iowa
Michigan
Washington

1978

1987

123%
109
119
100
113
101
113
98
108
101

146%
131
139
119
125
113
123
107
113
106

Percentage Point
Change 1978-87

23
22
20
19
12
12
10
9
5
5

93
96
88
87
99
84
94
102
87
102

82
85
79
78
91
76
87
96
81
96

89
86
90
86

98
95
98
91

9
9
8
5

117
124
107
107
113
114

89
111
96
99
106
107

-2 8
-1 3
-1 1
-8
-7
-7

com e fo r 1978 w o u ld equal 75 percen t. A state is
ju d ge d to have h ad an im p act on in com e in equ al­
ity if its relative p er capita in com e ch an ged by 5
p ercen tage points or m ore b etw een 1978 and 1987.
T h e in com e changes o f 20 states ten d ed to in ­
crease inequality. T en states w ith above-average
p er capita in com e in 1978 — C onnecticut, Massa­

-1 1
-1 1
-9
-9
-8
-8
-7
-6
-6
-6

Idaho, M ontana, Louisiana, Utah, N orth Dakota,
W est Virginia, Oklahom a, Indiana, N e w M exico
and Texas — that ex p erien ced substantially
slo w er than the average grow th . W e call these
states “ d o w n w a rd ly divergent.”

W e have also id en tified 10 states w h o se in com e

chusetts, N e w Jersey, N e w H am pshire, N e w York,
Virginia, M aryland, R h od e Island, D elaw are and
F lorid a — e x p erien ced substantially faster grow th

changes have ten d ed to red u ce inequality. Four o f
th em — Georgia, M aine, V erm ont and N o rth Caro­

b etw een 1978 and 1987 than the average. W e call
these states "u p w a rd ly d ivergent.” T h ere w ere 10
states w ith below -average p e r capita in com e —

b e lo w the average across states in 1978, but w h o
have grow n faster than this average since then.
Th ese states are called “ u p w a rd ly convergent.”


FEDERAL RESERVE BANK OF ST. LOUIS


lina — w e re states w h o se p e r capita in com es w ere

27

Table 1 cont’d.
No Substantial Change5
Illinois
Ohio
South Dakota
Kentucky
Mississippi
Nebraska
Arkansas
Wisconsin
Kansas
Pennsylvania
Alabama
Colorado
Missouri
Arizona
California
South Carolina
Tennessee
Minnesota

118
105
91
86
74
103
81
104
105
105
82
109
100
95
121
80
86
106

114
101
87
83
71
100
79
102
104
104
82
110
101
97
123
82
88
110

-4
-4
-4
-3
-3
-3
-2
-2
-1
-1
0
1
1
2
2
2
2
4

’States with above-average per capita income in 1978 and with a 5 or more percentage-point in­
crease in per capita income as a percent of the state average. For Rhode Island, a state with
below-average per capita income in 1978 and above-average per capita income in 1987, the rise in
relative income resulted in the state's income absolutely further from the average in 1987 than in
1978.
2States with below-average per capita income in 1978 and with a 5 or more percentage-point drop
between 1978 and 1987 in state per capita income as a percent of state average. For Indiana and
Texas, states with above-average income in 1978 and below-average income in 1987, the drops
resulted in the states’ being absolutely further from average per capita income in 1987 than in
1978.
3States with below-average per capita income in 1978 and with a 5 or more percentage-point in­
crease between 1978 and 1987 in state per capita income as a percent of the state average.
“States with above-average per capita income in 1978 and with a 5 or more percentage-point de­
cline between 1978 and 1987 in state per capita income as a percent of the state average. For
Wyoming, Oregon and Iowa, states with above-average per capita income in 1978 and belowaverage per capita income in 1987, the drop resulted in per capita income closer to the state aver­
age in 1987 than in 1978.
5States whose absolute percentage-point change in per capita income as a percent of the states
was less than 5 percent between 1978 and 1987.

Six states — W yom ing, Nevada, Oregon, Iowa,
M ich igan and W ashin gton — w ere “ d o w n w a rd ly
con vergen t.” Th ese states, w h o se p e r capita in ­
com es ex ce e d e d the average across states in 1978,
but w h o have gro w n slo w er than this average, also
contribu ted to red u ced inequality. O f all the
states, W yo m in g is the hardest to categorize. Be­
tw een 1978 and 1987, it ex p erien ced the largest
percen tage p oin t d eclin e in relative p er capita
in com e o f the 48 states. This 28-point declin e
d ro p p e d W yo m in g from an above-average in com e
level in 1978 to b elow -average b y 1987. I f the analy­
sis had focu sed on changes from 1984 to 1987,
W yo m in g w o u ld have been labeled as d o w n w a rd ly
divergent rather than d o w n w a rd ly convergent.
Finally, 18 states had relative p e r capita in com es
that ch anged less than 5 p ercen tage points b e­




tw een 1978 and 1987. Th ese states had little im ­
pact on the recent changes in inequality.
T o p rovid e a geogra p h ic o verview o f the results
p resen ted in table 1, a m ap is presen ted. As the
m ap reveals, states exp erien cin g relatively rapid
p er capita in com e grow th are, w ith ou t exception,
Atlantic Coast states. Since these states ten d to
have p er capita in com es above the average across
states, their rapid grow th tends to contribu te to
in creasin g inequality. On the o th er hand, states
ex p erien cin g relatively s lo w p e r capita in com e
grow th are scattered across the rem a in d er o f the
contin en tal U nited States. Th e fo llo w in g analysis
exam ines som e o f the p op u la r description s o f
regional grow th and som e m a jor eco n om ic
changes to see if they can explain this rising in ­
equality.

SEPTEMBER/OCTOBER 1988

28

Measuring Income Inequality
T h e m easure o f in com e in equality used in
this article is the coefficien t o f variation o f an­
nual state p e r capita in com es across the 48
contin en tal states (INEQ).' T h e coefficien t o f
variation is the standard de\iation o f a series
d ivid ed by its mean. For each year, IN EQ m ea­
sures the degree o f dispersion o f state p er ca p ­
ita in com es about the m ean state p er capita
in com e (M EAN). W ith each state w eigh ted
equally, M EAN is calcu lated as follow s:
48
M EAN = 1 SPCIt / 48,
i= 1
w h ere i = subscript den o tin g the individual
states and SPCI = state p er capita in com e.
Thus, the IN EQ is calcu lated as follow s:
48
IN E Q = [{ 2 (SPCI, - M E A N )2/ 47 H
i= 1

/MEAN,

A larger value o f IN E Q indicates greater varia­
tion b etw een state p e r capita in com es and,
thus, greater inequality.2 If p e r capita in com e
rose (fell) in a state w ith below -average p er c a p ­

'Data for the continental, rather than the entire, United
States are used because no consistent income series is
available for Hawaii or Alaska for the postwar period.
2Because state income data do not correct for cost-of-living
differences among states, the inequality measure may not
accurately reflect the real variations in per capita income
levels among states. No reliable state cost-of-living data
exist to make such adjustments. A related issue is interstate
differences in price changes over time. If states with aboveaverage per capita income in 1978 experienced substan­
tially higher inflation between 1978 and 1987 than lowincome states, the rise in inequality could be due to these
differences with no change in the inflation-adjusted distribu­
tion of per capita income. Price deflators for individual
states are unavailable: however, regional deflators show
little difference in inflation between 1978 and 1987. Using a
December 1977 base, the consumer price index (for all
urban consumers) for November 1987 was 186.2 for the

ita in com e o r d ec lin ed (rose) in a high p ci-ca p ­
ita in com e state, o th er things equal, INEQ
w ou ld d ec lin e (increase)/1
Unlike the standard deviation, the coefficient
o f variation used in co m p u tin g INEQ reflects
dispersion relative to the m ean and can be used
to com p a re the d eg ree o f in equ ality in different
years w ith differin g m eans. For exam ple, if per
capita in com e in each state d o u b led b etw een
1970 and 1980, the standard deviation fo r 1980
w ou ld be tw ice that o f 1970. T h e coefficien t o f
variation, how ever, w o u ld s h o w n o change
since it is stan d ardized by the m ean p e r capita
incom e.
For the coefficien t o f variation to be an u nbi­
ased m easure o f inequality, the u n d erlyin g data
must be n orm ally distributed.4 Using the
Shapiro-W ilk (1965) statistic, the state p er capita
in com e series w as tested fo r n orm ality for each
year. T h e null hypothesis, that the state p er
capita in com e data are a ran dom sam ple from a
norm al distribution, co u ld not be rejected at
the 5 percen t level fo r any years in the p ostw ar
period.

Northeast, 184.7 for the North Central Region, 185.1 for the
South and 187.4 for the West.
3A related measure of income inequality, the standard devia­
tion of the ratio of regional to national per capita income
was used in Browne (1980) and Ray and Rittenoure (1987).
The simple correlation between INEQ and the standard
deviation of the ratio of state to national per capita income
was 0.999 in the 1948-87 period. Williamson (1965) p. 11,
also used a related inequality measure: a populationweighted coefficient of variation of per capita income; the
measure is computed identically to INEQ except each
region's squared deviation from the mean is multiplied by its
share of the national population. For the 1946-87 period, a
correlation of 0.985 was found between INEQ and a
population-weighted coefficient of variation using state per
capita income.
4See Yotopoulos and Nugent (1976), pp. 242-43.

THE SHIFT TO THE SUN BELT

en ed in equality du rin g the 1970s. Businesses, par­
ticularly m anufacturing, m igrated to the Sun Belt

T h e shift o f industrial activity from the n a tio n ’s
Frost Belt to the Sun Belt contribu ted to the less­

from the Frost Belt fo r various reasons, in clu d in g
lo w e r w a ge rates.5 Since m anufacturing w ages are

5See Crandall (1986), pp. 124-27, for a brief survey of empirical
research documenting and explaining manufacturing’s shift to
the Sun Belt.


FEDERAL RESERVE BANK OF ST. LOUIS


29

States Classified by 1978-87 Per Capita
Income Change

Upwardly Convergent

I

I Downwardly Convergent

Upwardly Divergent

I

I Downwardly Divergent

w ell above the average w age o f all industries in all
regions o f the nation, this shift o f labor d em an d
from h igh er-w age to lo w er-w a ge states p ro d u ce d
h igh er relative grow th in per capita in com e in the
lo w er-in com e states and relatively lo w e r in com e
grow th in the h igh er-in com e states.6 For exam ple,
using on e listing o f Frost Belt and Sun Belt states
(see table 2), the Sun Belt’s share o f (continental)
U.S. m anufacturing em p loym en t in creased from
34.4 p ercen t in 1969 to 39.0 percen t in 1978, w h ile
the Frost Belt's share d ecreased from 51.3 percen t
to 46.2 percent. D uring the sam e period, average
relative p er capita in com e for the Sun Belt states
in creased from 91.2 percen t in 1969 to 92.6 percen t
in 1978; in the Frost Belt states, it fell from 112.4
p ercen t in 1969 to 106.3 p ercen t in 1978.
This shift has con tin u ed in the last 10 years. Th e
Sun Belt's share o f m anufacturing em p loym en t
in creased from 39.0 percen t in 1978 to 43.7 percen t

Non Substantial Change

in 1987, w h ile the Frost B elt’s share decreased
from 46.2 p ercen t to 41.1 percent. A lthou gh the
shift, by itself, tends to redu ce in com e inequality,
the actual p er capita in com es fo r the tw o regions
have not con tin u ed to converge over this period.
W h ile the average p e r capita in com e fo r the Sun
Belt states as a p ercen tage o f the average in com e
fo r all states rose slightly from 92.6 p ercen t to 93.1
p ercen t b etw een 1978 and 1987, it ju m p ed from
106.3 percen t to 111.1 p ercen t in the Frost Belt
states.
One reason w h y p e r capita in com es in the Frost
Belt and the Sun Belt have sto p p ed con vergin g
since 1978 is that the shift o f m anufacturing activ­
ity to the Sun Belt is less w id esp rea d than in p re­
vious decades; since 1978, m anufacturing trends
in m any states d iffered sharply from that o f their
region. For exam ple, the Frost B elt’s share o f m a n ­
ufacturing w orkers con tin u ed to d eclin e after

6ln 1987, for example, average weekly earnings for production
workers in the nation's manufacturing sector was $406, 30
percent higher than the private-sector average.




SEPTEMBER/OCTOBER 1988

30

Table 2
Impact of Sun Belt and Frost Belt States on Inequality
Sun Belt States
Alabama
—
Arizona
—
Arkansas
—
Delaware
—
California
—
Florida
—
Georgia
—
Kentucky
—
Louisiana
—
Maryland
—
Mississippi
—
New Mexico —
North Carolina —
Oklahoma
—
South Carolina —
Tennessee
—
Texas
—
Virginia
—
West Virginia —

No Substantial Change
No Substantial Change
No Substantial Change
Upwardly Divergent
No Substantial Change
Upwardly Divergent
Upwardly Convergent
No Substantial Change
Downwardly Divergent
Upwardly Divergent
No Substantial Change
Downwardly Divergent
Upwardly Convergent
Downwardly Divergent
No Substantial Change
No Substantial Change
Downwardly Divergent
Upwardly Divergent
Downwardly Divergent

Frost Belt States
Maine
New Hampshire
Vermont
Massachusetts
Rhode Island
Connecticut
New York
New Jersey
Pennsylvania
Ohio
Indiana
Illinois
Michigan
Wisconsin

—
—
—
—
—
—
—
—
—
—
—
—
—
—

Upwardly Convergent
Upwardly Divergent
Upwardly Convergent
Upwardly Divergent
Upwardly Divergent
Upwardly Divergent
Upwardly Divergent
Upwardly Divergent
No Substantial Change
No Substantial Change
Downwardly Divergent
No Substantial Change
Downwardly Convergent
No Substantial Change

SOURCE: Weinstein, Gross and Rees (1985) and table 1.

1978, but m anufacturing in m ost N e w England
states g rew as fast as, o r faster than, the nation.

these states, rapid in com e grow th w as fu eled by
the expansion o f constru ction and services, e sp e­
cially health, business and financial services.8

M anufacturing job shares rem ained constant b e­
tw een 1978 and 1987 in Maine, Massachusetts and
Connecticut, w h ile rising in N e w H am pshire and
Verm ont. Th e rapid grow th o f h igh -tech n ology
m anufacturing b etw een 1978 and 1984, particu ­
larly com pu ter- and defense-related produ ction,
was largely responsib le fo r the rapid grow th o f per
capita in com e in N e w England.7This grow th c o n ­
tribu ted to the Frost Belt’s relatively rapid in com e
grow th and the nation's increasing in com e in ­
equ ality since 1978. As table 2 shows, the higherin com e states o f Connecticut, N e w H am pshire
and M assachusetts are classified as u p w a rd ly
divergent.

At the sam e time, som e Sun Belt states have not
shared in that region's industrial expansion. M an ­
ufacturing em p loym en t from 1978 to 1987 g rew
substantially slo w er in W est Virginia and Lou isi­
ana and no faster in Kentucky, M aryland, Okla­
h om a and Ten n essee than it did in the nation.
T h e slo w er grow th in these states m ay have
stem m ed, in part, from th eir specialization in
en ergy-related industries, an issue discussed later
in this article. As table 2 indicates, Louisiana, Okla­
h om a and W est Virginia w ere am ong the d o w n ­
w a rd ly divergent Sun Belt states.

D espite a sharp loss o f m anufacturing jobs since
1978, N e w York, N e w Jersey and Bhode Island

T o sum m arize, m anu facturing activity has c o n ­
tinu ed to shift from the Frost Belt to the Sun Belt

have had relatively rapid p er capita in com e

states in the 1980s, but n ot as w id e ly as in p re ­

grow th, contribu tin g to the rising inequality. In

vious decades: in fact, a n u m ber o f states in both

7See Bradbury and Browne (1988). Manufacturing, however,
was not entirely responsible for New England’s per capita
income growth, especially since 1985. Rapid growth of earn­
ings in construction and in service-producing industries (espe­
cially finance, insurance, real estate, medical and business
services) combined with relatively slow population growth to
spur New England's expansion.
8U.S. Department of Commerce (1987), p. 2, and Ray and
Rittenoure (1987) p. 244, briefly discuss sources of growth in


FEDERAL RESERVE BANK OF ST. LOUIS


Mid-Atlantic States. Gross and Weinstein (1988) argue that the
rapid growth of the New England and Mid-Atlantic economies
in the 1980s is at least partially due to a rise in federal spend­
ing in those regions, particularly grants-in-aid and procurement.
The slower economic growth of some Sun Belt states, mean­
while, allegedly stems from a decline in the federal expendi­
tures they receive.

31

“b elts” have ex p erien ced m anufacturing grow th
cou n ter to that o f th eir region as a w h o le. Thus,
rather than con tin u in g to converge as they had in
the early and m id d le 1970s, the gap b etw een per
capita in com es in the Frost Belt and Sun Belt
states has w id e n e d since 1978.

THE BI-COASTAL ECONOMY
A cco rd in g to a stu dy released in 1986 by the
D em ocratic staff o f the Joint E con om ic C om m ittee
o f the U.S. Congress, national e co n o m ic grow th
betw een 1981 and 1985 w as con cen trated in states
on the East Coast and in California." T h e rapid
expansion o f these states relative to the nation's
in terior states led to the ch aracterization o f the
U nited States as a bi-coastal econ om y, despite the
absence o f O regon and W ashington from the list o f
fast-grow in g states. For exam ple, the study noted
that real earnings g rew at a 4 p ercen t rate in the
coastal states du rin g the 1981-85 period, c o m ­
pared w ith a 1.4 percen t rate in the non-coastal
states.
D oes the bi-coastal econ om y, w h ic h is prim arily
a d escrip tion rather than an explanation o f the
pattern o f grow th, p rovid e insights into the in ­
creasing in equality o f state p e r capita in com e?
T w o questions must be an sw ered affirm atively.
First, are the bi-coastal states ex p erien cin g m ore
rapid g row th o f p er capita in com e? T h e an sw er to
this qu estion is “yes." Table 3 lists the bi-coastal
states and their p er capita in com e perform an ce
fo r 1978-87. O f the 16 bi-coastal states, 14 g rew
substantially faster in p e r capita in com e than aver­
age. California, the sole W est Coast state, and
South C arolina ex p erien ced no substantial change
in th eir relative p e r capita in com e grow th.
Second, did these rapid ly g ro w in g states also
have above-average p er capita in com es? If so, the
rapid grow th causes th eir p e r capita in com e to
rise fu rther above the average, thus, increasing
state in com e inequality. O f the 14 states w ith ra p ­
idly g row in g p er capita in com e, 10 are classified as

9The study, The Bi-Coastal Economy, was released in July 1986
by the Joint Economic Committee of the U.S. Congress. See
U.S. Congress (1986).
,0The Joint Economic Committee study suggested a number of
reasons for the uneven pattern of regional growth during the
first half of the 1980s. The study suggests that “ a central cause
is trade and the current massive imbalance in trade that exists
between the United States and its trading partners” that dispro­
portionately affects interior states. U.S. exports of both agricul­
tural and nonagricultural commodities had declined to some
extent, according to the authors, because of increased compe­
tition from Third World nations attempting to earn foreign cur­




Table 3
Impact of Bi-Coastal States on
Inequality
California
— No Substantial Change
Connecticut
— Upwardly Divergent
Delaware
— Upwardly Divergent
Florida
— Upwardly Divergent
Georgia
— Upwardly Convergent
Maine
— Upwardly Convergent
Maryland
— Upwardly Divergent
Massachusetts — Upwardly Divergent
New Hampshire— Upwardly Divergent
New Jersey
— Upwardly Divergent
New York
— Upwardly Divergent
North Carolina — Upwardly Convergent
Rhode Island — Upwardly Divergent
South Carolina — No Substantial Change
Vermont
— Upwardly Convergent
Virginia
— Upwardly Divergent
SOURCE: U.S. Congress (1986) and table 1.

divergent; on ly fo u r o f these states are convergent.
In fact, tin; 10 divergent states accou nt for all the
u p w a rd ly d ivergent states in the contin en tal
U nited States and the fou r convergent states ac­
count fo r all the u p w a rd ly convergent states.
Thus, relatively rapid East Coast in com e grow th
w as a prim ary in flu ence in increasing the in equ al­
ity o f state p er capita in com e.
W h ile explanations fo r the relatively rapid
grow th o f in com e in the coastal states are specu la­
tive, explanations o f w h y in com e grow th in in te­
rior states lagged b eh in d are m ore p recise.10Fall­
ing en ergy prices and the agricultural crisis are
tw o frequ en tly cited reasons fo r the below -average
perform an ce.

The Influence o f Falling Energy Prices
Th e e co n o m ic grow th o f states e n d o w e d w ith
substantial en ergy resources tends to be directly
related to en ergy prices, w h ile the eco n o m ic

rency to pay interest on their loans. Also, increased competi­
tion from imported manufactured goods in domestic markets
was claimed to be partially responsible for the observed pattern
of regional growth. The study’s final explanation relates to the
strong job growth in the service industry, particularly in firms
engaged in importing, advertising, financing and selling foreignmade goods. Such industries are strongly concentrated on the
coasts, according to the study, and their growth helped boost
the coastal states.

SEPTEMBER/OCTOBER 1988

32

Chart 2
Relative Energy Prices and Relative Per Capita
Income in Energy and Non-Energy States
Index
1982=100
175

Percent
of average
105

150

Average per capita
income in non-energy
states
scale >

125

100

100

95

—-—/

75

/

Relative energy price
< scale

50

25
1968

70

72

74

76

grow th o f en erg y-p o o r states tends to be inversely
related.11As chart 2 shows, en ergy prices relative
to the general p rice level rose rapid ly from 1973,
peaked in 1981, then fell through 1987.12 If energyrich states are also gen erally lo w er-in com e states,
the d eclin e in en ergy prices in the 1980s has c o n ­
tributed to the increasing interstate in equ ality bv

"S ee Manuel (1982) and Brown and Hill (1987) for empirical
studies documenting the relationship between energy prices
and state economic growth. Miernyk (1977) and Manuel (1982)
discuss why energy prices and state economic growth are
linked. As they rise, energy costs become an increasingly
important factor in determining where to locate an energyintensive industry. Such relocation tends to shift employment
opportunities from energy-poor regions to energy-producing
states. Higher energy prices may also stimulate greater invest­
ment in energy production and exploration, increasing jobs in
energy-producing states. Although profits from relocating
manufacturing firms are likely to be distributed to owners
throughout the nation, the increased employment tends to
increase income in energy-producing states. In contrast,
energy-poor states are burdened with higher costs for fuel and
inputs in which energy costs are an important component.
When energy prices fall, the advantages shift to states that
heavily import oil rather than produce it.


FEDERAL RESERVE BANK OF ST. LOUIS


78

Average per capita \
income in energy
\
states
\
scale >
80

82

84

86

90

85
1988

slo w in g in com e grow th in these states relative to
those that pu rchase m ost o f th eir en ergy re­
sources from out-of-state sources.
Th e evid en ce supports this explanation. As
chart 2 shows, relative p er capita in com e in en ergy
states generally fo llo w e d the rise and fall o f en ergy
prices, w h ile the relationship w as an inverse one

12Relative energy prices in this article are indicated by the pro­
ducer price index for fuels, related products and electric power
divided by the GNP implicit price deflator for the private busi­
ness sector. The oil embargo in 1973-74 contributed directly to
the price increases for petroleum and indirectly to price in­
creases for other energy sources as energy users searched for
oil substitutes. Relaxation of price controls during the period
contributed to the price increases of natural gas. The easing of
energy prices in the current decade reflects a worldwide in­
crease in global oil supplies as international oil cartels are
unable to agree on production quotas. Also, heavy investment
to increase energy efficiency by car makers, businesses and
households has caused the quantity of energy demanded to
grow substantially slower than the rest of the nation’s econ­
omy, according to Schmidt (1988).

33

Table 4
Impact of Energy-Producing States
on Inequality___________________
Wyoming
—
West Virginia —
Oklahoma
—
Louisiana
—
Kentucky
—
Texas
—
North Dakota —
New Mexico —
Colorado
—
Montana
—
Utah
—

Downwardly Convergent
Downwardly Divergent
Downwardly Divergent
Downwardly Divergent
No Substantial Change
Downwardly Divergent
Downwardly Divergent
Downwardly Divergent
No Substantial Change
Downwardly Divergent
Downwardly Divergent

NOTE: Energy-producing states are those in which earn­
ings from oil and gas extraction and coal mining
produced at least 3 percent of the state’s total
earnings in 1981. States are ordered from those
with the highest to the lowest percentage.
SOURCE: table 1.

fo r the o th er states.13Table 4 lists the 11 en ergy
states in the continental U.S. in w h ic h earnings
from oil and gas extraction and coal m in in g p r o ­
d u ced at least 3 percen t o f the state’s total earn ­
ings in 1981, the y e a r in w h ich en ergy prices
peaked and oil and gas extraction and coal m in in g
p rovid ed its largest share o f total U.S. earnings in
the postw ar p erio d .14Th e en ergy states are listed
in d escen d in g o rd er a ccord in g to the p rop o rtio n
o f th eir earnings d erived from oil and gas extrac­
tions and coal m ining, ranging from W yo m in g
w ith 18.6 p ercen t to Utah w ith 3.1 percent.
In 1969, before the sharp rise in en ergy prices,
p e r capita in com e in the en ergy states averaged
88.7 p ercen t o f that fo r all 48 continental states.
This p ro p o rtio n rose to 95.4 p ercen t b y 1978 and
peaked at 96.7 p ercen t by 1981. By 1987, after e n ­
ergy p rices had d ec lin ed substantially, the average
p e r capita in com e in en ergy states d ec lin ed to 86.8
percen t o f the average o f all states.

13ln the 1947-87 period, the correlation between relative energy
prices and the average relative per capita income of energy
states is 0.54, significantly different from zero at the 1 percent
level. The correlation of relative energy prices and the relative
per capita income of non-energy states, - 0.54, is identical in
absolute value, but negatively signed. This correlation is also
significant at the 1 percent level.
14The validity of this classification is suggested by the substantial
overlap between this list of energy states and those suggested
in two previous studies. Nine of the 11 states shown in table 4
were among the 10 continental U.S. states with a ratio of
energy production to energy consumption greater than unity in




O f the 11 en ergy states, all but Kentucky, C o lo ­
rado and W yo m in g w ere classified as d o w n w a rd ly
d ivergent (see table 4).lr' In h a lf o f these eight
d o w n w a rd ly divergent states (Oklahom a, N e w
M exico, Louisiana and Texas), relative p e r capita
in com e rose from 1978 through the early 1980s,
then fell sharply in subsequent years, fo llo w in g
en ergy p rice trends. W yo m in g also exhibited this
pattern o f grow th : its relative p er capita in com e
g rew to 121 percen t o f the state average by 1980,
rem ained high in 1981, then p lu m m eted to 89
percen t by 1987. A lthou gh classified as d o w n ­
w a rd ly convergent, W y o m in g ’s p er capita in com e
fell b elo w the national average in 1984 and, thus,
has contribu ted to the greater in equality o f state
in com e since that year.
In the rem ainin g d o w n w a rd ly divergent en ergy
states (West Virginia, N orth Dakota, Utah and M o n ­
tana), relative p er capita in com e tren ded d o w n ­
w ard throughout the 1978-87 period. A lthou gh the
fall in en ergy prices u n d ou b ted ly con tribu ted to
th eir slo w in g after 1981, their sluggish in com e
grow th in previous years suggests that o th er fac­
tors w ere at w ork as w ell.
Th e im p orta n ce o f the en ergy price d eclin e as a
con tribu tor to in creasin g interstate in equality can
be seen m ore clearly b y con sid erin g the list o f
d o w n w a rd ly d ivergent states in table 1. Energy
states accou nt fo r eight o f the 10 d o w n w a rd ly
divergent states. In addition, W yom in g, has c o n ­
tributed to in creasin g in equality since 1984.
N on e o f the states w ith substantial u p w a rd
m ovem en t o f relative p e r capita in com e w ere
en ergy-rich states. Instead, these states w ere
heavy im porters o f en ergy resources w h o g e n er­
ally b en efited from the ch ea p er en ergy resources
in the 1980s. Since m ost states w ith substantial
post-1978 in com e g ro w th had above-average p er
capita incom es, the fall in en erg y prices also
ten d ed to increase in equ ality by b oostin g their
grow th fu rth er above the average. Thus, the de-

1976 (Corrigan and Stanfield, 1980). Eight of the 11 states
identified as energy states in our study were among the nine
continental U.S. states in which oil-price declines were associ­
ated with declines in total state employment in Brown and Hill
(1988).
15Research by Hunt (1987) suggests that Colorado’s economy
was not adversely affected by declining energy prices because
of its diversified economic base which captured enough benefi­
cial effects of oil price declines to offset the negative effects.

SEPTEMBER/OCTOBER 1988

34

Chart 3
Economic Indicators of U.S. Agriculture
Dollars
p er acre

d in e in en ergy prices w as an im portant factor in
increasing in equality in the 1980s."’

The Influence o f the “Farm Crisis”
T h e first h a lf o f the 1980s has been a cco m p a ­
n ied bv a w id e ly p u b licized e co n o m ic d eteriora ­
tion o f the n atio n ’s agricultural sector.17Chart 3
show s tw o sym ptom s o f the so-called farm crisis.
T h e value o f both the n atio n ’s farm exports and
farm land g rew ra p id ly d u rin g the 1970s but d e ­
clin ed du rin g the current decade.
A d eclin e in the farm sector affects non-farm
sectors d irectly linked to agriculture. T h ese in ­
clu de su ppliers o f fertilizer and farm equ ipm en t

16Ray and Rittenoure (1987) found that declining energy prices
contributed to the increasing inequality of regional per capita
income in the 1980s.
17See Petrulis et al. (1987) for a discussion of the reasons for the
farm crisis.
18Since the purpose of this analysis is to assess the possible
effects of the farm sector downturn on state per capita personal


FEDERAL RESERVE BANK OF ST. LOUIS


B illions
of dollars

as w e ll as firms that transport, process and market
agricultural produ cts. Less directly, a d eclin e in
farm ing and agribusiness co u ld adversely affect
o th er sectors as w ell, such as those p rovid in g ser­
vices to agricultural w orkers.
A d eclin e in the n atio n ’s agricultural sector
w o u ld m ost adversely affect state in com e in
agriculture-intensive states. One m easure o f this
intensiveness is the p rop o rtio n o f total state earn­
ings accou n ted fo r b y farm labor and p ro p rieto r
earnings.18Table 5 displays the 12 states that d e ­
rived at least 4 percen t o f th eir earnings from
farms in 1981, the m ost recent peak in both agri­
cultural exports and farm land values. N orth Da-

income, farm labor and proprietor earnings (a component of
personal income) is a more appropriate measure of farm in­
come than net farm income. While real net farm income is a
better measure of farm profitability, it includes corporate in­
come, which is excluded from the personal income series.

35

Table 5

Impact of Farm States on Inequality
South DakotaNorth Dakota Iowa
Nebraska
Idaho
Arkansas
Montana
Kentucky
Minnesota
Wisconsin
Vermont
Kansas

- No Substantial Change
- Downwardly Divergent
- Downwardly Convergent
- No Substantial Change
- Downwardly Divergent
- No Substantial Change
- Downwardly Divergent
- No Substantial Change
■No Substantial Change
- No Substantial Change
■Upwardly Convergent
- No Substantial Change

NOTE: Farm states are those in which 4 percent or more
of total 1981 state earnings were derived from
farming. States are ordered from those with the
highest to the lowest percentage.
SOURCE: table 1.

kota and South Dakota w ere the states m ost reli­
ant on farm ing, w ith 11.9 percen t and 15.1 percen t
o f th eir total earnings directly d erived from agri­
culture.
A verage p er capita in com e has d ec lin ed in farm
states relative to nonfarm states since 1978. Be­
tw een 1978 and 1987, relative p er capita in com e in
farm states d ro p p ed from 97 percen t o f the aver­
age to 93 percent. D uring the same period, the
average o f relative p e r capita in com e in all oth er
states rose from 101 percen t to 102 percent.
D esp ite this divergence, fe w farm states con trib­
u ted substantially to interstate in com e inequality.
As table 5 shows, on ly three o f the 12 farm states
— Idaho, M ontan a and N orth Dakota — are clas­
sified as d o w n w a rd ly divergent. On the oth er
hand, farm states accou nt for tw o o f the 10
convergent states. Belative p er capita in com e also
fell substantially in Iowa, a state w ith aboveaverage p e r capita in com e in 1978, and p er capita
in com e rose in Verm ont, a state w ith below average p e r capita in com e in 1978. Little change in
relative p e r capita in com e o ccu rred in the rem a in ­
in g seven farm states. Overall, the im pact o f the
farm crisis on the recen t increase in in equality
appears m inim al.

CONCLUSION
T h e 45-year d o w n w a rd trend in inequality
en d ed in the late 1970s. T w en ty states, even ly d i­
vid e d b etw een below -average and above-average




p er capita in com e states, are prim arily responsible
fo r the in creasin g inequality. A ll states w ith aboveaverage p er capita in com e and relatively rapid
in com e grow th are located on the A tlantic Coast.
The states w ith below -average p e r capita in com e
and relatively slow' grow th are scattered throu gh ­
out the nation's interior.
T h e Sun Belt-Frost Belt d escrip tion o f regional
grow th has lim ited success in explain in g this p h e ­
n om enon . T h e shift o f m anufacturing activity from
the Frost Belt to the Sun Belt, w h ic h contribu ted
significantly to the n arrow in g o f regional in com e
differentials in the 1970s, has con tin u ed in the
1980s, but has affected few'er states. In deed, in
recent years, m anu facturing has grow n relatively
rapid ly in som e N e w England states, w h ile g r o w ­
ing no faster than the national average in several
Sun Belt states.
T h e descrip tion o f the U.S. eco n o m y as a b i­
coastal e co n o m y w ith ra p id ly g ro w in g coastal and
slo w ly gro w in g in terior states provid es a better
insight in to the location o f states responsib le for
the rising in com e inequality, but not necessarily
the reasons fo r this result. T h e relatively p o o r p e r­
form an ce o f the in terior states has been attributed
to various p roblem s related to agriculture as w ell
as to falling en ergy prices. T h e agriculture crisis
has little explanatory p o w er. A lthou gh the agricu l­
tural sector has w eaken ed in the 1980s, farm states
accou nt fo r o n ly three o f the 10 d o w n w a rd ly diver­
gent states.
On the o th er hand, d eclin in g en ergy prices have
been a m a jor factor in increasing interstate in ­
co m e inequality. Energy states account fo r eight o f
the 10 d o w n w a rd ly d ivergent states. A n o th er
en ergy state, W yom in g, has contribu ted to in creas­
ing in com e in equality since 1984.

REFERENCES
Bradbury, Katharine L., and Lynn E. Browne. “ New England
Approaches the 1990s,” New England Economic Review
(January/February 1988), pp. 31-45.
Brown, S. P. A., and John K. Hill. “Lower Oil Prices and State
Employment,” Contemporary Policy Issues (July 1988), pp.
60-68.
Browne, Lynn E. “ Narrowing Regional Income Differentials,”
New England Economic Review (September/October 1980),
pp. 35-56.
Corrigan, Richard, and Rochelle L. Stanfield. “ Rising Energy
Prices — What’s Good for Some States is Bad for Others,"
National Journal (March 1980), pp. 460-69.
Crandall, Robert W. “The Transformation of U.S. Manufactur­
ing,” Industrial Relations (Spring 1986), pp. 118-30.

SEPTEMBER/OCTOBER 1988

36

“Federal Spending: The Northeast’s Loss is the Sunbelt’s
Gain,” National Journal (Government Research Corporation,
June 1976).

Shapiro, S. S., and M. B. Wilk. “An Analysis of Variance Test
for Normality (complete samples),” Biometrika (Volume 52,
1965), pp. 591-611.

Gross, Harold T., and Bernard L. Weinstein. “ Frost Belt vs. Sun
Belt in Aid Grants: Not a Fair Fight,” Wall Street Journal,
August 23, 1988.

“The Second War Between the States.’’
17, 1977).

Hunt, Gary L. The Impact of Oil Price Fluctuations on the
Economies of Energy Producing States,” Review of Regional
Studies (Fall 1987) pp. 60-76.

U.S. Congress, Joint Economic Committee. “The Bi-Coastal
Economy: Regional Patterns of Economic Growth During the
Reagan Administration,” Staff Study by the Democratic Staff,
mimeo (July 1986).

Manuel, David P. "The Effects of Higher Energy Prices on
State Income Growth,” Growth and Change (July 1982), pp.
26-37.
Miernyk, William H. “ Rising Energy Prices and Regional Eco­
nomic Development,” Growth and Change (July 1977), pp.
2-7.
Petrulis, Mindy, Bernal L. Green, Fred Hines, Richard Nolan and
Judith Sommer. How is Farm Financial Stress Affecting
Rural America? Agricultural Economic Report Number 568,
U.S. Department of Agriculture (June 1987).
Ray, Cadwell L., and R. Lynn Rittenoure. "Recent Regional
Growth Patterns: More Inequality,” Economic Development
Quarterly (August 1987), pp. 240-48.

Business Week (May

U.S. Department of Commerce. "Regional Differences in Per
Capita Personal Income Widen in the 1980s.” Commerce
News (August 20, 1987).
Weinstein, Bernard L., and Harold T. Gross. “The Rise and
Fall of Sun, Rust, and Frost Belts.” Economic Development
Quarterly (February 1988), pp. 9-18.
Weinstein, Bernard L., Harold T. Gross, and John Rees.
Regional Growth and Decline in the United States, 2nd ed.
(Praeger Publishers, 1985).

Reich, Robert B. “The Rural Crisis, and What to Do About It,”
Economic Development Quarterly (February 1988), pp. 3-8.

Williamson, J.G. “ Regional Inequality and the Process of
National Development: A Description of the Patterns.” Eco­
nomic Development and Cultural Change (July 1965), pp.
3-83.

Schmidt, Ronald H. “Oil and the Economy,” Federal Reserve
Bank of San Francisco Weekly Letter (May 27,1988).

Yotopoulos, Pan A., and Jeffrey B. Nugent. Economics of
Development: Empirical Investigations (Harper & Row, 1976).


FEDERAL RESERVE BANK OF ST. LOUIS


37

Michael T. Belongia anil Kees G. Koedijk
Michael T. Belongia is a research officer at the Federal Reserve
Bank of St. Louis and Kees G. Koedijk is an assistant professor of
monetary economics at Erasmus University, Rotterdam, The
Netherlands. Anne M. Grubish and Rosemarie V. Mueller pro­
vided research assistance.

Testing the Expectations Model
of the Term Structure: Some
Conjectures on the Effects of
Institutional Changes
T

■M. HE TR A D ITIO N A L expectation s m o d el of the
term structure o f interest rates attem pts to explain
h o w interest rates on a sim ilar debt instrum ent
are related across different m aturities. It posits
that, in a w o rld w ithou t risk or o n e in w h ich assets
are perfect substitutes, the o n e-p erio d interest
rate sh ou ld equal the ex p ected return to h old in g
an instrum ent o f lon ger m aturity fo r on e period.
Because the m o d el is based on the m ost fu n da­
m ental e co n o m ic assum ptions — rational behav­
io r b y individu als w h o act on all available in form a­
tion — it has h eld considerable appeal in a pplied
research. E m pirical tests fo r data across a range o f
cou ntries and sam ple periods, h ow ever, have
ten d ed to reject this sim ple statem ent o f the ex­
pectations m od el.' M oreover, exp a n d in g the basic
m o d el by a d d in g o th er explanatory variables, such
as a tim e-varying risk p rem iu m or latent in form a ­
tion variables, still has fou n d lim ited em pirical
success in explain in g interest rate behavior.2Thus,
a p u z z le rem ains: w h y is such a basic theoretical
m o d el so frequ en tly rejected b y the data?

In this article, using short m aturities in the
E u rocu rren cy market, w e isolate several institu­
tional factors that m ight explain som e rejection s
o f the expectation s m o d el. Alternatively, the analy­
sis m ay be view ed as an attem pt to suggest sp e­
cific characteristics o f p o lic y p roced u res that are
inconsistent w ith the theoretical m o d el's assu m p­
tions. O ur results suggest that sin gle-cou n try esti­
mates o f the expectation s m o d el m ay om it im p o r­
tant in form ation because financial markets are
h igh ly in tegrated across countries. M oreover, it
appears as if the m an n er in w h ich m on etary p o l­
icy is co n d u cted has effects on interest rates that
contribute to rejection s o f the theory. In particu ­
lar, the expectation s m o d el does not h old in co u n ­
tries w h e re the central bank — at least p e rio d i­
cally — fo llow s an exch an ge rate rule. A cco u n tin g
fo r relationships across markets and fo r the m a n ­
n er in w h ich m on etary p o lic y is co n d u cted re­
verses, in som e cases, the negative con clu sion o f
sim ple, single equ ation estim ates o f term structure
relationships.

'For a survey of these results, see Bisignano (1987).
2Examples of work along these lines are Shiller, et al. (1983)
and Campbell and Clarida (1987).




SEPTEMBER/OCTOBER 1988

38

THE EXPECTATIONS M ODEL
APPLIED TO SHORT MATURITIES
T h e em pirical version o f the expectation s m o d el
can be w ritten as:
<1* <r,., +, - r j = a + b(,F,,,, - r j + e,
w h ere rlt is the y ie ld on a o n e-p erio d bill in p eriod
t and ,FU+, is the current, observed fo iw a rd rate on
a o n e-p erio d bill, o n e p erio d into the future.3 C o ef­
ficients to be estim ated are d en o ted a and b; e, is
an erro r term w ith ze ro m ean and variance equal
to a2. Thus, in equ ation 1, the d ep en d en t variable
is the differen ce b etw een actual yield s on onep e rio d bills in con secu tive p eriod s and the explan ­
atory variable is the differen ce b etw een the cur­
rent fo iw a rd and spot rates on o n e-p erio d bills.
Equation 1 predicts that the change in onep erio d yie ld s sh ou ld be related to the forecasted
change, as rep resen ted by the fo rw ard rate — spot
rate spread. T h e expectation s h ypothesis im plies
that, if the forw a rd rate is an unbiased p red icto r o f
the future spot rate, the regression ’s slope c o e f­
ficient, b, sh ou ld not be significantly differen t from
one and its in tercept, a, shou ld not be significantly
differen t from zero.
This p oten tia lly rich area fo r em pirical research
has y ie ld e d fe w d efinitive results because tests o f
the expectation s m o d el inevitably have been joint
tests o f several m ain tain ed h ypotheses. T o cite
just a fe w o f the p roblem s that arise, the m odel
assumes a ze ro o r constant risk prem iu m . Th e
p rob lem fo r estim ation, h ow ever, is that the risk
(or, term ) prem iu m — som e system atic differen ce
b etw een the long-term interest rate and the ex­
p ec te d future values o f short-term interest rates
that reflects relative degrees o f u ncertainty — is
unobservable. Thus, if an em pirical test rejects the
h ypothesis a = 0 and b = 1, it is not possible to
discrim inate b etw een true m o d el rejection and
the possible effects o f a term prem iu m that has
been assum ed, incorrectly, to be zero. In part for
this reason, as w ill b e the case below , m an y stud­

3For one derivation of this result, see Mankiw and Miron (1986),
p. 214. Strictly speaking, this specification holds up to a con­
stant (the term premium), which we have ignored. The as­
sumption was that, for the short maturities used in this paper,
term premium effects, if any, should be negligible. Also see
Bisignano (1987). Cosset (1982) found that forward rates in
this market are unbiased, but not optimal, predictors of future
interest rates. He also found this market to be efficient in the
sense that past information on interest rates is not useful in
predicting future values of interest rates.
Values for the forward rate, ,F1t+1, were calculated as twice
the two-period interest rate minus the one-period rate. Because


FEDERAL RESERVE BANK OF ST. LOUIS


ies have ch osen to test a w ea k er form o f the e x p e c ­
tations m o d el (b = 1) and in terpret the statistical
significance o f the regression ’s in tercep t as in d ica ­
ting the existen ce o f a term prem iu m .4
Th ere are o th er testing p roblem s as w ell. W h en
data fo r lo n g er m aturities are studied, interest rate
data often are estim ated from a fitted y ie ld curve
rather than taken from observed market transac­
tions. In this instance, negative results m ight be a
rejection o f the form ula used to approxim ate un­
observable interest rates rather than the exp ecta ­
tions m odel. Finally, the rationality o f expectation s
by market agents is assum ed but, again, this is
difficult or im possible to test directly. A lthou gh
m ore attention has been paid in recent research to
m odels that isolate these assum ptions, it rem ains
im possible to say w h e th e r negative results in d i­
cate a rejection o f the expectation s m o d el itself or
sim ply one (or m ore) o f its u n d erlyin g assu m p­
tions.

ESTIMATION OF THE
EXPECTATIONS M ODEL
As n oted in the in troduction , equations sim ilar
to (1) have been estim ated w ith data fo r m an y
countries and sam ple periods. W e illustrate these
results b y estim ating equ ation 1 w ith Harris Bank
data on spot three-m on th dep osit rates from the
E u rocu rren cy market fo r the U.S., U.K., W est G er­
many, Japan and Sw itzerland; six-m onth d ep osit
rates also w ere used, as exp la in ed in fo otn ote 3, to
calculate values fo r the fo rw ard rate. T h e interest
rates are calculated as sim ple rates. T h e data are
Friday closin g quotes fo r the Friday closest to the
begin n in g o f each m onth.5 T h e sam ple p erio d
spans February 1981 through O ctober 1986. A l­
thou gh data p rior to 1981 are available, the
Euroyen market w as th in ly traded and, in 1980,
the C arter A dm in istration a d o p ted its Special
Credit C on trol program . Because these factors

the data in the study use three-month rates to represent the
theoretical “one period,” the forward rate is calculated as twice
the six-month (two period) rate minus the corresponding threemonth rate.
4See, for example, Shiller, et al. (1983).
5First-Friday-of-month data, rather than monthly averages of
daily or weekly data, were used to avoid questions about how
to treat partial weeks in adjoining months, months with different
numbers of weeks and the gap between three, four-week
months and a thirteen week quarter. See Hakkio and Leiderman (1984) for a discussion of these measurement issues.

39

that interest rate tiirre series closely approxim ate a
ran dom walk. Overall, these m ixed results rep re­
sent the typical findings o f previous em pirical
w ork on the expectation s m odel.

Table 1
Estimates of the Basic Expectations
Theory Relationship (monthly data,

T h e m ixed results in table 1 can be in terpreted
in tw o wavs. One in terpretation is that the e x p e c ­

1 9 8 1 . 0 2 - 1 9 8 6 . .1 0 )
a

b

R2

-0 .3 2
(0.92)
0.00
(0.00)
-0 .4 6
(3.25)
—0.17
(1.72)
-0 .2 3
(0.82)

-0 .2 6 *
(2.68)
0.90
(0.31)
0.42*
(4.13)
0.92
(0.27)
0.04*
(2.97)

0.01

Country
United States
United Kingdom
Germany
Japan
Switzerland

0.09
0.08
0.25
0.00

NOTE: Absolute values of t-statistics are in parentheses,
t-statistics for b apply to the null hypothesis b = 1. An asterisk
indicates a slope coefficient significantly different from one at
the 0.05 level of significance.

c o u ld adversely affect the test results, data p rio r to
February 1981 are not used in estim ation.6
Finally, a co m m en t on the initial approach to
estim ation is necessary. Because the data consist
o f observations on three-m onth yie ld s sam p led
m onthly, the changes in interest rates overlap and
in trod u ce a secon d o rd er m ovin g average process
into the data. Because this p ro p e rty o f the data
w ill affect the estim ated co efficien ts’ standard
errors, it must be co n sid ered by the estim ation
tech niqu e. T h e H ansen-H odrick p roced u re w e use
accounts fo r this p ro p e rty b y correctin g the
m o d e l’s error term fo r serial correlation .7

tations m o d el is rejected because it appears not to
h o ld fo r m ost o f the cou ntries exam in ed. A n o th er
in terpretation is that institutional o r o th er co n sid ­
erations, w h ich the pu re theory regards eith er as
given o r unim portant, m ay have had adverse ef­
fects on the em pirical tests. A m o n g others, im p o r­
tant structural changes that w ill affect the results
in clu de the co n d u ct o f U.S. m on etary policy,
changes in interest rate ceilin gs and general fin an ­
cial market deregu lation. Given the results sh ow n
in table 1, previous research gen erally has left
these results u n explain ed o r has a d d ed som e ad
hoc m easure o f risk to accou nt for the possible
effects o f an unobservable term prem iu m . In the
sections that follow , w e first revise the estim ation
p roced u re to see h o w this change affects the test
results. W e then discuss som e w ell-d efin ed events
and changes in institutions that co u ld affect the
term structure relations and p ro d u ce the results
that a ppear to reject the m od el.

ONE POSSIBLE REASON FOR
REJECTION OF THE
EXPECTATIONS MODEL:
CORRELATED ERROR TERMS
T h e in creasin g integration o f w o rld capital m ar­
kets suggests that an alternative statistical a p ­
proach sh ou ld be u sed to estim ate equ ation 1. As
capital flow s freely am on g nations, m on etary p o l­

power- fo r the equ ations is gen erally lo w (w ith the
notable excep tio n o f Japan).8This result is typical

icy actions (for exam ple) undertaken in on e co u n ­
try can be ex p ected to affect financial variables in
o th er countries as w ell. Consider, fo r exam ple, a
change in Bundesbank p o lic y that affects Germ an
interest rates and then is transm itted to interest
rates in the o th er fou r nations via capital flow s
cau sed b y the change in Germ an interest rates.
Th is effect, w h ic h w ill a p p ea r o n ly in the error
term o f the Germ an interest rate equ ation w h en
separ ate regressions are estim ated, co u ld be ex ­
p lo ite d as a n e w source o f in form ation fo r each

in estim ates o f the expectation s m odel, in dicating

regression if the cou n try equations w ere estim ated

6ln fact, the U.S. results are extraordinarily sensitive to these
few data points. The dramatic increase in interest rate volatility
during the first and second quarters of 1980, relative to the
remaining sample, would suggest this sensitivity in OLS re­
gression estimates.

account for the effects of the third-order serial correlation, see
Hansen and Hodrick (1980) and Campbell and Clarida (1987).

BASIC RESULTS
T h e results from estim ating equ ation 1 are re­
p o rted in table 1. T h e expectation s m o d el is
clearly rejected for the U nited States, G erm any
and Sw itzerland; their estim ated slope coefficients
are significantly differen t from one. In contrast,
the results fo r the U nited K in gd o m and Japan
support the expectation s m odel. Explanatory

8Durbin-Watson statistics are not reported because, as indi­
cated in the text, the reported standard errors reflect correc­
tions for serial correlation in the data.

7For an extensive description of the econometrics used to




SEPTEMBER/OCTOBER 1988

40

in form ation exists in the erro r term s is substanti­
ated by the co m p u ted value o f 56.34 fo r a likeli­
h ood ratio statistic testing w h e th er covariances

Table 2
Revised Expectations Model Estimates
Using Seemingly Unrelated
Regressions (SUR): 1981.02 -1986.10
Country
United States
United Kingdom
Germany
Japan
Switzerland

a

b

-0 .5 2
(2.26)
0.00
(0.02)
-0 .4 7
(5.62)
-0 .1 8
(3.07)
-0 .3 9
(2.37)

0.20*
(2.60)
0.93
(0.20)
0.45*
(4.15)
1.07
(0.42)
0.49*
(2.21)

am on g the erro r term s are zero: this value is to be
com p a red w ith the 5 percen t critical value o f
18.30. T h e erro r covariance and correlation
m atrices rep orted in table 3 in dicate w h ere the
significant correlation s b etw een countries w ere
found. Note, in particular, the high correlations
betw een the U.S. and G erm any and b etw een
G erm any and Sw itzerland. C on jectu res to explain
these correlations and, possibly, m o d el rejection s
are discussed later in referen ce to the table 4
results.
A lthou gh OLS and SUR sh ou ld p rod u ce sim ­
ilar coefficient estimates, both the U.S. and Swiss

NOTE: Absolute values of t-statistics are in parentheses.
For b, the t-statistic applies to the null hypothesis b = 1. An
asterisk indicates a slope coefficient significantly different
from one at the 0.05 level of significance.
F-test for null hypothesis: bus = bUK = bGER = bj = bsw =
1 is 5.63 compared with a critical value of 2.21.

jointly. In o th er w ords, the error term o f a single
equation (w hich reflects ' n ew s,” o r u npredictable
events w ith in that country) also m ay contain in for­
m ation — du e to linkages am on g markets — that
is relevant to explainin g interest rate beh avior in
an oth er country. T h e im portan t p oin t is that the
expectation s m o d el bein g tested assumes that this
in form ation is b ein g u sed b y the rational agents
w h o se co llective actions determ in e changes in
interest rates. Single equ ation estim ates, how ever,
exclu de the in form ation im p licit in these linkages
because they look at data for each cou ntry in iso­
lation.
One w a y to accou nt fo r this m issing in form ation
is to estim ate equ ation 1, as a p p lied to the live
countries u n d er study, as a system o f seem in gly
u nrelated regressions (SUR).9Th is p roced u re co n ­
siders con tem poran eou s correlation s that m ight
exist am on g the error term s o f the five equations
and, by d o in g so, im proves the efficien cy w ith
w h ich the coefficients are estim ated.

The SUR Results
T h e results from estim ating the five equations
bv SUR are rep orted in table 2. That im portant

9Edwards (1982) has made the same point and reported muchimproved results for a similar model applied to the exchange
rate. Krol (1987) also reported substantial integration of these
markets across countries. Mankiw (1986), however, finds little


FEDERAL RESERVE BANK OF ST. LOUIS


slope coefficien ts re p o rted in table 2 are m arkedly
differen t from th eir values in table 1. In v ie w o f the
lo w values fo r R- in both the U.S. and Swiss equ a­
tions, how ever, these changes m erely indicate
that, for these data, the basic specification o f the
expectation s m o d el sim p ly d oes not p rod u ce p re ­
cise estim ates o f the slope coefficient. T h e m ore
im portant p o in t is that, after using the SUR estim a­
tor, the h ypothesis that all five slope coefficients
are jointly equal to o n e still is rejected. Finally, the
Japanese intercept, w h ic h d id not change n u m eri­
cally, n o w is significantly d ifferen t from zero. Be­
cause the Germ an and U.K. results are largely u n ­
affected by the SUR estim ation, how ever, this
sim ple change in estim ation p roced u re to in c o r­
porate linkages a m o n g financial markets, w h ile
in dicatin g that significant in form ation exists in the
correlation s am on g erro r term s across equations,
still rejects the expectation s m odel fo r m ost o f the
countries exam ined.

OTHER SOURCES OF EXPLOITABLE
INFORMATION
A n o th er assu m ption b eh in d em p irica l tests o f
the expectation s m o d e l is that the data u sed for
estim ation w ere gen erated du rin g a p erio d ch ar­
a cterized b y a stable eco n o m ic structure. M o re ­
over, the data sh ou ld be draw n from markets in
w h ic h interest rates can adjust freely. Thus, the
basic m o d el shou ld not be estim ated w ith data
from period s associated w ith m a jor p o licy

correlation across countries and speculates that capital con­
trols may “ prevent effective international arbitrage (p. 66)” .
See Zellner (1962) for details on the estimation procedure.

41

Table 3
Error Correlation and Covariance Matrices From The SUR
Estimation
Country

United
States

United
Kingdom

Germany

Japan

Switzerland

Covariance Across Models
United States
United Kingdom
Germany
Japan
Switzerland

2.49
0.43
0.44
0.06
0.14

United States
United Kingdom
Germany
Japan
Switzerland

1.00
0.19
0.43*
0.08
0.08

2.03
0.25
0.43
0.07
0.11
0.49
0.30
Correlation Matrix
1.00
0.27*
0.10
0.29*

1.00
0.33*
0.38*

0.23
0.00

1.00
-0 .0 1

5 percent significance level for correlation is 0.25.
For the null hypothesis that the off-diagonal elements of the covariance matrix are zero, the
likelihood ratio statistic is 56.34 vs. a 5 percent critical value of 18.30.

Table 4
Revised Expectations Model SUR Estimates
Country
United States
United Kingdom
Germany
Japan
Switzerland

a

b

MTARGET

-0 .5 6
(2.23)
0.00
(0.02)
-0 .4 7
(5.50)
-0 .1 8
(3.07)
-0 .4 0
(2.42)

0.45
(1.08)
0.94
(0.19)
0.47
(3.83)*
1.07
(0.42)
0.58
(1.60)

-0 .4 9
(0.88)
—
—
—
—
—
—
—
—

EMS
—

—
—
—
-0 .5 6
(0.72)
—
—
-0 .6 2
(1.27)

NOTE: Absolute values of t-statistics are in parentheses. For b, t-statistic applies to the null
hypothesis b = 1. An asterisk indicates a slope coefficient significantly different from one at the 0.05
level of significance.
F-test for null hypothesis: bus = bUK = bGER = bj = bsw = 1 is 3.55 versus a critical value of 2.21.

changes o r im p ed im en ts to m arket adjustm ents.
In the case o f the form er, m ajor p o lic y changes

cu rred du rin g the p erio d used for estim ation and
assess h o w th ey affect the results re p o rted above.

m ay cause large discrete changes in expectation s
or changes in the variability o f expectation s that
can not b e m easured o r m o d elle d p rop erly. Simi­
larly, taking data from , say, a p erio d ch a racterized
by interest rate controls w o u ld be in ap propriate
fo r testing the m o d e l becau se th eory assumes that
interest rates can adjust freely in p erfectly c o m ­
petitive, efficien t markets. In w h at fo llo w s below ,
w e describe som e m ajor changes that have o c ­



Changes in U.S. Monetary Policy
Since O ctober 1979, the Federal Reserve has
used tw o distinct operational p roced u res in its
con d u ct o f m on etary p olicy. B etw een O ctober
1979 and O cto b er 1982, the Fed established a tar­
ge te d path fo r n o n b o rro w ed reserves; this a p ­
proach p erm itted short-term interest rates to fluc-

SEPTEMBER/OCTOBER 1988

42

Chart 1
Changes in Federal Funds Rate
Percent
4

Percent
4

1977

tuate w ith in w id e r bands than had the previous
procedu re, w h ic h had fo cu sed on k eep in g the
federal funds rate w ith in a n arrow range. In O cto ­
ber 1982, the Federal Reserve an n ou n ced that, due
to increasing u ncertainties about the defin ition o f
the M l aggregate, it w o u ld co n d u ct m on etary
p o lic y b y setting an objective fo r b o rro w e d re­
serves; this latter strategy resu lted in less variation
in short-term interest rates.10Thus, the first part o f
the sam ple p erio d used in the estim ation is char­
a cterized b y a Fed op era tin g p roced u re that p e r­
m itted greater variation in short-term interest
rates; this p erio d is fo llo w ed bv fou r years o f data
associated w ith a p roced u re that, o n ce again, re­
d u ced the variation in short-term interest rates.
T h e beh avior o f the fed eral funds rate, w h ic h su p­
ports this d ep ictio n o f events, is sh ow n in chart 1.
H o w w o u ld this sw itch in p o licy im p lem en ta ­
tion affect tests o f the expectation s m odel? A c ­

,0See Wallich (1984) and Gilbert (1985) for more discussion
about changes in the implementation of U.S. monetary policy
over time.


FEDERAL RESERVE BANK OF ST. LOUIS


1988

co rd in g to M an kiw and M iron (1986), Fed p o lic y
based o n sm ooth in g short-term interest rates can
be ch a racterized as:
(2) E, (Ar,+1) = 0
or, the exp ected change in the short-rate at each
m om en t in tim e is ze ro even if the Fed has been
observed to change short rates in response to, say,
real GNP g row th o r inflation rates that deviated
from p rio r expectations. If equ ation 2 describes
Fed p o lic y since O cto b er 1982 (and p rio r to O cto ­
b er 1979), the value o f (,F11+1 — r ,,) in equ ation 1 w ill
always be zero and short-term interest rates w ill
behave, approxim ately, as a ran dom walk. In this
case, the expectation s m o d el o f the term structure
w o u ld be in capable o f explain in g the b eh avior o f
short-term interest rates.
M an kiw and M iron (1986) investigated this p ro b ­
lem using annual U.S. data from 1890-1914 and

43

1915-79. T h e y fou n d that su pport fo r the e x p e c ­
tations m o d el varied w ith m o n eta iy regim e. W h ile
the expectation s m o d el “ h o ld s” fo r the pre-Fed
period, w h e n there was n o m onetary authority to
sm ooth interest rates, the m o d el is rejected fo r the
later p erio d w h en the F e d ’s approach to p o licy
ten d ed to sm ooth fluctuations in short-term in ter­
est rates. T h e ir results, therefore, suggest that the
U.S. results rep orted in table 2 — and perhaps
o th er rejection s o f the m o d el using post-1979 U.S.
data — co u ld be d o m in a ted b y the sub-sam ple
associated w ith the post-O ctob er 1982 change in
Federal Reserve operatin g procedu res.

Effects o f Exchange Rate Intervention
Rules
T h e fo u n d in g o f the European M o n e ta iy System
(EMS) is an oth er im portan t change that occu rred
in 1979 and is a possible source o f the negative
results for G erm any and Sw itzerland. T h e EMS
agreem ent established ranges fo r bilateral ex­
change rates o f the m em b er countries and called
fo r coop era tive interventions b y the central banks
o f the countries in volved w h e n rates deviated from
their s p ecified ranges. Thus, German m on etary
p o lic y since 1979 has been constrained b v its p a r­
ticipation in the exch an ge rate agreem ent and its
p led ge to in terven e." In practice, G erm any has
b ec o m e the lea d er o f the EMS due to the size o f its
e c o n o m y and its lo w inflation rate; oth er EMS
countries have fo llo w e d its n on in flation a iy m o n e­
ta iy policy. M u ch research lias sh ow n that the
EMS agreem ent really has beh aved as if a dollar/
DM o bjective w ere pu rsued b y the German central
bank.12
In addition, Swiss m o n eta iy p o licy is in flu en ced
by the DM/Swiss franc exchange rate even though
S w itzerlan d is not an EMS m em ber.13 Because
standard m od els typically explain the beh avior o f
the exch an ge rate as d ep en d in g o n the spread
b etw een foreign and d om estic interest rates, at­
tem pts b y the Bundesbank to in flu en ce the dollar/
DM exch an ge rate also w o u ld create a strong link

,1The history of the EMS and a discussion of how it functions can
be found in lingerer, et al. (1986).
,2See, for example, Fels (1987) for a discussion of the EMS as a
dollar/DM commitment by the Bundesbank.
"Because trade represents 39 percent of Swiss GDP and trade
with Germany accounts for one-fifth of total trade, the Swiss
franc/DM exchange rate has been particularly important to the
conduct of Swiss monetary policy. The Swiss National Bank, at
times, has abandoned its objectives for the growth rate of the
monetary base and, instead, pursued an exchange rate objec­
tive. See Rich and Beguelin (1985).

betw een Germ an and Swiss interest rates.14Sup­
pose, for exam ple, that the d olla r w ere d ep recia t­
in g against the DM because U.S. interest rates w ere
falling. T h e Bundesbank co u ld attem pt to stop or
reverse this dolla r d ep recia tion bv e x p a n d in g the
Germ an m o n ey stock and lo w e rin g G erm an sh ort­
term interest rates. Such an action, h ow ever,
w o u ld cause the value o f the Swiss franc to rise
against tin; DM. In the past, the Swiss N ational
Bank has resp o n d e d to this (or sim ilar) sequ en ce
o f events by fo llo w in g the Bundesbank w ith a
m ore expansion ary m on etary p o lic y a nd lo w e r
short-term interest rates as it attem p ted to re­
establish som e d esired value for the DM/Swiss
franc exch an ge rate. This close linkage o f German
and Swiss interest rates, from a Swiss objective fo r
stability o f the bilateral exch an ge rate, is likely to
be the source o f the h igh ly correlated Swiss and
Germ an erro r term s rep orted in table 3.15In sum,
both Germ an and Swiss m o n e ta iy p olicies are
in flu en ced b y exch an ge rate considerations that
cou ld affect em pirical estim ates o f the ex p ecta ­
tions m odel.

Empirical Implementation
T o investigate these possibilities, the system o f
SIIR equations rep orted in table 2 w as reestim ated w ith changes in the U.S., German and
Swiss regressions. For the U.S., the w h o le-sa m p le
slope coefficien t w as split to represent the tw o
distinct period s o f Federal Reserve operatin g p r o ­
cedures. A slop e du m m y (M TARGET) w as in tro­
duced, w h ic h took a value o f on e b etw een Febru­
ary 1981 and S eptem ber 1982 and a value o f zero
fo r the rem ainin g m onths. If the M an kiw -M iron
h ypothesis is correct, the slope coefficien t fo r the
first part o f the sam ple (b plus M TARGET) should
not be significantly d ifferen t from on e w h ile the
coefficien t fo r the latter p erio d (b alone) sh ou ld be
significantly d ifferen t (less than) from o n e.16
A lthou gh the p recise w a y to quantify the im pact
o f the EMS agreem en t on Germ an and Swiss finan­
cial markets is not clear, the p eriod s w h en the

15A related point that suggests this sort of influence across
countries is based on results from Belongia and Ott (1988).
They show that the dollar exchange rate risk premium and the
amount that the exchange rate adjusts to a given domesticforeign interest differential both vary with the choice of Federal
Reserve operating procedure (interest rate vs. money stock
objectives). If nothing else, their result would be suggestive of a
time varying risk premium in the expectations model.
,6An intercept dummy also was tried but it was not significant
individually and had no material effects on the magnitudes or
significance of other coefficients.

'“See, for example, the model presented by Dornbusch (1980).




SEPTEMBER/OCTOBER 1988

44

m em b er countries agreed to m a jo r realignm ents
o f the official exchange rate levels and ranges are
know n. O ther things the same, on e can h yp o th e­
size that interest rates m ade discrete adjustm ents
to these realignm ents w ith in one m onth after they
w ere ann ou nced. T o test the p rop o sitio n about
exchange rate linkages and interest rates, a
du m m y variable w as created to represent EMS
realignm ents and w as in trod u ced into both the
German and Swiss regressions. This variable took
a value o f o n e du rin g the m onths associated w ith
the eight EMS realignm ents and a value o f zero
du rin g all o th er m on th s.17As w ith the U.S. case,
m u ltiplyin g the forw ard rate — spot rate spread in
the German and Swiss regressions b y this du m m y
variable perm its the estim ation o f tw o different
values fo r the regressions’ slop e coefficients: o n e
coefficient fo r “ n orm a l” period s and the sum o f
tw o coefficients fo r m onths w h e n a realignm ent
occu rred.
In table 4, the revised SUR results are reported.
Th e null h ypothesis that all five slope coefficients
are jo in tly equal to on e is rejected, o n ce again, at
the 0.05 level o f significance. T h e expectation s
m o d el is re jected even after a u gm entin g the in for­
m ation set to in corporate changes in the im p le­
m entation o f U.S. m on etary p o lic y and the EMS
realignm ents.
Lookin g at in dividu al cou n try results, the ta b le’s
top row , associated w ith the slope d u m m y fo r the
p erio d o f m on etary targeting in the U nited States,
in dicates that estim ates o f the expectation s m o d el
are sensitive to changes in the F e d ’s operatin g
p roced u re. Even thou gh the M TARG E T d u m m y is
not significant, the m o d e l’s w h o le-p e rio d slope
coefficien t increases from 0.20 to 0.45 and n o w is
n ot significantly d ifferen t from one.
This apparent im p rovem en t in the U.S. results,
how ever, is in direct contrast to M an kiw and
M iro n ’s results in tw o respects. First, w h e n they
attem pted to investigate the effects o f post-1979
data on the expectation s m odel, th ey rep orted
that “w e obtain standard errors so large that one
can reject no interesting h yp o th esis” (p. 227).
M ore im portant, th ey h yp o th es ize d that the ex­
pectations m o d el sh ou ld not be rejected fo r the
p erio d o f m o n ey stock targeting, but sh ou ld be
rejected fo r the post-Septem ber 1982 period ; e m ­
pirically, this im p lies that b plus M TARG E T shou ld

’T h e dates of EMS realignments were March 23 and October 5,
1981; February 22 and June 14,1982; March 21,1983; July
22, 1985; April 7 and August 4, 1986 and are provided in Fels,
p. 217.


FEDERAL RESERVE BANK OF ST. LOUIS


not be statistically different from o n e w h ile b alone
sh ou ld be significantly differen t from (less than)
one. In fact, the results are reversed; the ex p ecta ­
tions m o d el is rejected fo r the p eriod o f m o n ey
stock targeting. Thus, w h ile the du m m y variable
im proves the overall results and provides perhaps
a stron ger test o f th eir m odel, the exact process at
w ork is in con sisten t w ith the o n e h ypoth esized,
leaving an u n explain ed p u zzle.
T h e revised estim ates fo r the Germ an and Swiss
equations p rovid e w eak su pport fo r the con jectu re
that the intervention p o licies o f th eir central banks
have significant effects o n tests o f the expectation s
m odel. T h e signs on the slope d u m m ies are nega­
tive and sim ilar in m agnitude, to the w h o le p erio d
slope coefficient, w h ich in dicates that the fo rw ard
rate-spot rate spread has zero effect during
m onths o f EMS realignm ents. M oreover, the w h o le
p e rio d Swiss slope coefficien t n o w both is larger
n u m erically and n ot significantly d ifferen t from
one. For Germany, h ow ever, the results are not
altered w h e n the dates o f EMS realignm ents are
co n sid ered and the data contin u e to reject the
expectation s m odel.

CONCLUSIONS
Th e expectation s m o d el o f the term structure o f
interest rates has been a p p lied to data fo r a n u m ­
ber o f countries and sam ple p eriod s w ith g e n er­
ally n egative results. In this article w e have investi­
gated som e con d ition s u n d er w h ic h the
expectation s m o d el m ight be rejected in the c o n ­
text o f its traditional single equ ation test. W e
fou n d substantial correlation s across the errors o f
the in dividu al equ ation s w hich, w h e n e x p lo ite d by
using SUR estim ation, im p ro ved the efficien cy o f
estim ation. W e also fo u n d that, although du m m y
variables used to represent changes in the a p ­
proach to m on etary p o lic y o r EMS exch an ge rate
targets w ere n ot significant individually, th ey c o n ­
tribu ted som ew h at to im p ro ved overall character­
istics o f the equations. A lthough, as in previous
studies, m any p u zzles still remain, these results
suggest that tests o f the expectation s m o d el
sh ou ld use m o re gen eral m o d els and m o re ef­
ficient estim ation p roced u res than the sim ple OLS
equation typically e m p loyed .

45

REFERENCES
Belongia, Michael T., and Mack Ott. 1The U.S. Monetary Policy
Regime, Interest Differentials and Dollar Exchange Rate Risk
Premia,” Journal of International Money and Finance, (Decem­
ber 1988), forthcoming.
Bisignano, Joseph R. “A Study of Efficiency and Volatility in
Government Securities Markets." Bank for International
Settlements, processed June 1987.
Campbell, John Y., and Richard H. Clarida. "The Term Struc­
ture of Euromarket Interest Rates: An Empirical Investiga­
tion,” Journal of Monetary Economics (January 1987), pp.
25-44.
Cosset, Jean-Claude. “ Forward Rates as Predictors of Future
Interest Rates in the Eurocurrency Market,” Journal of Interna­
tional Business Studies (Winter 1982), pp. 71-83.
Dornbusch, Rudiger. “ Exchange Rate Economics: Where Do
We Stand?,” Brookings Papers on Economic Activity (1980:1),
pp. 145-85.
Edwards, Sebastian. “ Exchange Rates and News': A MultiCurrency Approach," Journal of International Money and
Finance (December 1982), pp. 211-24.
Fels, Joachim. “The European Monetary System 1979-87:
Why Has It Worked?," Intereconomics (September/October
1987), pp. 216-22.
Gilbert, R. Alton. “ Operating Procedures for Conducting Mone­
tary Policy," this Review (February 1985), pp. 13-21.
Hakkio, Craig S., and Leonardo Leiderman. “ Intertemporal
Asset Pricing and the Term Structure of Exchange Rates and
Interest Rates: The Eurocurrency Market,” European Eco­
nomic Review (April 1986), pp. 325-44.
Hansen, Lars P., and Robert J. Hodrick. “ Forward Exchange
Rates as Optimal Predictors of Future Spot Rates: An Econo­
metric Analysis,” Journal of Political Economy (October 1980),
pp. 829-53.




Krol, Robert. “The Interdependence of the Term Structure of
Eurocurrency Interest Rates,” Journal of International Money
and Finance (June 1986), pp. 245-53.
Mankiw, N. Gregory, and Jeffrey A. Miron. “ The Changing
Behavior of the Term Structure of Interest Rates,” Quarterly
Journal of Economics (May 1986), pp. 211-28.
Mankiw, N. Gregory. “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity (1:1986),
pp. 61-96.
Rich, Georg, and Jean-Pierre Beguelin. “ Swiss Monetary
Policy in the 1970s and 1980s: An Experiment in Pragmatic
Monetarism,” in Monetary Policy and Monetary Regimes,
Center Symposium Series, CS-17, Karl Brunner, ed., Center
for Research in Government Policy and Business, University
of Rochester (1985), pp. 76-111.
Shiller, Robert J., John Y. Campbell, and Kermit L.
Schoenholtz. “ Forward Rates and Future Policy: Interpret­
ing the Term Structure of Interest Rates,” Brookings Papers
on Economic Activity (1:1983), pp. 173-217.
Wallich, Henry C. “ Recent Techniques of Monetary Policy,"
Federal Reserve Bank of Kansas City Economic Review,
(May 1984), pp. 21-30.
Ungerer, Horst, Owen Evans, Thomas Mayer, and Philip
Young. The European Monetary System: Recent Develop­
ments, Occasional Paper No. 48 (International Monetary
Fund, December 1986).
Zellner, Arnold. “An Efficient Method of Estimating Seemingly
Unrelated Regressions and Tests for Aggregation Bias,”
Journal of The American Statistical Association (June 1962),
pp. 348-68.

SEPTEMBER/OCTOBER 1988

46

Albert E. Burger
Albert E. Burger is a vice president at the Federal Reserve Bank
of St. Louis. Laura A. Prives provided research assistance.

The Puzzling Growth of the
Monetary Aggregates in the
1980s

M

l w i O D E R N m a croecon o m ic analysis assigns
the key role in aggregate d em an d m an agem ent to
m on etary policy. This role is carried out through
changes in the m o n e ta iy aggregates. Since there
are several m on etary aggregates — M l, M2 and M3
— con siderable confu sion m ay d evelop about the
m eaning o f th eir behavior, particularly w h e n they
d o not m ove in lock step w ith each o th er o r w ith
the grow th o f the m o n eta iy base. Such confusion
is esp ecially likely to h ap pen w hen, as has h ap­
p en ed in the 1980s, th eir m ovem en ts are quite
unusual bv historical standards.

In the 1980s, these relationships changed quite
dram atically. From 1984 through 1987, the m o n e­
ta iy base grow th averaged about 6 p ercen t to 8
percent. In sharp contrast to its previous historical
relationship, M l grow th averaged 7 p ercen t to 12
percent; in 1986 alone, M l g re w 4 percen tage
points faster than the base. M ean w hile, the grow th
rates o f M2 and M3 d ec lin ed relative to the grow th
o f the base: in 1986, th ey fell b e lo w base grow th,
and in 1987, base grow th ex ceed ed the grow th o f
M2 and M3 b y m ore than 2 p ercen tage points.

T h e m onetary base can be thought o f as the
fou ndation on w h ic h all the m o n eta iy aggregates
are built; it is also the set o f m on etary assets m ost

M a jor shifts in the p u b lic’s h oldin gs o f m o n eta iy
assets have a ccou n ted for these ch anged relation ­
ships. This article describes a fram ew ork that both
incorporates the relative am ounts o f different

closely related to Federal Reserve actions. Prior to
the early 1980s, there w as a fairly stable relation ­

m on etary assets the pu blic desires to h old and
relates the grow th o f M l, M2 and M3 to the m o n e­

ship on an annual basis b etw een the grow th rate

ta iy base. This fram ew ork is then used to analyze

o f the m on etary base and the grow th rates o f M l,

the unusual m ovem en ts o f these aggregates d u r­

M2 and M3. Th e m on etary base g re w about 1 p er­

ing the past fe w years.

centage point faster than M l; and the o th er tw o
aggregates, M2 and M3, g r e w about 2 o r 3 p ercen t­
age points faster than the m on etary base. Thus,
w h en Federal Reseive actions resulted in a 6 p e r­

SOURCES AND USES OF THE
MONETARY BASE

cent annual grow th rate o f the m on etary base, M l
w o u ld g ro w at about 5 percent, M2 at 8 percen t
and M3 at about 9 percent.


FEDERAL RESERVE BANK OF ST. LOUIS


T h e m o n eta iy base is essentially d erived from
the Federal Reserve’s balance sheet and can be

47

Table 1
Components of the Monetary Base: December 1987
(billions of dollars, not seasonally adjusted)
Sources
Federal Reserve holdings of
government securities
Federal Reserve loans
Float plus other Federal
Reserve assets
Other items'
Source base
Reserve adjustment2
Monetary base

Uses

$227.8
0.8

17.3
19.4
265.0
7.7
272.8

Depository institution deposits
at Federal Reserve banks
Currency held by depository
institutions
Currency held by
nonbank public

$ 37.7
30.9
196.5

Source base
Reserve adjustment2
Monetary base

265.0
7.7
272.8

'Other items include: Treasury deposits at Federal Reserve Banks, special drawing rights, Treasury
currency outstanding, Treasury cash holdings, foreign and other deposits with Federal Reserve
Banks, service-related balances and adjustments, and other Federal Reserve liabilities and capital.
Adjustment for reserve requirement ratio changes.

co m p u ted eith er from the sources side — the
item s that su pply base — o r from the uses side —
the item s that absorb base.1As table 1 shows, the
m a jor source o f the m on etary base is Federal Re­
serve h oldin gs o f govern m en t securities. Changes
in this item reflect the F e d ’s o p en market op era ­
tions; during the last 10 years, it has accou n ted for
about 80 percen t o f the total change and m ost o f
the vear-to-vear fluctuations in the base.
W h en the Federal Reserve makes an o p en m ar­
ket purchase o f govern m en t securities, o th er fac­
tors the same, m ore m o n eta iy base is su p p lied to
the financial sector and the public. This increase
in the base is then "u s e d ” by the pu blic and d e ­
pository institutions as additions to th eir h oldin gs
o f cu rren cy and reserves. Th e increase in reserves
form s the base from w h ic h to expan d derivative
m o n e ta iy assets created b y financial institutions.
Because the pu blic chooses the relative p ro p o r­
tions o f these types o f assets th ey w an t to hold, it
determ in es the relationship betw een the grow th
o f the base and the resulting grow th o f the various
m o n e ta iy aggregates.

'For a discussion of the concept and derivation of the monetary
base, see Burger and Balbach (1976). There are two available
measures of the monetary base, one published by the Federal
Reserve Board and the other by the Federal Reserve Bank of
St. Louis. The Board’s measure is a “ uses” concept and the
Federal Reserve Bank of St. Louis’ is a “ sources” concept. The
major difference is that the St. Louis Fed treats all vault cash
contemporaneously while the Board lags the vault cash com­
ponent of total reserves, reflecting its treatment as total re­




THE LINK BETWEEN THE
MONETARY BASE AND THE
MONETARY AGGREGATES
T h e relationship b etw een the m o n e ta iy base
and any m o n e ta iy aggregate can be expressed in
the fo llo w in g manner:
M = mB.
T h e m o n e ta iy base (B) is related to the specified
m o n e ta iy aggregate (M) by a m o n ey m u ltip lier (m).
Given the m o n e ta iy base, the m u ltip lier sum m a­
rizes the effect o f po rtfo lio decision s b y the public
and financial institutions on a m o n e ta iy aggregate.
In term s o f gro w th rates, this expression can be
w ritten :
iVI = ill + B,
w h ere the dot above each item den otes its grow th
rate. If the m o n ey m u ltipliers w ere constant over
time, then the grow th rates o f the m o n e ta iy aggre­
gates w o u ld fo llo w the sam e pattern as the grow th

serves. In analyzing periods of two or more quarters, the differ­
ences in results between the two base concepts is very small.
For a further discussion of these measures, see Burger (1979)
The source base is usually “ adjusted” to incorporate the
influence of reserve requirement changes into movements in
the adjusted monetary base. For a discussion of this adjust­
ment, see Burger and Rasche (1976), Burger (1979) and, for
the most recent method of calculating this adjustment, Gilbert
(1987).

SEPTEMBER/OCTOBER 1988

48

Chart 1
M1 Multiplier

1960

1965

1970

1975

1980

1985

1990

o f the m on etary base, and all aggregates w o u ld
g r o w together.

b etw een the grow th o f the m on etary base and M l.

As the next section shows, how ever, these m u lti­
pliers have not been constant. Consequently, al­
thou gh the grow th rates o f M l and the m on etary
base have b een h igh ly correlated, there have still
been period s such as 1974-76 and 1985-87 w h en
they diverged substantially. Th e grow th rates o f
M2 and M3 have been less closely tied to the
grow th o f the m on etary base and, although both

For the rem a in d er o f the 1970s, the M l m u lti­
p lier d eclin e slo w ed to about its 1962-73 pace.
Then, about mid-1980, the M l m u ltip lier flattened
out and sh o w ed little grow th on average until
early 1985, w h e n its beh avior ch anged m arkedly. It
rose at a 1.7 percen t annual rate in 1985; in 1986 its
grow th in creased to 4 percent. T h e M l m u ltip lier
d eclin ed som ew h at in mid-1987; h ow ever, w h e n

have been h igh ly correlated, th ey have frequ ently
diverged from the grow th o f M l.

EXAMINING THE BEHAVIOR OF THE
MULTIPLIERS
As chart 1 shows, from the early 1960s through
the 1970s, there w as a long-run d o w n w a rd trend
in the M l m u ltiplier. Th e m u ltip lier d rifted lo w e r
from the early 1960s through 1973, d eclin in g at
about a 1 percen t annual rate. D uring the next
three years, it fell faster at about a 3 p ercen t an­

FEDERAL RESERVE BANK OF ST. LOUIS


nual rate. This w as reflected in a w id e n in g spread

m easured on an annual basis, it still rose another
2 percen t in 1987. As chart 1 indicates, this p ro ­
lo n g ed and substantial rise w as w ith ou t preced en t
since the early 1960s.
Chart 2 show s that the M2 and M3 m o n ey m u lti­
pliers have fo llo w e d v ery different paths. T h ey
gen erally rose fo r m ost o f the p e rio d since the
early 1960s, w h ile the M l m u ltip lier w as falling. In
the last fe w years, w h ile the M l m u ltip lier has
been rising, how ever, the M2 and M3 m u ltipliers
have fallen. D uring the p e rio d sh ow n in chart 2,
three broad grow th patterns em erge in the M2 and

49

Chart 2
M2 and M3 Multipliers
Ratio
15

Ratio
15

Annual Data

14

14

13

13

M3 Multiplier
12

12

/

11

11

s '
10

10

'' M2 Multiplier

I

~

11
1
1
1
1
II1
1

w
1960

^

1965

1970

M3 m ultipliers. From the early 1960s through early
1982, they in creased on average at about a 2 p e r­
cent rate. In early 1983, th ey cam e to a halt, and
for the next tw o years, they sh ow ed essentially no
grow th . In early 1986, how ever-, the M2 and M3
m u ltipliers began a d eclin e that has lasted into
1988.

A Model o f the Money Multipliers
Th e substantial break in the usual beh avior o f
the m o n ey m u ltipliers in the 1980s w as reflected
in the unusual beh avior o f the m on etary aggre­
gates relative to the grow th o f the m on etary base,
and to each other. T o exam in e w h y this was the
case, on e m ust d ev elo p explicit form s o f the re­
spective m u ltipliers to analyze h o w the ch anging
po rtfo lio preferen ces o f the pu blic have affected
them.

1975

1985

1980

1990

m3 = M3/B,
R

t3

= reserves o f d ep o sito ry institutions adjusted
fo r reserve requ irem en t changes,
= cu rren cy h eld by the public,
= m on etary base = R + C,
= checkable deposits,
= the public's desired cu rren cy ratio = C/D,
= the p u b lic’s desired nontransactions bal­
ance ratio = IM2 — M l I/D,
= IM 3-M 2I/ D , and

r

= reserve ratio = R/D,

C
B
D
k
t2

the fo llo w in g explicit form s o f the m u ltipliers can
be d erived (see a p p en d ix 1 fo r this derivation):
ml = i ± k
r+ k

m , = 1 + k + t2

r+ k

m3 =

1 + k + 13
r+ k

In this fram ew ork, a distin ction can be m ade

Given the fo llo w in g definitions,

am ong three m a jor classes o f assets. As table 2
shows, M l represents transaction balances,

m l = Ml/13,

(M2 — M l) represents liqu id savings balances, and

m2 = M2/B,

(M3 — M2) represents m an aged liabilities o f de-




SEPTEMBER/OCTOBER 1988

50

ratio exert a dom in ant in flu ence on m ovem en ts in

Table 2
Components of the Monetary
Aggregates: December 1987 (not
seasonally adjusted)________________
Monthly
Average

M1

M2-M1

M3-M2

J Currency

( Total checkable deposits
1 Savings deposits
Small time deposits
MMDA
Money market mutual funds
, Overnight RP and Eurodollars
Large time deposits
Term RP and Eurodollars
I Institution-only MMMF

$199.4
560.1
410.0
914.6
525.2
221.1
78.1
485.4
196.3
89.6

pository financial institutions. W h en eith er the
specific characteristics or the relative yield s o f
these assets change, the pu blic respon ds b y alter­
ing the am ounts o f these assets th ey w ish to hold.
T h e k, t2 and t3 ratios capture the effects o f the
pu blic's shifting p referen ces am on g these assets
on the g row th rates o f M l, M2 and M3. A rise in
the r-ratio reflects an increase in d ep o sito ry in sti­
tu tion s’ d esired h oldin gs o f reserves relative to
deposits; h ence, a rise in this ratio redu ces all
three m ultipliers.
Given this fram ew ork, w e can n o w exam in e the
beh avior o f these ratios and d eterm in e th eir c o n ­
tribution to the m o n ey m u ltip lier m ovem ents,
esp ecially in recent years.

The Currency Ratio
A rise in the k-ratio reflects an increase in the
p u b lic’s desired h old in gs o f cu rren cy relative to
checkable deposits. For a given am ount o f m o n e ­
tary base, this m eans a redu ction in the portion o f
base held by d e p o s ito iv institutions (reserves) and,
consequently, a redu ction in checkable deposits.
Th erefore, a rise in the k-ratio redu ces all three
m o n ey m ultipliers.
It has been lo n g re co g n ized that, given the
grow th o f the m on etary base, variations in the k-

2See Cagan (1958).
3See Gutmann (1977).
4See Garcia (1978) and Dotsey (1988).


FEDERAL RESERVE BANK OF ST. LOUIS


M l and a strong in flu ence on m ovem en ts in oth er
m o n eta iy aggregates.- As chart 3 illustrates, m o ve­
m ents in the M l m u ltip lier are essentially the
m irror im age o f m ovem en ts in the k-ratio. Thus,
deviations o f M l grow th from base grow th are
pred om in an tly due to sharp changes in the
grow th o f the cu rren cy ratio (the quantitative ef­
fects o f these changes are d erived in a p p en d ix II).
Chart 3 show s that the cu rren cy ratio in creased
from the early 1960s until the early 1980s. On an
annual basis, the k-ratio sh o w ed no n oticeable
declin e in this 21-year p eriod ; in deed, there w ere
fe w years w h e n it d id not increase b y at least 1
percent. D uring the early 1980s, the cu rren cy ratio
sh ow ed little grow th . Then, in early 1985, instead
o f the public in creasin g its cu rren cy h oldin gs rela­
tive to checkable deposits, as had been its lo n g ­
term pattern, the pu blic began to do just the o p ­
posite. C onsequently, there w as a m ajor change in
the beh avior o f the k-ratio. D uring 1985, the k-ratio
fell 2.8 percent; in 1986, it d ec lin ed 7.7 percent;
and, in 1987, it d ro p p e d an oth er 4.1 percent.
Studies in dicate that m a jor changes in the
grow th o f the k-ratio are related prim arily to fac­
tors that affect the checkable dep osit co m p o n en t
o f this ratio. A lthou gh attem pts have been m ade to
trace the rise in the k-ratio in the 1970s to a sharp
increase in cu rren cy d em an d alon g w ith the rise
o f the "u n d ergrou n d eco n o m y ,”3 cu rren cy d e ­
m an d has b een fou n d to be stable over lo n g p e ri­
ods o f tim e.4
T h e am ou nt o f transaction balances that in d i­
viduals and firms desire to h old relative to oth er
assets is in flu en ced by such factors as current and
e x p ected rates o f inflation, relative yield s on oth er
assets and available alternative assets. In the
1970s, inflation accelerated, interest rates rose,
n ew form s o f savings accounts w ere o ffered to the
public and n ew cash m an agem ent techniques
becam e available to business. Unlike the dem an d
for currency, the d em a n d fo r checkable deposits
was substantially affected by these developm en ts,
particularly the financial innovations. For exam ­
ple, business h oldin gs o f transaction balances
relative to financial assets d ec lin ed from about 74
p ercen t in 1970 to about 38 p ercen t in 1981. This
d eclin e w as m ost closely related to the rise o f cash

51

Chart 3
Currency Ratio and M1 Multiplier
k-ratio

M1 Multiplier

Annual Data

m anagem ent techniqu es.1T h e m a jor effect of
these develop m en ts fell on the checkable deposit
co m p o n en t o f transaction balances, resulting in
an accelerated rise in the cu rren cy ratio from 1972

su per-N O W accounts (NOW' a ccou nts w ith no
m in im u m m aturity and no ceilin g on yield s) w ere
perm itted.

throu gh the rest o f the decade.

This deregu lation blu rred the sharp distinction
b etw een transaction and savings accounts that
had existed fo r nearly 50 years. Th e Banking A ct o f
1933 had p roh ib ited the paym en t o f interest on
d em a n d deposits, m aking the checkable c o m p o ­
n ent o f M l a relatively unattractive sav ings vehicle,
esp ecia lly in tim es o f rising interest rates. Som e
changes to this situation took place in the 1970s,
but d id not have a m a jor effect on the unique
transaction characteristics o f M l. Then, in the
1980s, checkable dep osits that y ie ld e d explicit
interest and had m an y o f the characteristics o f

In 1978 and 1979, sm all-d enom in ation tim e d e ­
posits o f varying m aturities, w ith interest rates tied
to Treasu ry certificates o f com parab le maturities,
w e re au th orized. In 1980, w ith the passage o f the
D ep ository Institutions D eregu lation and M o n e ­
tary C ontrol Act, a six-year phase-out o f interest
rate ceilin gs on tim e dep osits w as established11;
m oreover, n a tio n w id e N O W a ccou nts w e re autho­
rized at the en d o f 1980. In 1982, n ew types o f time
deposits that paid market interest rates w ere in ­
trod u ced and the Garn-St. Germ ain Act was
passed w h ich a u th o rized m o n ey market deposit
accounts. By the en d o f 1983, alm ost all interest

savings deposits w ere in trodu ced.
T h e yie ld s on these n ew checkable deposits

rates on tim e dep osits w ere deregu lated and

adju sted very sluggishly to changes in market

5From 1972 to 1980, the demand deposit share of liquid assets
fell at about a 6 percent annual rate. The decline in house­
holds’ holdings of transaction balances as a proportion of liquid
assets was relatively minor. The rate of decline of neither
household nor business holdings of transaction balances

seems closely tied to interest rate fluctuations in the 1970s
(Kopcke, 1987).




6See Gilbert (1986).

SEPTEMBER/OCTOBER 1988

52

interest rates.7C onsequently, as market interest
rates fell sharply in the 1980s, the spread b etw een
the rates offered on checkable deposits and m ar­
ket interest rates on o th er short-term liqu id assets
clo sed rapidly. Th e public resp o n d ed bv h old in g
m ore checkable deposits." T h e dem and for cu r­
rency, how ever, w as m u ch less affected by these
developm en ts, causing the cu rren cy ratio to flat­
ten out from 1980 to 1984, then decrease sharply
in 1985.
In addition to its dom in ant effect on the M I
m ultiplier, the k-ratio also exerts a strong in ­
flu ence on the m ovem ents o f the o th er m o n eta iy
aggregates. A com parison o f charts 2 and 3, h o w ­
ever, show s that the M2 and M3 m u ltipliers w ere
rising w h e n the k-ratio rose then flattened out in
recent years w h e n the k-ratio fell sharply. Clearly,
for the M2 and M3 m ultipliers, the in flu ence o f
o th er factors d o m in a ted the effect o f the k-ratio.

The t2-Ratio
A rise in the t2-ratio reflects the p u b lic’s desire
to h old m o re savings-tvpe deposits (M2 — M l)
relative to checkable deposits. Since the t2-ratio
enters d irectly into the n um erator o f the M2 and
M3 m ultipliers, a rise in this ratio increases these
m u ltipliers.” Chart 4 show s the dom in an t in ­
flu en ce o f the t2-ratio on the M2 and M3 m u ltip li­
ers. A lthou gh the rising k-ratio exerted a negative
in flu ence on these m u ltipliers fo r m ost o f the p e ­
rio d sh ow n in the chart, its in flu ence w as offset by
the m o vem en t o f the t2-ratio. (A p p en d ix II qu an ­
tifies the in flu en ce o f each o f these ratios on the
M2 and M3 m ultipliers.) T h e greater d isparity b e ­
tw een the m ean grow th rate o f these m u ltipliers
and that o f the base (than that b etw een M l and
the base) d u rin g m ost o f the 1960s and 1970s was
the result o f the 4 p ercen t annual rate o f grow th o f
the t2-ratio.
T h e 1985-87 period stands out in contrast to
previous periods. A lthou gh the t2-ratio declined ,
as sh ow n in chart 4, the M2 and M3 m u ltipliers
did not d eclin e as m u ch as on e w o u ld have ex­
pected, given the d eclin e in the t2-ratio alone. In

7See Wenninger (1986) and Roth (1987).
8A Federal Reserve survey of changes in the use of cash and
transaction accounts from 1984 to 1986 found that individuals
consolidated their accounts, increased their use of checking
accounts as a family savings vehicle and diminished their use
as a media for transactions. The study also found that average
cash balances increased with the decline in interest rates,
while portfolio considerations became more important and
transaction motives less important in how people managed
cash and transaction accounts between 1984 and 1986 (Avery
et. a l„ 1987).


FEDERAL RESERVE BANK OF ST. LOUIS


this period, how ever, the falling k-ratio, as show n
in chart 3, partly offset the t2-ratio's negative effect
on these m ultipliers.
As chart 5 shows, m ovem en ts in the t2-ralio
have been dom in ated by relative m ovem en ts o f
savings (SVC) and small tim e dep osits (S I D). Dur­
ing the 1970s, the sharply rising proportion o f
small tim e deposits relative to checkable deposits
ISTD/D) p rovid ed the m a jor im petus fo r the rise in
the t2-ratio. T h e stron g n egative in flu ence o f the
savings co m p o n en t in the late 1970s and early
1980s w as further offset by a sharp rise in o th er
liquid savings instrum ents such as MMDAs,
M M M Fs and overnight RPs relative to checkable
deposits (OL/D). W h en the t2-ratio d ec lin ed in late
1985 through mid-1987, it w as p red o m in an tly b e­
cause o f a sharp fall in the ratio o f sm all tim e d e ­
posits to checkable deposits.

The t3-Ratio
In recent years (1983-87), the spread b etw een
the grow th rates o f M3 and M 2 has been m u ch
n arrow er than it w as in the 1970s and early 1980s.
This change can be explain ed b y the beh avior o f
the t3-ratio. This ratio, w h ic h captu res the public's
d esired h oldin gs o f assets in clu d ed so lely in M3
co m p a red w ith checkable dep osits d eterm in es the
spread b etw een the M3 and M2 m u ltipliers. Chart
6 show s that, as this ratio rose sh arply from the
early 1970s to the early 1980s, the spread b etw een
the M3 and M2 m u ltipliers rose steadily. A fter
1982, h ow ever, as the t3-ratio fell, the spread b e ­
tw een the M3 and M2 m u ltipliers stabilized.
M ovem en ts o f large tim e dep osits have d o m i­
nated m ovem en ts o f the t3-ratio. T h e o th er c o m ­
p on en ts o f (M3 — M2) con stitu ted n o m o re than
20 p ercen t o f the total until 1977. A lth ou gh these
o th er m an aged liabilities (term RPs and E u rod ol­
lars and in stitu tion-only M M M Fs) rose rapid ly
enou gh to account fo r 36 p ercen t o f the total by
1987, fluctuations in large tim e deposits con tin u ed
to be the dom in an t cause o f t3-ratio fluctuations.
The sharp break in this ra tio ’s long-run pattern
that o ccu rred in late 1984 and con tin u ed o ver the

9To the extent that (M2 - M1) contains reservable liabilities, an
increase in time and savings deposits absorbs reserves and
reduces the multipliers. In previous formulations of the multi­
plier, a t-ratio appears in the denominator of all the multipliers
(see Burger, 1971). In the multipliers presented in this paper,
this effect is not separated out in the denomination of the
multipliers, but its effect is reflected in movements in the r-ratio.
This influence varies between the period before 1980 and after
1980, because of the definition of adjusted reserves that ap­
pears in the r-ratio. The exact nature of this influence is shown
in Gilbert (1987).

53

Chart 4
M2 and M3 Multipliers and t2-Ratio

1960

1965

1970

1975

1980

1985

1990

next n ine quarters reflected a slo w in g o f the
grow th o f large tim e deposits relative to the
grow th o f checkable deposits. A lthou gh the

affected the various m o n e ta iy aggregates in d is­
parate w ays. T h e fram ew ork p resen ted in this
article is o n e w a y to isolate the shifts that in ­

grow th o f o th er m an aged liabilities slo w ed in 1985,
it resu m ed its previous pace in 1986 and 1987.

flu en ced the m on etary aggregates and illustrate
th eir effects on the grow th rates o f the aggregates.

SUMMARY
Lookin g at past relationships, on e m ight be
tem p ted to con jectu re that, in the 1980s, the m o n ­
eta iy aggregates b ecam e totally d iscon n ected from
Federal Reserve actions as su m m arized in the
m o n eta iy base. Bv presen tin g a fram ew ork that
can be u sed to explain the m ovem en ts o f the ag­

REFERENCES
Avery, Robert B., George E. Elliehausen, Arthur B. Kennickell,
and Paul A. Spindt. "Changes in the Use of Transaction
Accounts and Cash from 1984 to 1986,” Federal Reserve
Bulletin (March 1987), pp. 179-96.

gregates both relative to each o th er and relative to
the grow th o f the m on etary base, this article has

Brunner, Karl and Meltzer, Allan H. “ Liquidity Traps for Money,
Bank Credit and Interest Rates,” Journal of Political Economy
(January/February 1968), pp. 1-37.

sh ow n this not to be the case. D uring the 1980s,
n ew financial assets w e re in trod u ced and m ajor

Burger, Albert E. The Money Supply Process, (Wadsworth
Publishing Co., 1971).

changes o ccu rred in inflation, interest rates and
tilt; basic characteristics o f m ost o f the traditional
m o n eta iy assets. In response to these events, the
public m ade sizable shifts in its portfolio, w h ich




_________“ Alternative Measures of the Monetary Base,” this
Review (June 1979), pp. 3-8.
Burger, Albert E., and Anatol B. Balbach. “ Derivation of the
Monetary Base,” this Review (November 1976), pp. 2-8.

SEPTEMBER/OCTOBER 1988

54

Chart 5
Components of the t2-Ratio

Burger, Albert E. and Rasche, Robert H. “ Revision of the
Monetary Base,” this Review (July 1977), pp. 13-23.

Gutmann, Peter. “The Subterranean Economy," Financial
Analysts Journal (November/December 1977), pp. 26-28.

Cagan, Phillip. “The Demand for Money Relative to the Total
Money Supply,” Journal of Political Economy (August 1958),
pp. 303-28.

Hess, Alan C. “ An Explanation of Short-Run Fluctuations in the
Ratio of Currency to Demand Deposits,” Journal of Money,
Credit and Banking (August 1971), pp. 666-79.

Dotsey, Michael. “The Demand for Currency in the United
States," Journal of Money, Credit and Banking (February
1988), pp. 22-40.

Judd, John P., and Bharat Trehan. “ Portfolio Substitution and
the Reliability of M1, M2 and M3 as Monetary Policy Indica­
tors,” Federal Reserve Bank of San Francisco Economic
Review (Summer 1987), pp. 5-29.

Gillian, Garcia. “The Currency Ratio and the Subterranean
Economy," Financial Analysts Journal (November/December
1978), pp. 64-69.
Gavin, William, and Pakko, Michael. “ M1-M1A?" Federal
Reserve Bank of Cleveland Economic Review (July 1,1987).
Gilbert, R. Alton. “ Requiem for Regulation Q: What It Did and
Why It Passed Away," this Review (February 1986), pp. 2 2 37.
_________“ A Revision in the Monetary Base,” this Review
(August/September 1987), pp. 24-29.


FEDERAL RESERVE BANK OF ST. LOUIS


Kopcke, Richard W. “ Financial Assets, Interest Rates and
Money Growth,” New England Economic Review Federal
Resen/e Bank of Boston (March/April 1987), pp. 17-30.
Motley, Brian. “ Should M2 be Redefined?” Federal Reserve
Bank of San Francisco Economic Review (Winter 1988), pp.
33-51.
Rasche, Robert H., and James M. Johannes. Controlling the
Growth of the Monetary Aggregates (Kluwer, 1987).

55

Chart 6
Spread Between M3 and M2 Multipliers and t3-Ratio
t3-ratio

A nnual D ata

Multipliers

S** --------

A
M3 Multiplier less *t
*
M2 Multiplier
*
scaie^

t
*

**
*■+
•

^lrl _.■------- " —

/
*
*

—

/r
y

/✓
/

/

v

/ v“

v
•

•

t3-ratio
< scale

—'''

1960

1965

1970

1975

1980

1985

1990

Roth, Howard. “ Has Deregulation Ruined M1 as a Policy
Guide?” Federal Reserve Bank of Kansas City Economic
Review (June 1987), pp. 24-37.

Tatom, John A. “ Recent Financial Innovations: Have They
Distorted the Meaning of M1 ?” this Review (April 1982), pp.
23-35.

Simpson, Tom. “ Changes in the Financial System: Implications
for Monetary Policy,” Brookings Economic Papers (Volume 1,
1984), pp. 249-65.

Wenninger, John. “ Responsiveness of Interest Rate Spreads
and Deposit Flows to Changes in Market Interest Rates,”
Federal Reserve Bank of New York Quarterly Review (Au­
tumn 1986), pp. 1-10.




SEPTEMBER/OCTOBER 1988

56

Appendix I
Derivation of Multipliers
M l m ultiplier (m l)

M3 m ultiplier (m3)

AM B = R + HAM + C

m3 =

C + D + M 2 - M l + M3 - M2

^ + C
ml =

Ml

C + D

AM B

R + RAM + C

K)
( ™ > ( e)
ml =

1 + k
r + k

M2 m ultiplier (m2)
m2 =

C + D + M2 - M l
R + RAM + C
( 1 + cK

m

^

)

/R + R A M \ V C \

{— ET-A d)
m2 =

y

R + RAM + C

Ml = C + D

1 + k + t2
r + k


FEDERAL RESERVE BANK OF ST. LOUIS


^M2 - M1^

D( ™

m3 =

)+ (C

1 + k + t2 + t3
r + k

M3 - M2^
) D

57

Appendix II
Magnitude of the Influence of the Component Ratios
on the Multipliers
T h e size o f the effect that each o f the ratios ex ­

e(m2,t2l = 12/I1+k + t2) > 0
elm3,t2l = t2/( 1 + k + t2 + t3l > 0
e(m3,t3) = t3/H + k + t2 + t3l > 0
e(m l,r), e(m2,r), e(m3,r) = - r / (r + k ) < 0

erts on the grow th o f the m o n ey m u ltipliers d e ­
pends hoth on the grow th rate o f each ratio and
the responsiveness o f the m u ltip lier to a ch ange in
the ratio. T h is responsiveness can be qu an tified by
calcu lating the partial elasticities o f each o f the
m u ltipliers w ith respect to its co m p o n en t ratios,
as show n below . T h ese results sh ow that, in this
form ulation, although the respon se o f all the m u l­
tipliers to a ch ange in the r-ratio are the same,
there are differen ces in the response o f the m u lti­
pliers to the o th er ratios.

Table A1 presents the co m p u ted annual
averages o f these elasticities. T h e values o f these
elasticities ch ange over tim e as the ratios change.
For exam ple, the rise in t2-ratio has affected the
relationship betw een the response o f m2 and m3
to a change in the t2-ratio. In the early 1960s,
e(m2,t2) and e(m3,t2) w ere both about the same.
By the early 1980s, the e(m2,t2) h ad risen to about
.76 w h ile e(m3,t2) w as still about .62. In 1985-87,
these elasticities fell as the t2- and t3-ratios
declined .

ELASTICITIES OF THE
MULTIPLIERS WITH RESPECT TO
THEIR COMPONENT RATIOS

T h e m agnitu de o f the in flu ence o f the p o rtfolio
shifts e m b ed d e d in the k-, t2-, and t3-ratios on the
grow th o f the m u ltipliers can be isolated using the
fo llo w in g form ula:

e(m l,k ) = k(r — 1)/(r + k)(1 + k) < 0
e(m2,k) = k ( r - 1 - t2)/(r + k )(l + k +12) < 0
e(m3,k) = k ( r - 1 - 12- t3)/(r + k ) ( l + k +12 +13) < 0

Table A1
Elasticities of the Multipliers with Respect to Their Component Ratios
Year

e(m1,k)

e(m2,k)

e(m3,k)

e(m2,t2)

e(m3,t2)

e(m3,t3)

e(m,r)

Year

1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987

-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 5
-0 .4 4
-0 .4 4
-0 .4 4
- 0 .4 3
-0 .4 3
-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 4
-0 .4 5
-0 .4 6
-0 .4 6
-0 .4 6
-0 .4 6
-0 .4 7
-0 .4 7

-0 .5 7
-0 .5 8
-0 .5 8
-0 .5 8
-0 .5 9
-0 .5 9
-0 .5 9
-0 .5 9
-0 .6 0
-0 .6 0
-0 .6 1
-0 .6 3
- 0 .6 4
-0 .6 4
- 0 .6 5
-0 .6 5
-0 .6 6
-0 .6 7
-0 .6 8
-0 .6 8
-0 .6 8
-0 .6 7
-0 .6 6

-0 .5 8
-0 .5 8
-0 .5 8
-0 .5 8
-0 .5 9
-0 .6 0
-0 .6 0
- 0 .6 0
-0 .6 0
-0 .6 1
-0 .6 2
-0 .6 3
-0 .6 4
-0 .6 5
-0 .6 6
-0 .6 6
-0 .6 8
-0 .6 9
-0 .6 9
-0 .6 9
- 0 .6 9
-0 .6 8
- 0 .6 7

0.63
0.64
0.65
0.65
0.65
0.65
0.67
0.69
0.69
0.70
0.71
0.73
0.74
0.74
0.74
0.75
0.75
0.76
0.76
0.76
0.76
0.75
0.74

0.60
0.61
0.61
0.61
0.62
0.62
0.62
0.63
0.62
0.60
0.61
0.64
0.66
0.64
0.62
0.62
0.61
0.61
0.62
0.61
0.61
0.60
0.59

0.04
0.05
0.06
0.06
0.05
0.05
0.08
0.09
0.11
0.14
0.14
0.12
0.12
0.14
0.16
0.17
0.19
0.20
0.18
0.20
0.20
0.20
0.20

-0 .3 5
-0 .3 4
-0 .3 4
-0 .3 4
-0 .3 4
-0 .3 3
-0 .3 3
-0 .3 3
-0 .3 3
-0 .3 3
-0 .3 2
-0 .3 0
-0 .3 0
-0 .2 9
-0 .2 8
-0 .2 8
-0 .2 7
- 0 .2 6
-0 .2 6
-0 .2 6
- 0 .2 6
-0 .2 7
- 0 .2 8

1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987




SEPTEMBER/OCTOBER 1988

58

m = e(m,k)(k) + e(m,t2)(t2) + e(m,t3)(t3) +
e( m,rllr).
In the above form ula, e lm ___I represents the
partial elasticity o f the respective m u ltip lier w ith
respect to the specified ratio. For exam ple, elm l.ki
w o u ld represent the partial elasticity o f the M l
m u ltiplier (m l) w ith respect to the k-ratio. Th e
dots above the ratios d en ote g ro w th rates. Th e
results o f this d ec om p os itio n o f the grow th rates
ot the respective m u ltipliers are sh ow n in tables
A2, A3 and A4. Th e results through 1984 w ere
co m p u ted using annual g ro w th rates o f the
co m p o n en t ratios that a p p ea r in the m ultipliers,
and the elasticities are the ones rep orted in table
A l. Q uarterly data fo r I/1985-I/1988 w ere
co m p u ted using quarterly grow th rates and
quarterly elasticity measures.
O ver the three years en d in g in 1984, the k-ratio,
on average, sh ow ed essentially no grow th . Then,
from fourth quarter 1984 to first qu arter o f 1986, it
fell at an annual rate o f about 5 percent; over the
next fou r quarters, it fell 10 percent. This effect is
sh ow n in tables A2, A3 and A4, as the negative
contribu tions o f the k-ratio to the g ro w th rates o f
the m u ltipliers becam e sm aller in the early 1980s
and then tu rned into large positive effects
beginn in g in 1985. This effect d om in a ted the
grow th o f m l, lea d in g to a p ro n o u n ced change in
the relationship b etw een the g ro w th o f M l and
the m on etary base. From fourth qu arter 1985 to
first qu arter 1987, the grow th o f M l ex c e e d e d the
grow th o f the m o n e ta iy base b y about 7
percen tage points.
In the 1985-87 period, the effect o f the d eclin in g
k-ratio on the relationships b etw een the grow th o f
M2 and M3 and the grow th o f the m on etary base
was not nearly as m arked as w as the case w ith M l.
Tables A3 and A4 sh o w that the ch anged beh avior
o f t2- and t3-ratios acted to offset the ch anged
beh avior o f the k-ratio on these m ultipliers.

Table A2
Contribution of the Component Ratios
to the Growth Rate of ml
Year

EEMK

EER

MULX

1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987

-0 .5 9
-0 .9 4
-0 .6 5
0.27
-0 .4 8
-1 .4 3
-0 .2 1
0.11
- 0 .6 7
-2 .3 1
- 2 .6 8
-2 .1 0
-0 .8 2
-0 .9 3
-1 .2 2
-1 .8 3
-0 .2 5
-0 .4 8
0.86
-0 .9 1
-1 .3 0
3.59
1.93

-0 .4 6
0.07
-0 .4 1
-0 .0 4
0.75
0.37
-0 .9 1
- 0 .3 4
-0 .3 7
-0 .6 3
-0 .4 1
0.18
0.43
-0 .1 1
0.51
-0 .1 6
-1 .3 6
0.83
0.37
-0 .1 8
0.43
0.51
0.29

-1 .0 2
-0 .8 5
-1 .0 5
-0 .2 6
0.30
-1 .0 5
- 1 .0 6
-0 .2 0
-1 .0 0
- 2 .9 0
-2 .9 9
-1 .7 9
-0 .3 1
-1 .0 2
-0 .6 7
-1 .9 9
1.16
0.33
1.17
-1 .0 8
1.74
4.04
2.19

Quarter

EEMK

EER

MULX

1985.1
1985.2
1985.3
1985.4
1986.1
1986.2
1986.3
1986.4
1987.1
1987.2
1987.3
1987.4
1988.1

2.60
1.97
3.50
2.55
1.50
5.27
6.15
5.93
2.47
- 0 .4 6
-4 .1 2
-3 .6 6
-3 .5 9

0.53
0.69
0.67
0.03
0.29
0.80
0.75
0.72
-0 .4 3
0.22
0.53
0.32
-0 .7 7

3.20
2.70
4.28
2.48
1.77
6.01
6.87
6.49
2.06
- 0 .2 8
-3 .4 8
-3 .3 4
-4 .2 8

EEMK = contribution of k-ratio to growth of m l

Since early to mid-1987, the k-, t2- and t3-ratios
all have risen, resu m in g patterns that are m ore in

EER = contribution of r-ratio to growth of m l
MULX = actual growth rate of m l

line w ith th eir historical behavior. Since the
relative grow th rates o f the aggregates d ep en d on
the in flu en ce o f each o f these ratios on the
respective m ultipliers, the rise in the k-ratio,
w h ic h has been esp ecially strong relative to its
historical pattern (from 11/1987 to 1/1988, the
k-ratio rose at an 8 percen t rate), has d om in a ted
the grow th o f all three m ultipliers, as sh ow n in
tables A2, A3 and A4. C onsequently, the M l
m u ltip lier has fallen and the grow th o f the


FEDERAL RESERVE BANK OF ST. LOUIS


m o n eta iy base has e x ceed ed the grow th o f M l, as
w as gen erally the case before 1985. Th e m u ltipliers
associated w ith M2 and M3, how ever, have fallen
since early 1987; as a result, the grow th rate o f the
m on etary base also has ex ce e d e d the grow th o f
these aggregates. This pattern is qu ite different
from that exp erien ced before 1985.

59

Table A3
Contribution of the Component Ratios to the Growth Rate of m2
Year

EEM2K

EEM2T2

1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987

-0 .7 7
-1 .2 4
-0 .8 6
0.36
-0 .6 4
-1 .9 1
-0 .2 8
0.15
-0 .9 2
-3 .2 0
-3 .7 9
-3 .0 1
-1 .1 8
-1 .3 6
- 1 .7 7
-2 .7 0
- 0 .3 7
-0 .7 1
1.26
-1 .3 4
1.89
5.12
2.71

3.86
2.15
3.00
1.13
0.41
0.78
5.13
4.95
2.75
1.94
5.71
7.80
5.00
0.72
1.12
2.59
2.06
2.76
0.86
1.22
-0 .6 1
-6 .2 2
-5 .4 5

Quarter

EEM2K

EEM2T2

1985.1
1985.2
1985.3
1985.4
1986.1
1986.2
1986.3
1986.4
1987.1
1987.2
1987.3
1987.4
1988.1

3.83
2.89
5.11
3.71
2.17
7.56
8.74
8.34
3.46
- 0 .6 4
- 5 .8 0
-5 .1 6
-5 .1 0

0.49
-4 .5 8
-6 .3 2
-5 .7 8
-3 .4 4
-7 .4 8
-8 .9 1
-10.51
-7 .5 7
- 3 .7 9
3.75
1.54
-4 .3 9

EER
-0 .4 6
0.07
-0 .4 1
-0 .0 4
0.75
0.37
-0 .9 1
- 0 .3 4
-0 .3 7
- 0 .6 3
-0 .4 1
0.18
0.43
-0 .1 1
0.51
-0 .1 6
1.36
0.83
0.37
-0 .1 8
0.43
0.51
0.29
EER
0.53
0.69
0.67
0.03
0.29
0.80
0.75
0.72
-0 .4 3
0.22
0.53
0.32
-0 .7 7

MUL2X
2.59
0.98
1.71
1.45
0.53
-0 .7 4
3.90
4.71
1.45
-1 .8 8
1.51
4.92
4.22
-0 .7 5
-0 .1 2
-0 .2 6
3.07
2.87
2.47
-0 .3 1
1.72
-0 .6 0
-2 .4 7
MUL2X
4.87
-0 .9 9
-0 .5 2
-2 .0 5
-0 .9 8
0.88
0.59
-1 .4 8
-4 .5 3
-4 .2 2
-1 .4 8
-3 .2 9
-1 .4 6

EEM2K = contribution of k-ratio to growth of m2
EEM2T2 = contribution of t2-ratio to growth of m2
EER = contribution of r-ratio to growth of m l
MUL2X = actual growth rate of m2




SEPTEMBER/OCTOBER 1988

60

Table A4
Contribution of the Component Ratios to the Growth Rate of m3
Year

EEM3K

EEM3T2

EEM3T3

1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987

-0 .7 7
-1 .2 5
- 0 .8 7
0.36
- 0 .6 5
-1 .9 2
-0 .2 8
0.15
-0 .9 3
-3 .2 6
- 3 .8 5
-3 .0 5
- 1 .2 0
-1 .3 8
-1 .8 1
- 2 .7 5
-0 .3 7
-0 .7 2
1.28
-1 .3 7
1.93
5.22
2.77

3.69
2.04
2.83
1.06
0.39
0.74
4.74
4.52
2.44
1.66
4.93
6.87
4.42
0.61
0.94
2.14
1.66
2.20
0.71
0.97
-0 .4 9
-4 .9 7
-4 .3 5

1.10
0.87
0.99
0.41
-0 .9 0
0.43
3.17
1.47
3.82
4.20
-0 .0 7
-0 .8 4
0.21
3.65
2.86
1.66
2.74
1.98
-2 .0 8
2.40
-0 .2 0
-1 .3 3
-0 .9 1

Quarter

EEM3K

EEM3T2

EEM3T3

1985.1
1985.2
1985.3
1985.4
1986.1
1986.2
1986.3
1986.4
1987.1
1987.2
1987.3
1987.4
1988.1

3.91
2.95
5.20
3.78
2.22
7.71
8.91
8.50
3.52
-0 .6 6
-5 .9 2
- 5 .2 7
-5 .2 1

0.39
-3 .6 6
-5 .0 7
-4 .6 3
-2 .7 4
-5 .9 7
-7 .1 3
-8 .4 4
-6 .0 8
-3 .0 3
2.98
1.22
3.48

-1 .8 9
-1 .7 0
-3 .3 6
-0 .7 3
1.75
-2 .5 6
-2 .9 1
-3 .7 2
-1 .5 2
1.33
2.58
1.95
0.85

EEM3K = contribution of k-ratio to growth of m3
EEM3T2 = contribution of t2-ratio to growth of m3
EEM3T3 = contribution of t3-ratio to growth of m3
EER = contribution of r-ratio to growth of m3
MUL3X = actual growth rate of m3


FEDERAL RESERVE BANK OF ST. LOUIS


EER
- 0 .4 6
0.07
-0 .4 1
-0 .0 4
0.75
0.37
-0 .9 1
-0 .3 4
- 0 .3 7
-0 .6 3
-0 .4 1
0.18
0.43
-0 .1 1
0.51
-0 .1 6
1.36
-0 .8 3
0.37
-0 .1 8
0.43
0.51
0.29
EER
0.53
0.69
0.67
0.03
0.29
0.80
0.75
0.72
-0 .4 3
0.22
0.53
0.32
- 0 .7 7

MUL3X
3.43
1.68
2.48
1.79
-0 .4 7
-0 .3 7
6.26
5.70
4.52
1.57
0.58
3.00
3.84
2.42
2.34
0.87
5.29
4.24
0.15
1.73
1.68
- 0 .5 8
-2 .2 2
MUL3X
2.94
-1 .7 1
-2 .5 5
-1 .5 6
1.48
-0 .0 2
-0 .3 7
-2 .9 6
- 4 .5 0
-2 .1 6
0.20
-1 .7 8
- 1 .6 4




Federal Reserve Bank o f St. Louis
Post O ffice Box 442
St. Louis, M issou ri 63166

The Review is published six
times per year by the Research
and Public Information
Department o f the Federal
Reserve Bank o f St. Louis.
Single-copy subscriptions are
available to the public free o f
charge. Mail requests f o r
subscriptions, back issues, or
address changes to: Research
and Public Information
Department, Federal Reserve
Bank o f St. Louis, P.O. Box 442,
St. Louis, Missouri 63166.
The views expressed are those
o f the individual authors and do
not necessarily reflect official
positions o f the Federal Reserve
Bank o f St. Louis or the Federal
Reserve System. Articles herein
may be reprinted provided the
source is credited. Please provide
the Bank’s Research and Public
Information Department with a
copy o f reprinted material.