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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 The Review is published 10 times per year by the Research and Public Information Department o f the Federal Reserve Bank o f St. Louis. Single-copy subscriptions are available to the public fr e e o f charge. Mail requests f o r subscriptions, back issues, or address changes to: Research and Public Information Department, Federal Reserve Bank o f St. Louis, P.O. Box 442, St. Louis, Missouri 63166. The views expressed are those o f the individual authors and do not necessarily reflect official positions o f the Federal Reserve Bank o f St. Louis or the Federal Reserve System. Articles herein may be reprinted provided the source is credited. Please provide the Bank’s Research and Public Inform a tion Department with a copy o f reprinted material. 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.