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Review
Vol. 66, No. 6




June/Julv 1984

5 A Perspective on the Federal Deficit
Problem
18 Money, Debt and Econom ic Activity
26 How Robust Are the Policy
Conclusions of the St. Louis
Equation?: Some Further Evidence

THE
FEDERAL
RESERVE
BANKof
ST. LOUIS

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Fed eral R eserve Bank of St. Louis
Review
June/July 1984

In This Issue . . .




T h e cu rren t d ebate over th e m agnitude o f th e fed eral d eficit involves n u m ero u s
m yths co n cern in g ho w it cam e to be so large, th e outlook for future deficits, and
th e likely eco n o m ic effects o f p ersistin g "large” d eficits. In th e first article in th is
Review, “A Perspective on th e Fed eral D eficit P roblem ," Jo h n A. T atom argues th at
triple-digit deficits in 1982 and 1983 arose largely from th e stron g cy clical d ow n ­
tu rn in th e econom y, n ot from policy actio n s su ch as in crea sed d efen se spending,
re cen t “c u ts” in p erson al in co m e taxes, o r bu rgeoning tran sfer program s.
Tatom p o in ts ou t th at th e rise in d efen se sp en d in g over th e p ast fou r y ears has
b een greatly ou tstrip p ed by th e rise in sp en d in g for federal tran sfer p rogram s an d
has co n trib u ted little to th e 1 9 8 2 -8 3 d eficit pictu re. M oreover, tax cu ts have b een
largely offset by bracket creep , so cial secu rity tax in crea ses an d o th e r tax hikes.
T atom explains that th e eco n o m ic effects o f d eficit in crea ses d ep en d u p on
w h eth er they are cau sed by ch an g es in fiscal p o licy o r by cy clical ch a n g es in th e
n a tio n ’s inco m e, output an d em ploym ent. M ost re cen t d iscu ssio n o f th e possible
adverse effects o f deficits co n c e rn s th o se ca u sed by fiscal policy actio n s, n o t th e
b u sin ess cy cle; this co n c e rn is b asically irrelevant to th e co n sid eratio n o f re cen t
cy clical deficits. F urth erm ore, T atom p o in ts out th at th ere is n o evid en ce su p p o rt­
ing m o st o f th e p u rp orted adverse effects o f h ig h er p olicy -related deficits, su ch as
h ig h er inflation o r in terest rates.
However, Tatom in d icates th at cu rren t p ro jectio n s o f future d eficits p o in t to an
u p tren d in th e stru ctu ral deficit — that part w h ich is related to fiscal p o licy — as
th e cy clical co m p o n e n t is elim in ated . W h eth er th e p ro je c te d grow th o f the
stru ctu ral d eficit w ill have adverse effects on th e eco n o m y is p rob lem atic. T h e lack
o f evidence th at h ig h er stru ctu ral deficits raise in terest rates m ay b e due sim ply to
o u r lack o f past ex p erien ce w ith “large” an d p ersisten t deficits.
In th e seco n d article in th is Review, “M oney, D ebt an d E co n o m ic Activity,” R. W.
Hafer n o tes th at th ere have b ee n in creasin g suggestions th at m o n etary p o licy ­
m akers should u se the inform ation from a variety o f eco n o m ic m easu res rath er
th an focu sing solely on th e behavior o f a m onetary m easure, su ch as M l. Although
th is ap p roach to policy is by no m eans new o r novel, su sp icio n that M l has
d eteriorated as a useful policy m easure in the w ake o f financial innovations has
re-kindled th e d ebate. Partially in resp o n se to th ese argum ents, th e Fed eral O pen
M arket C om m ittee (FOMC) at its February 1983 m eetin g estab lish ed a “m on itorin g
ran g e” for th e grow th o f total d o m estic n on fin an cial debt. Hafer investigates the
u sefu ln ess o f this debt m easu re for m onetary policy p u rp o ses by exam in in g the
relative abilities o f M l and debt growth in explaining th e behavior o f GNP growth.
For th e 1960-81 period, th e explanatory pow er o f M l is about 10 p e rce n t greater
th an that o f th e debt m easu re in its relation sh ip to GNP grow th. M oreover, Hafer
finds that, o n ce th e effects o f M l grow th on GNP grow th are estim ated directly, th e
d ebt grow th m easu re is red u n d an t: it adds n o ad d ition al u seful inform ation.
Hafer th en co m p ares the p erfo rm an ce o f M l an d d ebt in forecastin g GNP growth
d uring th e 1982-83 period. R ecen t velocity behavior suggests th at “th e d ebt m ea­
su re d oes n o t seem to b e a relatively m ore stable guide to GNP behavior th an M l
during th e p ast few y ea rs.” Thu s, forecastin g GNP grow th for 1 9 8 2 -8 3 using the
d ebt m easu re d oes n ot provide any significant gain over th e resu lts b a sed on M l . In

In This Issue ..




fact, th e au th o r n o tes th at if M l is a d ju sted for th e effects o f re cen t financial
innovations w h ich in crea sed M l grow th during 1982-83, th e forecast p erfo rm an ce
o f th is ad ju sted M l m easu re is significantly b ette r th an th at o f debt. C onsequently,
Hafer co n clu d e s th at th ere is little evid ence to su p p o rt th e u se o f a b ro ad debt
m easu re as y et an o th er in term ed iate target for m o n eta iy policy.
In th e third article, “How Robust Are th e Policy C on clu sio n s o f th e St. Louis
E qu ation?: Som e F u rth er E v id ence," Dallas S. B atten an d D aniel L. T h o rn to n poin t
out that, sin ce it w as first u sed in 1968 to investigate th e relative im p o rtan ce of
m o n etaiy and fiscal a ctio n s in in flu en cin g eco n o m ic activity th e St. Louis equation
h as b een su b je ct to m u ch criticism . O ne criticism is th at th e policy co n clu sio n s
may b e d ep en d en t on the eq u a tio n ’s eco n o m etric sp ecificatio n and, in particular,
on th e u se o f A lm on’s polynom ial distribu ted lag estim atio n tech n iq u e. T o investi­
gate th e serio u sn ess o f su ch criticism , B atten an d T h o rn to n co n d u ct a general
investigation o f th e sensitivity o f the St. Louis eq u a tio n ’s p o licy c o n clu sio n s to the
ch o ice o f lag stru ctu re an d polynom ial degree. Using a variety o f m odel selectio n
criteria, they find th at th e policy co n clu sio n s are virtually insensitive to alternative
lag stru ctu res o r polynom ial specification s. In every ca se exam in ed , they co u ld n ot
re je ct th e h yp oth esis that a one percen tag e-p o in t in crea se in m o n ey grow th leads
u ltim ately to a o n e p ercen tag e-p o in t in crease in th e rate o f grow th o f n om in al GNP.
M oreover, the hyp oth esis that h igh-em ploym ent governm ent ex p en d itu res had
no long-run im pact on nom inal GNP grow th w as re je cte d only w h en co n tem p o ra ­
neo u s governm ent sp en d in g grow th a lo n e w as in clu d ed in th e m od el; however,
this sp ecificatio n w as re je cted w h en tested against longer-lag alternatives for
governm ent spending.

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

A Perspective on the Federal
Deficit Problem
John A. Tatom

“ N o n e o f us re a llv u n d e rs ta n d s w h a t’s g o in g o n w ith a ll these n u m b e rs ."

— David Stockm an,
A tla n tic M o n th ly ,

D ecem b er 1981

EDERAL budget deficits o f $200 billion or m ore
have created co n sid erab le controversy and confu sion
am ong analysts, policym akers an d voters. T h e im p o r­
tant problem , o f co u rse, co n c e rn s th e co n se q u e n ce s of
cu rren t an d p ro jecte d spending, receip ts and deficits.
Public co n c e rn about th ese problem s began, however,
w ith the ballooning o f deficits in 1982 and 1983.
M any analysts co n je c tu re th at recen t and p ro jected
large deficits have d eleteriou s effects on the econ om y
— raising in terest rates, exch an ge rates, the inflation
rate, crow ding ou t private se c to r investm ent and e c o ­
n o m ic grow th and th reaten in g th e eco n o m ic recovery.
O thers are m ore sanguine, arguing in stead that recen t
deficits have n o t significantly affected in terest rates,
exch an ge rates o r p rice behavior.1
T h e p u rp o se o f th is article is to assess th ese c o n ­
trasting views on th e ca u ses and co n se q u e n ce s o f re­
ce n t and p rospective deficits. M ost o f the controversy
arises from d ifferences in th eo retical and em pirical
jud gm en ts abou t th e effects o f deficits on th e d em and
for goods an d services. After exam ining th ese relevant
co n cep tu al issues, re ce n t tren d s in th e federal budget
are taken up. T h e n th e se co n cep tu a l d istin ction s are
u sed to clarify th e so u rce an d potential eco n o m ic
effects o f re cen t an d p ro jecte d deficits.

John A. Tatom is a research officer at the Federal Reserve Bank of St.
Louis. Thomas H. Gregory provided research assistance.
1 example of the latter argument is the study by the U.S. Depart­
An
ment of the Treasury (1984). There does appear to be general
agreement about the possibility that deficits can be “ monetized,” that
is, financed by money creation. To the extent this occurs, inflation
would accelerate.



In th e view o f m any analysts, b o th cu rren t deficits
an d future p ro jectio n s in d icate a m a jo r break w ith the
U.S. p ostw ar ex p erien ce. It is suggested below th at this
view is u nw arranted w h en applied to re cen t deficits.
W hile re cen t deficits have b een large co m p ared w ith
earlier ones, th ey have arisen largely from th e u nu su al
cyclical ex p erien ce in th e U.S. econom y, not from u n ­
p reced en ted fiscal policy a ctio n s that raised spen din g
and/or red u ced tax receip ts. Fu tu re deficits, however,
may rep resen t a m a jo r break from th e cu rren t and past
exp erien ce. If so, p a st relatio n sh ip s b etw een deficits
an d eco n o m ic p erfo rm an ce m ay prove to b e o f little
u se in judging th e ir likely effects.

THE TH EO RY O F ACTIVE AND
PASSIVE D E F IC IT S
T h e federal budget deficit is th e ex cess of federal
governm ent exp en d itu res over receip ts. In analyzing
th e so u rces o f th e d eficit and its effect on th e econom y,
it is n ecessa ry to d istin gu ish betw een “active” and
"passive” co m p o n e n ts o f th e deficit. Spending, taxes
and, therefore, th e actu al d eficit are affected by both
d irect policy a ctio n s an d ch an g es in th e level o f e c o ­
n o m ic activity, p rices and in terest rates. T h e latter
ch an g es o cc u r passively, th at is, w ith ou t fiscal policy
action s. Active deficits, in co n trast, are th o se that arise
from legislated ch a n g es in sp en d in g or taxes, g ive n the
o th er eco n o m ic co n d itio n s that in flu en ce th e deficit.
O ne a ttem p t to deal w ith th is d ifferen ce is th e
m e a s u r e m e n t o f th e s o -c a lle d h ig h -e m p lo y m e n t
budget. It involves m easu rin g ex p en d itu res and tax

5

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

receip ts at a h igh-em ploym ent level o f real GNP, given
actu al p rices and in terest rates. T h is m easu re is useful
b eca u se it rem oves th at part o f th e actu al deficit that
arises from passive a d ju stm en t to cy clical flu ctu ation s
in real GNP.

crow ding out, sin ce it ca u ses a red u ctio n in th e supply
of p u rch asin g p ow er available from a given n om in al
m oney stock relative to th e d em an d for it. T h u s, in ­
terest rates rise fu rth er and m ore private sp en d in g is
crow d ed out.

F o r exam ple, as real in co m e exp an d s, tax receip ts
rise and spending (prim arily tran sfer paym ents) d e­
clines, so that the actu al d eficit shrinks. T his d ecrease
(or in crease w hen real in co m es fall) reflects a u to m a tic
m ovem ents th at are bu ilt-in to existing tax an d sp e n d ­
ing legislation. T h is au to m atic resp o n se o f th e d eficit to
eco n o m ic co n d itio n s is referred to as a ch an g e in the
passive d eficit. In co n tra st, leg islated in c re a s e s in
sp en d ing or tax red u ctio n s raise th e actu al d eficit at
any level o f GNP and p ro d u ce a ch an g e in th e active
deficit. At e a c h p o in t in tim e, th e observed deficit
reflects bo th an active co m p o n e n t — th e size o f the
deficit at, for exam ple, a h igh-em ploym ent level o f real
output — an d a passive co m p o n e n t — the part d ue to
th e b u sin ess cycle.

In sum m ary, a sim ple version o f con ven tion al theory
states that a rise in th e active d eficit raises n o t only the
level o f output and em ploym ent, but p rices an d in ­
terest rates as well. C row ding-out o f private investm ent
o ccu rs, slow ing th e grow th rate o f e co n o m ic capacity.

C onventional eco n o m ic analysis, w hich form s the
b asis for m u ch o f th e cu rren t p o p u lar d iscu ssio n , fo­
cu ses on th e effects o f a h ig h er active d eficit th at arises
from eith e r a d iscretio n ary in crease in federal ex p en d i­
tu res o r a cu t in taxes. T h e con ven tion al w isd om in d i­
c a te s th a t an in c re a s e in th e active d eficit cau ses
sp e n d in g on g oo d s an d services to rise. A federal
p u rch a se o f goo d s o r services d irectly raises total
aggregate spending; in creased tran sfer paym ents or
tax red u ctio n s allow g reater sp end in g in th e private
secto r. T hu s, a ch an g e in th e active d eficit is im portant
b eca u se it affects th e level o f real GNP.
At its sim plest level, the con ven tion al analysis in d i­
ca tes that, if the m oney stock is u naltered , interest
rates will rise along w ith real GNP. At h ig h er levels of
sp en d ing and in co m e, th e d em an d for m oney will be
higher. Thu s, in th is view, in terest rates m u st go up
to ration the available m oney stock. O f cou rse, a rise
in rates ten d s to choke off som e o f the exp an sio n in
sp en d ing and in co m e that resu lts from an in crease in
th e active deficit. T h is latter effect is called "crow dingo u t” b ecau se the rise in in terest rates discourages
(crow ds out) private investm ent and co n su m er p u r­
ch ases.
If in co m e and sp en d in g rise as a resu lt o f an in crease
in the active deficit, p rices are likely to rise as well. At
u n ch an ged prices, th e hig her level o f d em and for real
ou tp u t is unlikely to be p ro d u ced . T o in d u ce su ppliers
to p ro d u ce m ore output, th e general level o f p rices will
have to b e bid up. A h ig h er level o f p rices in d u ces m ore

6



A rise in th e passive deficit, in co n trast, reflects a
cyclical d eclin e in real GNP an d em ploym en t. Passive
deficit in crea ses do n ot exert an in d ep en d en t effect on
eco n o m ic activity.2 M oreover, su ch d eficit in creases, in
th e sim ple con ven tion al analysis, are typically a sso ci­
ated w ith a d eclin e in in terest rates and/or p rices, sin ce
cyclical d eclin es in real GNP reflect d eclin in g d em and
for goods an d services an d cred it.
T h ere are m any linkages in th e resu lts above th at are
o pen to qu estion. M ainstream m a cro e co n o m ic c o n ­
clu sio n s d ep en d heavily on alternative h y p oth eses
about th e sensitivity o f investm ent, co n su m e r sp e n d ­
ing, m o n ey d em an d an d aggregate su pply to in terest
rate an d p rice level flu ctu ation s. D epen din g on th ese
a s s u m p tio n s , c o n s id e r a b ly d iffe re n t c o n c lu s io n s
about the effects o f an in crea se in th e active deficit can
em erge.3
C entral to th e con v en tion al analysis is th e co n c lu ­
sion that an in crea se in the active d eficit raises the
d em and for goods an d services at u n ch an g ed p rices
and in terest rates. Even th is resu lt is, in p rin ciple,
problem atic. Som e an alysts em p h asize th at th e d e­
m and for goods an d services is n o t raised by an in ­
crease in th e active deficit. Federal spending, they
point out, m u st b e fin an ced — if not in th e p resent,
th en in th e future. Thu s, h o u seh o ld s will ten d to d is­
co u n t th e in crea sed fu tu r e tax liability th at arises from
an in crease in th e active deficit. In effect, h o u seh old s
m atch th e in crea sed d eficit by an equivalent in crease

2Movements in the passive deficit are endogenous with respect to
movements in real GNP, while active deficits are not. A rise in the
passive deficit, when real GNP falls, may reduce the extent of the real
GNP decline itself and the interest rate decline as well. Those adjust­
ments, however, are endogenous because they are built-in to the
structure of the economy.
3For illuminating discussions of these issues, see Carlson and
Spencer (1975), Cohen and Clark (1984) and Knoester (1983). The
latter shows that balanced budget increases in active fiscal policy
lead to larger structural unemployment, higher wages and prices,
larger future deficits and lower economic growth.

JUNE/JULY 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 1

Federal G overnm ent B udget as a Share of G NP

S o u r c e : N a t io n a l In c o m e a n d P r o d u c t A c c o u n ts
S h a d e d a r e a s r e p r e s e n t p e r io d s o f b u s in e s s r e c e s s io n s .
L a te s t d a t a p lo t t e d : 1st q u a r t e r

in p erson al saving (or cu t in co n su m p tio n ). Thu s, total
spending, given in terest rates and prices, d oes not
rise.4
If su ch d isco u n tin g o f future taxes occu rs, th e c o n ­
ventional co n clu sio n s about th e effects o f active defi­
cits fail to hold, ex cep t for th o se co n cern in g crow dingout, cap ital form ation and eco n o m ic grow th. O thers
have n o ted th e th eo retical am biguity o f m ainstream
theory in this regard.5 Thu s, w hile th e ch an n els of
influence o f a ch an g e in th e deficit are clear, esp ecially
the im p o rtan ce o f the active-passive d istinction , the
assessm en t of the effects o f a rise in th e active deficit
rem ains essentially an em pirical qu estion.

4This result is referred to as the Ricardian Equivalence Theorem. See
Barro (1974, 1978), as well as Buchanan and Wagner (1977).
5See, especially, the recent analysis by the U.S. Department of the
Treasury.



RECENT BU D G ET TREN DS
T h e federal budget deficit soared to $147 billion
(National In co m e A ccount, NIA, basis) in ca len d a r year
1982, th en rose to about $183 billion in 1983. P ro jec­
tions for the n ext several y ears range from a slight
d eclin e to a n ea r doubling by th e en d o f th e d ecad e. It
is useful to co m p are th e budget developm en ts o f the
past two y ears w ith p ast tren d s to gain som e u n d er­
stand ing o f h ow th e d eficit b eca m e so large.
Chart 1 show s the grow th o f federal spen din g and
receip ts as sh ares o f GNP from 1948 to 1983. T h e deficit,
the difference betw een ex p en d itu res and receipts, also
is show n as a sh are o f GNP. In th e fou rth qu arter of
1982, th e d eficit rea ch ed a p ea cetim e reco rd 6.7 per­
ce n t o f GNP. W hile th is p ro p o rtio n su b sequ en tly d e­
clined, it rem ain ed above 5 p e rce n t throu gh 1983.
T h e surge in th e deficit is asso ciated w ith an a cc e l­
eration in federal exp en d itu re grow th an d a d eclin e in

7

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Federal G overnm ent Expenditures as a Share of G NP
Ratio

S e a s o n a lly a d ju s t e d

Ratio

S o u r c e : N a t i o n a l In c o m e a n d P r o d u c t A c c o u n t s
S h a d e d a r e a s r e p r e s e n t p e r i o d s o f b u s in e s s r e c e s s io n s .
L a te s t d a t a p lo t t e d : 1st q u a r t e r

receip ts growth, w hen both are m easu red relative to
GNP. For exam ple, from 1980 to 1983, w h en GNP grew
at a 7.9 p ercen t ann u al rate, ex p en d itu res grew at an
11.1 p ercen t rate an d federal receip ts ro se at only a 6.0
p e rce n t rate. As a result, ex p en d itu res ro se from 22.9
p ercen t o f GNP in 1980 to 25.0 p ercen t in 1983, and the
sh are o f receip ts fell from 20.6 p e rce n t to 19.5 p ercen t.
T h u s, over this tim e interval, th e deficit w id ened from
2.3 p e rce n t to 5.5 p e rce n t o f GNP.

The Growth o f Federal Expenditures
T h e sharp surge upw ard in fed eral ex p en d itu res as a
sh are o f GNP is show n again in ch art 2, w h ere exp en d i­
tu res are broken into two m ajo r categ o ries: th e p u r­
ch a se o f goods an d services an d tran sfer paym ents
(including transfers to p ersons, state and lo cal govern­
m ents, n et in terest on th e fed eral d ebt an d su bsid ies to
governm ent enterp rises). From 1967 to 1979, th e share
o f exp en d itu res in GNP rose little (except for a tem p o ­

8



rary spurt in 1975), w ith th e surge in tran sfer paym ents
alm ost offset by the d eclin e in p u rch a ses o f goods and
services. Sin ce 1979, how ever, b o th co m p o n e n ts of
federal exp en d itu res have risen relative to GNP. Pur­
ch a se s o f goods an d services ro se from 7.0 p e rce n t to
8.3 p ercen t o f GNP from 1979 to 1983, w hile tran sfer
paym ents co n tin u ed th e ir previous tren d o f rising fas­
ter than GNP, in creasin g from 14.1 p e rce n t to 16.6 p er­
ce n t o f GNP.
T h e pattern o f fed eral p u rch a se s o f g ood s an d ser­
vices closely m irrors th at o f n atio n al d efen se ex p en d i­
tu res (not show n), sin ce th e rem ain d er, n on -d efen se
p u rch ases, h as rem ain ed abou t 2 p e rce n t to 3 p ercen t
o f GNP sin ce th e early 1960s. N ational d efen se p u r­
ch ases, after d eclin in g from 1968 to 1979, ro se from 4.6
p ercen t o f GNP in 1979 to 6.0 p e rce n t in 1983. T his rise
a cco u n ts for all o f th e rise in th e sh are o f p u rch a ses in
GNP, bu t only 36 p e rce n t o f th e in crea se in th e sh are of
exp en d itu res in GNP an d an even sm aller p ercen tag e
o f th e in crease in th e d eficit m easu red relative to GNP.

JUNE/JULY 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 3

Federal G o v ern m e n t Receipts as a Share of G NP
Ratio

L a te s t d a ta

S e a s o n a ll y a d ju s t e d

p lo t t e d : 1st q u a r t e r

Ratio

S o u rc e -. N a t i o n a l I n c o m e a n d P r o d u c t A c c o u n t s

Federal Receipts as a Share o f GNP

The Sources o f Recent Deficits

T h e sh are o f fed eral receip ts in GNP is show n in
ch art 3 along w ith its m ajo r co m p o n e n ts: p erso n al tax
an d n o n -tax receip ts, social secu rity co n trib u tio n s and
co rp orate in co m e taxes. From 1979 to 1983, th e share of
social security taxes in GNP co n tin u ed its upward
clim b, rising from 6.6 p e rce n t to 7.1 p ercen t. T h is in ­
crea se largely offset th e d eclin e in th e sh are o f p erson al
taxes from 9.5 p e rce n t to 8.9 p e rce n t over th e sam e
period. C orporate taxes d eclin ed from 3.1 p e rce n t to
1.8 p ercen t o f GNP from 1979 to 1983, a d eclin e that
reflected an actu al d eclin e in su ch receip ts from $74.2
billion to $59.3 billion. In large part, this w as due to a
sim ilar p ercen tag e d eclin e in co rp o rate profits from
$252.7 billion in 1979 to abou t $207.6 billion in 1983.

It ap pears th at th e re cen t b alloon in g o f federal defi­
cits has b een a sso cia ted w ith a co m b in a tio n o f adverse
b u d g etaiy d evelopm ents ra th er th a n a single cau se.
E xp en d itu res have surged upw ard relative to th e n a ­
tio n ’s GNP, prim arily b eca u se o f th e co n tin u ed rapid
grow th o f tran sfer program s su ch as social security
paym ents, M edicare, u n em p loy m en t ben efits an d in ­
terest on the n atio n al debt. At th e sam e tim e, receip ts
have grow n m ore slow ly th an GNP, largely b eca u se o f a
d eclin e in co rp orate in co m e and co rp orate in co m e tax
receip ts.




Sim ple exp lan ation s that attribu te re ce n t deficits to
th e d efense buildup th at began in 1979 o r to tax cu ts

9

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

C h a rt 4

Personal Taxes as a Share of Earned Personal In c o m e 1
1

S o u rc e : N a t io n a l In co m e a n d P ro d u c t A c c o u n ts
[X P e rs o n a l ta x e s in c lu d e s o c ia l s e c u r ity ta x e s . E a rn e d p e r s o n a l in c o m e is p e r s o n a l in c o m e le ss tr a n s fe r p a y m e n ts
S h a d e d a re a s r e p r e s e n t p e r io d s o f b u s in e s s re ce ssio n s.
L a te s t d a t a p lo tte d : 1st q u a r te r

are in a d e q u a te for u n d e rsta n d in g re c e n t d eficits.6
From 1979 to 1983, grow th in th e share o f d efen se
spen ding in GNP a cc o u n ts for only 1.4 p ercen tag e
p oin ts o f a 4.8 p ercen tag e-p o in t rise in th e d eficit as a
p ercen t o f GNP (from 0.7 p e rce n t to 5.5 p ercen t). O ther
expen d itu res, in p articu lar tran sfer paym ents, acco u n t
for a co n sid erably larger part o f th e rise.
T h e tax cu t argum ent is sim ply w rong. P ersonal tax
rates generally have risen sin ce th e passage o f th e 1981
tax cut, a “c u t” that evidently w as a p o o r su bstitu te for
indexing (w hich begins in 1985). C onfusion arises b e ­
cau se, w hile tax rates an d taxes obviously w ere cu t
from levels th at they w ould oth erw ise have attained,
a ctu al tax rates ten d ed to rise from 1980 to 1984. T he
cu t in person al m arginal tax rates w as largely offset by
in flation -ind u ced “bracket creep " and social security
tax hikes.7
B u s in e s s ta x c u ts , p ro v id e d p rim a rily th ro u g h

a ccelera ted d ep reciatio n (the A ccelerated C ost Recov­
ery System) su bstan tially red u ced effective tax rates on
in co m e from n ew in vestm en ts, b u t h ad only a m in o r
im p act on average tax rates o r on th e real tax b u rd en on
b u sin ess in co m e from 1980 to 1983.8 T h e lion 's sh are of
the observed d eclin e in co rp orate in co m e taxes as a
share o f GNP h as b ee n related to th e b u sin ess cycle.
Low er tax rates on co rp orate in co m e an d a ccelera ted
d ep reciation have b ee n largely offset by n ew in d irect
b u sin ess taxes. M oreover, th e taxation o f capital, w h ich
arises from th e u se o f h isto rical co sts in calcu latin g
d ep reciation in the face o f in flatio n -in d u ced b o o sts in
rep lacem en t co sts, h as co n tin u ed to in crease.
Charts 1 -3 sh o w clearly th at re cen t budget develop­
m ents are largely related to th e b u sin ess cy cle. D uring
the sh ad ed re cessio n period s, exp en d itu res (especially
tran sfer program s) typically rise an d receip ts generally
fall relative to GNP. Ind eed , w ith th e ex cep tio n o f the
1953— recessio n , w h en ex p en d itu res fell relative to
54
GNP as a result o f a sh arp d eclin e in national defense

6See “ How to Cut the Deficit” (1984), p. 50, for example.
7See Tatom (1981), McKenzie (1982) and Meyer (1983), for example.

10



8See Hulten and Robertson (1982) and Meyer.

FEDERAL RESERVE BANK OF ST. LOUIS

expend itu res, this p attern h as b ee n observed in each
postw ar recessio n . T h e g reater exten t o f th e recen t
re c e s s io n h a s am p lified th e cy clica l sw ing in th e
deficit.
A fu rth er exam ple o f the effect o f th e cy cle on the
federal budget is given in ch art 4, w here a m easu re of
th e average tax rate on "e a rn e d ” p ersonal in co m e is
given. T ran sfer paym ents are ex clu d ed from person al
in co m e in the chart, b eca u se they are n ot su b je ct to
federal taxes; social secu rity co n tribu tio n s are added
to federal p erso n al in co m e taxes, b ecau se they are
co n sid ered to be as d irect an d p ersonal as in co m e
taxes. A cyclically ad ju sted average tax rate m easure
also is show n.9
T h e rates in ch art 4 provide little in d icatio n o f the
so-called tax cu t. T h e actual rate rose from 22.9 p ercen t
in 1979 to 23.1 p ercen t in 1980, th en fell slightly to 22.7
p ercen t in 1983. T h ere is som e in d icatio n o f a d eclin e
after m id-1982, but th e average level for 1983 w as vir­
tually u nch an g ed from its 1979 and 1980 levels.
On a cyclically a d ju sted basis, th e evidence that
taxes w ere cu t is even w eaker. On th is basis, th e average
tax rate rose from 23.1 p ercen t in 1979 to 23.5 p ercen t in
1980 and reach ed 24.0 p ercen t in 1983. W hile the tax
rate d eclin ed som ew h at in 1983 from its 1982 level, it
was still above its 1980 level, th e y e a r before the "tax
c u t” began.
T h e 1.3 p ercen tag e-p o in t d ifference betw een the
actual an d th e cyclically ad ju sted average tax rates
rep resen ts a $30.4 billion shortfall in federal receip ts
based on the level o f in co m e in 1983. M oreover, su ch
in co m e w ould have b een su bstantially hig her if the
u nem p loy m ent rate had averaged 5 p e rce n t in 1983,
in stead o f th e actu al 9.6 p e rce n t rate. E ach percen tag e
point o f u nem ploym ent is asso ciated w ith about a 2 to
ZVi percen tag e-p o in t loss in real and nom inal GNP and
a 2V4 to 2% p ercen tag e-p o in t d eclin e in p ersonal in-

9The cyclical impact on the tax rate is found from the coefficient on
unemployment in a regression model of the tax rate. The equation
regresses the quarterly change in the actual tax rate on: changes in
the unemployment rate lagged one quarter, the inflation rate (GNP
deflator), a time trend, dummy variables for the 1964 tax cut (1 in the
first and second quarters of 1964) and the 1975 tax rebate (1 in the
second quarter of 1975 and minus 1 in the third quarter of 1975) and a
constant, for the period 1/1950 to IV/1983. When the equation is
estimated to 111/1981 and then simulated to IV/1983, it is stable and
reveals no significant errors. The cyclically adjusted measure “adds
back” the decline in the tax rate due to the excess of unemployment
over a full-employment unemployment rate of about 5 percent in
recent years. The cyclical effect associates a 1 percentage-point
increase in the unemployment rate with a 0.25 percentage-point
reduction in the average tax rate.



JUNE/JULY 1984

co m e less tran sfer p a y m en ts.1" Thu s, th e loss in p e r­
sonal tax receip ts alon e in 1983 w as abou t $72 billion, a
su bstantial sh are o f th e observed bu dget deficit.
C hart 5 show s th e d eficit as a p e rce n t o f GNP and
the h ig h -em p loy m en t d eficit as a p e rce n t o f highem ploym ent GNP.11 Typically, th e h igh -em ploym ent
deficit as a sh are o f h igh -em p loym ent GNP h as ranged
betw een plus or m inu s 2 p e rce n t.12 W hile actu al defi­
cits have risen su bstan tially as a sh are o f GNP sin ce
m id-1981, deficits m easu red on a h igh-em ploym ent
basis have rem ain ed w ithin th at range.13 F or exam ple,
using fiscal y ea r p eriod s (ending in th e third q u arter o f
ea ch year), th e 1.6 p e rce n t h igh -em p loym ent deficit
registered in 1983 w as eq u aled o r ex ceed ed in 1967 and
1968 (1.8 p e rce n t an d 1.6 p ercen t, respectively).14

10See Tatom (1978) for a discussion of Okun’s Law, the relationship of
unemployment to the GNP gap. The relationship of personal income
(less total transfer payments) to the business cycle was found by
regressing quarterly changes in the logarithm of the ratio of such
income to GNP on a constant and changes in the unemployment
rate adjusted for a high-employment benchmark. The optimal lag is
current and two lagged changes; no additional statistically signifi­
cant information is provided by introducing longer lags. In level form,
the sum coefficients indicate that each 1 percent of unemployment
reduces the ratio of personal income less transfer payments to GNP
by 0.28 percent.
1 The high-employment budget data are prepared by the Bureau of
1
Economic Analysis, U.S. Department of Commerce, following
methods described in deLeeuw and others (1980). Their analysis
uses a more disaggregated form of the cyclical adjustment proce­
dure described in footnote 9. The high-employment budget data
indicate the point above concerning “tax cuts.” In fiscal 1980, the
share of high-employment budget receipts in potential GNP was
20.7 percent. This ratio fell only slightly to 20.4 percent in fiscal
1983.
' 2The standard deviation of the high-employment deficit ratio is 1.17
percentage points for the period 1/1955 to 111/1983.
13The high-employment and actual deficit ratio are highly correlated
(chart 5). This raises the suspicion that either the passive deficit has
not been fully removed from the high-employment deficit or that
there are cyclical changes in the active deficit; that is, policymakers
respond quickly to changes in real GNP with active policies.
These cyclical movements in the high-employment deficit ratio
were verified by regressing its changes on changes in the unem­
ployment rate, using quarterly data from 11/1955 to 111/1983; (d, d, ,) = -0.012 + 0.417 (UN, - UN, ,), where d is the highemployment deficit ratio (deficits measured positively), and UN is
the unemployment rate. The t-statistics are - 0.2 and 3.07 for the
constant and slope, respectively. Lags on the change in unemploy­
ment are not significant. A first-order autocorrelation correction is
used. The unemployment rate (roughly the excess of the unemploy­
ment rate above 5 percent in fiscal 1983) coefficient indicates that
an extra 5.1 percent unemployment rate raises the measured highemployment deficit ratio by 2.1 percent, somewhat more than the
1.6 percent ratio observed in fiscal 1983. Thus, it appears that the
“ true” deficit ratio for 1983 would be near zero but slightly in surplus.
14These earlier peaks in the high-employment (and actual) deficit ratio
were of great concern to analysts at the time; in particular, they led to
the proposal of a temporary income tax surcharge in January 1967
and its passage in mid-1968.

11

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

C h a rt 5

Deficits as a Share of GNP

1956

58

60

62

64

66

68

70

72

74

76

78

80

82

1984

S o u r c e : N a t io n a l In c o m e a n d P r o d u c t A c c o u n ts
S h a d e d a r e a s r e p r e s e n t p e r i o d s o f b u s in e s s re c e s s io n s .
L a te s t d a t a p l o t t e d : H ig h - e m p lo y m e n t - 4 t h q u a r t e r ; A c t u a l - l s t q u a r t e r

TH E D E F IC IT OUTLOOK: FROM
PASSIVE TO ACTIVE D E F IC IT S ?
W hile re cen t budget deficits ap p e ar to have b een
largely th e result o f th e 1980 and 19 8 1 -8 2 recessio n s,
p ro jectio n s o f future exp en d itu res, receip ts an d defi­
cits sh ow a different p ictu re. Su ch p ro jectio n s are
show n in table 1, w ith earlier actu al data for co m p ari­
son p u rposes.
T h e first co lu m n in table 1 show s th e estim ated
d eficit for fiscal y e a rs 1983 to 1989, b a se d on th e
a ssu m p tio n s u sed in th e p rep aratio n o f th e fiscal 1985
budget for th e eco n om y on a "cu rre n t serv ices” b a sis.15
T h e cu rren t services bu dget m easu res assu m e th at all
federal program s and activities in th e future rem ain th e
sam e as th o se ad o p ted for th e 1984 fiscal y e a r (ending

15See Council of Economic Advisers (1984), p. 36.

12



in S e p te m b e r 1984) a n d th a t th e re a re n o p o licy
ch an g es in su ch program s.18 T h ey also in co rp o rate
assu m p tio n s about future spen din g, real GNP growth,
inflation, in terest rates an d u nem p loy m en t.
T h e p r o je c te d to ta l d e fic its re m a in s u b s ta n tia l
throu gh 1989, providing su p p o rt for re cen t co n cern s
about “large” deficits. Note, how ever, that relative to
th e size o f th e eco n om y o r GNP, th e actu al deficit
d eclin es after 1983.
T h e table also provides a breakdow n o f th e deficit
into “cy clica l” an d “stru ctu ra l” co m p o n e n ts. T h is d is­
tin ctio n is sim ilar to th e h ig h -em p loy m ent vs. actual
d eficit categ o ries u sed previously. In th is in stan ce,
however, th e cy clical d eficit arises from th e d epartu re
o f real GNP from its 1969-to-1981 trend , ra th er th an

16For a detailed discussion, see Office of Management and Budget
(1984), pp. A-1 to A-38.

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 1
The Cyclical and Structural Components of the Deficit: 1980-89
(dollar amounts in billions)

Fiscal
year

Total
deficit

Deficit
as percent
of GNP

Structural
as percent
of trend GNP

Cyclical
component

Structural
component

2.3%
2.0
3.6
6.1

$ 4
19
62

$ 55
39
48
101

2.1%
1.3
1.5
2.9

5.3%
5.3
5.1
4.8
4.1
3.6

$49
44

$138
163
171
187
187
197

Highemployment
deficit

Highemployment
deficit as
percent of
potential
GNP

3.7%
4.2
4.1

Actual

1980
1981
1982

$ 60
58
111

1983

195

95

$16.7
1.0
20.2
56.8

0.6%
0.0
0.6
1.6

Projected1

1984

$187

1985
1986
1987

208
216
220
203
193

1988
1989

45
34
16
-4

3.9
3.8
3.8

'Deficit estimates for 1984-89 are from the current services budget, January 1984.

from a high-em ploym ent level. T h e stru ctu ral deficit is
th e level th at w ould exist if real GNP w ere at its tren d
level; th e sm aller h igh-em ploym ent d eficit m easu res
th e d eficit th at w ould exist w ere real GNP at a highem ploym ent level.
W hile th e total d eficit d eclin es relative to GNP in the
table, th e stru ctu ral d eficit ballo o n s up relative to GNP
until 1985, th e n rem ain s qu ite high as real GNP ap ­
p ro ach es trend. T h e se estim ates show an u n p re c e ­
d en ted rise in th e stru ctu ral d eficit an d reco rd levels
persisting through th e decad e.
T h ere are a n u m b er o f reason s for viewing su ch
co n clu sio n s w ith extrem e cau tio n . First, estim ates of
the stru ctu ral d eficit ten d to be raised by th e u se of
tren d GNP, sin ce it is som ew hat below th e path of
h igh -em ploym ent GNP. T h e table also in clu d es highem ploym ent m easu res o f the d eficit for 1980 to 1983,
for co m p ariso n p u rp o ses.17 T h e tren d -based estim ates
o f the stru ctu ral deficit in 1980-83 average about 1.3
p ercentage p o in ts h ig h er th an stru ctu ral deficits that

17High-employment budget measures exist only through the third
quarter of 1983, following the methods described by deLeeuw and
others. Beginning in December 1983, the Bureau of Economic



are m easu red on a h igh -em ploym ent b asis.18 T h e size
o f p ro jecte d stru ctu ral deficits in th e cu rren t budget
estim ates are likely to be sim ilarly overstated; thus, the
p ro jectio n s for 1984 to 1989 do n ot rep resen t a m ajo r
break from th e reco rd show n in ch art 5 .19 A djusted for

Analysis switched to a new measure called a "cyclically adjusted”
budget. It is not comparable with the earlier series since the bench­
mark level of GNP is an interpolation of “ middle-expansion” phases
of the business cycle, at which points unemployment rates have
different structural/cyclical components. See deLeeuw and Hollo­
way (1983). This measure also is not comparable to the trend-based
GNP measure analyzed by the Council of Economic Advisers
(1984) and used in table 1.
18The budget data in table 1 are for the unified budget, while the
high-employment measures are on an NIA basis. For a discussion
of the differences, see Pechman (1983), pp. 17-18. The principal
difference is that the unified budget is measured on a cash basis,
when outlays or receipts are actually made, while the NIA budget is
measured on an accrual basis; that is, receipts are measured by an
increase in tax liability, whether paid or not, and expenditures are
measured by purchases, whether cash outlays have been made or
not.
19Barro (1984) arrives at the same conclusion. He develops a model
that explains deficits in terms of expected inflation rates, the busi­
ness cycle and temporary changes in government spending. His
estimates for the period since 1920 indicate that 1982-83 deficits
and projections for 1984 are consistent with the previous structure
and do not indicate that there has been a shift in fiscal policy toward
higher deficits.

13

FEDERAL RESERVE BANK OF ST. LOUIS

th is d iffere n ce, th e p r o je c te d 1988— d eficits are
89
slightly m ore th an tw ice th e stand ard deviation o f the
high-em plovm ent deficit ratio from 1955 to 1983, in ­
stead o f over th ree tim es as large.
Also, the deficits in table 1 are cu rren t services esti­
m ates. C urrently p ro p o sed A d m in istration p o licies
w ould red u ce th e stru ctu ral deficit show n for 1989 to
about 2.3 p e rce n t o f actu al or, roughly, tren d GNP,
in stead o f th e 3.8 p e rce n t show n in th e table.20
Third, if actual e co n o m ic co n d itio n s differ from the
eco n o m ic assu m p tio n s used for th e p ro jectio n s, future
deficits cou ld b e h ig h er o r low er th an ind icated . Som e
analysts have b een critical o f a d eclin e in in terest rates
assu m ed in m aking th e p ro jectio n . If in terest rates are
h ig h er th an p ro je c te d from 1984 to 1989, the actu al and
stru ctu ral d eficits w ould be larger.21 O thers have criti­
cized th e p ro jecte d rate o f eco n o m ic grow th as too low;
a h ig h er grow th rate w ould low er th e actu al and p ro­
je cte d deficit 22
E co n o m ic assu m p tio n s are extrem ely im portant to
deficit p ro jectio n s. C arlson (1983) d em on strates, for
exam p le, th a t ch a n g e s in a ssu m p tio n s abou t e c o ­
n om ic co n d itio n s for fiscal 1986, betw een p ro jectio n s
m ade in M arch 1981 and p ro jectio n s m ad e in Jan u ary
1983, a cco u n ted for m o st o f a nearly tenfold rise in the
p ro jected deficit from $21.0 billion to $203.1 billion.
Policy ch an g es b etw een th e two p ro jectio n s re d u c e d

20The Administration proposals would do this by reducing a projected
23.0 percent share of outlays in GNP by 0.9 percentage points and
raising the 19.4 percent share of receipts by 0.4 percentage points,
reducing the projected actual deficit to 2.3 percent. The proposed
spending reductions include paring back 0.2 percentage points of
the rise in the share of national defense outlays. The rest of the
reduction is in net interest (0.2 percent), social security and Medic­
aid (0.1 percent) and other transfer payments and non-defense
expenditures.
2 This criticism is subject to a fundamental qualification, however. The
1
assumed lower interest rates from 1984 to 1989 are largely prem­
ised upon a decline in inflation. If recent or higher interest rates are
assumed because inflation is assumed to be the same or higher,
then the impact of the higher interest rates on the interest compo­
nent of outlays and the deficit would be more than offset by the
positive effect of inflation on receipts relative to expenditures.
22Foremost among the critics has been the Congressional Budget
Office (1984). Its principal departures from the assumptions used by
the Administration are that: interest rates decline much less for
1984-89 and real GNP growth is slower in 1986-89. As a result, the
deficit generally rises in the CBO projections, from $186 billion in
1984 to $248 billion in 1989.
The CBO does not discuss the structural deficit issue. Nonethe­
less, under its more pessimistic assumptions the deficit declines as
a share of GNP from 6.1 percent in 1983 to 5.2 percent in 1984, to
about 5 percent in 1985-87 and to 4.8 percent and 4.6 percent in
1988 and 1989, respectively (p. 2). Moreover, its discussion of the
consequences of “ large deficits” indicates that financing of such
deficits will take a substantially smaller share of gross and net
private domestic savings in 1984-85 than in 1983 (p. 19).

14


JUNE/JULY 1984

the p ro jecte d d eficit by about $39 billion, bu t d ow n­
w ard revisions in th e p ro jecte d levels o f p rices an d real
GNP for 1986 raised it by $221 billion.
Even d ep artu res from n ear-term assu m p tio n s ca n
have relatively large effects on p ro jecte d deficits. For
exam ple, at th e en d o f Ju ly 1983, the Office o f M anage­
m ent and Budget (1983) estim ated that the unified
budget d eficit for fiscal 1983, w h ich en d ed two m o n th s
later, w o u ld sh o w a d eficit o f $209.8 b illio n . Tw o
m on th s later, th e actu al deficit en d ed up at $195.4
billion, prim arily b eca u se outlays w ere abou t $13 b il­
lion low er th a n estim ated tw o m o n th s earlier, w hen
m ost o f the fiscal y e a r h ad b een co m p leted .

THE CONSEQUENCES OF
LARGE D E F IC IT S
C onventional e co n o m ic theory suggests th at rising
deficits m ay ten d to raise p rices, ou tp u t an d in terest
rates, w hile d ep ressin g cap ital form ation. O btaining
em pirical su p p ort for all but th e last o f th ese h yp oth ­
eses h as proved quite difficult, how ever.23
In 1981, co n c e rn over rising deficits asso ciated w ith
the E co n o m ic Recovery T ax Act o f 1981 focu sed on th e
an ticipation that in creasin g d eficits w ould overheat
the eco n om y an d raise inflation, ju st as inflation m ea ­
su res began to p lu m m et an d the eco n om y en tered the
w o rst re c e s s io n sin c e th e 1 9 3 0 s.24 S in ce th en , in ­
creased atten tio n h as b een focu sed on the effect of
deficits o n in terest rates an d cap ital form ation d uring a
period in w hich, u ntil recen tly, in terest rates w ere
d eclining an d cap ital sp en d in g w as unusually high
relative to GNP 25 In part, finding evid ence on th e c o n ­
seq u en ces o f d eficit in crea ses b eco m es difficult b e­

23Carlson (1982) presents evidence supporting the view that deficits
crowd-out private sector capital formation.
24Hein (1981) explains the shortcomings of the hypothesized link
between deficits and inflation. Essentially, as he notes, the funda­
mental linkage in such a hypothesis is the extent to which deficits are
monetized; that is, the share of the deficit financed by the Federal
Reserve through money creation, primarily open market purchases
of government securities. There has been no such linkage since at
least 1974. For a contrasting view, see Hamburger and Zwick (1981,
1982). McMillin and Beard (1982) have pointed to some shortcom­
ings of the Hamburger-Zwick analysis.
25Curiously, analyses of proposals to deal with large future deficits by
raising taxes or cutting federal spending growth emphasize the
effects of such programs in avoiding rising interest rates that pur­
portedly could choke off the current expansion. Higher interest rates
resulting from future deficits, to the extent they would occur, are
already part of the existing structure of interest rates. Such analyses
typically ignore conventional thinking, which emphasizes that such
fiscal programs directly retard spending and, hence, expansions,
despite any effect of lower interest rates. Kopcke (1983), for exam­
ple, has emphasized this point.

JUNE/JULY 1984

FEDERAL RESERVE BANK OF ST. LOUIS

cau se o f a failure to a cco u n t for the active/passive defi­
cit d istinction. T h is problem is m ost apparen t w hen
o n e looks at th e investigation o f th e d eficit-interest rate
link.
T h e actual p attern of d eficits an d in terest rates over
the past four y ears ru n s co u n te r to the higher-deficit,
h ig h er-in terest rate h y p o th esis. In te re st rates sky­
rocketed from III/1979 to III/1981; long-term T reasu iy
security yields, for exam ple, rose from about 9 p ercen t
to 14 p e rce n t. D uring th e sam e p eriod , th e highem plovm ent deficit for the m ost recen t four quarters
fell from about $2 billion to $1 billion, and th e actual
d eficit rose from about $14 billion to $56 billion. Over
th e n ext tw o y ears (III/1981 to III/1983), lon g-term
T rea su iy security yields fell from 14 percen t to 11.6
p ercen t. Yet, in th e latter period, th e actu al deficit
ballooned up to $186 billion and th e high-em plovm ent
d eficit rose from n e a r zero to about $57 billion.26
A p rincipal difficulty in interp reting th ese m ove­
m ents in interest rates and deficits is th e failure to
a cco u n t for th e active/passive d eficit d istin ction . In the
past, deficits have b een in large part passive, as ch art 5
ind icates. Thu s, it is not su rprising that, during and
follow ing periods o f recessio n , deficits w ere rising or
“h igh ,” an d in terest rates w ere falling or rem ained
“low .” T h e d o m in an ce o f this negative cy clical rela­
tion sh ip betw een passive d eficits and in terest rates
in terferes substantially w ith em pirical investigations of
the im pact o f deficits on in terest rates. An exam ple of
th is confusion is d etailed in th e insert on pages 16 and
17.
T h e seco n d problem w ith testing th e in terest ratedeficit hyp othesis is that th e U.S. eco n om y has had
only lim ited p eacetim e ex p erien ce w ith eith er large or
variable active deficits, m easu red relative to GNP. As
ch art 5 ind icates, deficits o r su rp lu ses rarely have ex ­
ceed ed 2 p ercen t o f GNP on a high-em plovm en t basis.
Thus, should future federal stru ctu ral deficits be
larger th an they w ere in th e earlier p ostw ar exp erien ce,
past em pirical evidence w ould provide little guidan ce
co n cern in g th e p otential adverse effects on inflation
and in terest rate levels. Although past evidence sug­
gests th ere are n one, th e eco n om y h as had no p e a ce ­
tim e ex p erien ce w ith large, p ersisten t stru ctu ral defi­
26Another such striking parallel occurred in fiscal 1975 (measured
here as IV/1974 to 111/1975) when the deficit ballooned to $58.4
billion from $6.9 billion in fiscal 1974. This set a postwar record,
exceeding even the 1943 budget deficit of $54.9 billion. As a share
of GNP, the 3.8 percent 1975 deficit also set a postwar record, not
exceeded until fiscal 1982. Nonetheless, 3-month Treasury bill rates
fell from about 9 percent in the fall of 1974 to about 5.5 percent at the
end of 1975. See Carlson (1976) and Lang (1977) for a discussion of
this episode.



cits, as som e analysts have suggested will o c c u r from
1983 to 1989. Thu s, th e past m ay offer little relevant
evidence for a ssessin g th e future effects o f deficits. Of
c o u r s e , fin a n c ia l m a rk e t p a r t ic ip a n t s h ave b e e n
w arned o f the p oten tial m agnitu d e o f future deficits
and, to th e exten t su ch d eficits cou ld be ex p ected to
raise interest rates, su ch effects already sh ould have
b een in co rp o rated in to th e stru ctu re o f rates. In terest­
ingly enough, how ever, in terest rates have generally
fallen sin ce late 1981, even though it has b een only
sin ce th en that th e adverse d eficit inform ation began to
be d iscern ed and d issem in ated .

SUMMARY
In 19 8 2 -8 3 , fed eral d eficits surged to triple-digit
levels. M oreover, ad m in istration an d CBO p ro jectio n s
in d icate they will rem ain so, at least th rou gh 1989.
These deficits have arisen from the u nsatisfactory cy­
clical perfoi-m ance o f th e U.S. eco n om y. Typically, fed­
eral exp en d itu res are raised w h en u nem p loy m en t is
h ig h er and tax receip ts are low er. R ecessio n s in 1980
an d 1 9 8 1-82 have left th e u n em p loy m en t rate at u n ­
usually high levels sin ce 1980. Suggestions that eith er a
rise in d efen se sp en d in g or cu ts in tax rates have
played m a jo r roles in th e creatio n o f re ce n t d eficits are
m isleading.
P rojection s tend to sh ow deficits d eclin in g as a share
o f GNP, b u t stru c tu ra l d eficit p r o je c tio n s sh o w a
w orsen in g tren d in 1984— an d little im provem ent in
85
1986-89. Should th e cu rren t cy clical d eficit b e tra n s­
form ed into a stru ctu ral deficit, it is n ot clea r w hat
co n se q u e n ce s su ch a developm ent w ould have. T h ere
is little evidence su pportin g th e adverse co n se q u e n ce s
o f a sharp in crea se in th e stru ctu ral deficit. T h e lack of
su ch evidence, how ever, m ay arise from th e fact that
the United States h as h ad no ex p erien ce w ith “large”
peacetim e stru ctu ral deficits.

REFER EN C ES
Barro, Robert J. "The Behavior of U.S. Deficits,” National Bureau of
Economic Research Working Paper No. 1309, March 1984.
________ “Comment From An Unreconstructed Ricardian,” Jour­
nal of Monetary Economics (August 1978), pp. 569-81.
________ “Are Government Bonds Net Wealth?” Journal of Polit­
ical Economy (November/December 1974), pp. 1095-117.
Buchanan, J. M., and R. Wagner.
Press, 1977).

Democracy in Deficit (Academic

Carlson, Keith M. “The Critical Role of Economic Assumptions in the
Evaluation of Federal Budget Programs,” this Review (October
1983), pp. 5-14.
________ "The Mix of Monetary and Fiscal Policies: Conventional
Wisdom Vs. Empirical Reality,” this Review (October 1982), pp.
7-21.

15

________ “ Large Federal Budget Deficits: Perspectives and Pros­
pects,” this Review (October 1976), pp. 2-7.

Lang, Richard W. “The 1975-76 Federal Deficits and the Credit
Market,” this Review (January 1977), pp. 9-16.

Carlson, Keith M., and Roger W. Spencer. “Crowding Out and Its
Critics,” this Review (December 1975), pp. 2-17.

deLeeuw, Frank, and Thomas M. Holloway. “Cyclical Adjustment of
the Federal Budget and Federal Debt, " Survey of Current Business
(December 1983), pp. 25-40.

Cohen, Darrel, and Peter B. Clark. The Effects of Fiscal Policy on
the U.S. Economy, Staff Studies No. 136 (Board of Governors of
the Federal Reserve System, January 1984).
Congressional Budget Office. The Economic Outlook, Congress of
the United States (U.S. Government Printing Office, February
1984a).

_________ An Analysis of the President's Budgetary Proposals for
Fiscal Year 1985, Congress of the United States (GPO, February
1984b).

deLeeuw, Frank, and others. “The High-Employment Budget: New
Estimates, 1955-80,” Survey of Current Business (November
1980), pp. 13-43.
McKenzie, Richard B. “ Supply-Side Economics and the Vanishing
Tax Cut,” Federal Reserve Bank of Atlanta Economic Review
(May 1982), pp. 20-24.

Economic Report of the President

McMillin, W. Douglas, and Thomas R. Beard. “ Deficits, Money and
Inflation: Comment,” Journal of Monetary Economics (September
1982), pp. 273-77.

Greider, William. “The Education of David Stockman,” The Atlantic
Monthly (December 1981), pp. 27-54.

Meyer, Stephen A. “Tax Cuts: Reality or Illusion,” Federal Reserve
Bank of Philadelphia Business Review (July/August 1983), pp.
3-16.

Council of Economic Advisers.
(GPO, February 1984).

Hamburger, Michael J., and Burton Zwick. "Deficits, Money and
Inflation,” Journal of Monetary Economics (January 1981), pp.
141-50.
________ “ Deficits, Money and Inflation: Reply,” Journal of Mone­
tary Economics (September 1982), pp. 279-83.
Hein, Scott E.
3-10.

“ Deficits and Inflation,” this Review (March 1981), pp.

“ How to Cut the Deficit.” Business Week, Special Report (March
26, 1984), pp. 49-106.
Hulten, Charles R., and James W. Robertson. “Corporate Tax Poli­
cy and Economic Growth: An Analysis of the 1981 and 1982 Tax
Acts,” Urban Institute Discussion Paper (December 1982).

Office of Management and Budget, Budget of the United States
Government 1985 (GPO, February 1984).

_________ Mid Session Review of Fiscal 1984 Budget (July 25,
1983).
Pechman, Joseph A.
Institute, 1983).

Federal Tax Policy, 4th ed. (The Brookings

Plosser, Charles I., and G. William Schwert. “Money Income and
Sunspots: Measuring Economic Relationships and the Effects of
Differencing,” Journal of Monetary Economics (1978), pp. 637-60.

Knoester, Anthonie. “Stagnation and the Inverted Haavelmo Effect:
Some International Evidence," De Economist, volume 131, no. 4,
(1983), pp. 548-84.

Tatom, John A. “We Are All Supply-Siders Now!” this Review (May
1981), pp. 18-30, reprinted in Bruce Bartlett and Timothy P. Roth,
The Supply-Side Solution (Chatham House Publishers, Inc.,
1983), pp. 6-25.

Kochin, Levis A. "Are Future Taxes Anticipated by Consumers?"
Journal of Money, Credit and Banking (August 1974), pp. 385-94.

________ “ Economic Growth and Unemployment: A Reappraisal
of the Conventional View,” this Review (October 1978), pp. 16-22.

Kopcke, Richard W. “ Will Big Deficits Spoil the Recovery?” in
Federal Reserve Bank of Boston, The Economics of Large Gov­
ernment Deficits, Conference Series No. 27 (1983), pp. 141-68.

U.S. Department of the Treasury. The Effects of Deficits on Prices of
Financial Assets: Theory and Evidence (GPO, March 1984).

In te re st R ates an d th e D eficit: 1955—
83
W hen th e level o f in terest rates is related to the
size o f th e deficit, m easu red relative to GNP, the
relationship is generally negative in stead o f positive,
as is often co n jectu red . M oreover, th e negative rela­
tion ship is often statistically significant. T h is result
arises becau se o f the sim u ltan eo u s o cc u rre n ce o f
cyclical deficit in creases and recessio n -related d e ­
creases in in terest rates, esp ecially sh o rt-term in ­
terest rates.
T his p attern clearly em erges in an exam in ation of
quarterly ch an g es in b o th th e 3-m on th T reasury bill
rate an d th e Aaa b o n d y ield for th e period II/1955 to
III/1983 and th e su bp erio d s II/1955 to IV/1969 and
1/1970 to III/1983. T h e se ch an g es w ere regressed on
cu rren t and past ch an g es in the actu al federal deficit-GNP ratio and on cu rren t and past ch an g es in
th e h ig h -em p loy m ent deficit/potential GNP ratio.
Although up to fou r past qu arterly ch an g es w ere

Digitized 16 FRASER
for


exam ined, no lagged values w ere statistically signifi­
ca n t in eith e r case. T h e table show s th e eq u ation s
for ea ch in terest rate, for ea ch period, for ea ch deficit-GNP ratio.1
'The omission of other variables that influence interest rates does
not bias the coefficient estimate of the effect of the deficit on
interest rates unless the changes in the omitted variables are
correlated with changes in the deficit ratio. For example, failure to
control for an effect of the rate of money growth on interest rates
does not bias the coefficient estimates here unless changes in
money growth are correlated with changes in the deficit ratio. For
the periods examined, they are not. The simple correlation coeffi­
cient for changes in M1 growth and in the actual deficit ratio is
-0 .1 2 in all three periods. The coefficient for changes in M1
growth and the high-employment deficit ratio is -0 .1 5 for the
1955-to-1969 period, -0 .1 0 for the 1970-to-1983 period, and
-0.11 for the full period. None of these correlation coefficients
are statistically significant at a 95 percent confidence level.
Plosser and Schwert (1978) provide a useful discussion of the
advantages and limitations of differencing in assessing economic
relationships.

In virtually every case, a rise in th e actual o r highem ploym ent d eficit is inversely related to th e level of
interest rates, though not, in m ost cases, statistically
significant. In all th ree periods, in creases in th e
a c tu a l deficit-GNP ratio are significantly asso ciated
w ith low er 3-m on th T reasu ry bill rates. E ach 1 percen tag e-p o in t in cre a se in th e actu al deficit-GNP
ratio is estim ated to low er in terest rates by 21 to 53
b asis points. T h e negative effects o f the actu al deficit
on the long-term rate, th e Aaa bo n d yield, are not
significantly different from zero.
Surprisingly, th e resu lts w ere little ch an g ed after
con trollin g for th e im p act o f th e b u sin ess cycle by
using the high-em ploym ent d eficit ratio. T h e effect
on long- and sh o rt-term rates o f a rise in th e highem ploym ent d eficit ratio generally rem ained nega­
tive, but not significantly different from zero. As
expected , the m agnitu de o f th e in terest rate effect is
less negative th an for th e actu al deficit ratio. T h e

negative relation sh ip m ay arise b eca u se the te c h ­
niques u sed to m easu re the h igh-em ploym ent defi­
cit fail to fully rem ove cy clical in flu en ces.2
T h e se resu lts illu strate th e difficulty o f identifying
the effects o f d eficits on th e e co n o m ic perform an ce
w h e n th e p a ssiv e/ a ctiv e d e fic it d is t in c tio n is
ignored. Taking the d istin ctio n into a cco u n t, how ­
ever, still d oes not su p p ort th e con v en tion al p ro p ­
osition that th ere is a positive link betw een deficits
an d in terest rates.
2When the high-employment deficit ratio is cyclically adjusted
following the equation in footnote 13 in the text, the point estimate
of the effect of changes in this adjusted deficit on interest rates
becomes more positive. For the Aaa bond yield, the coefficient on
such an adjusted deficit is 0.01 in all three periods, but this
positive relationship is not statistically significant (the t-statistic is
below 0.3 in all three cases). The effect on the Treasury bill rate is
positive in the 1955-to-1969 period but insignificant: 0.13 (t =
1.29); in the later sample and for the full period, the Treasury bill
effect remains negative and is statistically insignificant
(t-statistics less than 0.70 in absolute value).

Interest Rates and the Federal Deficit

11/1955-111/1983

actual
actual
actual

11/1955-111/1983

high-employment

11/1955—
IV/1969

high-employment

1/1970-111/1983

high-employment

11/1955-111/1983

actual

11/1955—
IV/1969

actual

11/1970-111/1983

actual

11/1955-111/1983

high-employment

11/1955-IV/1969

high-employment

IV/1969—
111/1983

Change in Aaa bond yield

Deficit and
GNP measure

1/1970-111/1983

Change in 3-month
Treasury bill rate

Period

11/1955—
IV/1969

Dependent variable

high-employment

Constant

0.092
(1.10)
0.104
(189)
0.090
(0.56)
0.077
(0.88)

Change
in the
deficit
ratio

R2

SE

DW

0.11

0.885

1.92

0.08

0.422

1.63

---

0.12

1.198

1.98

---

0.03

0.924

1.78

--

-0.01

0.418

1.73

0.35
(2.82)

0.03

1.255

1.84

P

0.107
(1.30)
0.051
(0.30)

-0.419
(-3.81)*
-0.213
(-2.41)*
-0.530
(-2.85)*
-0.277
(-1.98)*
0.053
(0.50)
-0.394
(-1 .6 6 )

0.088
(189)
0.079
(2.78)
0.103
(1.12)

-0.069
(-1 .5 0 )
-0.047
(-1 .5 1 )
-0.079
(-1 .0 0 )

0.01

0.374

1.95

0.02

0.146

1.77

0.00

0.523

1.95

0.085
(181)
0.079
(2.66)
0.096
(104)

-0.031
(-0 .5 7 )

-0.01

0.378

1.94

0.25
(2.68)

-0.012
(-0 .3 3 )

-0 .0 2

0.149

1.74

-0.038
(-0.42)

-0.01

0.527

1.94

0.36
(2.79)
0.23
(1.73)

“

0.25
(2.67)
0.34
(2.60)
0.23
(1.74)

NOTE: t-statistics are given in parentheses; * indicates a deficit measure whose coefficient is significantly different from zero at a 95 percent
confidence level.




17

Money, Debt and Econom ic
Activity
IV. Hafer

T

M - HE Fed eral O pen M arket C om m ittee (FOMC) d e­
cid ed in O ctober 1982 that, at least for th e im m ed iate
future, less im p o rtan ce w ould be attach ed to m ove­
m en ts in th e narrow ly defined m onetary aggregate
(M l) in establish ing m o n etary policy. T h is departure
from previous p o licy w as m otivated prim arily by in ­
creasing ex p ectation s that th e in tro d u ction o f SuperNOW a cco u n ts w ould distort M l ’s u sefu ln ess as a reli­
able policy guide.

T h e n o tio n th at M l m ay n ot be approp riate as the
in term ed iate target m easu re is n ot co n fin ed to th e
period sin ce 1982. Som e eco n o m ists long have argued
that policy should n ot be based on a single variable,
but on a variety o f "in fo rm atio n al” variables. If one
target variable disp lays "a b n o rm a l” behavior, o th er
target variables can be co n su lted for sim ilar irregular­
ities. R ather th an basin g policy on a target variable
gone astray, policym akers can th u s evaluate a diverse
set o f inform ation an d assign th e p ro p er w eight to ea ch
in term ed iate target variable.1

R. W Hafer is a senior economist at the Federal Resen/e Bank of St.
.
Louis. Larry J. DiMariano provided research assistance.
'Kareken, Muench and Wallace (1973), for example, conclude that
the monetary policymakers should use all the information variables
to which they have access. To some extent, knowledge of economic
activity does play an important role in the FOMC's decision calculus.
One need only read the “ Record" of the FOMC meetings to see the
extent to which economic conditions, such as real economic activity,
price developments and recent changes in interest rates, influence
monetary policy decisions. On the question of using several in­
termediate targets, Kane (1982), p. 204, draws the opposite conclu­
sion: “ I doubt very much that systems that employ a multiplicity of
intermediate targets constitute efficient ways to organize decisions
about monetary policy.”

18


Su sp icion o f re cen t d isto rtion s in M l has p rom pted
som e eco n o m ists to suggest th at th e Fed eral Reserve
target a broad d ebt m easu re.2 T h e ir argum ent against
too heavy a relian ce on m o n etary m easu res is th at su ch
m easu res cap tu re only th e asset side o f th e non fin an cial se c to r’s fin an cial b a la n ce sh eet; inform ation from
the liability side is bein g overlooked. C onsequently,
ch artin g th e p ath o f a broad debt m easu re in addition
to a m o n e ta ry aggregate, th ey argue, w ill provide
policym akers w ith in form ation n o t revealed solely by
m on ey grow th. Partially in resp o n se to th ese argu­
m ents, th e FOMC at its February 1983 m eetin g esta b ­
lish ed a m o n ito rin g ran ge for th e grow th o f total
d o m estic n on fin an cial debt.
T his p a p er investigates th e u sefu ln ess o f adding this
d ebt m easu re to th e co lle ctio n o f targets alread y used
to d ecid e th e d irectio n o f m on etary policy.3 B ecau se
any variable u sed as an in term ed iate target sh o u ld be
closely related to th e goal o f m on etary policy, w e will
first co m p are h o w w ell th e grow th rates o f M l an d debt
explain th e behavior o f GNP grow th in th e past two
d ecad es.4 We also will co m p are ea ch m e a su re’s ability

2This position has been argued by Benjamin Friedman in a series of
papers (1981, 1982, 1983a). See also Kopcke (1983) and Morris
(1982, 1983) for further arguments in favor of using the broad debt
measure.
3The analysis in this paper draws on Hafer (1984a), where the issue is
investigated in greater detail using a variety of statistical tests.
4During the past 20 years, numerous papers have investigated this
link between different monetary measures and GNP: see, among
others, Friedman and Meiselman (1963), Hamburger (1970), Carl­
son and Hein (1980), Hafer (1981), and Judd and Motley (1983).
Another feature of an intermediate target, one that is not dealt with
in this paper, is that it should be controllable by the policymaker. In

JUNE/JULY 1984

FEDERAL RESERVE BANK OF ST. LOUIS

to forecast GNP grow th during th e 1 982-83 period.
F orecasts o f GNP using an M l m easu re that abstracts
from recen t financial innovations that may have d is­
torted M l growth (here called ad ju sted M l) also are
reported. T h e evidence reveals that th ere is insufficient
evidence to su p p ort th e u sefu ln ess o f th e d ebt m ea ­
sure relative to tw o m e asu res o f narrow ly defined
m oney as a potential in term ed iate target for m onetary
policy.5

TOTAL D O M ESTIC
NONFINANCIAL D E B T
Total d o m estic n onfin ancial debt, put simply, is a
m easure o f the cred it m arket debt ow ed by d om estic
non fin ancial secto rs o f th e U.S. econom y. As th e defini­
tion suggests, th e m easu re ex clu d es debt ow ed by
fin a n cia l in s titu tio n s , in c lu d in g U.S. g o v e rn m en tsp o n so red cred it agen cies, federally related m ortgage
pools and private fin ancial institu tions. It also exclu d es
trade debt, loan s for th e p u rp o se o f carrying secu rities
and funds raised from equity so u rces. On th e o th er
hand, th e d ebt m easu re in clu d es d ebt secu rities, m o rt­
gages, bank loans, co m m ercial paper, co n su m er credit
and governm ent lo an s ow ed bv non financial sectors.
Table 1 p resen ts a sum m ary o f th e co m p ositio n of
this debt m easu re by m ajo r se c to r as o f IV/1983. In that
qu arter, to tal d o m e stic n o n fin an cial d ebt stood at
$5,218.96 billion. Of this am ount, debt ow ed by the
h o u s e h o ld s e c t o r a n d n o n fin a n c ia l b u s in e s s e s
a cco u n ted for 70 p e rce n t o f the total. T h e governm ent
secto r ow es the rem aind er, w ith th e U.S. governm ent

other words, changes in the “tools" of monetary policy, that is,
changes in open market operations, reserve requirements and the
like, should have reliable consequences on the intermediate target.
Thus, although a measure may be closely related to the goal vari­
able, this is of little solace if it is uncontrollable. Some evidence on the
controllability of debt with respect to M1 is presented in Friedman
(1983a) and Kopcke. Kopcke’s evidence, based on one-, two- and
three-month-ahead forecasts of an M1 and debt multiplier, suggests
that the forecast errors of the debt multiplier are not offsetting as they
are for the M1 multiplier. For example, the average error for the
one-month-ahead forecasts for the period November 1979 through
June 1982 are 0.06 percent for M1 and 0.23 percent for debt. When
two- and three-month forecast horizons are used, the debt multi­
plier’s average forecast error is at least twice that for M1. Although
the mean absolute value of the two series’ forecast errors are similar,
the relative biasedness of the debt multiplier’s forecasts could, if
used for policy, produce incorrect signals. This is especially true
because, as Kopcke notes, the debt data are available only with a
lag, while the M1 data are calculated on a weekly basis. Moreover,
there appear to be large revisions in the debt data unmatched by any
of the relevant monetary measures.
5A similar conclusion is reached by Porter and Offenbacher (1983),
and Davidson and Hafer (1983).



Table 1
Total Domestic Nonfinancial Debt:
IV/1983 (billions of dollars)
Percent

of
Amount

U.S. Government
State/Local Government
Households
Nonfinancial Business
Total

total

$1,177.95
395.54
1,832.21
1,813.26

23%
8
35
35

$5,218.96

NOTE: Total does not equal 100 percent due to rounding.

secto r's sh are bein g abou t th ree tim es th at o f state and
local governm ents.
As show n in ch art 1, th e relative sh ares o f th e total
d e b t m e a s u r e o w ed by th e v a rio u s s e c to r s have
ch an g ed over tim e. F or exam ple, in 1960, th e sh are of
total debt a cco u n ted for by h o u seh o ld s an d n o n fin an ­
cial b u sin esses w as abou t 30 p e rce n t and 27 p ercen t,
respectively. By 1983, th eir sh ares ea ch had risen to
about 35 p ercen t o f th e total. T h e p roportion o f debt
ow ed by state and local governm ents h as rem ain ed
relatively u n ch an g ed d uring th e p ast 20 years, d eclin ­
ing from about 10 p e rce n t in 1960 to aroun d 8 p ercen t
in 1983.
D uring the sam e period, however, th e p ercen tag e of
total d ebt a cco u n ted for by th e U.S. governm ent has
varied con sid erably. From 33 p e rce n t in 1960, th e U.S.
govern m en t’s sh are d rop p ed to abou t 17 p e rce n t in
1974. Sin ce th en , it h as in crea sed to nearly 24 p ercen t.

WHICH EXPLAINS ECONOMIC
ACTIVITY B E T T E R : M l O R D E B T ?
T h o se w ho advocate th e u se o f a d ebt m easu re as a
target variable have p resen ted evid ence in d icatin g that
the level o f debt relative to th e level o f GNP (debt veloc­
ity) has b een relatively co n sta n t over th e past few d e­
cad es, in co n tra st to th e M l-G N P relatio n sh ip . They
argue that the stable relatio n sh ip betw een d ebt and
GNP ca n b e exploited for policy d ecisio n s ,KIf th e goal of
m o n etaiy policy is to achieve som e desired grow th of

6See, for example, the evidence presented in Friedman (1981,
1983a,b) and Kopcke.

19

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

C h a rt l

Com position of Domestic N o n fin a n c ia l D eb t
Percent

Percent

n om in al GNP throu gh th e u se o f interm ed iate growth
targets, however, th e salient q u estio n is how w ell do
th e g ro w th o f M l an d d ebt explain variations in the
g ro w th o f GNP? T h is issu e is critically im p ortan t in th e
selectio n o f a viable in term ed iate target m easure.
To investigate th is issue, a variant o f the St. Louis
redu ced -form GNP equation is u sed .7 T h is equation

7The basic equation is described in Tatom (1981). The model is
written as:
M
N
GNP = a0 + Pi 2 m, M,_i + p2 2 g, Gt_j
i= 0
j= 0

Q
+ (33 2 pek Pf_k + p4 S, + e,
k= 0
where M represents money, G is high-employment federal expendi­
tures, Pe is the relative price of energy and S is the strike variable.
The dots above each measure denote rates of change, measured
here as logarithmic differences.

20


relates th e grow th o f n om in al GNP to a m easu re of
m o n eta iy action s, fiscal a ctio n s, ch a n g es in th e relative
p rice o f energy an d a m easu re to a cc o u n t for lost
p ro d u ctio n due to lab or strikes. By su b stitu tin g the
d ebt m easu re for M l in th e eq uation, w e are able to
co m p are th e two m e a su re s’ ability to explain m ove­
m en ts in GNP growth.
E qu ation s o f th e form d escrib ed above w ere esti­
m ated u sin g season ally ad ju sted , quarterly d ata for the
period I/1960-IV/1981. T h is sam p le period is u sed b e ­
ca u se it pred ates th e 1 9 8 2 -8 3 perio d in w h ich m any
believe M l ’s u sefu ln ess as an in term ed iate target d e­
clin ed con sid erably. T h u s, o u r sam p le period en ables
us to co m p are ea ch m e a su re’s relative cap ab ilities in
explaining GNP d uring an "u n tro u b led ” tim e. Also,
th ese estim ates ca n b e u sed to fo reca st GNP grow th to
see w h eth er th e d ebt m easu re b e tte r p red icts GNP
during th e perplexin g 1 9 8 2 -8 3 period. Sum m ary re­
su lts o f th e estim atio n s are p resen ted in table 2.8

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 2
Regression Results for GNP Equations
1/1960—
IV/1981
Intermediate Target
and Lags Used
Variable

Constant
Strike
2X,
SGi
2F>k
e
R2
SE
DW

M1

3.285
-0.580
1.266
-0.192

(3.03)
(3.36)
(8.13)
(1.39)

0.019 (0.45)
0.59
2.64
2.12

Lag

3
10
5

Debt

-1.961
- 0.546
1.148
0.088
-0.530

(1.43)
(3.03)
(6.92)
(1.97)
(0.96)

Lag

0
0
11

0.54
2.79
2.21

NOTE: Absolute value of t-statistics appear in parentheses. FP is
the coefficient of determination adjusted for degrees of freedom;
SE is the regression standard error; and DW is the Durbin-Watson
test statistic.

Tu rning first to th e results based on M l, w e find that
th e equation acco u n ts for abou t 60 p e rce n t o f th e vari­
atio n in GNP grow th. T h e regression resu lts in d icate
th at a 1 percen tag e p o in t in crease in M l grow th p ro ­
d u ces a 1.3 p ercen tag e point in crease in the grow th of
GNP after th ree q u arte rs. A lthough th is estim ated
“lo n g -ru n ” effect is som ew h at larger th an th e usual
value o f unity, a test o f th e h y p oth esis th at th is estim ate
d oes n ot differ statistically from on e co u ld n o t be re­
je cte d at a stand ard 5 p e rce n t level o f sign ifican ce.9 Th e
fam iliar result that fiscal actio n s exert n o lasting effect
on GNP grow th is revealed in th e estim ated coefficient:
the su m m ed co efficien t’s value o f —0.19 is n o t statisti­
cally different from zero at th e 5 p e rce n t level.10 Finally,
the results in d icate th at th e long-run effect o f a chan ge
in the relative p rice o f energy is zero, as th eory p red icts,
an d th at days lost due to w ork stopp ages have a signifi­
can t, negative im pact on th e grow th o f GNP.

8The equation is estimated using ordinary least squares. The lag
lengths M, N and Q in footnote 7 were determined using several
statistical tests: Mallows Cp, Akaike’s Final Prediction Error criteria
and the Pagano-Hartley procedure. Where lag lengths selected by
the procedures differed, F-tests were used to pick the best lag for
each variable. For further discussion of these lag length selection
procedures as they apply to this type of specification, see Batten and
Thornton (1984).
9The calculated t-statistic is 1.71.
10Evidence on the long-run insignificance of fiscal actions on GNP is
investigated more fully in Hafer (1982).



T h e seco n d set o f regression resu lts reported in table
2 rep laces M l grow th w ith the grow th o f total d o m estic
non fin an cial debt. It is in terestin g to n o te that the
lag-length selectio n p ro ced u res ch o se only co n tem p o ­
ran eou s values o f d ebt grow th. T h e estim ated co e f­
ficient on th is term is 1.15, in d icatin g that a 1 p e rce n t­
age point in crea se in th e grow th o f debt tran slates into
a 1.15 p e rc e n ta g e p o in t in c re a s e in n o m in a l GNP
grow th in th e sa m e q u a rte r.11 A lthough w e again find
that th e cum ulative effect o f th e ch an g e in th e relative
p rice o f energy is n ot statistically different from zero
(t = 0.96), th e resu lt for fiscal a ctio n s suggests a m argi­
nally significant co n tem p o ra n eo u s effect (t = 1.97).
This effect is, how ever, quite sm all in m agn itu d e: a 1
p ercen tage poin t in crea se in th e grow th o f governm ent
e x p e n d itu re s y ie ld s o n ly a 0.09 p e rce n ta g e p o in t
ch an g e in GNP grow th. M oreover, b ec a u se o f th e c o n ­
tem p o ran eo u s n atu re o f th is result, it is difficult to
tra n s la te th is fin d in g in to a m ean in gfu l lo n g -ru n
outcom e.
A co m p ariso n o f e a c h eq u a tio n ’s overall explanatory
pow er in d icates th at M l o utperform s d ebt in exp lain ­
ing variations in GNP grow th. T h e R2 o f th e estim ated
equation using M l (0.59) is about 10 p ercen t h igher
th an th at u sin g d eb t (0.54). T h is difference, however, is
n o t large an d h as led som e to argue th at th is relative
clo sen ess d oes n o t p reclu d e th e u sefu ln ess o f debt as
an additional policy variable. As B en jam in Friedm an
has stated th e case, “th e evidence d oes not w arrant
in clu d in g th e m on ey m arket but exclu din g th e cred it
m arket o n th e groun d s o f th e clo sen ess, o r lack thereof,
o f th e observed em pirical re latio n sh ip s.”12
Of cou rse, a co m p ariso n o f relative explanatory pow ­
er o f GNP eq u atio n s using M l o r debt m ay not provide
an ad equ ate test o f th e ir relative abilities to explain
GNP. A m ore ap p rop riate test w ould b e to co m p are
th eir m arginal inform ational co n ten t. In o th er w ords,
after w e have a cco u n ted for th e effects o f M l (debt)
grow th on GNP, is th ere any statistically significant,
a d d itio n a l explan atory p ow er gained by adding debt
(M l) grow th to th e equation ?
To test th is n otion, a co n tem p o ra n eo u s debt growth
term w as ad d ed to th e M l eq u ation sh ow n in table 2.
T h is expand ed eq u ation th e n w as co m p ared statisti­
cally to th e previously estim ated M l eq uation. T h e
result reveals th at adding debt grow th d oes not en-

11Testing the hypothesis that the estimated coefficient on debt equals
unity yields a t-statistic of 0.89. Thus, we cannot reject the null
hypothesis that the coefficient equals one.
,2Friedman (1983b), p. 186.

21

FEDERAL RESERVE BANK OF ST. LOUIS

h a n ce M l grow th in explaining th e grow th o f GNP: the
calcu lated F -statistic w as 1.72, far below th e 5 p ercen t
critical value o f 3.99. T h e reverse test, that o f adding a
co n tem p o ran eou s an d th ree lagged term s o f M l to the
debt equation in table 2, also w as perform ed. T h e
calcu lated F -statistic w as 3.33, large enou gh to exceed
the 5 p ercen t critical value o f 2.50.
T h ese resu lts d em o n strate th at th e ap p aren t c lo se ­
n ess in explanatory pow er betw een red u ced -form GNP
equations using M l o r d ebt derives from th e clo se
relationship betw een th ese tw o m easu res; that is, debt
grow th reflects th e behavior o f M l grow th w h en the
latter is a bsen t from th e estim ated eq u atio n .13 O nce the
effects o f M l grow th are estim ated directly, th e debt
growth m easu re is red u n d an t; it co n tain s no ad d itio n ­
al statistically useful inform ation.

M l AND D E B T :
THE 1 9 8 2 -8 3 EXPERIEN CE
Som e have argued th at th ere h as b een a d ram atic
breakdow n in th e m oney-GNP link during th e last two
y ears and, th erefore, th e u se o f an o th er, n onm onetary
in term ed iate target is required. Presum ably, th e debt
m easu re w ould n ot be su b je ct to th e sam e ch an g es in
its relatio n sh ip s w ith GNP; co n sequ en tly, it w ould b e a
m ore reliable in term ed iate target. To test this p re­
sum ption, w e co m p are the behavior of M l and debt
velocity grow th rates sin ce the recessio n trough (IV/
1982) w ith historical p attern s to see how well the eq u a ­
tions estim ated earlier forecast m ovem ents in GNP
during the 1982-83 period.

Velocity Behavior o f M l and Debt
during the Recovery
T h e re cen t behavior o f velocity grow th h as b een
cited as an illu stration o f the su p p o sed d eterioration in
the money-GNP lin k.14 To put velocity behavior in a
historical perspective, the quarterly grow th rates o f M l
velocity in th e trough qu arter and the follow ing four
qu arters for th e m ost re cen t and four previous re c e s ­
sion s are listed in th e u p p er p anel of table 3.

13This result gains further credence if one examines the causal rela­
tionship between M1 growth and debt growth. As reported in Hafer
(1984a) using a slightly different sample period, the evidence over­
whelmingly indicates that M1 growth Granger-causes debt growth.
Also, evidence based on the lag length selection procedures indi­
cates that, when M1 and debt growth are included in the GNP
equation, no debt terms are significant.
14Analyses of the recent behavior of velocity include, among others,
Hein and Veugelers (1983), Judd (1983) and Tatom (1983).

22


JUNE/JULY 1984

T h e m ost re cen t beh avior o f M l velocity (IV/1982)
clearly has b een slow er th an th e "average” recovery
p h ase. T h e negative grow th o f v elocity d uring th e
trough qu arter an d on e q u arter into th e recovery are
u n m atch ed in th e sam ple. T h e behavior o f M l velocity
during th e next th ree qu arters also diverge from the
average. M oreover, the average grow th o f M l velocity
during the four qu arters after th e trou gh w as 5.36 p er­
ce n t d uring th e previous four recoveries. In con trast,
M l velocity grow th sin ce IV/1982 h as averaged only a
0.45 p e rce n t rate o f grow th.
T h e behavior o f d ebt velocity d uring th e cu rren t
recovery, rep o rted in th e m idd le p an el o f table 3, also
ap pears unlike its average p o st-tro u g h period . Follow ­
ing th e IV/1982 trough, debt velocity grow th, like M l
velocity growth, w as co n sid erab ly below th e average
rate for several qu arters. F or exam ple, th e average rate
o f grow th for debt velocity in th e y ea r follow ing the
trough w as 2.06 p ercen t. D uring th e first y ea r o f the
re ce n t exp an sio n , d eb t velocity grow th averaged a
negative 0.27 p e rce n t rate.
T h e m ost re cen t ex p erien ce is n o t w ith ou t h isto rical
com p arison , how ever. T h e recovery follow ing th e 1970
recessio n , for exam ple, reveals a su b stan tial d eclin e in
debt velocity well into the ex p an sio n p h ase o f the
cycle. Thu s, the debt m easu re d oes n o t seem to b e a
relatively m ore stable guide to GNP behavior th a n M l
during the past few y ears.

Velocity Using an Adjusted M l Measure
Several re cen t stu d ies have suggested th at th e p ro b ­
lem w ith th e M l velocity b eh avior d uring th e recen t
recovery is that “effective” m o n ey grow th — grow th
that rep resen ts in crea ses in tra n sa ctio n -o rien ted h o ld ­
ings — h as b een overstated b eca u se o f fin an cial in ­
novations like th e Super-NOW a cco u n ts in tro d u ced in
Jan u ary 1983.15 O ne ap p ro ach to investigate th is c o n ­
ce rn is to u se an ad ju sted M l m easu re th at exclu d es
a cco u n ts w ith the dual ch a ra cte ristics o f tran sactio n
and savings a c c o u n ts .ui
W hen th is a d ju sted M l m easu re is u sed to calcu late
velocity grow th during th e re cen t recovery, th e results
are con sid erably different. For exam ple, as sh ow n in
th e low er p an el o f table 3, a d ju sted M l velocity grow th

15See, for example, Judd and McElhattan (1983) and Hafer (1984b).
1
6The approach taken here follows Hafer (1984b); that is, the adjusted
M1 measure omits interest-bearing checkable deposits. This
approach admittedly overstates the savings nature of interestbearing checkable deposits relative to the more sophisticated tech­
niques of, say, Spindt (1984).

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 3
Velocity Growth During Recovery
Quarters after trough
Recession Trough

0

1

2

3

4

-1 .02
0.53
-4 .9 6
-1.11
-1 .6 4

7.85
5.49
8.81
3.68
6.46

6.52
4.47
-1.01
8.55
4.63

3.11
7.00
-0 .2 7
7.64
4.37

7.93
5.91
3.22
6.86
5.98

IV/1982

-12.64

-4.67

1.02

1.54

3.91

11/1958
1/1961
IV/1970
1/1975
Average

-3 .17
-1 .3 8
-4 .7 9
-5 .6 7
-3 .7 5

8.70
3.52
8.19
1.56
5.49

2.13
-0 .8 6
-2.43
6.25
1.27

0.58
4.22
-3 .4 2
0.59
0.49

2.88
1.73
-2 .3 9
1.66
0.97

IV/1982

-6.56

-0 .7 2

0.56

0.87

-1 .8 0

11/1958
1/1961
IV/1970
1/1975
Average

-1 .0 2
0.53
-5.15
-0 .9 3
-1 .64

7.85
5.49
8.92
3.81
6.52

6.52
4.47
-0.96
8.63
4.66

3.11
7.00
-0 .2 8
7.82
4.41

7.93
5.91
3.22
7.21
6.07

IV/1982

M1

11/1958
1/1961
IV/1970
1/1975
Average

-6.72

3.08

5.80

5.12

5.35

Recession Trough

DEBT

Recession Trough

ADJUSTED M1

in the IV/1982 trough qu arter is —6.7 p ercen t, co m ­
pared w ith —12.6 p e rce n t using M l. T h e average ad ­
ju sted M l velocity grow th rate in previous trou ghs is
— 1.64 p ercen t. D uring th e four qu arters after IV/1982,
the grow th o f ad ju sted M l velocity averages 4.84 p er­
ce n t p e r quarter, co m p ared w ith th e 5 4 2 p ercen t aver­
age quarterly rate from previous recovery p h ases. In
co n trast, th e grow th rate o f M l velocity as cu rrently
d efined averages only 0.45 p e rce n t d uring th e four
qu arters after th e IV/1982 trough. Thu s, relative m ove­
m en ts in debt velocity d uring th e post-IV/1982 recovery
suggest that th e behavior o f an M l velocity m easure
that red u ces th e in flu en ce o f financial innovations d u r­
ing th e post-IV/1982 period is m u ch clo se r to previous
norm s.

on th e coefficien t estim ates und erlying th e results re­
p orted in table 2, quarterly forecasts o f GNP grow th for
th e 1 9 8 2-83 period w ere m ad e using th e actu al grow th
rates o f M l an d debt, as w ell as th e o th e r explanatory
variables. T h e out-of-sam ple fo reca st errors derived
from the M l and debt eq u atio n s along w ith actu al GNP
grow th are reported in table 4 .17
T h e forecast errors from th e M l eq u ation in d icate
th a t M l c o n t in u a lly o v e r p r e d ic te d GNP g ro w th
throu ghou t 19 8 2 -8 3 . T h e m ean erro r is a negative 5.49
p ercen t w ith th e largest quarterly errors appearing in
1/1982, III/1982, IV/1982 and 1/1983.18 It is interestin g to
n o te that th ese latter errors o c c u r about th e tim e w hen
d iscu ssio n s about th e effects o f fin an cial innovations
on M l suggest th at M l grow th m ay b e overstated.
M oreover, the ro o t-m ean -squ ared erro r (BMSE) is 5.93,

Forecasting GNP
A co m m o n te ch n iq u e u sed to asse ss th e viability of
alternative target variables is to exam in e th e accu ra cy
o f out-of-sam ple forecasts o f e co n o m ic activity. Based



17The errors reported are actual minus predicted GNP growth.
,8These errors exceed two standard errors from the regression equa­
tion (SE = 2.64).

23

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 4
GNP Forecasts: 1/1982- IV/1983
Quarter

Actual GNP
Growth

Forecast Errors Using:
M1

Debt

Adjusted M1

1/1982
II
III
IV

-1.43%
6.41
2.66
2.44

1/1983
II
III
IV

7.88
12.48
10.88
8.71

-6 .9 6
-3 .2 6
-1 .5 0
-5.19

0.54
0.85
5.11
-4.71

1.28
3.45
5.68
-1.12

Mean Error
Mean Absolute Error

-5.49
5.49

-3 .4 8
5.11
6.22

0.16
2.95
3.33

Root-Mean-Squared Error

-7.18%
-3 .9 3
-7 .5 8
-8 .2 9

5.93

-6.07%
-2 .9 5
-9.54
-11.10

-1.95%
2.02
-3.42
-4.68

a value m ore th an two tim es th e estim ated eq u atio n ’s
standard error (2.64).
W hen th e d ebt eq u ation in table 2 is u sed to forecast
GNP grow th, there is a slight im provem ent in th e a b so ­
lute forecast errors. Relative to the 5.49 p ercen t m ean
absolu te error using M l, using debt yield s a m ean
absolu te forecast erro r o f 5.11 p ercen t. T h ree o f the
q u arters’ errors (1/1982, III/1982 an d IV/1982) also ex ­
ceed two tim es th e d ebt reg ressio n ’s stand ard error
(2.79). T h e relatively m in o r im provem ent in th e m ean
errors from using th e d ebt m easu re d isap pears w hen
RMSEs are co m p ared . T h e RMSE derived from debt
forecasts o f GNP is 6.22, som ew hat larger th an that
from M l. Like th e RMSE for M l, this value is m ore than
tw ice th e eq u atio n ’s stand ard error, again ind icatin g
little gain in th e u se o f th e debt m easure over M l.

GNP Forecasts Using Adjusted M l
B ased on th e foregoing velocity co m p ariso n s and
previous em pirical findings, it m ay prove useful to
investigate th e GNP forecastin g reco rd o f M l w hen the
effects o f the fin ancial innovations are rem oved. T o do
this, M l w as rep laced by ad ju sted M l in th e regression
equation an d u sed to forecast GNP g row th.19 T h e fore­
cast results using th e ad ju sted -M l m easure, also re­
p orted in table 4, co rrobo rate the evidence based on
com p aring relative velocity m ovem ents. T h e GNP fore-

19The estimated equation is identical to the M1 equation, except that a
dummy variable term is added to capture the intercept shift in 1981
due to the introduction of NOW accounts on a nationwide basis. The
cumulative effect of adjusted M1 (using the same lag structure as
M1) is 1.21, compared with 1.27 for M1. The R2 for the equation
using adjusted M1 is 0.56, compared with 0.59 for M1.

24


cast errors from th e a d ju sted -M l equation are n o tice ­
ably sm aller th an th o se for M l o r debt and, m ore
im portant, are n ot co n tin u ally on e-sid ed . T h e c o n s e ­
qu en ce o f this latter property is that th e m ean error
using ad ju sted M l to forecast GNP grow th is only 0.16
p ercen t. M oreover, th e m ean ab solu te erro r is 2.95
p ercen t, well below th at for th e o th e r two m easures.
Finally, the RMSE is calcu la ted to b e 3.33, alm ost oneh alf the value found u sing M l o r d ebt to forecast GNP.20
T h e evid ence in d icates th at th e debt m easure pro­
vides little o r no im provem ent over M l in forecasting
GNP growth during th e 1 9 8 2 -8 3 period. M oreover, u s­
ing a tra n sa ctio n s definition o f m o n ey that ab stracts
from the effects o f re cen t fin an cial innovations on M l
provides forecasts o f GNP grow th that are statistically
su p erio r to forecasts b ased on debt.

SUMMARY AND CONCLUSION
Som e analysts have suggested that inform ation from
the liability side o f th e eco n o m y ’s b a la n ce sh eet m ight
be useful in the form ation o f m on etary policy. In this
paper, w e have investigated th is co n ten tio n bv co m ­
paring th e relative abilities o f M l and total d o m estic
n on fin an cial d ebt to explain th e grow th o f GNP. Based
on evidence from th e sam p le p eriod 1960-81, M l b etter
explained m ovem ents in GNP th an debt. M oreover,
o n ce th e effects o f M l grow th w ere a cco u n ted for, debt
grow th did n ot significantly in crea se the explanatory
pow er o f th e GNP eq uation. In co n trast, M l provided
significant inform ation to explain GNP growth, even
after the effects o f d ebt w ere in clu d ed in th e ex p lan a­
tory equation.
O ut-of-sam ple forecast resu lts o f GNP during the
1 9 8 2-83 period also in d icate that th ere is no advantage
to using th e d ebt m easu re. R ecen t debt velocity b e ­
havior ap pears as equally at od d s w ith historical p at­
tern s d uring p ost-trough p eriod s as d oes M l velocity
behavior. W hat little im provem ent th ere is in using
debt in stead o f M l to forecast GNP stem s from recen t
fin an cial in n o v atio n s w h ich b loated th e m easu red
grow th o f M l in 1 9 8 2 -8 3 . W hen an M l m easu re that
a d ju sts for su ch effects is used, GNP grow th rate fore­
casts b ased on th e behavior o f d ebt fare poorly co m ­
pared w ith th e ad ju sted M l m easure.
Thus, th ere is little evid ence to su p p ort th e u se o f a
broad d ebt m easu re as y et a n o th e r in term ed iate target
variable for m o n etary policy.

20Judd and McElhattan, based on a different measure of adjusted M1,
also find an improved forecasting record relative to the published M1
growth rate during 1982-83.

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984
ments and the Evidence,” American Economic Review, Papers
and Proceedings (May 1970), pp. 32-39.

R EFER EN C ES
Batten, Dallas S., and Daniel L. Thornton. “ How Robust are the
Policy Conclusions of the St. Louis Equation?” this Review (June/
July 1984), pp. 26-32.

Hein, Scott E., and Paul T. W. M. Veugelers. “ Predicting Velocity
Growth: A Time Series Perspective,” this Review (October 1983),
pp. 34—
43.

Carlson, Keith M., and Scott E. Hein. "Monetary Aggregates as
Monetary Indicators,” this Review (November 1980), pp. 12-21.

Judd, John P. “The Recent Decline in Velocity: Instability in Money
Demand or Inflation?" Federal Reserve Bank of San Francisco
Economic Review (Spring 1983), pp. 12-19.

Davidson, Lawrence S., and R. W. Hafer. “Some Evidence on
Selecting an Intermediate Target for Monetary Policy," Southern
Economic Journal (October 1983), pp. 406-21.
Friedman, Benjamin M. “The Relative Stability of Money and Credit
Velocities’ in the United States: Evidence and Some Specula­
tions,” Working Paper No. 645 (National Bureau of Economic
Research, 1981).
_________“ Money, Credit and Nonfinancial Economic Activity: An
Empirical Study of Five Countries,” Working Paper No. 1033
(National Bureau of Economic Research, 1982).
________ “Monetary Policy with a Credit Aggregate Target,” in
Karl Brunner and Allan H. Meltzer, eds., Money, Monetary Policy,
and Financial Institutions, Carnegie-Rochester Conference Series
on Public Policy, (Spring 1983a), pp. 117-48.
_________"The Roles of Money and Credit in Macroeconomic
Analysis,” in James Tobin, ed., Macroeconomics, Prices, and
Quantities: Essays in Memory of Arthur M. Okun (The Brookings
Institution, 1983b), pp. 161-89.
Friedman, Milton, and David Meiselman. “The Relative Stability of
Monetary Velocity and the Investment Multiplier in the United
States 1897-1958,” in the Commission on Money and Credit,
Stabilization Policies (Prentice Hall, 1963), pp. 165-268.
Hafer, R. W. “ Selecting a Monetary Indicator: A Test of the New
Monetary Aggregates,” this Review (February 1981), pp. 12-18.
_________“The Role of Fiscal Policy in the St. Louis Equation,”
this Review (January 1982), pp. 17-22.
________ “Choosing Between M1 and Debt as an Intermediate
Target for Monetary Policy" (a paper presented at the CarnegieRochester Conference Series on Public Policy, April 13-14,
1984a).
________ “The Money-GNP Link: Assessing Alternative Transaction Measures," this Review (March 1984b), pp. 19-27.
Hamburger, Michael J.

"Indicators of Monetary Policy: The Argu­




Judd, John P., and Rose McElhattan. “The Behavior of Money and
the Economy in 1982-83," Federal Reserve Bank of San Francis­
co Economic Review (Summer 1983), pp. 46-51.
Judd, John P., and Brian Motley. “ M1 versus M2: Which is More
Reliable? ” Working Papers in Applied Economic Theory and Econ­
ometrics, No. 83-04 (Federal Reserve Bank of San Francisco,
October 1983).
Kane, Edward J. “Selecting Monetary Targets in a Changing Finan­
cial Environment,” in Monetary Policy Issues in the 1980s, a sym­
posium sponsored by the Federal Reserve Bank of Kansas City
(August 9 and 10, 1982), pp. 181-206.
Kareken, J. H., T. Muench, and N. Wallace. “Optimal Open Market
Strategy: The Use of Information Variables,” American Economic
Review (March 1973), pp. 156-72.
Kopcke, Richard W. “ Must the Ideal Money Stock’ be Control­
lable?” New England Economic Review (March/April 1983), pp.
10-23.
Morris, Frank E. “ Do the Monetary Aggregates Have a Future as
Targets of Federal Reserve Policy?” New England Economic
Review (March/April 1982), pp. 5-14.
_________“Monetarism without Money," New England Economic
Review (March/April 1983), pp. 5-9.
Porter, Richard D., and Edward K. Offenbacher. “ Empirical Com­
parisons of Credit and Monetary Aggregates Using Vector Autore­
gressive Methods,” Federal Reserve Bank of Richmond Economic
Review (November/December 1983), pp. 16-29.
Spindt, Paul A. “Money Is What Money Does: Monetary Aggrega­
tion and the Equation of Exchange,” (Board of Governors of the
Federal Reserve System, 1984; processed).
Tatom, John A. “ Energy Prices and Short-Run Economic Perfor­
mance,” this Review (January 1981), pp. 3-17.
_________“Was the 1982 Velocity Decline Unusual?” this Review
(August/September 1983), pp. 5-15.

25

How Robust Are the Policy
Conclusions of the
St. Louis Equation?:
Some Fu rth er Evidence
Dallas S. Batten and Daniel L. Thornton

I N a previous issu e o f th is Review, w e provided som e
evidence th at th e policy co n clu sio n s o f the St. Louis
equation are robu st w ith resp ect to bo th th e sp ecifica ­
tion o f its lag stru ctu re and th e im position o f p oly n o­
m ial restrictio n s: m onetary policy has a significant
long-run effect on aggregate inco m e, w hile fiscal policy
does n o t.1 T h is result is im portant b ecau se it provides
evidence th at th ese policy co n clu sio n s are not d ep en ­
d en t on th e eq u atio n ’s eco n o m etric sp ecification , a
su b ject o f co n tin u ed d ebate sin ce th e equation first
appeared. T his co n clu sio n , however, w as based on the
use o f only one tech n iq u e — developed by Pagano and
Hartley (1981) — for selectin g th e approp riate lag stru c­
tu re and polynom ial degree. C onsequently, th e general
sensitivity o f th e policy co n clu sio n s to th e sp ecifica­
tion of lag lengths and polynom ial degrees rem ain s an
issue.
T h e p u rpose o f this article is to use various m odel
selectio n criteria to investigate th e im p act o f m odel
sp ecification on th e policy co n clu sio n s draw n from
the St. Louis eq u ation.2 T h e evid ence p resen ted here

Dallas S. Batten and Daniel L. Thornton are senior economists at the
Federal Reserve Bank of St. Louis. Sarah R. Driver provided re­
search assistance.
1See Batten and Thornton (1983).
2Since there has been an increased interest in techniques for specify­
ing lag lengths of finite distributed lag models, our results, although
data and model specific, should provide an experiential starting point
for those interested in using these procedures.

26


d em on strates that th ese co n clu sio n s are extrem ely
robu st w ith re sp ect to ch a n g es in eith er th e lag stru c­
ture o r the polynom ial restrictio n s. Thu s, argum ents
that the general policy co n clu sio n s o f the St. Louis
equation are d ep en d en t u pon an ad h o c eco n o m etric
sp ecification are w ith ou t m erit.

THE PR O BLEM O F MODEL
SPECIFICATION
To investigate th e ap p rop riate lag lengths for the St.
Louis equation, w e em ploy the grow th rate sp ecifica ­
tion, p resen ted as eq u ation 1 in table 1. T h e d ots over
e a c h v ariab le re p re s e n t q u a rte r-to -q u a rte r a n n u al
rates o f change, an d Y, M an d G are n om in al GNP,
m on ey (the M l definition) and h igh -em ploym ent gov­
ern m en t exp en d itu res, respectively.
T h e first p rob lem in estim atin g th e St. Louis eq u a ­
tion, or for th at m atter, any finite d istribu ted lag m odel,
is to specify th e o rd er o f th e d istribu ted lags (I, K).
M odel selectio n criteria typically trade off th e bias
associated w ith specifying too sh ort a lag (or too low a
polynom ial degree) against th e in efficiency asso ciated
w ith selectin g too lon g a lag (or too high a polynom ial
degree). In general, if eith e r th e lag is too long or the
polynom ial d egree too high, th e estim ates will b e u n ­
biased bu t inefficient. If eith er th e lag is too sh ort or the
polynom ial d egree too low, the estim ates will be biased
but efficient. F urth erm ore, sin ce the St. Louis equation

JUNE/JULY 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1
Various Equations for the PDL Specification of the
St. Louis Equation
(1 ) Y, = y. +

I
K
2 Pi M,_i + 2 "Y G, j -tj
i=0
j=0

E,

*
P, — oto + a,i + a 2 i2 + <3 i3 + ... + apip;

i — 1, 2, ..., I; P — 1
0,

■j = Xo + X-j + \ 2 j 2 + X3 P +
Y

j — 1, 2, ..., K; Q < K
0,

(2 )

(3)

NOTE: Z„ =

Y,

=

H.

+

+ ^oj0 :

P
Q
2 arZrt + 2 XsWst +
r= 0
s=0

et

I
K
2 ir M, , and Wst = 2 js Gt H ,
i= 0
j= 0

where, for notational purposes, 0° is defined to be 1.

has two d istribu ted lag variables, th e resulting esti­
m ates w ill b e biased an d m ay be inefficient if on e lag is
too long an d th e o th er to o short.3
B ecau se different criteria give different w eights to
this bias/efficiency trade-off, they m ay select different
lag stru ctu res (and polynom ial degrees). In the co n text
o f th e St. Louis equation, th is m ean s th at different
policy co n clu sio n s m ay be obtain ed sim ply becau se
different w eights are u sed for the bias/efficiency trad e­
off. In particular, th e co n clu sio n that fiscal policy is
ineffective in th e long run m ay result largely from the
lack o f efficiency o f the estim ator. In ord er to investi­
gate this issue, w e exam ine the general co n clu sio n s
co n cern in g m on etary and fiscal policy effectiveness in
m odels selected by six different m odel selectio n cri­
teria. T h ese criteria w ere ch o se n eith e r b ecau se they
are am ong the m ost co m m o n ly suggested or becau se
they rep resen t a definite ordering o f th e bias/efficiency
trade-off.

LAG-LENGTH SELECTIO N
T h e criteria em ployed h ere are: Pagano an d H artley’s
t-test (PH), M allow s’ (1973) C p -statistic, Akaike’s (1970)
F in al P red ictio n E rro r (FPE), Gew eke an d M e e se ’s
(1981) Bayesian E stim ation C riterion (BEC), Sch w arz’
(1978) Bayesian Inform ation C riterion (SBIC) an d the
stand ard F-test. (See th e ap p en d ix for a b rief d escrip ­
tion o f th ese criteria.)
E ach o f th e six alternative criteria for d eterm ining
th e appropriate lag len gth s is u sed to select th e lag
lengths (I, K) for m on ey an d governm ent expen d itu res
grow th.4 To assess the sensitivity o f the various te c h ­
niques to the selectio n o f th e m axim um lag length (L),
th ree values o f L (8,12 an d 16) are specified initially for
ea ch variable.

Empirical Results o f
Lag-Length Selection
T h e St. Louis eq u ation is estim ated over th e period
11/1962 to III/1982.5 T h e results reported in table 2 show

3The actual conditions are somewhat more complicated than is indi­
cated here. Let 9 and a* denote the assumed and correct lag length
and p and p* denote the assumed and correct degree of polynomial,
respectively. Estimates of the parameter vector will be biased if (a)
9=9* and p<p*, (b) 9<9* and p = p', or (c) 9>9*, p = p* and
9 - 9* > p*. In the instance when 9 - 9* < p*, the polynomial distrib­
uted lag estimates may be biased, but need not be. That is, there are
restrictions that may or may not be satisfied by the data. Further­
more, PDL estimators will be inefficient if 9 = 9* and p > p*. See
Trivedi and Pagan (1979).



4While it is unclear how the various criteria will select lags in the
general case, it is possible to order the selection when only two
alternative lag specifications, p and p + q, are considered. The crite­
rion would pick p, using an F-test, in the following way: Cp if F < 2;
FPE if F < 2T/(T + p + 1); SBIC if F < 1 + [(T + p + 1)(Tq/t - 1)/q]; BEC
if F < 1 + [(T —p 1)lnT/(T p —q —1)], where T is the sample size.
5The sample period is chosen to conform to that employed in Batten
and Thornton.

27

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 2
Lag Lengths Selected by Various
Model Selection Criteria

Table 3
Tests of Policy Effectiveness for
Various Distributed Lag Models

Maximum Lag Length (L)
Criterion

8

12

16

Lag Length
M
G

Chosen by

IM

i.G

M G

M G

10

9

PH, FPE

1.16
(0.62)

-0 .0 4
(0.26)

5
0
5
2
5
2
1 0
2
0
1 8

10
9
5
2
10
9
1 0
2
0
10
8

10
9
5
2
10
9
1 0
2
0
1 0

10

8

F-test

1.03
(0.11)

0.08
(0.62)

5

2

Cp, FPE

1.00
(0.00)

0.07
(0.92)

5

0

PH

0.98
(0.09)

0.11*
(2.38)

2

0

SBIC

1.19
(0.97)

0.09*
(1.99)

1

PH
Cp
FPE
BEC
SBIC
F-test

M G

0

BEC, F-test

0.95
(0.29)

0.10’
(2.05)

1

8

F-test

1.10
(0.57)

-0.01
(0.11)

that th e ch o se n lag lengths differ by criterion and, to a
le sser extent, by th e m axim um lag length specified . F or
exam ple, w h en th e m axim um lag length w as eight, the
PH criterion selected th e lag on m oney grow th (I) to be
five an d th e lag o n governm ent exp en d itu re grow th (K)
to be zero.6 Both th e FPE and Cp criteria ch o o se the
sam e lag on M bu t a slightly lo n g er lag on G. W hen the
m axim um lag is in creased to 12 an d 16, b o th th e FPE
a n d PH criteria select lo n g er lags on M and G (I = 10
an d K = 9). T h e Cp statistic, however, is u naffected by
ch an ging th e m axim u m lag length. T h e Bayesian crite­
ria also are u naffected by th e ch o ice o f th e m axim um
lag length; how ever, they select lags th at are extrem ely
short. Perhaps th ese criteria give too m u ch w eight to
efficiency in th e bias/efficiency trade-off.7
T h e F-test ap pears to be th e m ost sensitive to the
ch o ice o f th e m axim um lag length. It ten d s to in ­
d icate sh o rter lags w hen ever th e last significant lag
coefficien t is follow ed by a n u m b er o f insignificant
o n es. T h e insignificant co efficien ts ten d to d ilute the
d iscrim inatin g pow er o f th e F-test. T hu s, it ch o o ses a
m u ch sh o rte r lag w hen L is in creased from 12 to 16.
T his is to be exp ected , how ever, given th e general n a ­
ture o f th is test.

Absolute value of t-statistics in parentheses for testing 2M = 1
and XG = 0.
'Statistically significant at the 5 percent level.

Policy Effectiveness and the
Lag Structure
To test for th e long-run effectiveness o f m onetary
and fiscal policies, sim ple t-tests o f th e su m s o f the
d istribu ted lag w eights are p erform ed . T h e results of
t h e s e t e s t s , for t h e lag stru ctu res rep o rted in table 2, are
p resen ted in table 3. T h e su m m ed effects o f m on ey
grow th on n om in al in co m e grow th range from 0.95 to
1.19, an d th e h y p oth esis th at th ere is a o n e-to -on e
relation sh ip betw een m oney grow th an d grow th in
n om in al in co m e in th e long ru n ca n n o t b e re je cte d for
any o f the lag stru ctu res.

T h e su m m ed effects o f governm ent exp en d itu res on
n om in al in co m e range from —0.04 to 0.11 and, in c o n ­
trast to th e estim ated im p acts o f ch an g es in m on ey
growth, are n ot significantly different from zero in ev­
ery in sta n ce w h en th ere is a lagged effect o f G. This
suggests that th ere is no long-run effect o f G on n o m i­
nal
6
Actually, the PH t-ratio for the second lag of G is 1.91 when the lag in co m e grow th. In th e th ree m od els w here only
co n tem p o ran eo u s G is in clu d ed , how ever, its coefon M is five. Thus, the PH technique nearly selects the same lag
structure (five on M and two on G) as does the FPE criterion.
7The Bayesian criteria are designed to be asymptotically efficient in
that they select the correct lag length in large samples (see Geweke
and Meese for details). It appears, however, that they give this
property too much weight in small samples and select lags (and
polynomial degrees) that are too short. In a Monte Carlo experiment,
Geweke and Meese found that the probability of underfitting is about
50 percent even with a sample size of 50.


28


Furthermore, for this analysis, the equation is constrained to con­
tain both variables. That is, the possibility that one of the criteria can
select a model in which either M or G is excluded completely
is precluded. If this constraint is removed, however, bpth Bayesian
criteria indicate that not even contemporaneous G should be
included in the equation.

FEDERAL RESERVE BANK OF ST. LOUIS

ficient is always significant, a result in d ep en d en t o f the
lag on M.8 T h is suggests that h igh-em ploym ent govern­
m e n t e x p e n d itu re s m ay have an im m e d ia te an d
p en n a n en t im pact on nom inal output. W hen th e m o d ­
els w ith “long’' lags on b o th variables (M and G) are
tested against a m od el w ith a “lo n g ” lag on M and no
lag on G via a likelihood ratio test, how ever, th e latter
m odel is re je cte d at th e 5 p e rce n t sign ificance level.9
T h at is, th e m odel w ith long lags on both variables is
preferred. In th e preferred sp ecification, G has a sig­
n ificant sh o rt-ru n effect, bu t no long-run effect on
nom inal output.
T h e above resu lts suggest th at th e long-run policy
im plications o f th e St. Louis equation are relatively
insensitive to th e lag sp ecificatio n and, h en ce, to the
relative w eighting o f th e bias/efficiency trade-off. Only
in th e m od els ch o se n by th e Bayesian criteria d oes
governm ent sp en d ing have a p erm an en t effect on in ­
com e. T h e data suggest, how ever, that lon ger lag sp e ci­
fications are preferable over the short o n es ch o sen by
the Bayesian criteria. C onsequently, it ap pears that
th ese criteria give too m u ch w eight to efficiency in the
bias/efficiency trade-off.
It should be n o ted that, even thou gh th e long-run
(equ ilibrium ) p ro p e rties o f th e eq u atio n are qu ite
robust w ith resp ect to th e lag stru ctu re, th e short-ru n
dynam ics differ considerably, esp ecially for a ch ange
in m on ey grow th. In p articular, th e sh o rt-ru n im p act of
a ch an ge in m o n ey grow th is con sid erably larger, and
lasts longer, in th e m o d els w ith relatively long lags on
m oney grow th th an in th e sh o rte r lag specification s.

POLYNOMIAL-DEGREE SELECTIO N
T h e problem o f p olynom ial-d egree selectio n is co m ­
pletely analogous to that o f lag-length selectio n . T o see
this, w e n o te that th e polynom ial distribu ted lag (PDL)
estim a tio n te c h n iq u e a ssu m es th at th e reg ressio n
coefficients on M and G (i.e., th e (3s and ys) fall on
polynom ials o f d egrees P and Q, respectively, w here
P < I and Q 5~ K. T h e se assu m p tio n s are given by the
equations (2) in table 1. Given the lag lengths, I and K,
the eq u ations in (2) can be co m bin ed w ith (1) to obtain
the PDL equation (3). T hu s, selectin g th e polynom ial
degree am o u n ts to ch o o sin g o rd ers (P, Q) o f equation
Estimates of the equations that include only contemporaneous G and
lags of M from 1 to 10 are not qualitatively different from those
reported in table 3.
9When models with 10 lags on M and 9 or 8 lags of G are com­
pared with a model with 10 lags on M and only contemporaneous
G, the implied restrictions are rejected at the 5 percent significance
level. The calculated \ 2 statistics (5 percent critical values) are 24.39
(x2(9) = 16.9) and 17.28 (x2(8) = 15.5), respectively.



JUNE/JULY 1984

(3). As w ith th e sp ecificatio n o f lag lengths, w e m u st
specify th e m axim u m polynom ial degree th at will be
co n sid ere d initially. In this in sta n ce , how ever, the
ch o ice is not arbitrary b eca u se th e polynom ial degree
can n o t b e larger th an th e lag length o f th e m od el w e are
consid ering.
T h e ap p lication o f th e above p ro ced u re to all o f the
m od els in th e previous sectio n w ould b e ted iou s sin ce
seven different lag stru ctu res w ere selected by th e vari­
ous criteria for different m axim um lag len gth s. T h u s, to
sim plify ch o o sin g th e polynom ial degree, a " b e s t” lag
stru ctu re is ch o se n . To do this, ea ch lag stru ctu re in
table 2 is tested against th e oth ers and against arbi­
trarily ch o sen lags o f four, six and twelve on both M
and G using a likelihood ratio test. T h e resulting
statistics are rep o rted in table 4. B eca u se som e o f the
lag stru ctu res rep o rted in table 2 differ only slightly
from ea ch other, th e results o f all th e te sts are not
reported.
T h ese resu lts in d icate that the m odel w ith 10 lags on
M and 9 lags on G d oes well relative to all the others.
F or exam ple, w h en th is m odel is tested against the
arbitrary m od el w ith six lags on b o th variables, th e null
hyp oth esis that the add itional fou r lags on M and the
additional th ree lags on G are all zero is re je cted at th e 5
p ercen t sign ifican ce level. T his is also true o f th e o th er
“sh o rt” lag m od els. F urth erm ore, w h en th is m od el is
com p ared w ith on e w ith twelve lags on b o th variables,
th e null h yp oth esis th at th e ad d itional two lags on M
an d th e ad d itional th ree lags on G are all zero ca n n o t
be rejected . Indeed, only th e lon ger lags ch o se n by the
PH an d FPE criteria ca n n o t b e re je cte d relative to all of
th e o th e r sp ecificatio n s. Finally, it is in terestin g to note
that th e extrem ely sh o rt lags o f th e Bayesian criteria are
generally re je cte d relative to th e lo n g er lag sp ecifica ­
tions. W hile no am ou n t o f testin g can be conclusive,
th ese results suggest that th e lon ger lag stru ctu res
selected by th e PH an d FPE criteria are th e m ost ap p ro ­
priate. C onsequently, th e resu lts o f polynom ial-degree
selection , w h ich are rep o rted below , are b ased on a
m odel w ith 10 lags on M an d 9 on G.

Empirical Results o f
Polynomial-Degree Selection
T h e sam e six criteria u sed to d eterm in e th e lag
len gth w ere applied to th e selectio n o f th e polynom ial
d eg ree.10 T h e resu lts are p resen ted in table 5 .11 T h ese
10Because of their spurious nature, the endpoint constraints are not
imposed; see Thornton and Batten (1984).
11
The polynomial degrees chosen by the PH criterion here differ from
those reported in Batten and Thornton. In that article we attempted
to account for the preliminary test problem.

29

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE/JULY 1984

Table 4
X 2 Statistics for Lag Specification Tests
Lags on M and G

Lags on
M and G

12
10
6

12
9
6

5
4
2

10 9

2
4
0

6

6

5

2

3.33
—

N.A.
21.10*

29.78*
26.45*

—
—
—
—

—
—
—
—

5.35
—
—
—

4

4

N.A.
32.13*
N.A.
—
—
—

2

0

43.39*
40.06*
18.96*
13.61*
7.94
—

0

0

N.A.
—
N.A.
—
N.A.
18.14*

N.A. indicates that the likelihood ratio was not calculated between arbitrarily chosen lags.
‘ Statistically significant at the 5 percent level.

resu lts are sim ilar to th o se ob tain ed in th e lag-length
selectio n in th at th e FPE an d PH criteria (and in th is
in stan ce, M allow s’ Cp) select relatively high p olyno­
mial degrees, w hile th e Bayesian criteria select ex ­
trem ely low degree polynom ials. T h e Bayesian results
suggest th at estim ates o f th e 11 co efficien ts on M (co n ­
tem p o ran eo u s plus th e 10 d istribu ted lags) and th e 10
on G ca n b e obtain ed by estim atin g only 2 p olyno­
m ial c o e ffic ie n ts o n M a n d o n ly 1 o n G. In d eed ,
w h en th e polynom ial restrictio n s im plied bv th e m od ­
el selected by th ese criteria are tested , th ey are re je cted
at th e 5 p e rce n t sign ifican ce level. On th e o th e r hand,
w hen th e im plied polynom ial restrictio n s o f th e FPE
and PH d eterm in ed sp ecificatio n s are tested , they c a n ­
n ot b e re je cte d .12

Table 5
Polynomial Degrees Selected by
Various Model Selection Criteria
Polynomial degree
Criterion

M

PH

6
6
6
1

Cp
FPE
BEC
SBIC
F-test

G

7
8
8
0
0
3

1
6

NOTE: Based on a specification including 10 lags on M
and 9 on G.

Table 6
Policy Effectiveness for Various
Polynomial Distributed Lag Models
Polynomial degree
M

6

8

6

7

Chosen by

SM

SG

Cp, FPE

1.09
(0.34)

-0.01
(0.06)

PH

1.08
(0.31)

(0.02)

G

—

6

3

F-test

1.08
(0.30)

-0.01
(007)

1

0

BEC, SBIC

1.00
(0.00)

Policy Effectiveness and the
Polynomial Degree
T ests o f th e policy im p licatio n s from th ese PDL m o d ­
els are p resen ted in table 6. Again, the results confirm
th e ro b u stn ess o f th e policy im p lication s o f th e St.
Louis equation. T h e su m m ed effects o f m o n ey growth
on nom inal in co m e grow th differ only slightly from
th o se reported in table 3 an d range from 1.00 to 1.09.
Furtherm ore, a test o f th e h y p oth esis th at th ere is a
o n e-to -on e relation sh ip betw een the grow th rate in
m oney an d n om in al in co m e grow th ca n n o t b e re je cted
at th e 5 p e rce n t sign ifican ce level for th e various sets of
polynom ial restrictio n s.

0.02
(0.14)

NOTE: Based on a specification including 10 lags on M
and 9 on G. Absolute value of t-statistics in paren­
theses for testing 2M = 1 and £G = 0.
— indicates less than .005 in absolute value.

30


12The x2 statistic for testing the polynomial restrictions selected by the
Bayesian criteria is 52.64, compared with a critical value of x2(18) =
28.9. For the FPE, PH and F-test selected PDL models, the x2
statistics (5 percent critical values) are 8.62 (x2(5) = 11.1), 11.19
( X 2 ( 6 ) = 12.6) and 23.21 (x2(10) = 18.3), respectively.

FEDERAL RESERVE BANK OF ST. LOUIS

Also, th e su m m ed co efficien ts on G are nearly zero
an d th e h yp othesis th at th ey are equal to zero can n o t
be re je cted at the 5 p ercen t significance level. T hu s, the
p o licy im p lica tio n s o f th e St. Louis eq u atio n also
ap p ear to be u naffected by the ch o ice o f polynom ial
degree.

JUNE/JULY 1984

m o n eta iy p olicy is effective an d fiscal policy is in effec­
tive in influen cin g th e grow th o f GNP. T h is result is
alm ost totally insensitive to alternative lag stru ctu res
or polynom ial sp ecificatio n s.

R EFE R E N C ES

CONCLUSIONS
T his p ap er has investigated the ro b u stn ess o f the
policy co n clu sio n s o f the St. Louis equation w ith re­
sp ect to its polynom ial d istribu ted lag sp ecification . Six
alternative m odel sp ecificatio n criteria have b ee n used
to identify lag lengths and polynom ial degrees, and
tests o f policy effectiveness have been perform ed on
ea ch o f th ese specification s.
In ea ch case, the h yp oth esis th at a 1 p ercen tage
poin t in crease in m o n ey grow th lead s ultim ately to
a 1 p ercen tag e point in crease in th e rate o f growth
of nom inal GNP can n o t be re je cted at conventional
levels o f statistical sig n ifican ce. Alternatively, highem plovm ent governm ent sp end in g h as a perm anen t
im pact on th e rate o f grow th o f n om inal GNP only
w h e n c o n t e m p o r a n e o u s g o v e r n m e n t s p e n d in g
grow th alon e is in clu d ed w ith the d istribu ted lag of
m oney grow th in the m odel. T h is sp ecification, how ­
ever, is c o n siste n tly r e je c te d w h en te ste d against
h ig h er o rd er sp ecificatio n s. C onsequently, th e general
co n clu sio n from this study is that, in th e long run,

Akaike, Hirotugu. “Statistical Predictor Identification,” Annals of The
Institute of Statistical Mathematics (no. 2, 1970), pp. 203-17.
Batten, Dallas S., and Daniel L. Thornton. “ Polynomial Distributed
Lags and the Estimation of the St. Louis Equation," this Review
(April 1983), pp. 13-25.
Geweke, John, and Richard Meese. “ Estimating Regression Mod­
els of Finite but Unknown Order," International Economic Review
(February 1981), pp. 55-70.
Hsiao, Cheng. “ Autoregressive Modelling and Money-lncome
Causality Detection," Journal of Monetary Economics (January
1981), pp. 85-106.
Mallows, C. L. “ Some Comments on Cp,” Technometrics (Novem­
ber 1973), pp. 661-75.
Pagano, Marcello, and Michael J. Hartley. “On Fitting Distributed
Lag Models Subject to Polynomial Restrictions,” Journal of Econo­
metrics (June 1981), pp. 171-98.
Schwarz, Gideon. “ Estimating the Dimension of a Model," The
Annals of Statistics (March 1978), pp. 461-64.
Thornton, Daniel L., and Dallas S. Batten. "What Do Almon's End­
point Constraints Constrain?” (Federal Reserve Bank of St. Louis,
1984; processed).
Trivedi, P. K., and A. R. Pagan. “ Polynomial Distributed Lags: A
Unified Treatment,” Economic Studies Quarterly (April 1979), pp.
37-49.

Appendix: M odel S electio n C riteria
T h e criteria em ployed h ere can be outlined w ith ­
in the fram ew ork o f th e follow ing distribu ted lag
m odel:

norm al b asis for X, an d N is an u p p er triangular
m atrix w ith positive d iagonal elem en ts. E qu ation (1)
can now be rew ritten as

(1!

(2)

Y = X0 +

e

,

w here X is a T by (8 + 1) m atrix o f distribu ted lag
variables, | is a (9 + 1 ) by 1 v ecto r o f param eters and e
3
is a T bv 1 vector o f d istu rb an ces. T h e initial step in
im plem enting any o f th ese te ch n iq u e s is to specify a
m axim um lag length, L.

Pagano-Hartley t-test
T h e Pagano-H artley te ch n iq u e em ploys a GramSchm idt d eco m p o sitio n o f th e observation matrix.
Specifically,
X = QN,
w here Q is a m atrix w h o se co lu m n s form an ortho-




Y = QNJ3 +

e

= QX +

e

, w h ere X = N .
|3

To select th e ap p rop riate lag length, Pagano and
Hartley suggest ch o o sin g the sm allest j for w hich
the hypothesis,
HL- j : ^ _j = 0,
ca n be re je cte d . T h e PH te ch n iq u e also en ab les
efficient calcu latio n o f th e o th e r lag-length selectio n
statistics d iscu ssed below .

Mallows’ Cp-statistic
An alternative to th e PH te ch n iq u e is to co n sid er
m inim izing som e fu n ctio n o f the residual sum of
squares. O ne su ch statistic is M allow s’ C p-statistic,

31

w hich is based u p on a m ean squ are error pred iction
norm . T h e C p-statistic is defined as

c PL-j = ^

RSSL_j - T + 2 (L + l - j ) ,
j = 0, 1, ..., L,

w here RSSL_j d en o tes th e resid ual su m o f squares
w ith j restrictio n s im p osed and s2 = RSS1/(T—L —1).
As j in creases from zero to L, th e C p-statistic trades
off som e red u ctio n in th e variance o f p red iction for
an in crease in th e bias. T h e value o f j for w hich the
C p-statistic is a m inim u m is th e o n e that m inim izes
the ex p ected m ean squ are error o f p red iction . It can
b e show n th at th e C p-statistic will attain a local
m inim um w henever th e t-statistic on th e m arginal
distribu ted lag co efficien t is g reater th an o r equal
to V T .

Akaike’s FPE Criterion
A nother criterion based on a m ean squ are error
p red ictio n norm is Akaike’s Final P red iction Error
(FPE) criterion, defined as
T + (L + l - j )
FPE-—* = T - ( L - H —

RSS!

Tw o B ayesian criteria have b een suggested th at
s elect th e co rrect lag len gth asym ptotically. T h e first
o f th ese is Sch w arz’ B ayesian Inform ation C riterion
(SBIC) and is given by
RSS l _ j
In T
SBIC = In U . V . ■ + ( L + l - j )
)
T
T -L -l+ j
j = 0, 1, ..., L.
T h e seco n d , suggested by Gew eke an d M eese, is th e
Bayesian E stim ation C riterion (BEC) given by
BEC =

RSSL _ j

T -L -l+ j

T + (L + l —j)s2 ( l n T )
T -L -l
j = 0, 1, ..., L.

Sin ce ch o o sin g a lag length th at is too long d oes
n o t result in biased estim ates o f th e d istribu ted lag
param eters, th e only advantage o f th e Bayesian cri­
teria is asym ptotic efficiency.

The Standard F-test
A final p ro ced u re involves calcu latin g a sequen tial
F-statistic, defined as
F,,_ j = (R S S ,,-j_ , —R SSj/lj + l)s~,

......L-

Like M allow s' C p -sta tistic, th e FPE crite rio n a t­
tem p ts to b alan ce th e “risk’' d ue to bias w h en sh o rt­
er lag len gths are selecte d against th e “risk” due to
th e in crease in variance w hen lo n g er lag length s are
ch o se n . Hsiao 11981) has show n that m inim izing the
FPE is equivalent to applying an ap proxim ate se ­
quential F-test w ith vaiying sign ifican ce levels.




Bayesian Criteria

j = 0 , 1 , L,

and selectin g th e lag length as th e first L —j for
w h ich th e null h yp oth esis, pL = ( 3 l - i = ... = (JL- j
= 0, is rejected .
T h ese p ro ced u res also ca n b e applied to th e p ro b ­
lem o f polynom ial d egree selectio n . O n ce th e lag
length is selected , d eterm in in g th e polynom ial d e ­
gree am o u n ts to n o th in g m ore th an selectin g the
length o f th e vecto r o f polynom ial co efficien ts.