Full text of Review (Federal Reserve Bank of Dallas) : May 1991
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fEDERAL RESERVE BANK Of FEDERAL OF DALLAS May 1991 1991 May • • cononnc CVICW Money Growlb, Growth) SUjJjJ~y Jl101lr!) Grou Ih, SUjJjJl) Malle), SUfJPl:v 5lJocks, Sbocks. II/jlaliol/ l~l)ocks. (mel and 1J 17 ?flation Joseph H. H. Haslag and D'Ann M. Ozment O'Ann M Ozment lVodeling Trend) in 110deling 7J'ellcL' ill 1 11odelil/g n'el/ds il/ ;v!acroecoJlornic I1facroeCOllOtJlic ,1/acroecOI/OIll ic 7i'777e Series 7l'1ne 7lllle Serie'i S. Balke Nathan S This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org) Economic Review Federal Reserve Bank olDal/as --- ...--...... Roben D. MeT"" Jr. .._--... -,- H.ney RoM..I.... .s.--~"-- .. C.r.td P. O"Driscoll, Jr . ..... -.-... ~o- w. Michllel tox 1....,Ad<_ SI.phllt P. A. 8rown _l'a~" Economists NIJ/Il)I13/ /Jrld ill /f)frnJllOOIJl John K HIli Evan F Kocn 9 Robe" T Clall Joseph H Haslag """"" M ""'" QaVJ;l M Go\;Id MMkA Wyme KewlJ Yeats IIegovI M1 CIWlfW Robert W Gilmer WI'Lam C Gnb!n Mire II: Yuce K!:I\ R PhIllips lonL TayOl riona 0 S.galla O-AmM Onnem Edil0rs Rhonda HarrIS D,al'\il W Palmer VIlIlnla M Rogefs T~ ~,I fct)fIIIfIIIC Rrvoew.s p..b-lst.:I by the AeseM!IIN; at [)flits 11'41_ t.t ))"USed ... those 01 .... a.t.'v$ n de Iw;JI _lor rtI*I t'If PCB ,.eN Ii ... fO'ili .... ~ ' ..... at Oat.1S or , .. feotr. IIetene SUa'II'!_ IN _-IIbiI!", It ctwv~11 , _ : , 'et S"'i' cac:'/ ... Pltne ... a..,. r'••hp_IeGPr RbIa«-. lID loIoaS. ..0 WI N PoIJIe: A't.J 1lftIIn-..I. ~ IIrtsrot Broc otOdllS.Svor '0.-... T_15271 (1141651 6289 MItIrs ... 011 MP'oI'IIQ • t'II mndIIo> :$ 0lIII:.I II'd " ~ ~ q IJf'C'o'dIa ... " • "'" 04 ;te hi :-. IOoI'C1I p!.bIQIOl>~II'e~NIeI'iII Contents Page I Money G1'owth, Supply Shocks, and Inflation Joseph H. Haslag and O'Ann M. Ozment Reccnlly, economi:-.Is have cX:lmin(:d the monetarist and the cX(X.'Clalion!)-;llIgmcnl~d PhilJips-curve modds of innation to determine which modd i., a bener pr~dictor of the inflation mIt!. These smdies r:.lise an important qlh:stion: Does money growth conwin information Ihal is LL$l.:flll in predicti ng the inl1,nion rate? Joseph H. Haslal-( :lIlti l)'Ann M. Ozment s[X.'Cify :l general model of (he inflation rolle Ihal cncompasscs both (he Phillips+Curvc :lnd the monetarist models. They find that their general, encompassinR model is a hener predictor of the in flation rate than cilhc..-'f the 1l'lOl1CC1rist model or the c:xrx:<:tations-augmentc..-cl Phillips-culVc model of infl:nion Furthcnnon:, the authors find thai changes In money ~rowth play an import3nt, independent role in prt.·{hcting the innalion r.He Page 19 Modeling Trends in MaC1'oeconomic Time Series Nathan S. Balke How pr(::dictablc arc real G;'>lP, prices. and Ulher macroeconomic d:lta over long time horizons? The answer depend'i on the nature of th\.'ir trend..., In this article, Nathan S. Balke describes altern;Uive modds of trend for economic data, disclIs."cs thl.! implk'ations of thcs~ models for forecasting and Imsincss-cy<.:1c 'lnalysis. and revil.!ws soml.! of the I.!xist ing evitk:nce for and agllinst various models of treno. In addition, Balkc conducts ;I ca.'iC study of real GNP and the price kvel. He finds that a simple linc:lr time trend m:ly :Idequatcly renl.'Cl the long-nm heh:lvior of re'll GN P. '111e price levcl. o n the other hand. appc;II'S to Ix; .. ffected by infrequent hut dr;unatic event.. th.1I have lon~-I;I...ting effects ConSl."qucntly. the prit'e level is mud1 more dimnlll to fOn"C'.J.sl . Joseph H. Haslag D' Ann M. Ozment Senior Economist Federal Reserve Bank 01 Dallas Assistant Economist Federal Reserve Sri of Dallas Money Growth, Supply Shocks, and Inflation hal rok' doe:- Illorn.: ~ WO\\ th pby in dt.:to.·nllinin).: tIll' mllation I~ U (.·;' EmpIrical :-'[lI(hl':-' l'xam inin~ thl' inll:nion r.LI".. (htli.:r in thl'ir :m"\H'r to th i:qul·..tioll. ~)Illl' model .. .. tre ..... thl' rok·.. that \\':I)':l' Wu\\ th and I;tt'[Of 'o(~lrL'itr pb y in dl'lcnnin ing Illl' inlbti"n r.lIl· Tlll'''l' 11\()(k+..--o]k n n:];,:r,.,,:d to ;1." tIll' l·xp,,:t·t;ltillll:--:HIgl1H..'nh_xl I'llillip." 'l·ur.'l· 1I1( )de!'" -gl'ner.llI~· Oll1il 111011(.'), gfo\\lh from the l·:..l imato.xl 1'l·gn: ......iol1.. on thl' Woun<i:-Ihal any I1lfimnation COnlaim:d in monl'Y W'O\\lh i .. ;llr(.·ad~ :Kl'OllllllXI for hy I;:'lIhc.:r III(' ulll'mploYlIIl'nt or OUlput gap In ollll,"r Ill()(!d:... ho\\eH·r. changl'" ii' Ihl' inll:llioll r.Ul' "ll'lll from [0 0 nllKh Il'IOnl'~ d ,;I:"lIlg too fl'w good .. ~Udl "],X'llfiCllion.. an: oll,,'n ;1 ....'>()('i;Ul'tl \\ Ilh 1II0Ill'tal'''' Illo( kh '\ot .. lIrpri .. ..,}:.. 1ll0Iu.1:lrt'>l 1Il0 (k+. of till" mll.lIton r.lh,: l)('onllnl'l1ll~ fl':'lhm: thl: d1i..'l1 of dl;mgL':- In lHon(.·~ WO\\lh ' Ikno.:. llu.. lllon(.·I:m ..1 1l'H )(Il'i:.. p];Kl' "UIl:'>l,1ll11.11 \\l'ight o n thl: IIlfonn:llion l.:ont:lUllxl in n'HIIlL'~ }:.lu\\lh fur pl'l.."<lit1in).: inlbt ion I)irrl·n..:nt :-.r'll"(·ilit~ ni( J1l " ,11\: 1IIuk·",l;lmbl,k· IX'l·:ItI:-.<.· Ihl') ;If(.' t!t'n\L"(1 frollll'C"llr'll1in).: thl·on(.·.. '(.'\·t·rthdt·:-.... all imponalll tjlll·..tion i:-. r.li:-.<."tl. DllO,::o. monc.:\' gnm th t'()nlain information that i..; 1I ......-r1l1 in prl"tli(·hll).: [Ill' inll:l1ioll I~ t[l'! RlTcl'l ly. li[l·I~ lllIn.: ha ...; dC\·l·lllpl.'d [hal ;Iddrl·.. :-l·.. ;1 do:-dy f(.·bll.'d qUl':-I;on : I h:11 b . which lll(xkl- IJ\(.' t.:XIK·( t:ltil m"':luWIII:nll'd Ilhi ll ip:nll"(.' or till' mOIW[:tri:-I-b :1 IX'lIl'r pfl'diclor o f tl\(.' inlb[ion rate!' Thrn' rt'n'n\ 1"':1]1<..·1.... iJlu:-lr.lIl' tl\(.· findin).:.. Jnlhl' Ii ...... [ of tlll·"t.: ;Irtklt·~. Y:l:..h l' ;\Jdn:l (II.)HX) ('(unp:lfl'd ,I 1ll0nl'l:lIi ..1 Il}()(]d wilh [ilt.: I'llillip:-'('I1r.'l' !llotlt'l ..pt,t·i f,cl1ion:- to tlt·ll'r· min(.· which lll(x ll'l ".1" :1 IX'lIl'r pf(.·dktor of Ihl' innation r.1l1' ,\h.'hr.1 fo und Ih:1[ 111(.' IlItJlll'l:llbt lllo dd ·:-. pt'rformann' d(.,],x·lult"(i on w hkh lIll';I.. lIfl' of mo m.:) \\ .1." lI ......·d in till' :m.l ly.. i .. \X'!tl'n thl' moo(.'} Ille;I~t11\.' \\'a .. \12. thl' l'\ i<lt·nl'(.' .. U1-:J.,:l·..Il'C..l Ihal till.' Illonelan"l Illo<ld prlx lit1l'd inlltlion IllOf(.' :It'nl r.udy 111:111 Ihl' J>hiIlIP:--<. IIr\l' :-1'X"t ilk;Uioll \'1;'111.'11 lilt' 1l10nl'l;lrl'>[ Illl )(ki mdu( kd M I in IlK' W f.cono m ic Rl."Yl.,w _ !olay 199 1 " 1'X"t· ili(~,tlfln. hO\\e\·... r . i\khr.I·" Imdings suggested tll:Tt till' I'hillip:..·(.·ur.·c nuxld W:I'> a more ;1('<:\ll'::ltc.: prl'tlktor of inll:ll ion ~ I n 1111' :-'l'omd artidt·. Jolin K Ilill and Kl'n nl... t ll J ]{ohi n..on (19H9J (.·o!l\p arl.'d prcdklioos 1'1'0111 11111.:1..' t·OtHIX·til'g 11l()(k l..; of I Ill' ;nn:lIion 1:11(."" In [ht' fi r." 1 m()(ld. M1. ).:1'O\\[h \\':I'>lhl' .-.ok l'xpl:tnatory vari:lhl!.:'. In tI\(: S(.·t'on<l modd. \\'age ).:f()\\tll fl.'plan·d 1' 12 :I~ til(.' imk,pt.'ndl·n\ \'aliabk. \\ lIill.' in till' th ird lll(x!t'1. f:ll·tor .'>(·:lrciIY 1ll~:I:"llres \\ tTl' thl' indcl'X'ndenl \·:Iri.l blc,..; Ilill :md 1~(~l ; nMm l'Imdmkd that !Hu cit: !" nJnI;lining \\':Igt' gl'()\\ th (II' .1 l'( )mhin:lIT(1Il ()f Ihe ullemployment mtt' and 11ll' ('ap:lClt)' llliliL:l\ lon r.lIC mor(.' :lCCllr.lld~ prl"th('lt'd IIlILitlol1 Ih;lll ;I m(xld whose :..oll.' l':-.pl.ln;tllI'1 I ;l riahk, \\;lS 1'12 gnlwth. In the third p'lpcr. I):wid J Stockton and We ...SIlIO /hank Nathan 88l1o:e Cdu3ld BcmhoIf. Ketll HIM. and esneoaJ/y Cvan F Kcwrwg fat helpful eotrfflC(lts on eatl.., coptes Of tillS af/1C1e Any rema.rnng fJrrors Bre solely our rCSpOfIs,blllty Samo rnonelsnSl models SfJ«dy B reduced· form equarlOfl IOflhe mlletlOn r/jIB &Jeh 8 Speed'CIJllanIS cons,s /unt W!/h ChS/'IfI(!S If! mon.ty growtn mlluoncll'lg mfl81100 through 8 re/JI balance clfCX:;1 Altems/IVI'/)'. Eugene F Fama ( t982} u.ws the quantity lheory framc.vrxk as the bas'S for a mtXicI 111 which changeS 111 11'1118/>011 (osull when money·supply grOWlh 6JtCe«lS money.oemand grOWlh MelVa comparn forecasts lI$II1Q lIIIema/rvu modelS of the /(IflallOll rate /rom 1977 I 10 1987 ~ focuS"'f} on /he rool squared CfrOf (RM$E) oi/he dlflerent torecast.ng mocJeiS !-Its rank.ngos cnanoe IWler> he consrders a.Hetenl svt>perIOOS FOfthepetltX1 1911 110 1982 3.lhemooet/Jl1S1 mooe: ".,It! M I as the money mea_e has /I /t;M'ef RMSE ltuJn the """'PS-<:UlVtI ff'IOdeI which 111 /um fillS III /ower me"" RMSE I1l¥ItheWmodei FOflhftsarrPe 1981 110 1987 4 me e.tdMce SIJ9(16Sts IfI9l the PhIj'rp$<tJtVe ff'IOdeI IS ,_a Ch:lrle~ S. Slru(:knll.:),er (19H<Jl lI-.cu nooneslL-U spcdlk:uion le~ls IOl"()l1lpaf\.: m()net~ri~1 models :1 ~.lin,"'1 IhL' expcct:uion.... -allgrm: nled Phillip~-<.·ur\'e modd • St(x:kfon and Stntcklllep:r did not find evidcnn: Mlpportinf.: one model over :LnotllL'r nathcr, tbey condu<.kd thai tlleM: " re~lIlt ... ~lI~~esl th:u o.::l<.'h mo(k'i identities some <."rilil':.1 delenninanl of inn'Ll ion hut Ihat no one ~llL'l'iJ1c;lIion is Mlflldently gem:r.ll to 'encompa~s' the re~ lIllS of it~ eompelitors" (Slo(:kton :Lnd Stnll"k me)'er 19H9, 2H3) . J The V(J(SJOtl 01 the expcct8/lOfIs,augmenteci Phll/'OS-Gurve model est,rna/co by Stockton allo StruekmByer IS (JIe' Slfltedoflglll(l//y .... Gotdort( !985) Nola/hal Gotdon (1982) also fJxar"fWlCd tho fol8 thatlhe CxCIlar>ge filla played .... (1elern'WIII"IQ ....fiatiOfl ThttoocfllClCfllon IN fJXchiJngf;t vat" aOle. fIoweWJf• ...as fIO/ SlatJSlICMI)/ dtffCfCflf from 1/1#0 • ThttP'rrodeIfJIsopioposeslha/moncyt!lf'ldlNou/peJIgBP JfJIfII/y determne rnowmenIS .... IN IflIIabCn falO In /heff "general" $p«lflClJllCJ(I. Jclfruy J l-Ia/i"rlan. RIchard 0 Pbtter, ttnd DaVId H Small (1991) cs/nla/a. model .... wtwch cf"I8nt;}8$ If! the If)f/a/ICJ(I fat8 aut II tuncflOfl 0I1hff deviatIOn If) vetoc' /y ffom 'IS /fend vaJue fJf!d the OUtpul gap The authots hnd 1/IallheselWO sepMalo effccts W8 no/ SlgfHf" canrly (f,fforlfll Ifom one af"lOlflef W,th the pllCO QaP term ('hal IS. P-P' ) capluflng boIh M2 effects lind output gap 8ff«;IS. the e..-.dE1nc8 SUf1f1C$Is that 00Ih money IJf>d ItIa oulpu/ gap JfJIfII/y (and SIf1"'t.cMW/y) delemwne Cn.JngeS n Iho nIIa/JOn falO J RecMIIy. Yash Mehta (1990) .xlifTWl«J Iho role /hall.lfll' labor COSIS and Ifle output gap played If) plc<1tcltng m0vements .... /he If)//aflOfl filla MelIta concludes lhall.lfllliabot COSIS do flO( help 10 prC01C1 the 111/18/0'1 ral(l, 001 lhal Cl"IBnges in IheOUIPUI gap do IIaIp 10(JIedtCI Chat'lflesllllhe inflatIOn rale He also slales Ihal 'Ihe 'Increments l prCOIC- ,,1'(1'COfltrlbulJOfl of lhe OUtpu/ gop femalnS srgrnlICanl oven al/er on(IlIIlQws lot the ....f/v9tlc. 01 morHt//tf)' faclOfS on th8 pllCO level- (Mehra 1990, 38) Malva fll"ldS 8V><1ence thaI fflOf'I8f(Jfy varlables-speoflCally IN tnl6tesl falc-are "9fI'ficwll .... a modeI...rtl /lie 0/APUl {lap also IflCluded TIIe~presenlcd .... ltIos.tJCIedlHcrsfTtJmMehtaS nSO\ltilfallleyasp«;ls TherTrOSlmootlanteJrff6tflf'lCelSthal ht$ lSt.matng equalO'l IW$I d,HfJffJl"lCes Ihc tn/la/JOfl fa/8. awu/tng 10 /he a/lseflce 01 Sl.!11OflM1/y ll'llhe .orrpIIc,r prICe def/al(}( We measure lhe 1fIfIil10'l fal8 U$IfIQ the fOledW(Jtfl"t pllCC d6fiaIOf. and /flo ....!la10'l la/a IS slatlOflal"y MOtCCVflf. If! Mellta's anaIysrs mono)' altaels tll& (XICt! k1vc1 ifldlfeclly through /heP- Ctrot-GOfrtICIO'I /elm II IS fIO(cleat. lhere/ote. IIIaI a monelary V3(,~ addS $If1IIIt.c""If)!or- malJOfl .... lerms of predlCllfl9 !he 111114/1OtI fale based on MBIIta 'Sfesvtts , The purpo~ of thi~ :mide is to specify a gener.LI Illodel o f Ihe innation r.Ue Ih:1I answers IWO qUL'Mion.. , Fir~I, i~ there enough u:.eful infonn:lIion nmt:linL'(1 in money f.:rowth II) warr:.tnl indudin~ thL.. variahle in an inflation-r.lIc L'qtl :Hi()n~ SL'coml. docs a gener.LI model Ih:1I L'n("lJlll p:I.~~es Ix)th Ihe eXfX.'t."I:ltion~';l uAmented Phillip~-('"lIr\'e Illtxld :md thl! monel:lri:'1 mo del pn.xlict inllal!(m more ac<."ur.lldy Ih:1Il eilher of Ibe two individual models? O\·el"":,11. the c \'idcnct' prt.'M:ntL-u in this artide i ... ("Im ... i~lcm with tht' nOlion that the l..'IK(llllp:ls:-ing m(xld is sllfX'rior (in the .......n ....... Ihat it is a heller predictor of the innalion r.ne) 10 eit her IhL' mtlllet:l risi or cX I"X:I..·lalions-augmented I'hillip:--L'urve models found in Ihe liter.lIu re.' In P:H1il.:lIl:Jr, Ihe e\'iden<."e sll)..:J,:esls Ihal change.s in money growlh do play an import:tnt. indL'!lc.:nden! role in prL'tliclin).!: i nfl:Llion. A theoretical model of inflaHon TilL' tiN aim of this artide.: i~ to pmvidc a Iheort.:tk':ll MrtLl..'llire 11t:1I encomp:ls....es hOlh Ihe m(lIlt:lari~1 and l..'xpe<.'lations-:tugmentL't1 Phillips<.·l Uye thL'orics of inn:llion. We liSe :I Iht."Oretic:II fl~ l mew()rk of a~rcf.:alc de.:m;l nd and ; I~ regale supply 10 d(.'rive Ihe ~enl!r.ll innation-r.lte model. By asslllllln~ th:11 the bbor markel :llway~ Clt':l rs :11 it:. full-t.'mplo~'mL'nl 11.:\'1..'1 . l1l:J.kin~ the :I).(gregate supply elln'e \'t..'nk':ll. we oht:lin and e~t imate.: a monet:trlst ~fX."<."Itlc:llion, By a~Munin).!: Ihm prices ~re markL"<.I-up over w:L~e~ , ll1akin~ Ihe aggregate suppl y nllve horizonl al. we oblain :md ~~tim:lte :111 eX lx,\:t:ll ions-:mgmentL-u Phillips-cllrvc mOOc!. The j.(ener.ll inlblion-r.lle model. with a posil ively ..loped a~regale supply CWVL'. L'ncompas.'iCs hOlh of the~e .. hernafive.: modds in Ihe St.'n.'iC tha t hy rc~l ri<."ling p:micular coefficienls in the gener.11 nuxld to L'qual zero, the ).!:cnel"":ll model colla pses to one o r the other o f Ihe spc.."'l'ial C:lSL':., \Vhat arc Ihe fllnd:lI11ent:11 fOrl..'L'S that cause movelllcnt~ in Ihl..' inflation r.Lle? \Ve :ls-sume Ih:1I Ihe innalion r.lle mo\'e~ to prevent Ihe emergencc o f disequilihrium in the commodities m:trkel . For e.:x:lIllplc, s llrpo~e Ih:1l dt'm:md growth excLocds suppl y growlh :11 the current r:lle of inflation. Our inl uilion tdls U:oi thai fhe innal ion 1"":111,: incre:tscs 10 depres..s dcmand growth (a nd pcr h:l ps to stimulate supply Amwlhl. thcrcby mainlaini n~ equilibrium . Corn I,:"d},. If "uprl) gnl\\ Ih exo•.'l.·d,.. d ...'m:md gl"O\\ Ih, Ihe inllllion r:lIc tk'n·k'r:llc .. 10 induce gl\.":I1 ...·r delll.lnd growth and 11m .. prt:\"\:nt di~'IIUlhhnlllll IHIIII l'llh.:rwnj.! \\' ...' pnx.x.,...'tl h} "1'X'01\ ing ;t ..impll.' llJ(xk.'1 of a).:J.:I"\.'g,II ...' dCIll.lI1d ;md ;It-tWl·).plt' "uppl), tllll~ ilk n lll }' l0~ 1111.: ';Il'\()" Ih;1I Inll uerKc lk'm:lnd /-tm\\ Ih ,md .. uppl}' WO\\ [11 Aggrt:g.nl· lk'lll:md .111<1 ;1t-twcg.lIl.' I'>uppl) ;Ifl,.' ;1'''"Illl.,1 til I'X' gin"n hy [Ill.' lollo\\in).: l·xprc,.. iOlh : (I) ( 1) I' "'.I' -~,( /I ' -/),-(01, \\ 11CI"l.' .1' til 'nl IlL'" (lUIPI U, d dl'Il(IIt:.. dl'm:Illd, .,' dl'I10Il'S ." "ppl},. I i .. Ihe ("lll"t"l.'n[ liml.· Ix'riod, .11 i~ Ihl' I1IOnl'}, I'>lIpply, p i~ 11ll' rnn: k\\:1. ( ; i~ gO\crnml'IlI l'xlx·mhllll\:.. , .1'1' i .. Ihe potentia) kVI.'1 o( Olltput. I/' i .. till' nomin:1 1 \\ ;'gl' r.llc. to· i.. the (ulll.·mploYllIem 1"1.":11 \\,lgC r.I[l·. :lIld " ,. (/!' ami 9, > 0 .11"1.' 1).:Ir:Ulll'[l·r- '· 1:'.Il'h \ ;In;(hk' Llll.'qu:nitilb I :tnd .? il'> IlIl-:'I~UI'l.·d III )og k'\d ... EqU:l lioll I ''';111 "A).:rl't-t;l[e UUlplll dl'l11:md '>I.hl'lluk·, II1dil, .lIlO).: Ih.n o Ulput i .. IX)!O;lIiH:ly rcbtl,llo I Ill' kH'! of 1"1.,,:,1 mOil\.:} hal.II1H·" and gl)\I,.'ll1l11l.'l1I ~ 1"M,.'l1d i llg ' In .. hI m . t ..·'tlu;nioll I indiLl\l'" [h.L1 an ;IAAreg.ul· lk·lIl.tnll nln'l' d,,Jwn in P -.I·"P:ll"l· '" d()\\n\\;lnl, .. lelpinJ.: and .. hift-, 10 the rij.!hl ." 1\.·.. I'XIrl .....• 10 inl"fl':I......·.. in either nominal 1l1l1ll...·y l );lbll~I,.·~ (Ir /-:O\l;fIlllll'll1 .. pl.'nuin/-t E<[ll:Itiotl .? I" .In :IAArl.."g;Ul· !'>uppl) .'>I.·hl.'<.llIk. rdalil1/-: 111:11 out put ~lIr pl) I" ro .. il;\'dy rd:lIl."{1 10 till" k\'d of pOIl·nli:.1 O1l1plll hut inH."J"X·ly r...·btl·d 10 dl'\'i:II;OIl' in Ihl' fl.'al \\;lJ.:l' r:lll' from it:-. rull -l'lllplo)'ment !l'\"cl I:qu:niorl 2 i nd lGlleS Ihal [he : 1~~rl·I.::Ltl· .. upply sdll'dllk' will 11:1\'1,.' :1 posit il ...· .. ll ll)\,.· in /" .1' sp:1l'l' '1')ll' :I/-:/-:'"l'!ptl; .. upply .....·heduk· .. 111f... 10 thl.' ri).:h[ in rl'''rOllw to inll\.·a""· .. in pOl l'mial OIl[ PUI :l1ld [he J.:rtmth r.lll· of mart..l'H:k.lnng fl',,1 \\a).:c" :lnd 10 d l·n...~I.'>C" in l1olllin.II \\ .1J.:1...·.. TIll"<llllpk'll' Ihi .. modd. \\e "lx'of}:111 l.'tl\l;ltlon Ih.t1lk.·...e: nbc.. hOIl 1I.Ij.!l·/-tIll\\·lh ,.. d ..." ...·ml inl.' 1. \V...· ;""lIl11l' Ih.1I 11.1).:1....... II\;' l'<1Il1r:K1l.""l1 Ix:ll.lfI.' ;III th...• ,hod..s 111;11 ;llle.'tt thl' ...'t"tIl'lOllly :Ire l"I.';IIi/~'t1 In l ..........· 1)(."...•• \\Orkl'r- ;11\.' ;\11 ...·mpling 10 ......'t UI"c.' ;1 1\.";11 II a)':l' r.Ut' u ..ing l.·:l.l'x'l1 ...,1 Inlblinn :ntd tlll'dl'lll.lI1u pll".. \lI\.· .. ollM..·l"\l.'{II.I'" 1'X'riod 111i.. [~I x' e)( nOlnllul II ;lJ.:C l l>Olr:Il1ing I .. fl mn:lliz..., 1 in F.conumic It""·k ....· -May 199 1 the folloll U1J.: rt:PI'l.~·nt;llion of 11':1).:1..' growlh: \\ IK·I"I.· If' I" the eXI'X"('IL,1 innallcm r:lle. W·· is the l.·xlll.·ll ...'t1 ).:nl\\·th r:lIl.· III t ile markl.·t-<.)earin/-: I"\.·al II a);l.· r:lle.:. I ' dcno\ ...•.. tht! unempl()}'Illent r:lIl·. t · i~ the n.llur:I) faIL' of uncmploy-tnl·llI. :mu ). and ~ > 0 .11\: p;l r:une[l·r-. \,\'.... :t:-....l.IIlK·lh:t1 wage growlh ;1'> pc )....11I d) 1\.·!a[l.'{l to bAAl.""l1 \ alII ...·.. u( W:I).:l· wow1h . thl' eXfX.'t.1l.'tl ).:nlwlh r:lIl' of the markel· dearint-t I\.·al 1I :I).:e .-;11 ...' . :md [hl' gap hel\\een Iltle' nallll~11 :lOd :KtII:d IlIlemp)O}'llll'n\ r:ucs [)o[)lIn:ll \\ age g rowth arc l':IAAl.·d \' ... Illl'" im:) lldl'tllo :U:(Olltll for !:thor l"ont r:u:ts thaI do no[ Icnll in:ne ~itll ll it arl eou ..ly John Ii Taylor (1979) fi r~1 proposed l11at "..'nl l in:lliun IXlIIlts for labor l·Ontl~ll"t .. arc !'>1:lgJ.:l.')\.'(1 Work er~ altcmpl 10 1\;'l"OUP rcl:ll il'l' wage deterior:l1ioll and tim.. in..tigale per-bll'nn: in l1omin:d \\:Igl' growth O\'cr time ~ TIlt' ruuO\\ ing condition.... :.II\.' .. : lIi.~ fil."{1 in 11K' ....1I::llIy ..1:lIc· I - l I;', - 1/'., ,', If" - If," Ind 00·" In the "Il';,dy ~ ... Ie. l.'tlu:llion 3 illlplic.. [hat li',-If, ., 00·. 1'1111'>. Ihe ....tcady--statl.· (omhlion !'>ays th:11 or . .. .... w· - 1'hr$ spIlClllCMlOfl uses gover~ purchases 01 goods measure 01 fISCal poIK:y Othet re- ana _ _ as N 5Hla...s ha.vused /he iedeflll budgef deltCIf as /he fiscal poIK:ymcasurc lndccd·lJfIfIf89"todcmand mal' be SE!I'lSI11V1t1O"OOI$III/t1(f~'btXJgClconsllaIllIO/hefman fUst sptIf'IOlfI!1 en QOOCtS ana SCfVICes When "'18 usee the hK;h ~I govenYl"lCl'll OUdgol dellCll as !he fiscal (X)4cy measuro. nowcvor. ,fie fe~lIls a,o flOl subslantlVeIy d,f'CfOn/ Irom /n0s6 ff¥}Of/od In tnlS IIrtlCl6 Tho IJQprf1l)ate domand scllOdulO IS esson/lal'Y me same liS lIle OIJlpul domanrl scllOdulO speclllfJd by John B Taylor (1979) One concern \\-.1Il 1110 Spec'/ICIlIt()(l 01 equalt()(l "S thall/omits Jaggcavalucs 01 real baliJfICOS andgr:NCfnmer>t spendlfl!1 YI!!. ecOflOn'llS/SQM4HIIl/ybeitove thai mccffects 01 chMIgcs III monelat)' vdftables are dtS/nOulod over II1T18 L~ ViIIws aI rnone)' Ql'tMlIl Sfe III/Toducod 111/0 me modeilhtougfl eJ<ptH;liKJ onIJdtlOfl We do flOllllJ.et>d IfIaII1lo lII/etpt@l4/lOflol/fltlcooHICIeflfSOfIlaggedvallesalrnone)' Ql'OOtlh be IItnted 10 haw /I1Or'Ie)' alleels 1tlfIa/JOO through f!l(J)fICteci "'~"M Ra/1lel. Ihe Illterptefll/1OfI 01 coeIfioents 0fI ~ mont!)' Ql'0WI7I1fl tne ,eOVCeCJ-IOtm selt""9 :nat WV e5tmale $houIt11)e I hybrid 01 /fI(! expected IfIIIaIJOn c;hiJrtt1e18fIO the ltfIQI'egIIle demand cIIarw>eI s... GtB)' ('9761 ¥1d Ft!iJC/Iet (19m lot 8 trO'e dela<ied IlKOOStIlOfl 01 the wage-cort/T8ICfIflg models , changes in thl' growth r:.Lt\.' of n:'Ll wag\.os e<IU.ll the growth rJ.tc of the markeH'I~:Lring ~II w:lge rate. Equations I, 2, and 3 together <Ieflne the inflatio n-r.ue equation implied hy this model. Scuing output dt:mand equal to output supply, differentiating with res (X.'Ct to time, a nd suhstituting for \V:lge growth with equation 3 yields the fo llowing e xpression for the inflatio n r::IIC: (4) 1C, =l /« (l I +~I ) [ a,"-f, +(llG,-Y;+4'I[A/il, +(1- A)1C~ 1- ~ I IAW I or +(w· - W or )1 + 4',8( U,_, -V, ! )]. With ~! > 0, equation 4 indicates that the inflation rate is po sitivdy rdatt:d to change.~ in money growth :1nd ~o\'ernm~ n t-spt:nding growth. each a factor th.ll influt:nces the growth r.lle of aggregate dem:md.9 Funhennor~ , the equation indicates that the inflation r:.lle is positivdy rcl:II(,"<I to changes in last period's wage growth and the llllc mploymentr.IIC gap but nl'g:lIi\'dy rd.It\.-o to ch:mgL-s in p<>{cntial output growth and th~ a(.1ual growth r.ue of the markel -clc-.uinR r~:tl wagl.! rate. Funhermore , with A < 1, equ:uio n 4 indiC::llcs that the inflation rate hi flOSit ively related to the eXJX--'Cted infhllion rate and tht: e"[X.-'Cted growth r.IIC of market-clearing re:LI w:tg~s, Why b there a qualit:Hlve difference between th~ effect thai a change in the growth rate of the f!.\1Jl!Cled markct-de;lring re;L1 w;Lge rate ha.~ on the inflation rate and the effL'C1 that a c hange in the growth r:lle of the aellla{ m:uket·cle:Lring real wage r:.Lle has on the inflation nlle?'o The expected growth rate of market-dearing rca1 w:lges is haSl.-d on all inform:Hion :lv:Li1:Lble 10 workers in time pcriod I - \. The workcrs infon11:Ilion set consists of eXfX,:ctct! clwnges in productivity growth. lalXlr force growth, and the growth rale of quantilil.!s of r.LW m:lleri:lls ConS<..-quently, • Wo 8SSt.mIJ thtougllOut Ihts 8f/1CkJ thaI /lIB parametCfS are cons/8nI over /me T1lus. t1'I(1 derlV8lNe 01 each palamtJler w>/h r.spec/IO tme 1$ zero • See Gcxdon (/985} /oF • ""'8 COfT¥)Icto drscU$SO'l 01 poIen/.aI Output end In.IIPPIOP£,.,to IfIterpteldllOfl 01 ~ duc:IMf)''''' such 8 framcwotf< 4 t:,,~cted c hanges in W· :Ire built into the labor contr:.lCts that dctennint: today's nominal W'dge growth . In contrast, une"pcct\."{1 changes in roO are not huilt into today's 1:Lhor contr.Jcts. (ke.Jusc lalxlr Confr.K1S are not perfeL1ly indCXl'd to accommodate unexpected changes, the impact on the inflation rate due to CXpccK"<I and une"pected ch:lnJ(es in the growth r.Lte of the market-clc-.Jring real wage rate will differ. Equ:1tion 4 represents a gcner.tl theoretical nl(xld of the inflation rate. 111e ch:Ir:.lCt~rization of the 'Iggreg:lle :,upply function di.'<tinguishes this gener:LI model from two 1)~ci al ca:.es: the cxpect.ltions-;Lugmented Phillips-curve model and the monctarist model. In particular. the slope of the agwt'g:w: su pply Cll TVC (th"t is, 1/ rpl) diffe re nti:IlCS (he:: e::stim:Lle::d infl:llion cq U:llion . In (he fo llowing scctions. we detai l th~se cliffercnces for the mont.'taris! :Ind the expectations-augmented Phillips-cuTVe models. Fo r cach .~pcci;L1 case, the appropriate specification of the lInd~rlying inflation L"qu:ltion is dcri\'L"{1. The monetarist model In the monerarist model, the innation rate is primarily d('tennined by ffiOVem~nL" in the output demand schedule. The key assuffi]')(ion is that w;LgcS :m:.' flexible so that the labor markt::t 3lways dears (fonnan}" w,-p, - w;). With rl!al wages always equal to their markc.,t-d\.'arinEt level, equation 2 implies that the aggrc~ate supply sdK'(lulc i.~ :1 ,·crtical line. intersecting the horizont:11 axis al polenli:LI OUlpU!' Note that, for Ihe purpose :11 hand, 10 assume that the labor market alw'lYs dears is equivalent to scnin~ ~! equal to zero in equation 2. Thus. the monetarist modd of inflation Gm be regarck-d as :1 specia l case of the gener..1 1 model developed IH: fI.;. Figure I depicts the mOOl.:tarist mood gr.Lphically with thl' downw:lrd-sloping aggregate demand schedule and a v(.'rtic.';Ll aggrt:ga(e supply sl'lll."<Iule. '111(:' intt:'rSl."'<1ion of tht:' aggregate dcmand and aggreg:lI(.' supply "'liNes dctennines rhe price le\·ct To ilIustr.lte the cffe<.1s of ch:mges in aggregate demand , con:.ider thc t:ffects o f an in<.Tcasc in the money supply As Figure;: I s hows, a larger money :.(ock tmnsl:L1es into a rightward shift in thc aggreg:Ltc dem:md CllrvC from q, to 0t ' rcsu lting in an cxces,..; demand for commodiFederal R~rve Ibnk of Dallas Figure t Monetarist Model In shon. th .... 11l0net:trist mood cmphasizes Ihl' role of money growth through its impact on aggrt'g:lIt' delll:md wowth. Because wages are flexible. Ihe lahor m:lrh'l dears at its full-l'mploy~ ment level. Inne:!sl· . . in pnxluctivit}' wowth, employment growth. or the :tvail:tbility of r.tW m:lIerials. for instance. tr:tnsbte into a lower inflation mle ht.·cauSl: output su pply growth incn::I.'ieS relati\'(:: to OUlput demand growth ..... P.i------"""''+__ • f-- - - - - -"'+__ The expectations-augmented Phillips-curve model 0. ;u IIH.: initi:ll equilihriul1l prio:! It:vel. P", To pn':\'L'nl tile emergenct' of di:-.\:quilihrimll. tht: price lev...·1 ris,,-'s 10 PI' thu .... fedu(:inj.! real mont:y h:llam·e ..... l()\\crinj.! :lggrej.!;lI ...· quanlily dem:tnded. :lnd maintaining cquilihriulll Tim..... \\'h ...·n cxoj.!t'nous furt·c ... incre.tse :I!!J.!rCj.!:lIe demand. the ohsl·ly...·d imp:lCt is bJghl.'r pril'l.'..... In thl' Illont'tari:-.t Illodel. shifl .... in the outpul .... uppl)' ...dll'dule arise ht..'C:HI~ of f:lclors that ;,ffl·...·1 till' levd of pol""nlial oUlpU\. To iIIu:-.tr:.lll' 11ll' dT...·...·[ of a changto' in aJ.!gr",·gale :o.u rply on th ...· price k·\·...-I ....·on.-;idt'f :1 dl:tng.... III pnxluclivity \X/ilh 11ll' full-...·mplo}'l11l·nt nmditions ~ati:o.fit:d. an inct"l.:;t ....l: in pnxlucli\"il}' gn)\\lh. for eXilmpk. r.... :-.ulls in till' output supply . . ...·hedule shiflinj.! out :t . . pOlential outpul in('fl.'as~...;. Olher things being (Xlual. W"-'ater productivity IIl1.'anS Ih:ll ~tggregal .... :-.upply incn::ases, and Ihen,: i.... an l'XCCSS supply of cOIl1!1)oditil':o. at the initi:ll prio..: lev ....l. To prevent the l·l11ergl'no.' of disc·quillhriul11 in the commodi tit' .... mark .... t. the price le\·...-I would f;lll. With 9," O. the g ...·n...-rall11(xlc1 of Iht: in/lit ion r:t1 .... (tllat is ....·qualion ,I) f ...·duces to thl' (111()\\ ing t'xprl:ssion: ti~ .... Equation') inclic:ltc . . tllat th .... in/btion r.llc is a function of money W()wth. gon:rnillent-:o.pending g1"Owlh. and f:KlOr.... thaI :I(fl'''''[ the:,' gnm·th mle of potl'nlbl output. Ec ono m ic Rc \,jc v.·_ l\t ay t99 1 In this seclion. we assume thaI there is some degret' of wage stil'kincs.~ Ihat permits under- and ovt:remploymcnt as potential outcomes. This m ....;tns th:lI we relax the key assumption imposed in the monetarist rcprt:sent:llion , namely th:1I the IalX)r m:lrkct dears al the full-employment levd. In ;Kldition. we incor]xlr:IIC the notion of:t pricemarkup schemt', in which firms are \villing to supply any qu:tnlity of output, pro\'idt'd th:1I the output price s:lIisI1o..·... :1 reservation-markup nmdition. Gr.lphicIlly. :t price-markup schl'm.... implil's a horizont;J1 :tggrt:gate supply l'llf\'l' al a ltc"'\'d equal to Ihtc"' wagtc"' mIt: plus :t re:o.er...ationm:lrkup le\'d In thl: l'XIX'ct;lti(ms-augmenlcd Phillips-cuf\'e scuing. WO i. . no longt'r appropriately int .... rpretd\ as th(.' markl't-d ....aring real wage r.1I ..... Instl':1d. it is mort· ;\ppropri;1\.... 10 interpret WO :IS :t target rc:11 wage r:lle Ihat rcfl ....(,"\s the desired markup of price ahove unil-blxlr costs As equ:Hion 2 shows. ;111 innea~e in Ihe rl':1l wagt' r.ue abov .... tht' targel level reduces output supply. Conversely. \vhl'1l thl' m:trket ft';ll wage mIt' falls Ix:J()w target level. output supply ri ....e . . To :ts.~\.lme th:ll finn.~ adh(:!r(:! :-.Iriclly to tht:: m:lrkup scht:me is equivall'nt 10 lelling if'1go to infinity. so thaI thl' :tggrl'j.!:tlt: supply curve lx.:coml's horizontal at Iht, kv...-l /I' - WO Figure 2 pre...enl.... :1 gr:lphical d .... piction of till" CISe:: in \\·hi ....h ¢I, - 00. In this setup. :t ch:1I1ge in money gro\\lh--or anything else Ihat :Iffl'...1s :tggreg:Ht' demand growth-h:ts no immedi:tte df"-'Ct on thl' infl:llion r. uc. To iIIu:o;tr.l1e. nm . . idcr tilr.: effect of:t riglltw:trd shift in Ihe :t~re,l.::tte llo..·mand sch...->t:lul.... fRlm ~. to D,. fl.'Slilting from an increase in mone}, growth. Uec:tllSC the aggTl'g:tle ... llpply scheduk- is horizonlal. more lllonl'Y , Figure 3 Figure 2 - - General Model- Shift in Aggregate Demand Phillips-Curve Model ',-.' f---------=~~,--- ~~Z( •.,, 1-0, 0, v. 1r:11I ...1:I1e..:'" HlIIl moT!..' o\llpul. I rom y III .1'" hlll prietO dtl'l,.'''' 110! th.m}.:l.· Formally. \\llh 9 .. 00. Ihe..: i nll;u iol1 r:lk' I.-qual ion (th;l! j .... t'qu;uion I) i ... c\.pn..· ......'xl :h (6) IT, =1).1;' ,+CJ- A)IT']-I..lw ·' +((;' 0_(;' 0") 1+-81/, _ ( , ,) In }.:t'nt:r:11. l'tlll.lllon 6 Indicllt·... Ih.n thc IIlI1;nion r:llt: I" do... t·l, n.-btt'(it() b(lnr... Ih.lI ... hilt Ih..... :1I-Q.:.rC:-j.(,lIl· ... upply ...,:ht'(lull..·. ,uL"h .1 .. \\ .I).:~· j.!.!ll\\lh If mont:} WI)\\ Ih I, \II .ll fnl Inflation In till' ~'\PI..·(,:I:lli()I1"'-.I U1-tllh:I" l·d I'h ill,p' ~1l1"'\1..· 1ll,)(ld, it j, through Ihe ul1erllplo) rlll·nt·r:ltt: j.(ap terril . A ... .. \10\\ n in I :i gl.lr~' 1, an h\(TI.':I!>o.: in mon~'~ ro.:","lls in higlll'r OllllHIl .\ htl!>. J1l01~' money 11J\\~'r!> the une..:lnploYlllt·1l1 1~1 1 "': ~Ind l"ln .. l:ll e.... inlo high(T inlblion Ihrough f~I'II.·l \\ :Igl' ).,:f()\\'lh Ally i llfOf1ll:llioll rnllll :1(':I.'o.:lt.'r:lI inj.t 11j()1\(.·} grt)\\ 111 i .. :l l re;ldy l·;I Pllln..'d III thl.' 1lI11.'mploymt·llt-r:u..: j.!.;lp !I.'flll I k nce. Ihl' t·\I"X.'l'I:lIillll,-:IUj.tIllI.·lltc:-d Phillilh-('l!f\I.· Illodel 1ll.lint:Ulb Ih~lt lI\onl.·) grrm lh don not COni;!'" .lIl)' ltldept'ndl.·nl mlorrn:uion rl.'ll.·\.\llI for pn..'(./iCi ing tltt, inn .. tion r:11(.: The general model Tht' "t·~ k:llun.: ot Ihl' ~L·ncr:.I1 modd I'" Ih~' ;lh"":lll.\: 01 (ol1(i1lion ... on Ilw ,lope l'O••·tlKknt. 0 \lor ..... l-\~,Iwr.tl l y. the ... Iope otthe .IR~rl.·g.llt.· ...upply 6 v, ..elK·dull: i .. tWilh ....r inlinil~' nor / .... ro ,.\ ..... \ld, . ..·tllI.lllon li ... :1 1I\0r.... l-\~· ner:11 \1.'1'1011 01 hOlh Ihe IIIllIll.·t.ln'l .tnd I.·Xpl'll.Uitlll ...·.llIgllll'lltl."(1 I'hillip,,nit; I.' Illl x h,:b Figurl.· .~ d~'Pllh Ihi!> gL'tK·r.ll f~·rr........... nt;ltion ., .. ;m up\\.m.l-.. loplllg "upph ('unt' \n inn,,';l"-t' III Ill()ne..:~ .. upph .. 111ft .. tin- .1).!J.:fq,pll' dem.lIlt! ">tlwdult' nghl\\;lrd from f) 10 J) .md lr.m!>l.ul..'''' 11110 an iIKfl-;I"I.· in hoth tlw pri('e k\I.·llIrolll/~. [0 /') :md output (If0111 .1', 10 Y,) Both pfi('~' .Illd oulplll Illo\\,.' in r,,'''rxm:-t·lo., .. hlft in Ihl.· a).!J.:reg.,II.· dt"lll.md ..... Iwdule .•I"l"()lllp.lr~-d to th ..: lIlor.... ~pl..·l'Ific lindmg... pre ... ent~·d III Ihl" monel .ln ...1 C I......·- 1I1 \\ 1m h only prin'... \\1.., .... ,tlTel·ted-.lnd lilt· ~'Xpt:l'I:ll illll,-au!-\n\I,.'nled 1'lllllip'-( lIn I.' C I!>I..'in \\hil'h onl, outpul \\:1 .. :It'f...TII.·d. IIl'illl..'. IhL' gelwr..tl tlll xkll.·tln)IllI).I ...... ~·' I~Jlll Ihe 1ll(11l~·I.I,.isl :1 nd \;.'XIX.~·I :l1 i()lh-:lIlgI11elllt'd 1'llill ip,'-n ll'\"...· nll)(k·b I~Jlll !lw ml)l\el:!ri"l ;tllti ~·S Ix.'Cl a t i(IIl" :11lJ.{m...·ntl..,d I'hillilh-turvt· 1I1I)(t...·I ... illlp()... ~· It·"I.lhlt' r~' ..lntlion .. 011 Ihl.' !-\ener.11 !lllxkl For Illl' mOIlt:1:lfi ... 1 lmxlel. 11"'llhl'r 1.1).!J.:..:d \ .Ih)t'~ of \\ .Il-\t· gflJ\\ til nor Iht' Ull('mpl()~ llll.·nl · r.I!e l-\.Ip :In''':~t Ihe mll.llion r:t1t· I'(Jf Ihl' eXpt,(I.llilln~-_IlI!-\ln~·nted I'hillirh ..nln~· 1Il( )(lci . nc:ilh ..·r 1l1(II1C:-Y gnmlh nl)f ~()\I.·mnwnl ~llC..'ml 1(1~ ,f.:ro\\lh .1!lC:-l·' till.' IIltl:llion r:lIe II o ne l,lIl ' .....It'(·llhe h\ llt)l!tI.·-..c.. 'L"-.(XI;II~·d \\ Ith 1.·llIlI.'r ollhl.,......· ,pt.'"f.:i.tI (":I,t' IIxxkl .... Ih~'n the ~1..·nl.·r::1 l1lodd I" 'lIpc:rior 1(1 II.·nll!> of jlrt"(h(1inl-\ inil.lllllfl • An empirical specification ThL' Ih.....()r.....licll :,pl-><" iI1catitlil derivL'd al')!)\'L' incilldl's SL'\'LT:d \ ·: lriahk'.~ lh:lt do not tr:tns!:tlL' di r.....nly intI) ()h., ..... rv:lhlc dal a. Cl m .... eqtlL·111 Iy. l·.'lil11:nin).! L'qu;lIion I a:- "'Ialt:d is :'01llL'\\'h:lt ditl ku h. SIll'cilk:l l ly. Iher..... are faclors Ihal dlkr111ine IhL' gn)\\lll o f m:lrkl'l -clL'a ring rL':11 \\':lgL'S tlt:lt should lx' lIlcl udl.:d in :l SIX'cifiGl1ion or I Ill' inlbtiol1 1.111:'. ,\ bny of thl' S;1111 ..... \·ari:lhl ..... s \\ ill alkct I ltL' Icvd of pot ..... lltia l OUl p ut growl h In th is :'L'l'llon. \\ 'L' propose "L'\'l'r:d oh,'L'I'\';Jhk \ 'ari:lhlL's t it;n sho uld lx' included in;1I1 ..... m pirical an:l l}',..is of the infl:l1ion r:lte Gl·t1l'r:l l1y. ti ll' growtlt l~l1e of the 11l:l rkl'l · ck:lring IX:;II wagg r:ltL' dqx·nd:. Oil faclors til:\! L'ntl'r into Ihl' p ro<iUl'Iio n fu nn;oll and into either thl' bhor ,km:md or bhor supply spt:dlk:nioth Spt,:dfkl ily. p roduct h 'ity gro\\11t ;llld till.: gro\\'t h 1:1lL' of l~l\\' 111:lIl'ria1:-; :llkc! th ..... elL-manti for bho!'. :l1ld bl')!)f fore..... grO\\ '11t :lfli..'<.'ls IhL' .~ urpl}' of !:thor H T IlL'sL' fac[ol'» al...o may in!lllL'no: tltl.: inlbtion l~lIe through tllt'ir dli..'l:ts on potL'nti:t1 Olllplll To illll:-tr:t[(.:. l'on,~idL'r the dfecI 01';1 ch:mgt: in Pl'Odll(·ti \-'il), gn)\\ll l on 111 ..... grl)\\·t h t~l[e of Ih..... 1l1:1rkct-do,,:;tfing real wagl' An inlTea.'>;l' in produc[ivity growth 1'L'~l1lt .... in grl';lIl'r dl'm:tnd fo r workt:r ... To pn,:n:nl di........quilihrillm in Iht: lahor m:l rkct. tIll' growth r:lIl' of ll1:trkL'l-dt!arin).: r..:;l1 \Va).:L'S Ill U ,~ t ri.sc in rl-.'l)(lll,W to till' inl'n.:;l.~e in tlt(dl'llland for workt:rs An inlTt!;lSc in t ill' supply of 1: 1\\ mal ..... rial:- (dUl' to M)ml' t!xogL'nou:- f;ll'l nr) Silllibrly 11~1n.~bh,:S into ~ rcat\!r d ..... mand for \\'ork\!r.... th till' gro\\lh r:.ltc or r: t\\· l11:l\L'rials itll't\.'a~l.:s. the m:lrkl'I-C'lt!:lring rl'al wagl' r:llt:: rbes, tr:ln ,~ la l ing into:l IO\\l'r intl:ttioll 1:1tto'. Sitni1:tr!Y,:l!l inn'l'a:'l' in eithl'r pl'lKlu('li\ 'ily growth or tltL' g rowth 1:1tt: or r~lW m:llt:ri als will in('l'l';l'>l' till: gro\\·th ratL' 01 pOll'nl ial out p ut. rl'~ulting in a lO\\'l'r inlltlio n ratl' Thus, to the cxtent Ihal producth'ity ).:l'o\\'tll ;l1ld lhl' ;l\ ':l ibhililY of r:t\\' ll1:lIL'ri:lb art: illll)()11;l!lt f:KlOr~ alrl'cti ng thl.: markel-dL';lring rt!:ti wage raIl:. L'qu:ltiol1 -I prl'( llns thaI i nlTe:lse~ in tile growtlt r:lIe:- of th ..... sc \·ari:thlc.~ Iransbt .... into a lo\\'er intl:ltion rat ..... \'\' ItL'n 1:lhor rOl'l'e growth i nlTe:1.~cs. howL'\'l'r. till' dfl'Ct.~ on tlte m:lrkl:l-cll-aring I'L'al \\:lg(;" l~l"'" and 1)()tl:nl i:tI output :l r.... OPI)():.ite in sign Con~ i dl'l' an i11lTt::l:-..... in !:thor lore..... growth To prl.'\'cnl d iwquil ih riwll in tlte lahor llI:lrkel, a f.co nomk Re view - Ma y 199 1 h~t(;"r p;ro\\'ing lal')!)!' foro..' means that I hto' growth mIl.' of tile market-cll-aring rcal wagl' r:ll C f:tlls and thl' inlbtion 1~1I1.: risl·s. Alteftlath'cJ}', a higher growth rat ..... o r lilt, bl')!lr force Illl'aIlS Iha[ the )..:(()\\th r:lte or 1)()tt:l1 tia l o utput rbes, :l1lJ llll' inllnion l~ll ..... IllU.~[ l;r!J to pre\'l'nt diSl'qllilihrilltn in till' goods l11:lrket. On nL't, t h\.' d'fec[ on POIL'llti:tI output growl h \\'ill dotl\itl;lle .~o tllat intl;uion i... dirL'ctly rd :lIl:d 10 lahor forl'L' growt h TIll' next qUl'sllon i~. How do \\'1.: Ille:lsure IllL'~ f;ll'tor:.? Follo\Vin)..: Gordon ( 19H5), S!<Kkto n :111d Struckllll'Yl'r (P)H9), and ~khr:l (199Cl). Wl' Ille:tsurl' pnxluc[!\'ity as out put per hou r o r all pL'rsorh in thl' nonfarm hll .~int::.s .... ector. Labor rorct" /-:I'o\\,[!t is measured ;1... till' pen.'l:nt:lge ci1:mgl' ill thl' !:thof force participation 1.111.: . F()llo\\'i llg T:L[ o lll (19HI) :lnd I·b rel' (19H3), supply .~h()cks 10 r.l\V IlKltl'ri:tls ar.... Glptll !'<,:d by 1lI0Vl'111cn[S in tile pril'C of food rcla t iv..... 10 Ihe gent:r:tl price k-vd :lnd in [he prin: of l'ncrgy rdative to the gL'llcr:d pricL' Ievd. ](ebtive pric.... tHOVL'I11l.:nt~ s..... rvc :I,~ proxies will'n till' dominant 1ll00·t!llll'nt.s it, the qu:rnl itiL'.s stL'nt f rOIll cxog\.'nOLl:. :.hock.s [0 thl' Mlpply of raw matL'rial s. Ik-l.:;l llse th ..... price tnOVl'ment.~ :l rt! 1101111L' rt!~ult of major c h:l ngl.:.~ in dot1tL'stic demand , exogenous shift:. in the ... upply nl l'\'C me,ln [11:11 tltt" relative prict! of r;t\\' lll:t[l:rials i.~ tK'g:lli\'dy rdatctllo eC]ui lihril ll n qU:ll)titi('s. lkClU.'i<.' Ihe l:.'xpL'<.1\:.'<.1 vallll' of thl' growth 1.111.: of till' m:lfkL't-l'Ic:lring n'::ll W:lgC r.ltl' i~ in t"quation -t. l'Xl)(,:cIL1:1 ":ll llL',~ of tlK' growth r:lte.~ of produclivity, tit .... labor force. and raw m:tlc.;:t1s :tlso enler into Ihl' inll:lIion-r:llc equation. \VL' choo.o;,: to U."": Ihe Ullcondi[ion:ll cXJX'(.'It.:d v:l lu('--the sample llK':ln-: l ,~ cXlx'ctcd value , TIlliS, l'adl of th ........;...variabll's ." .,.'rit;"s (.'nler tilt: 1::-li111:l1ing t.'<.[uation tlK'aSufl'd :IS dc\'iation.... fn)1ll tilt" mean value. InveSlfnC<iI would al50 M<,cIy affOCI Inc growlh ralO 01 !he mar/WI-clearmg real wags rale We omll 1118 If/veslmenl vanable from our diSCUSSIOn because II IS not easy 10 the demand CIJfV6 ()( the supply curve Shlfls ,n the demand curve Bre already lmp/re,11y emtx;JdIed If! 1M aggregale IdBtlllfy whe!her movements are mc rcsult 01 sh,IIS If! demand curve cqualoon tn/olfYCMg the coeffrel(!{ll on the ,nveSlmefll vanable is very dlffreult wIwn shocks occur 10 bolh Ille ckm8nd IOf and supply o/lIlvCSlfOOfIl 7 Anothl!r variahk Ih:11 is not direc.1ly ohservahlt' is thl' CXpcx11..'li inflation r:.lte. In !-,'CIlt:'r:.li, one woukl I!Xpcct that the fac.10rs includl.."<.l in !'"'quation 4 would al...o he u!>C.:o in fOI'(.'Cl!lting the inflation mte. We :L..sume Ihat cx(X."Ctcd inflation is (.'o ooition!.'<..1 on jnronn.ilion ;lVuilahle 31 (iITIt.' t-1. Thus. eX(X.-'<..·It.:"<.1 infl:ltion i~ rcpl'l,....oo.,cnt(.'(] a~ Ix.-ing depencknt on lagged \'::l lut.~ of all the vari:lhlt.-s that enter into tht! }tcneral inflation-rJte specific.nion . 111l1s, the variahles in cqu:lI.ion 4 :llong with I:tAAt'(\ \",.. lues of the inflation rate com,tilLlI.e the infonn:llion set that a}tents 1I.'>C to fon.'ca.'>l the inflatio n ,,,'e, In addition, u~ing lagged valut!s 10 Clptllrc the CXIX."Cted inflation r:.1It.: is :I ~imple w:ly to imroduce dynamic effecls of thl!St' \~ lriables on Ihe intl:Ltion mle.1! Thus, tl.~ing observable dat:1 to GlptUI"C the efTe(·ts of change~ in the growth ratt' of rhe l11arketcle:lring re:11 W:lge rate :Ind the e:IQx."<.1!."<.1 infbtion r:.lle condi tiolK-o on infonnation availahle in ~riod (-1. the inflation-r:.lte I..-"(Illation e~ imatt-d i.. represented hy the following t.:xpn:ssion: (7) 1C, = Cu + . . . 'L pl" , + 'L ... D,G,.... + L.,., T, K", +LAIi, + L'.UJI; ., +til,P(;,.,+ t V,RPE,-. + :t~,RPI';" + IO,Rap, 1+ rD,. ,., p, where c, 8, r. A.. (. 11, '01, ; , 0, and rare p:lr:.lmcter estim:ltes; i - I , ..., 9 r..:prcscnt Ihe lag lengths o f the variables induded in tile infonn:ltion .~:I used to "'I' v An ahemawo way 10 /TIllodVcll d)InamIc$ /TIlo /he KlflallOfl- r/110 cqtJal lOfllS IOVSft fhccondlllOflal eJtptXlcd value oI lhe var",b/c$ /fuJl ~ me cJtpcclcd grow", rale 01 lhe marl<ot-dcar.ng IBIJI W3g0raro Indeed. " 1he000pet;fallOflis cond,f1OtIC(;/ 00'l ",. H/f'1eS ' hl$1OnCN be/'la1'!(Jr (lor ltlSIance an aJfOItJOtC$$IVO ptO(;eSS). /hen laflfllld val.oes 0( ptodVc/Mly fITO'Iotn. 1.1001 Ioree growth. /II1d me growth r81e 0( raw matetlSls INOCJId enrer It1IO IIwJ IfIfIaIICll eq<allO'llhmugh . -· lO$Iea<l cllhrovgh CllpCCICd rlIallCll &cause IIwJ qualail' we oHccts 00'l.nn.11OtI due 10 cn.nges .,. -. WId If" are /tie s.ne we cIlOOSCI fa ITIlroauce the dynamrcs Ihlough the OJtPCClcd /nfta!JO(l rale • (';.Ikulatc the .... xpectcd inflation r:.ill!: SliP d ....no(L'S th .... unemployment r:lte le:-.." it~ n:llur:.11 r-.ue; and D L.. :1 dummy \'::Iriahlc that [<lkes on Ihe v:J.lue of 1 from 1971:110 1972:4 when price (:ontrol .. were in effect. Other v-. . riahlc." a«: defined III the Appendix. Wilh 11K.' s(X.'(.·iflc:'llion of the empirical modd. it b useful to identify Ihe implicit rl,.'Str1ctions imposed on t.'<-Illation 7 fhal yield the monetari..t :lnd CXpI..-'<..1.a tion..-:llIgmentcd Phillips-curve model... t\hhou~h (he: expt"<.1L'Ci inflation r:.ue d(X.'S not appear in Ihe: mone:tarist rnode! prescnt!.'(1 in t'quation 5, il is f;l irly common in the literature to indude l:iggl:."<.1 v:llues of Ihe infl;uion ,.III! :1I,d money gro\\1h in e.:slimatinR the L'qualion to :lccount for d)'n:llu ics. In ;l ddition. supply-shc.X'k v.. riablcs-such :IS the relative prk:c of encrgysometimes apfX!ar in the monetarist s(X'CiflC:ilions. Sllpply sh<X'k~ would ;l ff(;!(1 pott:ntial output. which appear:; in I..'qu:ltion 4. TIlliS. tht: kt.:y diITen:ncc IX"1.w(."(!n thc 1ll0111..1:lri..t ...(X.'Cifk";.ltion... and the gent:r:.11 o ne is tlml the unemployment-ratc gap and I;IAAI,.'(] valut:~ of wage growlh 00 not appear in the monetari...1 tnodd The de facto restriction pbcc..'<..1 on Ihe gene-r.11 mooel is that IX'lthcr (he uncmployment-rate Rap nor wage gRm1h l'flfltain infonnation th:1I. signifl!'';.J.nllr help to predi<.1 infbtion. In other words. the gt.·nt:r:.ll model is nOI ~upcrior to the mont.-1arist srx..'d fk alion if we (.";.Inllot n..'jcct the null hypothese. 1t);lt the coemcient~ Oil bRSL'(\ \'3lucs of wage gro\\1h :md I:tggL'Ci \':llues of the unemployIlK'nt-r:ltl' g:lp :Irc ~Jintly equal to zero. How doc... I..'qu;nio n 7 diffl!r from the cxpcctal ion ..-mlgmt:nlL"<.I I'hillips<ur\'e modds thai are e... tim;lK'Ci? Mosl important is the.: inclusion of demand-sclll.."<.lull..' shift par:llllelt.:fS, ~uch :I ~ lllont:y growth, [hat :Ipf>l:ar in the Outplll dema nd sdledule. MO\'t'ments in the aMr<::gatc dl!llland curve :lffect the prict: IcYeI wht:n the aggregatc supply curve is 1101 horizont:ll . Con!>C..'q llcntly, lht: etTl,.'(.'l" of changes in hoth money growth ;lnd govemmt:nt-spcnding growth :ITC implidlly assuJll<:."<.1to he I,.'qual to z~ro in the expt.'c talion:--:lugmcntl.."tl Phil lip:.-Cl.lrve ...(X.--cific-.. lion. fonn:llIy, hy imp().."in~ the condition" lh:1I the CQI..""ffi,.'il..,nts on contempo raneous amI bgg!.-"(\ \";.lllIC~ of nlOney gmwth and tht: contempor:.ml,."Otl~ \";.J.lue o f ROvcrnment-spcndin~ growth ~)intl y equ;11 zem, I..-flu;ltio n 7 t'ol1apscs to the t:xrx'ct:llion...-au~mented Phillip~-curye model. I-Icncc . lhc Rener:11 spt."<.·ific:uion of the inflation , .. tc pn:scntcd in thi~ scl1ion encomFede ral R<'lICn 'C" 1b.nJr. o(OaUas Table 1 Simple Correlation Coefficients Between the Inflation Rate and Selected Variables Vanable CorrelallOl'l Coeftidenl P·value' ", .506" .000' RPE, .393" .000' RPF, .183" .045 PG, - .383" .000' w.. .681 " .000' U,., - a." LSF.. , - .006 .114 ,9519 .217 , P. ...aIue is the tigmicanoe ptObdity 01 the correlatioo .. The correlabOl1 coeffiCMlt II tigf'IItieaIllIy dift8fent lrom lefO p:I .... ~· .... Ix)(h till' mOtll'l ,ln:-t ;tnd 11ll' l".. pl'l'l :ltton .... • ,IU).:lIIl·l1ll'd PIlllltlh"'lln e.: 1lltJ(ld .... 1":C:lII!'ol..· it f'l.·I.I'\l· .... l ·lIndnio\) .... IllIpO~l..,1 hy ~';Il'h t11(J(lel TIll' ).:L·IlL·I';lllllodd f'l.·dun.: .... to I Ill' 1110rll'I.lr1:-.t l11tJ(1t:1 if till' Ltl)tll' 1II:1")."l·1 (k·:I, ..... in~t.lnlalll·t)u ." l y ~I) that \\':I).:l· gl'tm Ih :111<1 t ill' lHK·lllploy n ll'IlI·f;n l· gap do not (ontain info1'1n,uioll Ih,ll i ........ ignificllll i n !L'rm :-o of pn.'{ht'lillg inlltlion . On IIlL' o lhL'r ha nd . IIlL' gl'l1l'r:11 Illll~k-I t\.:(I U l'l· ~ III IIIL' l ·X lx·(·l alill11.". :1\,11-\llll'IlIL'd P h illip~ ·n lrn.· IllIKk·1 if .w ilhl·r 11l01ll'Y ).:l'o\\·th nor ).:1)\ l·nlllw1lI·. . . lx:n di llg 1-\ro\\'1It ol11t;l ill intill'l11aliolllhal i.; .... iJ.,:llitk:ml in Inllh o f p rnlit·t · in).: intblioll \\ ht:lhL'" I ilL' ).:L·Ill'r:11 Il\IKk-l i.... .... llIX·rior 10 L'll lwr 11K' Il\OnL·t:u·j...,1 IlllKlt:1 o r till' l·'IX'i..·\:tIUljh :llI).:IlWntl·d Pllilllp~-nl""L' l111J(ld dqx·nd .. lin \\ I1l·IIII..'r till' l'\ ld...'n..'l' ....UggL·"I:-- Ih:1I IXllh of Ilw ......· Ilull hnXlI1K· ......·.... :Ift,· n ..'jn·h.'i..1 APIX'mhx , Thl' .... 1')Cotk:ltion Ihal \\(.: e.::--limal .... i:-- ""'lll;\ll0n - . TIll' rd,ltl\ l' pl'il'l..· of r..!\\ lll:lIl'riab ..·oll:--i ....!:-- (If Ix~h Ihl' n..'\;tli\L· pril'l' (If t.·IlI..· r~ y :md 11ll' rl,Llli\t· p rKt.· of ft)(J(I. " Tltl· ...... fl·:lIun.::-- arlO nl\lllllOIl tn IXlIh lilt.' lll()nl'I:II'i~1 :Ind l·Xpt.:C1:tlion:--· all).:IIll'lltl'i..l j·hlllip....·nln l' mudd ... in Ihl' lil<:r:llurc T ahle.: I rqxlI1:-- tIll' {'(Jrn..'I:!tion codl'ide.:nl:-O hl..'l\\'l'l'n t ilt.' inl1:lI iorl 1~ lI l' amI ....... \·l·1l POII..'IlI1:11 l ','l:pl:tn:ltol)' \ ·:t ri:thk·.~ : till' ftlllwth r:llc of the.: :Idjll ... ll·d 1ll0Ill 'l:tl)' b:l ...l' UIl. thl' gl~)\\'lh roUe.: u f the rd:II1\·1..' pricl' n l e.:lll'f).:y ( J</'/:·'. Ihl..' ).:f()\\Ih 1~1\l' of lilt.' rd,1\i\l' pril'l' o f food (HI'I-'). Iltl' ~rowlh r:.tll' (.1' p rodmlinlY (Ii,' ). tIlt.' la).:).:l·d \·:tlUl' of I hl' ).:T0\\ th r: 111..· of \\:t).:l· .... (II' J. the.: I:!ggl'd \,:thll' of 1111..' 1I1ll'lllplo) rlll'IlI·r..Ue.: ).:ap (l -I J. :t lld tltt.· LIAAl'd \ ,tim' 0 1 , Ill' I.lhor fort.'l' p:lrlil'ip:tlion Issues in model specification -11ll'd.II;! 1I......·d III lIur :111:11) ... 1:-. .... p:1I1 1 9';9~ .tnt! .Ir..· qll;ln ..:rl) .md ........ "'tJll,llI} adjl"'....'i..! (Fllr:1 (k'I;lllt.-d d ..·....nipllllll (.1111 .... \, l ri 'lllk·~ ......: ..: Ihl..· f ..c:ononlk Hl·' ·ic .... - ~t ay 1''') 1 Afenra (f990J proposes tnt;;Jud,nfJ a durTmy var.able /0 IIOCCIU'II lot cI1MlQeS ", /he .nIlaf1Oll rate lot me t)elK;Jd IfflInCf:1Ialoly allet pI~ CQr1ltois were Mtcc:J • s-:rowth r.tt~· (/.111-" ).1' Exn:pt for the unemployment-r.Ue g:lp ~lOd labor fo n:e IXlnidpation growth. tilt: l'orrdation co.:ffkil·nt is significantly different from z~'ro in eac h ('';.I.'>C The.: l:vidl:nce ~uggest' that 11\'(.' of the sc\'cn pOienli:11 explan~t tory variahles arc s ignificantl y l'orrelated with the inflation r.ttl·, Thb find ing docs not nile out the po!'>:-.ibility th:II IIU1l'Ri11ll1 infofln:ltion is contain~'ll in the unemploynK'nl-r:.ue ~ap ~lOd lalx lf for(,e panicip:tti(ln W( )\\,th, Indl: ...'<.I, tllultirle regrc~ io n is a direct way to sllt."<.l light on \Vhl·th~·r change:-. in ;lny of the expl:lna!olY \'ari.lhle,' contain marginal infornl:l1iOl' alx llLt the inlllliotl rate while holding all other explanatory v:triahk:s constant An import:lIlt isstLe in e,~tilllating equ:ltion 7 is identifying thl' :Lppro priate bg k:ngth for th..: variabks Ih:1I arl' a ,~ S lllllcd 10 h:tve d'fects distributed over lilllt::, Daniel L. Thornton and Dallas S Bancn (19H5) provide l'vjdenct:: that sugge:-.ts that J10licy conc1u:-.ion:-. arc "..:nsitive to the lag stnK'lure sJ1edfied , To l'Imfrnnt this problem , the Schwa rtz criterion 1llethOO W:lS l'mplo}'ed to :-.el<.-ct the ('orreCf lag len}.tth of the: inde:pe:ndetll \':Iri:lhlc:-.,I\ Tht: Schwanz critcrion indicl\l's th:1I ("qllation 7 :-:ho uld indud(.· thl' (.'(lIllempor:lnl·ou:-. value and one 1:IAAl.:d value: of Itlone), growth. :tnd it abo indicate:-. that tht;: l'onlempOr,lIleoliS value of s-:()\'crnm~'nt-spending j.tfm.... th he indlld ..."<.l in the t.'qu:ltion <th:l\ is. 1111 I and 11/1 '" 0 ), The Sc h\\'an z criterion further indic.ues Ihat tlw mod!:.'l :-;hould indude two bAAed v:llm:s of the inll:llion r.ue . thl' ltnemplo}'IllC/lI-r:ile gap, wage growth , :lOd the Arowth r.t1e of lilt' feb!inc: prit'~· of energy (thai i", III , - III, 111_ - m~ - 2), For productivity growth, !:thor forl:e parti<.'ipation r:lle growth , and the growth r.lle of tht:' relaTive pric,:e of food, tht;: Schw:lrtz niteri{ln indi(';t1e,~ th at one J:tggcd v:t1ue of e:Kh should be inc1ll(kd in The model (that is, JII \ - I1Ih _ 111,,_ 1), 11> The general specilk:uion estimated in this ;lnkle i,,, rcpre:-. ...·nted hy Ihe following expres:-;10n : , (M) .. We UM IhfJmonci8ryNself'l/hlsanaiysiS If'lSleadolanolher mone.'lIryIW6g81e lot pstSlfJlOfly cornpMlSOfIS 01 /tie mone.'sry See HssJag (1990) lot Tho baSe 10 M I 8nd M2 evrdence Plcscnlod If'l thBl 8T11CJe SuggeSIS /hal ITIOfI(Jy mulbpl,. QrOWftl (as mcll5l.Ked oye,1I'wiN M I or M2J was not II uulul V8T<able lot prcdlCllfIg If'lllatlOt1 81 very shorl lag /<8fIg/fls, such liS tllO:SO chos8<l Oy the Schwartz c/Jlcrion In acid,'IOt1, Rooorl G K"'9 and Challes I PIoS58f (1 984) malfl18J1l 11181 Ihe monelary ""se '5 relll/OO more clouly to .,flatlOfllhan arc tho Otoadolll monelary aggregateS ChCrIf/ H SIao (1981) oolllflCS 8 proceduro lor choosmg /fie opllmal /sf/leng th m B mullJVllflalB fBgress/Ofi SOiling Ho inc/vdcs uPI08ffJhl laggcdvalvcsolcach of/fllllfldependBn l vafl8bios m /fill Spec"JC/l11()tI '" Another IIIlpOftllnl economcllJC ISsue 'S whether SJm()llane· Ilyisa concern, resulting If! b<ascdcocll/ClCflIS Tofl'lJ(lJ(TltLe /fie pofollflll8l smul18l'lo!ll1y boBs. we fJ6fI6fal/y used /sg gcd v8lues 01 eJlo/llfialory V8TllIOI6s In fSCI, the only conlempo. rMl60US vlltvcS 01 r/flhl·hant;j.S/CkJ vllrl801cs JfICJudcd., this model we po#K;y variables NIII/fler ITIaItly growIfI nor fJOVt/"fWl'lCI'll·speiIdIfIg flTOW/tt BID contcmpor8flCOUSJy cor· rclated .../1'1 IfIIIafJOtl al lhe 5-perC8fl/ s~ level t::)njlllllg /he conromporaneous valueS dotM; not affect Iho rcsults repotted II'IIhls arllCle " We I~sted ItIo model errots lot seflltl CQfrelall(Kl us.og the ,. Btcusch Godlrlty lest In /Ills case, /tie 81"1wsch-Godlrey IC, = cu + I P,,j/, ,+/)"G,+ I ., +{ILBI';_I + J.l 1, i·,_,+ , T,IC,_, + L A,lii ., I L., v,RPE,_, +~ , RPI'~ I + L 8,l-IaPr., + yD" ., Empirical resuJts In thi:-; Sl'ction we report the findings ohtainl'd by estilllatin).,\ equation 8, We u:-;e these n.:,~ults to dl'aw infefl'rll'eS Oil the role that money growth plays in tietl:nnining the innation r:He, In :rddition, these rl'sults :-;hed light on thl: ahil ity of the gcncml modd \() predict inl1ation better than either the monetarist or the expcctarion:-;-auglI1ellted Phillips-curve 11ll xle b , 1':lhl<.' 2 R'portS Ihe re,.. ulh of c:-.rimatin~ equation 8 1- \,\/hat do the res ults sllgge..,t :tbOllt partkul:ir variahles in the ge neral mood? 111cre i., :It lea:-.t o ne :->t:lli:-.tietlly :-.ignific tnl coefficient (:11 the 5-pcrcent level) on I:tgged \';rllle:-; of mon..:y growth. inl1:ttion . the gro wth r:Ue of rhe rciative price o f l'llefgy , and wage growth The(.'oellkient on the b~ed value.: of the prodlK1ivit}' gro\vth rate is ,.. iAnificallt at the to-percent Federal Reserve Hank of OalJas level. In addition. the I.:ocffidenl" on the fir..t and second l a~~t--<.I v:llul..'." of the unemployment-rate gap are signifi(,.'anl al Ihe 6-pcn,.'cnl and H-pcret:nt level. rc'ipt.'ltivcly Thl;' l"oefficient... that arc signifit."ant al the S"rx·!'t:l;'nt level indic.ltc thai increase:-. in money growlh, waAe growth, :md the growth r::ItC of the rebti\'1;' prkc of ent.·r~y result in higher inflation. which I.:orresponds 10 the Iheorelic:al predktion.... Nex1. we con .. ider the null hYflothesis Ihat C(x:fficicnL" on the v:lriahlcs :Ire ~)intly equal to zero. Efft.:l.:tivcly . this I(.'..ts fo r Gr.IIl~t·r c:lusality. Under the null h Yflot h(.'sis that the coeffidcnts on contem por.lncous :lIld laggl.-<.I val lies of money growth jointl y cqual ZC f( l. Ihc F sl:lt islic is 1001. which is grc:Llcr Ihan the critka l va lu!.: 0 1' .3 07 at the 5-pcrcc:nt sij.!n ific:lnl·c Icvcl. Simil:lrly. we ~par.ltcly (cst whcther thc coefficient:-. on lagg!.:d values of wage growl h, the unl'm ploYl11ent-r..l1e gap. and the growth r.lte o f the relat ive price o f energy arc ;oint I)' equal to Zl'ro. The Fstalistics for I:tgged v;lluc:.'s of wagt' growth and the growth r.HI;' of the rd:ll ivc prkc of energy an: 6 1'5 :md <159. rcsIX'<.1ivdy. \\hi(:h b l:Irger than the '5IlCn'cnI c riti cal value of.3 07 . For laggc. .d values of Ihe llOernploymen\-r.lte S{ap. l ile F sl:ttbtic is 1.90, which b :.malier than the S-pcn:cllt critic.11 \':llUt'. 11)(: evidence, Ihercfon.:, sllAAe't:. th:1I mont'y S{rowth. wage growth, :lIld Ihe growth r.tlC of the rcl:lli\'l..' pric..·\! of encrgy arc cadI useful pn..'dictors of (Gr.lngcr C:H I~) the innation r.lle. 111e evidence abo is c.:on:-.istl.!nt wi th the notion that productivity growt h t.'ontrihllte,.. u:>.l".'ful infonnation for predicting (Gr.lIlger causi ng) i nll:nion , The cvidctKe :-.uggcsl:-. Ih:1I governtm.:nt-:.pending growth, Ihe u11c..'l11ploymetll -r.ne j.!:tp, l:!IX)r furce partidpation growth, :.md IIle growth r.lte of the rel:itive price of food, huwever, du not predict (Gr.J.nger cau.sc) Ihe inflation r.l te. Is the evilit'nce consistent w ith the notion th:\I the gL·ner.d model expl:l ins inlblioll l)Clter 11I;m thl;." monet:II';"t model? Thc gt.'ller..d model rt-<.llICC:' 10 the monel :l ri ..1 model if the coefficients on w:lge growth :Ind the unemploymentr.1\1;' gap :Irc ~lint l y equal to I.t.·ro. fonn:llly, this condition :1I110unIS to restrit.'ting tht' l'<X!fficienl:. on 1:IAAt.:d value, of wa).!l.' !-lfowlh :In([ laggl.-<.I v:llue:-. of thL' unempl0)'lm:nt-r.lle j.!ap 10 jointly equal i'.ero Under the null hypothesi:-. th:lt AI - A. - ¢, - 9: - D. lhe /,':-olal;"lic is 4, 14, whidl is Economic Ih.'Vlcw_May 199 1 weall:r than the 5-pcrccnt critk"al value of 2.45. l 11U:', the evidence SUAAcsts that the gene..!! modd is stali:-.tiC:llly superior to Ihe monetarist mrxld in tcnns of prt."dicting inf1:Hion. The !-tener,1i model collapses 10 the expect:llioll:.-"ugmented Phillir-..-cun,'e modd if tht! coefficients on moncy gmwth and govemmcntsllCnding growth arc jointly (.'qual to zero. Under the null hypothe:.is that the coefficicnts on contempc>r..IOL'oUS :Ind I:tggl;'d val llcs of both money growth and government-spending growlh are jointly equ:ll to zero,lhe Fstat istic is 7.13, The S-percen t cri ticOl I v;lluc is 2.68, so the resu lts arc consistt:nl w ith the hypol hesis that moncy growth and ~overnrl\(:nt -s pending growth ;m~ systenwtical1y reb ted to inn:ltion, Thus. the evidenc!.: sllj.!gest,", Ibal llll' gcner.!l model is statistic.ll1y superior to the cxpcct:L1ions-:lugmented Phill i ps-nl lVe modd in terms of prt--dict ing the inn:Jtion r:lle 1M 5l8/JSloClS • 64, Iessfll¥lthe5-pcft;cflIamcalvawat2 37. Thereforll. /he ~ /$ CO'ISISIBtlI -..tIl /he II)pottIc$I$ /tId1 /he errors •• not $CnIIIty CJC)ffOOlcd See Godfrey (1978)1or II dcscnpllOflollhts IfISlIot serl8lcorrelabDrt Wi/tl lagged depcfrIdenf vlJIl8bIe$ on /lie nghI-hlInd SIde 01 /tie /csl /$ II morll gsnetBi test lot $CfIlfI correl8llOf1 AA.mallwllflsts, such lIS Durbns h 1OSl. /csl spcohcBfy for IhB ptllset'tU at fitst-()(dct 8UIG- BQW'1Of!. ".,. BtBtnCh-Godtroy -,....... aortBl.t.1Ofl III .". t~ WII uk:vIBlcd the lest IcsuIfs lepotled III /tits "toCle USII'Ig' 6IOhI18fJ06d values oIlh9 In additlOfl, under /he null hypolhC$J$ /hal none 01 the flxpltJM/Ory vlJ(labics help /0 cJCP/alll Ihe vanallOl'l oIlflf1a· ll(ll'laboul its melJfl, thB F $tatlS/.c /$ 37 76 /"hccnlica/valuo allhe 5-percent $Igniflcllnco level is I 75 The flVldence, thelefoff}, suggests that the adJl,)s/cd AO (083) is Slgmfl_ cantly dllfSfCf1t flom ~efO Ovural/, lhe IIvldence SuggeSIS /IlDt 1/)0 general mtXlel.xpllMS sane of the VSflallOfl of the IfIfI~11Ofl late about If 11$ moat! Mehra (I990) IIX8flIIfICd 1110 <S$UO 01 wflClhcr fJ'O(JvCtl"'/),/tie IllfiatlOfl ,alII In OU' generaJ acJtv$ted wages affected ~, Mehta's lestses.wnflBl1y amoun/ /Odclertnnng " )", ")" "", • 0 t.nc:/III'lhBnulItypolheSlS/llafproductlv· 1fy'8dJUSfBd wages dO not alfecl /tie IfII/aIJOtl rate, Ihe t statIStIC; 1$ 3 46 The 5·perCBfll crrllCal vaMt /$ I 96 Thus. IfI(l evidencB suggcs/$ thai II char>fIC III /f8fld~ed waoo {JJONtII doo$ alf8CI .../Lt1JOtl The maIO difference Me«a's spcdIic.alJOtl and otn I$IhBI he usasone /af19cdl'aWoIuontJ.MltuSledptOdt.lcrMtygrOWl1l. wnereas 11-. US(} two /agQcd V8t1es ot wage growIfI and <n'Y one lagged VIIW 01 ptoducWlIy growth be~ " Table 2 Coefficient Estimates for the General Inflation·Rate Equation, 1959-88 Coefficient Standard Variable Estimates Eo", Intercept - .215" .097 <" .394" .097 <" .144 .089 M, - .018 .057 .21S·· M" -.005 RPE" .059 .014 .038" .014 PG r" - .098' .048 w,_, .049 .068 w , .202" .063 D - .173 .117 G, ,021 014 RPF, .013 .'''' D, 1 - .205' .108 U,~ - U,... 192' .112 RPEo--l U,., - LSF", - .064 .098 DIAGNOSTICS: Breusch-Godfrey test al8 lags. 1.64 • indicates sqvfocance al the 10~m •, il1dleatel sigl'lllicanoa 31 the S.perC80t level . ~el. NOTE , The vanables ate defined In the AppendIx lZ Federal Reserve: & nk of I)allas Table 3 Sum of Coefficient Estimates and Tests for Significant long-Run Effects , ~) ••II._. Sum of the Coefficienl Est.mates t statistICs' 200 396 .02 ' 1.47 ~ • The tatautic is calcutated ur'lder the null hypolnll$ls Ihallhe s.um ot lhe coatfioenlS Is 8Q\JaiIO zero NOTE, The ~ariables are defined In Ihe Appench. \\ 'h~H .•rl' till' 101\).: ru n dl',,·l ·t .. 0 1 (·h angl.::-' in poliq \ M u hk· .. IJIl I h l ' I1ltl.lI io n r: lIl'~ T ahk :\ prl' ''l'IlI''IIll' I\.· .. ull .. ol Il'''1 "1;1 1 j.,l1l~ t';tku l:lIl'(l Fort.- casling ex perime nt umk 'r till' n ull h~ I~" hl.·" ' " Ih al Ihl' ,'\UIII o f tl w l 'IIt:l1kil'nh l't lu;!!" /l'ro ·nli.. Il'''1 (il-Il ·l'lni n l·.. 1111,.' iI1-"':Ullpk' prolx'!1il'" of I IIl' gl'nl'r:rI lUodt'l '111l' 1l1''>;1 qlll..·'l lon t·,>;.II11int'" Ihl' lIu t ..of-.·.alll p ll' p ro lx'nil ' " :-'lx't.·i /k •• h O\\ do forl'l';hh f n ull Ihi.. m odd ('omp~lrl' 10 Ih o'ol' ~l' lll'r: llt:d hy mont:lar i.~1 \\ hl'l hl ' " Ihl' 101.11 (or IOrl).:"nlll) mult i pltl'r I" .. t).:l1Ilk.l1l1l~ d ill'l'rl"" from /l'nl A .. '1';lh k' :'t .. ho\\ ... until'1" ti ll' null h~ ]l()lht,,,,, Ih:Ullw "lIlll of Ihl' ttlt.'ffit·ll'l1I .. for l'llllll'mpor:rnl 'oll" :Ind IlIll' I:r~l't l \ .11\ll ' l,f Il aw 1llIml'} ,r.:n)\\ Ih I.. "lgI1ilkam l} dlfl\:t'o.:nl fnllll/l'rn. lIK' null h} I~)l h ":" , ,, i.. n: jl't.·ll ·d .11 ')-l'lI.:'\ ·l ·1I1 ." 'gllil ll';111t 'l' Fl,r gt,n ·nll lll·n t- " Ix·ndin ,r.: ).!lll\\ lh . hm\l· \ l·l'. ilK' n \l 11 II n~ llh l· .. i.. C l1l nOl Ix' 11,' 1,,' j H.'d .11 u .. u.d .. i).!nilit :l 11t l' 1v11..'1... '1hi.; 1.'1 i{\l'lll'l' "11).!).!I.·"t... Ih.11 .• IK'1'Tll:l llt'llI dla n gl ' in IllOl1l ' } ).!1lJ\\ lh h a .. a 1)I.·I'III.l no.:nl dfnr o n l hl' in l1:lrio 11 '~ lI l·. Ili it ,I 1X' 1'111.11ll'lll ~ l l.l n ~l· II' gt )ll'1'nnll'lll " p l·n d i ll).! ).:rO\\ 11t dot'" nol In 'hlIt1 . ! 1 k.· l·\ld~·nl·l· "1 1 ~1'''1'' 1 !1:11 rnC 'lll'~ ).!rll\\lh i ... 1 u .....'tu l pl'\.'t.lil\C lf Clf till ' inl1:u ion r:. lIc. \\ltidl ... tlrn.. i'I~·nl \\ il lt th ..: l1lClIll..'I:l n ..r llll)(td \\ . I ~l· ~ro\\ III .lIld thl.· dt')':l'l 'l' 01 tk'm :rnd pn.·...,un.· ;11\.' ;.1..... , 1I"'l:f1l1 p ''l''l.ht-lI,r'' I If 11ll' m ll.llic Hl .. Ill'. \\ tliclt I' l'( IIbl""111 \\ 1111 till' t" IX 't1~ll ic Ilb-.lll).!Tllt1110..'t.1 I'hilhp''''I. u n l ' 11)1 Kld _'I1n l" . t ilt· ... \ Ilk'llt'l' "U).:,t.:l·"" Ih:II.1 J.,'t-'l'It.'I: llll1tllk-l. \\ Ilith ~· I)tI'Ill IX l ..., ..-, .. I'NlIh (}j' th ..·.....· "IX·.... II CI .....·... I" .1 "ulx'nor rnodd of inll;rliol\ \\I)I.'n llllllll:lr..'tilo d rhl" o/rlll' Ill·"l"<.l 1110tk+.. 'n ll' n.· ..ult .. prl.·wllll'tl in till" .In idt: 1'0(,'(1" on l1r. :' I)(II"lx't.'~rt lon"-:II IAn ll· IlI I..'t.t I'hill ' ll...-l'tll"\'l' 1llc xlds o f Ihl' In lb l ;on r: 1 1I..·~ In Ih i.......'l·\i.m. Wt· l ·OlllP:Irt.: Ihl' hla .. :Ind .1Cl'l1r:lq ' of f()I'..'t.~ ""h ).:l ·lll·r:tll..'t.l hy Ihl' Al'nl'r:11 m CKkl 10 tho...... of forl't~ I ..h Al' nl'l~ I\ I..'t.1 h~' llll' I..'Xlx't1;1 I h Hl .... ~ 1\ l/-:tlll'llll 'd Phi Iii 1'I'o- Cli I"\'l' :1 1l( I 1ll0IK·I:lri .. IIIIOdds T Ill' hOl'i/cln l1sl'tl li)r th i.. I..·Xlx 'ri nll·1I1 1." l")HO: 1- 11)Hli: I Th l' 19i·{O.~ :11'1.' an il1lpOl'lanl 11..'., lill).: ,groulld for 11K' ).!l·l1l'f :11 IIl1 x k l. p artinrlarl y l'IlIllp:lrl'd 10 l h t: l·." I)1,.·l ·I:11it l1l .... allgllll·n l l·d l'hil li p ,,,-ol f\ 1..' " 1X'l il lCn ioll T Ill'fl' i .. ).:l'l ll· r~rI ('onl 'l'rn t har Ihl' 1'1.'1 :11;1111 .. 1111 1 1)('1\\ l..·l·11 !llI m l') ~n)\\!h and l'CO nom It' :It·t i\ il} lhangl..'d "llh.~ I , II' t i;lll }' d unng Iltt: I I}HO .. I f Ih i .. i .. ">II. Ihl' ~l'nl'r: ll IlltKld 1ll:1}' nol rll:rfo n n a n ~ !)I.'Ul·r Ilu ll I !ll' I'Xpt..'t·t:,l ion .. :nl.L:lIIl·llll·d Ph i ll i pvl'U!'\ l' Illodd In ",hidl 1lI01l1..'}, WO\\lh ,.. !dl oul oj Ihl' " IX't.·i lk: " IOIl -':oll' lhal lilt' 1ll ~lin di ll l..'rl'lll·l· !X'I \\l't'n ti ll ' L·XIX ·l ·l ;u i()n .. augllll 'llll '(1 Phill ip....n l .... t: rll(xld .In d Ih t: ~l'nl'I~ 1 1 111I1I1...'! ... 1111,.' Pl'l·"l·'U'l· III 1ll011Q ~rtl\\ l h in I hl' ).!L·n l'r:,1 modd ·1111'rdi)rl..·. If Ihl' ""'mI1lK' n l " Table 4 Forecast Summary Statistics, One-Step-Ahead Forecasts (Forecast Horizon, 1980:1-1988:4) Root Mean Squared Error 192 .087 Expectations·augmented Phlllips--curve model .259 .156 Mooe!arisl model .442 .165 General model rC){:lrdin).: llIom:}' ).:1"1)\\111 I'" torn.:CI. I IIL'n 11K> rei:l!io!) ... llip Ix:!\\ L'L'n Im ,m'}, grll\\·tll and inllllilJ!) ... hou ld not add imp"nam In fo rm;u ion dunng till" I~. C()n ....... quL·IIlI}, till" L·'l:p ...·t·t ;i 'II)rl .... ;lU~r1ll"nl ...·d Phi llip:. nil' ...· 11Iodd \\ Ilu ld dtl ItI ..1 a" \\ ....II in pn:ditIU1~ mtl;I\lf1ll ,I" 11ll" ~l' I ll'r: 11 .In lIl"I:IIKC. for...·l;i"[., f roUl ,I mudd In "tlt"h mo{ k'l nUlI,lIning i11Ol1e\ ~n)\\lh 1Il10nn,IIIOl\ \\ollle! not Ix: an} llIore ,ll"lUralo.: Ih.m l "r""LI"'" ).:l·n ...·I·;lI\.-<:1 h~ a m odel [hat I" Ilk·nl it.,1 III .... \ t· .. y \, "Y e\;t"ept for [h.... OIUI ..... !C)ll (,' m\'I1") ).:nJ\\t h Th...• (orl·chllll).: <'·'I)I,:ril11..:lIt elilplo} ..."<.1 11.......... b a /l'li/-filll!' n'r"lon Thi.. m ...·an~ Ih.lt one-:.\cp ah!.":ld f()rccl .. l~ o f [ill.' I1ltlalioll r:llt' In li llie period f ll.'t.· :1 11 1111.' inl ()rt1ulic Ul :1\;lil" I,I...- Ik.'t·:lll ...... [Ill' Ill(Kld indu{I...-.... J.I).!gl·d \ :Iiuo.: .. or t·;I1.."h 01 t lli.: \ ·ari:lhk ... 1110.: )"\:."." .... ardll· I· I ~ :1..... 111111.·<.1 10 1I:" .... lh...· 111"[01"1" :"·a i1:lhl .... \\ 11,'11 Illah:ill).: 11ll' .....· 1"01"1.'(":1.. 1:. In .Idllili(\I1. till" P; II":'l l))l·l o.:l" ...·... lll ll:l [l·.. can Ix: upd:l t.... d ...·: lth p .... nod.b IIl'\\ 1Il10rllLlt i(lIl hl'l"ol1lo.: .. :1\".lI bh!v. Th ll". lo r ...·l":1't, lor 11)1">0: 1 U"l" ~. I111 pk illfonn:ll ioll TIr gotlC"ill model 1If7~)IOy1'd 'S not (Neclly ~iItlIe 10 me P' r1JOdC1II'.1I H.lRrrloJll Potrer and Sma'i used 10 lorc casllfw> u)ll.llo(W' "II, In p..l'/oeiJISt I7If'SC' iWlflOtS used 1.12 85 1'19 r11()'1t.,), '""'1<".... /JasIIlfJ m-s S~"'".l·"'" Or! ltl<.> <lSSIM'1f)II(ll' /I~., M2 ,1'1(/ ,"/01 ....1,)1 GNP 8rc CC»ltegril'cd TI>{> COO'>lflJr,IIIOI' 1''CIIIIl>Iog~ '5 110t app1rC,lI)'o ,,1>(>(1 Of"'" .,Sl'$ /til) " mot!( fary b.l~/' Mean Error ,lS me ~ mei.ls,"c for till' r><.:ri(KI 11)')1): 1-11)- 1); 1.1111"\,\,1'[" lor 11)1">0:2 U't.· ~, u llp k IIlformal ioll for tilL" lwriod 11)"i\): 1II)1">O:I . •md '-I) on T .lhk I rqxm ... [Ill" "UI1I111:1i! ,t.H! .. 'il"~ o f lon.·CI"I" ).:l'!ll·r:II ...1.1 h} 11 lL" ).:l·Ill"r:d lll(Klt.-1. Ih .... l·'I"lI..1..·I.1\IIJ1l .. ·.I II).:I1lL"llwd 1'll illlp"·(III"II.· Ill(xll'l. ;l l1d ,h..· lllon,,·[;m ..1 lIIodd 'Ill\" Il W.1!l O':In".... r .... jx)rted III nllullIll 101 T.lhlo.· I ,I r..· nlll "1).:lllhcanll} lhfkrl'nl Iroll1 I.<.·ro TIll' l·\ldl·ntl·. IIll'rdol\.". .. tI.~t: ..·.. t"l h ,1\ !orl.1.-:'I"I:. ,11"1: \lnhi.I....1.l lor L"lt.:h of Illl·.....· thre .... lllo!.ld .. 1hI.' 1(\1:-.1-" (Omp.I I",·.. ,ht· 10l"l1..I ..tll1).: .IUll!":I!.)" 0 1 tilL" thl\"l' 1110dd .. 1\" T;lhlt.- ... .. hO\\ ... Ihl.· ).: ...·llc..'ral modd h ,I" Ihl..· 10\\ ..·..1 l{\bE. .. lI).!gl· ..li n g lh.[1 it i:..1 iliOn.' .1lnll~1l~· prt·d ic.·IO)" o( inl1.l1iol1 durin).: Ihl.· 11)l{t1.. th,1Il "'I[I1\"I" til\" .... xp ....l·taII( ,n... n l).:llll'IlI,·d I'hilll p ..-llin t' Ill< >lId 01" Ih l" 111I1I1I."Lll"i .. t l1uKlt.-1 " ~I I II .Iddilioll. [Iil' K\I:-.!': for thl' gl'm'l'all1l()(ld i~ I"ougldy Iht.....I.··louI11" :1 .. l:1r).:o.: :I~ tIll' I{\ISI ': lot" th t" t.''l: l""1l'<.1 ,l\\I)lh.,11I).!1l11·nt ...·d I'hillip~ CUT' ...· l1l(xl...-l T hi .. L'\ Itk·))t· ..· lll l lhvr .. ug,I.(I.·"'" 111:11 [lie inli)rll1;tlinrl lon t;tirl\."(1 III 1I101ll"~ ).:r()\\lh umtrihuto.:., III impl~'\"1.1 t() ...... ~,I ..[.. (ll l ill' ill11.llillil I~ IIo.· til .. hoI1. Ihl.· rl.'''lIlh frol1l 11ll" lorn·.. , tlllg t·'p..:riltll.·nt ).:o.:llI..'r:l lly t·(ln ul>llcll,· [iiI.' 1.'\ ic.lt·IKo.: pl"t·"~·Il1I.·d Inllll thl' \\1111111 ... lrllpk l",ltlll.l\ lI ln. Ilhol.ll" " .. thl' ).:L·n <,·r:llIllIKld ..·,Il·nd .. [Ill' ...·xl"ll...-<:'1:I[i.IIl .. ·.lu){llll·nt ...-<:1 Philhp:'o-('III"\~' .. t"lt:llnl ~I I ion hy indlldill~ mOIlI.·y gnl\\th. 1llon~'~ ).tro\\lh :tPI"X':tr-. to p1:t\ .111 imp{I11.lllt rol...- In jlT\·ditlin).: IllI..' inlb[illll r:11...· .... illlilarh . In ..ol:1l ;1 .. Iht· g~'nl'r:'1 1 nl(xld l·,l l·nd .. tIll' 1ll11ll\.·I,ln ..t IllcK1t.-111~ Imhldlll).: 1"lt>l. ll "dditl< lIu l input pnl ..· ).trt1\\th \.111,,111...-... 111(1 :l(.klition:lII1le-.t~ul\.';,> of Ihl.: dl.:grcc uf clem:mcl prc1>.'>urc. thc~ f:lf.:I","" ,LpPC:1r lu play an importanl role in prt.-"(Iiclin}l IOfl.tll()n. Conclusion The aim of thi~ an.l ly~i'i is to 'ipecify a of Ihe IOfl:ltinn r:lle Ihal cn he lI:.t:u 10 Icst \\ hcther or not monl..'Y growth pb)"S an lll1pot'l:1nl role in pn.-dil1I11g lnfl'llion TIle model 'ipecIOl..-d hl.."n.' l'Omhmc:- fc-.Itures of two different thoones uf inflallon "10 that l.."3ch is nc...tl.."tl in our Rcner.tl mood. A ~lInpJe thl..'OTetll":.LI fr.lmcwOfk characterize-. infl:nion a~ :l functiun of change-. in monel' ~rowth. mput prin:: ~R}\\th . :Jnd mcasun..--s of slack in Ihe ...·conomy. 1111: cvidl.'fK."C prcsellied m this .Inlcle .. uggcst:. thaI hoth mo netary and nonmorH..'1;lry :l.'ifl'.."t1." im::lud ...-d in the mooel are lI!o.t.'ful for pr("tlictinjOt inflatinn. lk"CJU'JoC moncr l'tR)\\1h is :& lL-.cful pl\.-dk1or of inflation. the c\ idence is ron~i.'>tent "itll the nOlio n Ihm the gcncr.IJ model ~ :,ufX;!rtnr to a .. pt."Cia/ ClSe model In which inpul pnl"C ~ro\\1h and ..l:ick 11lC".lSures. ;,>Udl :I!> Ihe uneillploymenl-r.llc gap. alone :11"(' u'>Cd to prt.'<.Ikl infl allon. likewise. Ix:c::tuse input pric.:e growth and slack ml';t~ures :Irc useful prccliClors of inflation. tIl(' evidence is a lso cnnsblcnl with th~ notion th~ t the genera l nux.ld L." , ,uJ'krior 10 ;I ~IX-"t.;~l G.IM: model in which only moncy ~rowth ill IN_-xI 10 prt..x1kt mflatiun 111US, Ihe evidence .. uggests Ih:LI :t gcne!':ll fmlllcwork that enco lll p;t~s both modd .. w ill betlcr expbin variation in Ihe in fl ation r.l le Ihan cilhn the ~t:ner.lIlllodcl Eronomk: Rc:viI:'oto. - May 199 1 expt.'t.T.llIOllS-augOlentr.:d I'hil!ips-cu rve model or till' monctart.';\ model. I n addit ion 10 the wlt hin -'iampl~ t::valuation, we a lso comp:lrt..-d the threc mooels in an o lll-ofs.:un p ll' cxpc:rlmcnt U :. IO ~ the 19ROs as the forc:.' c:ts t hurizon. F()rrt"'lsti n~ ;K'C U rdCY was highest when we uSt..-d the Kt:nem l model This Onding also pro"id~'i indirt..'Ct evidence that moncy growth rcmainl..'tI a useful prc.-diaor of inflation during me 19f1Os Indeed, if thc sped,li C'".t.')C model empha'iizing mput pnce growth and :.Iack mC3sures had Etcner.lIf.."t:I equaUy accurate forL"CaSts of inflation. then the eVIdence would suggt.."St lhal adding monl'y growth to the mooel did no t comribule u.-.cful infomlatlo n for p redicting inflation. The rt.'Su l ~ pn......cnlf..-d in this :Inicle suggt$t that a gel1Cr.ll. encompassing model will yield bener predictions of the: inflation rate man the altC'ma tl\'c 'JX.-'cial C-.I~ models. namely. the mont..'l3n..'iI :md the e.xPl-ct:uiOn .. augmented I'hilh~ CUf\'C mood.. of inflation. Because moner gw\\1h is Includdl in th~ cnCOIllfXb.'i.ng model, the rc... uhs indicate that the effects of monetary pulil), on inflation should he dirt.."'Ctly measured As our {'vidence MIAAI!MS, relying solely on movements III slack mC:bUTCS ;tnd inpul price Jtmwth omits u!)Cful mfonnatio n. panku larly from mo nt.'Y growth . 1110;,>. policymakers may judge the impact of mo nctary policy actions on mflalion fmm these pammeter cstimates and do not nf..,,(·c,-.:o.lrily have to ;nf~r the cff...'Cts of different policies rro m nlovcm\!nt~ in dlher the in p ut p rice vari:tbles o r ~I:tck vari;1bk·s. " Appendix men! of Commerce publication - fixed-weight GNP price deflator. Business Conditions Digest.) (Source: U.S. Department of Commerce, Bureau of EcooomicAnalysis.) loA = St. louis adjusted monetary base. (Source : Federal Reserve Bank of SI. Louis.) RPE _ price of energy in the fixed-weight personal consumption expenditure deflator relative to the fixed-weight consumption expenditure deflator excluding food and energy. (Source: U.S. Department of Commerce , Bureau of Economic Analysis.) PG "" • w mean-adjusted output per hour of all persons in the nonfarm business sector minus its sample mean. (Source: U.S. Department of Labor, Bureau of Labor Statistics.) '"' average hourly compensation of all employees in the nonfarm business sector. (Source: U.S. Department of Commerce publication BUSiness Conditions Digest.) ... high-employment government expenditures. (Source; U.S. Depart- .6 RPF '" the price of food in the fixed-weight personal consumption expenditure deflator relative to the fixed-weight consumption expenditure deflator excluding food and energy. (Source: U.S. Department of Commerce , Bureau of Economic Analysis.) LBF '" labor force participation rate ; the ratio of people included in the labor force relative to total population. (Source: U.S. Department of Labor, Bureau of Labor Statistics.) u _ the D '" civilian unemployment rate . (Source: U.S. Department of Labor, Bureau at Labor Statistics.) natural rate of unemployment. This series is constructed using the methodology developed by Peter Clarl< (1982). NOTE All Vinabla Irl IvdibIe orWle trom ClnBASE. Ihe Cibblnil All seI HI lS lbove 1he ....18bIe cI8noIe grOW'lh liI!n. which I" CllculiI!ed \.ISIfIg In! dllter.notS of tI'Ie ..."""'. F.:dc ..... 1 RC'M:n ·t· lbnk of OaLl;I$ References Clark. Peter K (1981). ~Ok lln'" 1.:'1\\ ant! POh:ntial GNP. ~ ( \X'3shinglon. D.C.: Uo:ud uf Govtmor.. of the Fcdcr:d I{c.;en I.' !'!)':-I\::IlI. Onnl'llo'rl Failla . Eugene F. ( 198.n. - I nn:nio n. OutpUi. and MUlle)·.- .I(Jllnwl (J/lJlIsillf.'SS. :\pril. 201-31. Hill . John K . Jml Kenneth J . Robin.-vn (989), "Munt'),. \YI>1f,l ....:-. :lOd Factor Scart'iry :lS Pre<iictnN of lnfl:ltio n . Feder:11 Rt'5('T\'C Hank of ])a[b .. £CCJIlomic Hetlleu ~ May, 21- 29. M I "i:au. Chcn~ ( 19tl 1). -AlIIOn:gres...;!\,c illodcling and I'olnnC'y. lncomc uus::dit}' Oi.'tCClion. jounmJ 0/ M 011erall' &:onomles. January. 85-106 M Fischer. StJnlcr ( 19- ). -lonA-Tenn Cunlr..K'L';. Rmional EXpL't.1:::nion:- :lnd the Optim:11 Money Supply Rule: j cmnwl 0/ Pohlicall:.cr)l1omy 85 o.la),); 26 1--5 Fril-·(hn:.m. Bt:nlamin M ll98H). -t\IOIlCI:Ir) Policy \\7jthuUI QU:::lnlil) Variable:-.- AIII('nall/ Ecorl()1111C HemeII' 7X IMa~' ); l-jO-·6. Godfn..-'}·. L G. 0 978). ·Tl-...... inSl for H1R11I:r Order $tori;d Correlallun in RcAn........ lon Equ:ni(In..; \':'hen the RcArt:'o....or.. lndudc: bRL.'t't1 fX:p:n· den! V:lrl:lhb.: Ecmmm('/nCIl 16 ('\(I\'(.-"mlll.·r): 1303-10. Gor(lon. Roben J 1I~-;)' - Und("N1:mding Inn:niun IIllhc 198Q:..: B",(K)kil1.~s PlI/)('I"S UII Ecollomic Actit'l~I ' I. 263-99 - - - (1982). - l n03Iioo. Fkxiblc EsdlanRt' Ra tc:o;. :lnd Iht" Natur:11 ft:.ue of Unemplll}'tnent .- III 1l 'ol'kt:I's.j(lbs. (/I/ll llljlmioll. t'd Manin l' Raily (\'\Ia..,hinAton. O.C.: The BrookinA:In:-titlltionl. Gr:ly • .I0 Anna (1976). "W:'IAt' Jnd...'xatio!l : ,\ M:H:rOt:l'ono11lic Approach." ./ollma/ uf MOllelmy £Co l/ o m ics 2 (April ); 22 J-jS HafC'1'. It \YI (191=13). "[nl1:11ion: A';'<;(;'!i...;inp: Its Rcccnt Bdl:.Lvior :md 1~·lLIurl.! I'rosp•.'cls," Fcderal Hl.!sc tvl.! lbnk Ors! l.Olli:- /(1.."'I 'iell'. l\ lL~tLM . 36-41 Hallman. Jeffrey J.. f~Kh:.Lrd D . I'on..-r, and Da\ iel H SIII:.tll <t99 JI. - M2 PC'r L'nil of Putentbl G;\'l' ;\.., :tn Andl(lr for thl' Pril"c Lc\'eI: Americall £COIlUIII/(: Rel'iell', (onhcolllinp:. Kin}.:. Rohen G" and Ch3rles I I'los,.''t:r (1984). ~ I'olnne)'. Crt.'<.Iil , and I'm.e, in a Re:lI Business C)·de.- American Economic Rl!l,ieu'7·j (May); 363-HO. MchrJ . Y~:-h I'. (199C», - Rc;11 OutpUl :md Unit Lahor C()~ l" ;i:- Pn..-dictors of Inflatio n.· Federal R~I"\'e U:.IOk of Rlchmo nd Eco"om;c Revil!ll'. Sl.!f>l:t'mlkr Deloher. 3 1-39. - - - ll9HH). 111C Fun!cJst Pcrfonnance of Ah ...'rn:III\t' !\l odds of Inn:ttion: Federal l<C!'>en'c Bank o f Rlt'hmond EcOl1omic Rel'll!u'. ~ph:mhcr/ Octohcr, IO - I ~. SUkkton. 1);lvid J.. ;lnd Ch.l rlt'~ S SlnlC'kmc),cr ( 19HC»). ~Tc~t., of the ~pt.."Cific;lIion and Pre· d"11Vt' A('('ur:lty of Nonncsled :o.'lodcls o f Innali{IO .- Hel'icll ' 0/ t:cOllomi CS (lIId StrlfWio. May. 275-H3. ~ Enerm' Prices and Short· Hun EC(U10mic PC lfonn3ncc.~ Federal Rcsetve Hank of St l.olLis ReF/eli'. Janu:1ry, 3- 17. Tatom , Joh n A. (I9R I). T'l ylor . .John B (1979). " 1 ~l il1l ;lt ion and Contro l of :l Mal'rot:(:onom ic Model w;l h Ral ional Expt.:ct:Ui()llS,'· ECO ll om et ric(/ 47 (Scptember): I 267-HG. Thornton, D:ll1lcil ....Ino D:llla:-!:l. Bauen (1985), - 1... !"H.en~th SdeCljlln :1I1e1 Test o f Gmnger C;lu.":llil~' lktwt,'cn Money and Income," .Irmnwl (1· Mmu!,Y. Credit, culd &mkillg, ,\by. 164-7H. llaslas:t. Jo.·..cph I I ( 19')O). ~ \I()net:try A~n:p::u ...·" and tht." k.u(.' of Inn;!!iun: Frtl..-r:al Ik~'T\'t' It.Ink of 1):111,1'; £n)IIOlllic Rt'l'iell'. M,m:h. I-I!. ,. Nathan S, Balke AssIstant Professor of Economics Soothem Methodist University VISIting Scholar Federal Reserve Bank 01Dallas Modeling Trends in Macroeconomic Time Series r:ldHilH):llly, bll"ln~ ....~-q'dc analyst ... and Jll:lO~)i:-IS h: I \ e.: d...'c( )111 1')( >sI::d macrOt.:n m( )mi .... lim . .· ,..e l'k ... , sud l :1,.. re.:al gro.,'" nation:ll prod uct (GNP). into (,ydic tl ;lIld trend ('oltlpo ne nls The.: cyclil':ll n)m rX)Ill'l\l captllfl.:d h.::mpora ry tlul1 ualic)I1s ;1:-.... o<:iall"<.1 with the b llsi ne,....... cycle, w hilc.: Ihc {rend C(II11J'lCme.:nl <k :-('rilx:d lell1g-[enn ","COll(lmi<: J.,:1l)wth Befort: [ill' !'>l..·!llln:11 p;lper of ~el..;()n and Plosscr (19H2>. Irend {'OIliI')()IK'nl:- wcre typic.llIy nJ(xklc.:d ;I .. :-1111pk' Iin"":11' lill1e.: tl'l'nll.. Simple l in~: l r time.: trend .. Illiply til;11 mosl of the \'Oblilil}' of tim\.: :-0.:0...•.. :-u<:h :... G\:1' i .. :t~'o(x'ia1l.."<.1 wnh fluctuation ... in thl' q'l"iiell <:ollll')(Hl ...'nt and not with flllctu::lIion ... in the.: x"(1.liar lfl.:nd \~.:bon .Uld 1'1n...-.cr h,,\~ ch:IIII'nJ.,:l'tl Ihi ... nm('I,.·p'lOIl of 11K' hu:-lIx· ..... cycle by :llf!uinJ.,: th:!t tfl.:n(b in m:Ul}' m,Kf<It.'l"Ollomi<: lin"l<: X'Ol':'>. .. Udl :1... n.-;ll G\1I', prin.~ .. , m01l1..1', :lnd in\(:re,.;t r:.ttl·:-. r.lndomly tluC·tll:tle over time 'I'll ...· )In...:-,hilit}' thaI tl'l'lld:- are r.lIldOIll . o r :-toCh:l .. tk, llI ;lY 1I:I\'l' IlIlporta nt im pliclI ion... for m;lnOl'l'OIlOmi{':- \Vhl..'lher I r~nds arc dctenninistil or ,.. \oc.'h:t:-I1t· h;I." inll,)()11:tnl implicllions for Ihe.: n:lllIl'l' o f tlllCtU:ltioll." in economic lillie se.:rie.::- a nd GI ll It'ad to <Illite.: di t'k-fl..'J\l <· h; II~KI l..' riza l ion:- of the.: hu:-in ..::-s cycle.: Fu rtlll..·nlloTe ..~ t och asli c ITem'" a re.: ml ld l tHIJr ...· <Ii llk ll h tel fo re.:CI ... t: COrlS\..'quem ly. thl' uncl..· rt ai nt )· a ...."<X'ialed with lo ng-teTm forcca:-b i:m udl ).:n.:al ..:r th:1fl thai for dl·t~rmini~l it· IT""nds [n tlli:-. ,lr1llk'. [ I'l'\'le.:\\· th~ dislinl·tion hl·twl,.'l:n dl·tennlll'''l1(· .ll1d .. t( ll"lu";lic tremb, I abo I'l'\ ie.:w :-Imll' of Ihl..' fl"<.l·n\ l·\i<k-no.~ l'OnceminX thl..· PI'l':-o.:Il('I..' 0 1 dl·tl..'llllini:-til: :lnd :-tocha-.tic trl..·ml...., In ;ldclttilll1 I~ I I'l'\ Il'\\ lflJ.,: the.: l·xi .. till~ litl..·r.llure.:. I nln.... ilk:r;t !lKllk·ll1f tn.·od in \\ hich jlht :1 fe\\ Impolunl l'\'l'llls (If .. hod, .. (k'll..·nnil"k' meN (If Ihl.' long-Il'nn \ol:!lihlY in l'(:onoillic (ll!;! \hxlds of tn.·nd ill \\ ludl thl'~ l' ;1ft' infn.-'(IUCnt pennaTlI.:nt :-h{ll·k .. nl:!} l';I I)tIIn.: 1l11(1u:t1ion'i III Ihl' 1I\;nd h,,:ttl'r T ....'(.'()J1()ill F.(.'O lIomio; R(.'\·icw - May 199 1 Ihan :-Iocha:-tic Irend,> in which :-h()I.'ks (XX'llr (;'\' (' '1' pe ri(xl: yet. they m:l}' provi(k' :t tn ler piCIUTC o f the unl·e.:11:tinty associate d wit h IOIlR-te.:rm ( )TCGls ting than do dete rm inistic trl:nd... Fi nall y. I l:xa tllin<:; n:al GNP :lnd GNP deflator <1:11:1 from IK69 to 1988 While Ih~ evidencc :-.t1~e.: ...,ts 111:11 :t dch:nnini... til' tre.:nd adL'(.!lI:lId~' char.lClerizes the he havior o f real GN P. I fi nd tbal Iht: GN P ddl;uor is better C.'h:lr:lCteriJ;I.."(1 :L" a Mocha ... tic lrend I\II"'t of the long-teml \'o!:tlliity III tht.· GNP dl:tlator. illm'e\'cr. Gill ht" Uc.""",·rilll"<.1 hy jll~ a ft:w impurtanl t:\'l'nl.s Deterministic a nd s tochastic trrnds [n this .'><.."CI;on, I highlight ....Ollle.: impon :mt diffe.:rcnn.·.. bctwt"Cn dt:t~mlini:-ti<: Irl'nd:- and :-I<X-ha:-lil' trend ... by con ... idering :-tOIlle.: sim ple e.:x:ll11plc:-. As a point of depanlln..'. (,'onsidcr the ff)l l()win~ 11l(xld: '" I', = r, + c:,. w he.:re r, is Ihe tre nd COlllfX )Ill'nt and c:, b tht: 1r.1I1sitory or cyd icaJ com poncnt. Lei the.: cycl ica l ('( lIn polle.:llt. (.~, he a ml':t ll-Zc)'(). s t;llion:u)' 1~l!ldo m varia h ie ( In gl:lllT.l1. the tre.:nd and (,'ydictl componl'nls can IX' correl:ttt:d 'I'll<..' most rotllmo n l~' lls\"'d dl'te.: nni nbtic tro.: nds ,In.' polynomiat.. in time Con.. i(ic.-r Ihl' ... impic /'MSh IOlhanJ,. Thomas B fornoy. JoIrIK HJt. and EvanF KOMIg fot fIfIIpIt6 COI'1J'I1eflI$ The ~ond'lt(Jt'IlII mean V/Jf.ant:e. and auIOCOVo!II<aneeS 01 a stallOl'lMJ' random ~lf(tiWIfJ aI' consrant t:7IIef Itme " Figure 1 Figure 2 Example of Stochastic and Deterministic Trends in a Time Series Cumulative Impulse Responses for Stochastic and Deterministic Trends '" " - " .. " r . ..,; ~, --:....•. ... , ~ .. ,. , " - ' +--r--~~~--~~~~~~ ~ ~ ~ ~ I~ I~ I~ I~ __ ~ ~ r, =r +111 . 11K' (:h:m).:1.: m In.:nd (r, - r, ,) , .. 1.:qu;11 to :1 ('on't:ln( (11) . II (1Illl' 'i.:ril·' I ~ nll1laln.., .1 lil·ll'rlllini'I!!.; Irl.:nd. IIK'n thi, .....:m:.., can Ix: madl..· :-t.lIlonar), hy dl.:tn.:ndm),! wllh :1 Iml'M timl' Irl.:nd A ,to(:h:l..,tll· tn.:nd (,;.IIl Ix: dl·",,·nlx.'d hy the l'tllUllllO r, =I1+r +E I ;\) \\ hl·]'l..· E, i, a llle:1I1-I.I.:I'O ..... l:lIiona ry r:mdom \,;rriahk . I krl·. Ihl' dla n).:l· 01' ~r(J\\ til in thl.: Irl.: nd flunu:t tl's around a (;on:-I;l11I 1lI1.::1n \'\' 1.: can fl.:wrilt: tlte lrt:nd (;0111ponl'nl a:- r,= r,, + JI I+ :t E,. ."' Ih.:n.:. the l1\:n<l C01l1polll.: nl dqx:nd ... nOI only on the ;I\·t:ra).!e gr()\\ lit r: lI e ( JI) lmt :11'0() ()1\ all p:l~t , ·:lllIl..·.., of E" T lms. shoc: k:- 111 till' tn'nd ('ompont:nt :Irl' lX.'nnalll·1l\ Oll l' 01 tl1l' .. impk· ... t l":l1npk's of a ,. rhal,s Ichooset1lepai_s$O/fIar lrommesameltlJl.a/ moc1els y.ek:I the same 1orf!C4$1 pro/de p(/dII Ihc . +-~~~~-r~~~~~~--2 3 ~ I • 7 • p""", • 10 II 12 13 I. 11 :-toch.I"II\· tfend 1" :1 r:tndont \\.llk (\\illt dnft if J1 dOl.:" not l'(lll;11 OJ In thl:- GI:-t:. E , I'" -.erially linn Irfl.:I;lll'tl To pro\ Ilk Ihl' realkr \\ itb 'o(11l1l' Ide;1 of \\ h.11 Ihl' ;llIl·...,.1I il l' ImKkl .. of trl'nd llIiJ.thl look Iikl..·. ri":ll1'l' I tll"'p].I) .. ""11U I.lll'(l p;lIh .. fOf thl' t1'l'ntl t'(mlrMlIll..·nl for Ix~h "1<1(' ha"lL~ :lOd dl'll..·rmini .. til· Ir..:nd mudd ... TIll' "III( h,I~I1\' trend I" :1 r:mdu1ll wall.: \\llh tlnti . :md the P:1r:lllll..·tn:- 1l">l,."(1 in till' .. imublion ;ll"l' dlo'ot..'n 'o() that. tn !Ill' :1b.'I..·I1\·e of .my .. hoc k .... hOlh llIodeb imply !Ill' :-a1111' Ifl'nt! hill' ! Tltl' pre.w nn.· of :-b(K· k.~ tor thl' :-IIK·h,l..,tic Irend . hl)\\l·\\· ... !e.ld .. (1):\ Ifl'nd O I1l1p01ll..'t11 thaI IIM)k.., "1..'1) dlflerl'lll from the delenn inbm Ir..:n<l In PI~Kl i('e. it I'" nOI :tlw:ly:IlllI illll .. r"()llll'x:t 1l1 ining:1 pilI! III' I Ill' lbla \\ he thl..·r a .- .erie' ha:-:I ~Ioc h :t ..l it· 01':1 dell..·rt11ini:-tk Ire nd IX.'I.::lll -.e thl' prl'''l'nn' til' Iht.: l"ydil':llcompoIll'nl Gi ll (111.'oI.·url· Ille trend nllllj>(tnl..·nt. St:tll ..lk'al tl..'l"lllllqlll.·' h.lll·l'1l·ell l]e\eIIIIWd tIl 11)' III dbl in,,:uI..,1 1 1'Il'I\\l'l..'n ... IIKila .., ic :Ind ddenllL11i..,li(· trl..·nd ... r di""·u .... ~lIllll' III' Ihe~l: technique.., l)elo" . !'>t( X· h.I"l l ~· .llld dl·ll·rmllll .. tl( Irend:- imply I l'1) dill'l·fl.·1l1 IOIl).:. run n..·'fM)\l">l,.·' 10 :-htx·k .. III linll' 'l'ne'" Shf K k:- 10 :, liml' "l·rie... Ih.1I ha~ .1 "lo dl.I ..lll trl.·nu .trl'. in p;ln . l>cnnanl..·nl: Ihl'~ dl:I1lj.tl.· Iltl' Irl·nd. or 100lj.t·rull k·\d . of 11K' limt.: "l·ril.·, lX'ml;\nentl~ '11Il' tlitkl\.·!ll·e in IlC .... bll..·nn· Gill Ix: dr:l111.I1I \ Fi).:u1'l· llr:lt"e.., Ihl.· n,· .. pon ....: (If:\ IIllK' "Cril· .... I;. 111.1 :-hIK'" (thl' l·umu!.1ll1l· impube Ft'tlc:ral Kl'SC n -c H:lnk of D:lllas ro.::srxm~ function) for;1 GI:.I:.' in which.\', h;l!'> :1 !'>impll' detennini:.tic In.'nd lllodel and for a C:ISL' in \\hich .r, is:1 r.mdolll -w:l lk (willl drifl) :o;t(x'h:!slic Tfend • O"I.;r lime. tlw fI,·:.pon."i(.· of)" to:l :.hock for Illl' d(.'\l·rmini:.llc In.'nd e\'entually appruadl e. . . Ihl..' origin:!1 trl'nd lim' For the :.toch;lslit' m,'nd C'.I.:-.t:. Ihere is no It.:n<kncy for )" 10 f(.'lurn 10 its originallrt..'nd Iml' Thus. :.h(l<:ks 10)" :lre JX'ffil:lnl'nt for the :'((l('ha!'>lic Ifend Implications for business-cycle analysis and forecasting De1L'nninin~ if Irends afe delerministic or !'>1{l('hastic Illay I}\.: irnpo!1ant for se\·er.11 re:1 .. .011s Firs!, wl1\.:II1\.'1' sho(:k." to:1 time ser ie:> an:: Pl'fsj:.. lent may h:IVl' implicalions for dt.:termining I hl' nature and .. .()llfn:... I)f hllsines.... -c.:ycle nllt'lllatilllls. St:cond. tht: 1I1Kl·rt:lint~' a:'MX'iated wil h lon1-\-1L~nn foreca"ting of a tinK' s<:ri<: . . . IS \'t:f)' differenl for ;1 dt:lermini:-.tic Ifl'nd :lIld for ;1 "Ioch:l:.tic trend Third. Iht: ahility of (.'()m 'l·ntion:11 eamoIllCl r i(' rllethods to make :.1:lIislil<tl inferenc.:cs ;thoUI IXIr.llllett:r:- in a rt:gre:,sion model- thaI is. \0 k ·:.t IlYIXlthc:->L':' ahout fI:grl·"'''illll cocfficiems--<.Iiff(;'r:Mlh:.tanti;tll) dqx:nding on whdlwr o r not a :.locha:.l1<" tn:nd i:. prL·:-.cnl l ien: . I will fex:us on Ihe implk;uinn . . of .~ I Ix:h:l.. . tk :Inti dClerminil'oll(' lrem!:. for hu~ine:-""-<,·yd,.' :ma l),:;;:; and fon"(';t~l i ng Ullcer1 ainlY· ' Ont: implic:.llion of thl' pcr..i:'lellcc unplit"d hy :1 sloch:l:-;Iic tn.:nd io; til:11 IIIL' tr.l(lilional appro;'K h (thm is. Ihe :l ppro:\ch Ixofore Ndson nnd I'los..~l:f 19H2) of descrihing bu:.inc:.." (.)'ck:. as nll(.1ll:ll ion... around :\ dct<:nnini. . l ic 11'L'nd i:-; no longer :Ipp ropriale. Tht: preserK<: of a .~toc.:ha:-;tic Iff.:nd il11]1lic." thai nuctllation~ in ;c liml' SI..'ri..:... art: till' rc;:.ult of .~ hoc k." nOI only In Iht! tr:lIlsitor), or cyd ical cOllllxlIll'nl h ut aiM) to thl.' trl'nd t'(Jlnpollent. Inck,,-'(I. the d(;'gn.·e of Ix:rsi..,tenc.'l' and till' relali\'(;' ,'oblility of Ih...' lrend lX)1llp<IIlt:nl Illa)' h:l\'l' impliC:llinns for expl:tn:ui()Jlo; of IllIlpUI nlll,..111:llions For t:xamplc. in Iht: tr:ldlllon:11 lllon...1:lri.... t or cven n...·o-Kcynl·:.i:ln 1II:ll"I1M.:ollll lmic Illodel. :lggrt:g;lto: suppl}' detl·n11ine:. 11K' long-nm level of output .. AggTej.\:l1c tk'm:md (:md , thel'l.:fort', mon...·tafy poliq) doc::. not :llk't.11he long-nlO Ie\'c! of output If nUdliations in G~ P ;Irt.' p rim:lril}' penn;lIl(;'nt, tlten supply-.,idt: ... ill X"k...,. :.lId, a:. :.hocks to Il.-"dmology :lIld boor !<upply, arL' impo rt:11lI for t:xphining thl-'SC F.conom;c RC\'iew - ~by 1991 nlKl liations Aggrcw"e delll:lnd nUCIlIations, whidl would ty piC:llI}' indlldl' tile eO'('(,1:-; of monetary IXllic)', Ill:l}' nOI: b...' as imp<)llanl in exp laining OUlput nuctU:llion ... as \Va:. om,'e thought if much of th(;' :-;hOI1-lcnn vul:ll:iHly is dll<:" to nllctu:ttions in the stochastic trend ~ Anotht!r impl ical ion of a . . t(lCh:lstic lrend is Illat the degrt!e of uncl'naint)' a.·••·.ociatCd with lonA-lenn for(;,GI:.ling is very different from that of a deh.:nllinistic trend Figure 3 p lol:> Ihe fOr<:.-"Glst :iIld the 9;-perccnt fOfl·C .."t txmfidt:nce interval.... for timc-scri(;'S 1l1(Klds w ith;l S\(K'h:l:.fic trend :me! ;I dt:ICnllinistic tr(;'nd Thl' ldt pand shows Ihe opl il1l:11 fonx: 11>1 wh!:n ,l', (,(lIltains a dctennin islic trend : lite right pand shows 111L' 0plim:11 fOflX:I:.t w hen .l ~ conlains a sl(K'ha.. .l il· Irend. For bolh sels of forl·clst ~. the forec lster is assu med 10 know the IXlr.lIll<:tCrs of Ihe Ill<xlt.:l. Figun: 3 .:;h"ws that w h ile till:: confidence illlerv;!1 for Ih(;' del t:n11i ni~l: ic.· trend rc:lChes :t tl\;lxim llm intcf\'al ( in Ihi:. (;'X:UllP](;', fairly quickly>. ~ An example 01 a dellVTlllltlSbC trend serieS IS a SIfI1DIe ftrS/· Ofder 8Ul'OICgfesslOfl 0I1hc form y... a+/JI.8y" I Il" .mere 0 < ,,< I This can 00 fowrltlen 115 Y, - a '+JlI+ 2: $8... wherca' _ at'(f clllcompOtlllilt -"J -(Mlrt -"r and jJ - /JIp 's g'ven oy r ..,{, e {,) Tlfecycl,· FOf FigCJfCS 21100 3. I set " cqCJalto 0 8 , See Sloek and Wit/SOIl (1988) IOf II nOt!/cchmcal d,seUSSIOfl of the impIICII/K)(IS of stOChastIC t,ends fOf econometrl(; prac/!CII For II formal eXllmmstl()fl 01 the Suns. SlocJc. and WatSOll (Hl90) impIlCst,onS see • Most IfIlermed,alc macfoecotlOrllfC IlIxtbool<S such as Gordon (1990) 8nd DomCUSch and Fischer (1990) conraO'l models w,th these ch8IIJClcr,st>es • Nelson and PIosser (l982) Oftginally wggesred thIS lfI/e" prefal!Of! B/at>chard and Oush (1989) have used Ihrs conccpllC tdcnltly agg'egate SCJppty shocks If! a rnJ/INSf, /atll con/ext HoweYeO'. Campbell and ManI<lW (1987) and West (/988) have fXJIfIled 00/ thar. If!Ihc context 01 other models. li1e petSl!;lence 0'1 feal GNP COtJId also CO'I1E! from aggregate demand shocks " Figure 3 Forecasts and Confidence Intervals A. Determu"I!Sl1C Trend ".., .., B StochastIC Trend " ., " . .. " , " , Ihl.· tunfidl.·ncl.· 1Il1l.·r.al for Iho.: ,Itx:h:t . . tic tn:nd cOlllinually intTl.·:ho.:, :h thl.· fo rl."t";.I. . t hori/on innea.-.c:-. In I.ICt. th ...· \,;tr;ann' ;t . . ~l)dat ...·d w;lh till" 0pullla! fOI"l....c.t.. . ( of a :-.tOl.h:hIIC tro.:nd inlTl..·.hl..·~ I;no.:arly \\'llh Ih ...· liml.·lliJrl/'lm and 1ll1J\l.·~ I()\\:lrd infi n il }' a:- Ihl.· tlmt· !lo ri /.on Io..·n~tho.:rh. ·1111... hell:1\ ior ,lIM...·.' I.' thai l.·\'l.·11 w hen tlK' forl.·ct"Il·" h:h pt:rfL'cI II1fO(lll:l1ion :Ihout Iht' n:ll l lr...· of thl.· I;rno.:-.......:r; ...·. . Illodd. \ ' 0.:1)' hm).:-IL·rlll forl.."t~b l in).: flf :1 v;lriahlc wnll a . . tc)(.·lla . . tit· trt'nd I .... I r:HI).!hl \\ ;th ha%;1I'(1 .•.....•. .. '......_----_.-• . (';) De.;pitl.· :1 l:I1W': 1'...·., ...·:1 1'.. 11 (.:fforl d ...·\·otnl 10 thl.· .... X:l1l1l!l:lIion of lr ...·n(b and :-Ollll' ...·:HI}' ...·v i - 111\,.':111 • r, = a + "flr+ 'L '')' I, . " ,,11\,.'1"\,.· (', i:-:I !':Indl)Jll ...·r'!'CU'. :tntl SIOChaS/JC Ilene SIC saIO 10 nave IWOIJf'II 'OOIS ()1 +(' " ,11IX'k. IIl:11 Ila.. . J'....·nl i ~ .,000ri:lIl), lIll\,.'WTcl:lll'd Till' dl'l ...· rlllini.~lic :lI1d :-h)(.·li:I.,lic If...·mb m ;IY nlllt ...·xt 111'1111 . . /I r CO'lloUlS a UI'lIlIOOl II r J r , IIIen r has a $IQCIlilS/'C " erw:I Modcis '" w/'wcn /he "'"OW", Of change IISeif nas a -- d t:nl'(: ~ UPI)(lnlnJ.t . . 11 K'11:I.'tlt' Irend ~. til ...· ...·\'KIt·nc.... in 1.I\·or of :-1IK'ha .... \II,: tn:mb i . . im·omlu,iq.: In 'hi... .'>l.·CI; OIl. I hnt:tly rl'\;l.·\\ Ihl.· two (.'(lllllllonly 1I'>l.'(1 ;lpprc ladK· .... tIl d ...·t ...·(,:IIIl).! \\h ...·"I. . r: l ....11X'11;1 ....li"· tr...·nd ;. . pl\::-...·nl.;'" " ...·11 :1.' '>IHII .... o r 11K' \.'\·id .... rK .... ro r O f ;t).!;lin't 111l' .... tIX: h"'.lil· tr...·nd 1111\\ h;l\ ...· f(.· ......-;II"l.·h ...·,.... tr i ...·d II) d blinJ.,lubll ho.:l" ...,.:n a .. .Iol.'ha:-II(,' tr...'nd and :t lk'I...·rlllini . . l it' trt'ml- '1\\\1 appro.ldlo.:, h:I\l.' lI'll:llIy Ill.."l'n lI.-.cd Oltl·n ....·1.'01l01ll;....1 .. t k "l.·rilll..·IIIII ...• .'oCr; .... ~ \\llh .IUII)(cWl':-M\ ...• 1111)(.11,.'], (lllllc (Ilnll Tescing fo r s toch astic trends: che c urrent s ta te o f de bate Note lnal r can De uumtten as ____ - 2~~ 1)1,: d\.'scrihct! within Ill\..' mlx!...·l . lfl~ :'" r.! i . . !l's, than 1.IIK·n .1; l'otll:!in~ :1 dl.:ll.:rlllllli.. . lil· tr...·nd plu, :t ....1:llion:Il1' II: Uhittll), l'OIllI')(I1l ...·nl In t h; .... Cl.. . l'. :t .... lIlx: k 10.1 ; \\ i ll l·\o.:n ll1,t Jl~ di...• IIUI. :md.l; \\111 r...·!lI nl to it., o l;,l.:in:1I Irm ...· tr...·nd If r.1 nlll<!l . . I (and {J ...'<Iual . . 01. Ih""n I; contalll, :t lillit (oot. :l11d lIa . . :1 .. . lllf.ha:-l il tr.... nd Ir:" '1II1ll;t r to l.·qu:llion .t:", \\ ....II:h:1 ,t:llion.H) 1r:I!l .. i[III: {"(11lI1)(HK'l1t' IIt·rt·. ,I ,Ix)(:!.. II) .1; \\111 h.l\·l':1 lX;nll:m...·nt. dl ...."t1 11m.' . on .... \\;lY III (k:t ...·l1Il1n .... \\ 11\,.·lh...·r :1 NIX·h.lo,[ i... Irt'nd i . . pn.: ....... nl I~ III Il.·'" . . 1 :llio,[i(~llIr \\ IK·lh...·r.1 tlllli IHIII l·xi ..I ..... \h:1I i..... tl."" i( Ir:_. r.: ..."tlll:lb I III "''''III.II;lIn I ·111.... Did,.... y-Fulk-r 1",'''1 CFu lkr 19'7(,) :tnt! Ih...· I'hill ip:--Po.:lTl ln 1\..·....1 Fl'dcr :lt Rcscn 'c 8:lnk o f Da tla~ (PllIlIip-' :md Pl'rron 19HX1 :Ire two of tIl\.' mo~1 commollly u ......'(IIL·'h to dl..·II..'t.1 Ihe pR'X'nn: of a unit rool.~ AnotlH:r nH:lhod of evalu:lling the prCM:'IlCl' of:1 :-.todla,lll· Irl..·nd i, In dclcnninl..· the dq.':R"C of )'X'r;i:-.tenl·l..· III IhL' lbt:1 ~lea'l1n·:; of I,,:r:-.i'h:ncl· l":.lIl IX' ohl.linl.."ll h) l·,lilll.lling:1 liox- Jl·nkin:-. (J9;(») Alni\IA modd and thcn tf':lcin!l,thc dfL"l'1 of :I !'Iux:k on Ihe k,d of Ihe \,;u;ahk·. :-.imilar 10 whal W:h dOlll' in I'iKlIrl..· 1 By dle'lenmning Ihe lonjot-rull rl..·'I}(Jrll'ol..· 01':1 tinK' :-.erie!'> 10 a !'>hock «hI..' l·l1rllU!alh ..: imilltl'e fl"'I')(Jrhe funclion). 1m...• Gill ohtain an ...·,tilll:lte of t lK' dewee of per:-.htenn', I\n ;tl!l'mati'l' ll1ea'llfl..· of persi,tencl..· is the "arrarlCl' l~rti() P("OI}(ISl'd hy Ox:hrane (19M). Tlli., "arrant'l' l~l1i() i, ]..(i'·l·!l by If.l; ha, a ddl'11l1inhlil' tr",nd. \ ~ appruache., O. :r~ I.. appnJ:ldll.."' 00 One :ld":1tllagt: of tht: v:lri:lIlu.! r.llio Illea:-.un..' i, Ih.u it dOl.::-' no( R"(luirc the ..."':'>llIu:llion of a :-.p<..'(.·ifk p:u: IIII...·uk 1llolkl For the r.lfK.lom-walk :-.lo(:h:I.-.tit· In:nd u'I.:d 10 Fi~lIrc:-. I and 2. !""It the UIIllU];lli' ...· IIllpul....c I\.·,pon~ fur"l<..1ion :lnd Ihl..· COdlr:tnl..· \;lri:lIln' r.ltJO (:L, k:lppro:IChl~ - I imply pe"'i~",·m\.· 1ll1..':1.'1I1\..... I..'(IU:II to I Ix'l';Ill ......· 01 IIIl' imphl'ation, a~sociall..·d with a ~t(x:h:l~til' ITI,.·nd. ;1 l:tf1.(e amounl of reM!:lrdl h:I"; heen l·onUll~·tL'(llo 1.'\ ;IIII;II~ whether dL'll'fm inistil' Of :-.Iodl:htil' !fL'nlh ;Il\" pre:-.enl in ma("r(x.'conolllic dal:1 Fol' th~ mo~t p:111 . the cvidencc b m ixed Nd!'>llll ;Ind 1·lo.,:-. ...·f (1~2). thing annual <lal:1. found th:1I m l111L·rOlI:-. 11l:Il'rOl.'l·ono111il' time ......... ril.·~. indudil1l-l rl.·:Il GNP, the GN P pricc ddlalOf. till..' 111ont:)' ~t\x· k. and inlcre~1 1~111e'~. showed evidcno.: of a ., tot:h:!:-.t iL· tn:nd :-.dlwcrt (19H7l. tL~in~ postWorld \X'af I I qllal1erlr dal a. a1.'>() fou nd widt.:" pn.::ld I..·,idl·rll..'l· of ullil root, or a :-.1(x:ha'l ic trend Ot l1l·r:-. h:IH: .11I1..·lllptt.'d 10 dctermine Iht: dq.:ree of pc.:f.,i,tence in m:K'rol.'Conomic <1:11:1. CamplX'U and i\ 1:u,ki\\ (11)1-17). using c";lim:lle:-. of Ihe CU1l1u!:tIl\ ...• irnpul ...... re"'fXlIl ...e function. found "llh'l antial 1X'r;i,'It:nl'e in po"" ....ar qllarterl)' n.::I! GNP C:.ullplll..'l1 and ~l.lnki\\ (1989), Komlcndi and I\ kqllin.: ( 11)901. and Cogley (990) h:n'c found e\idt:IK...• of ",uKh:I:-.II{' In.:nd~ and :-.uh:-.I~ln tial rcr.btelll.:l· in re:11 GNP for many counlri"". In :I !I11llthariate l·Olll ...·"!. King. PI(j~'it:r. SI(x:k. :Lnd \X'al:-.on (1l)H;). :-.II;IPlfO :md W:1L"'Dn 09BtH. :md &:O llomlc Review _ May t99t B1:tndlard and Quah (1<)H9) havc .lIlriblll ...'l! a :-.ub~t.tnti;ll alllount o f thc volalilit}' in rcal GNP to fM..'nn:lnenl Ouclu:uion:. .... R<"'Ccnlly, hUWC\'l:f. othef author:. lta"C quc,lion..."<.Ithe !'trengl h of thc c\"idenn: in fa\'or of :-.todl:l-.tic tn:nd~. COl.'hr:tne (11)HH) found Ihat thc degn..'t:: of per.i!'tenl.'e in •.IImual U.S. ft.'":ll GNP <I:U:I from IH69 to 19S6 w:., ~lIh:-'lantjally lower Ih:1I1 wa!> ,uAA",sted hy Ihe 'tudic' of C;lInphd l :lnd Mankiw (19!i7) ll,in~ jlo:-.I- World War 1\ qll:1I1 ...·rly data . Dl: I..on~ ;md SlIlllm...·rs (19M) :llso ha\'e found tha t \!vid ...·Ill'I..· of;l S(o(':h:l:-.tic Ifend in ("L'a! GNP i., :-.ul~t:lnli:.I1) wcaker for :mnual dal a than fo r qU:1l1el"ly data. Wa tson ( 19H6) :md Clark (19H7). usi ng ahcmatiH' Irl'nd-cydl' dn'omposilions. found ~l1h~l ant i :tlly lc:-.s I"x.'r:-.i.'itcnce i n qu:t11erly GNP than d id C:m1phdl :md ~lankiw. St.·v",r:.1authcJr..-Citri....tiam J and Eidlenbauln (1m) :md Itudehw-.<:h U9'XH·-h:tw :tl"}lul.'t.lth:tt it is nl..·arly illlpos..... ib1e \\ ith a finile amount of data 10 di!'>tinguish hetwccn :I !'>\(X'ha,lic In.:nd model and a delennini:.li<; trend ITKx.lcd Ihal indudes :1 cycliC:l1 l'Illnponen{ Ih:1I i, "l'1")' rc"'I!>lenl (or I£ ~_, >;1 dose to I). '111l' ''l' :lulhor; :IT}lue tl1:11 Illany "",n",s that '\erle' initi.tlly idenlilk"<.l;l:-. having:1 :-.\(x:h:l ~t ic tfend l'ould he 1ll()(.lek"<.l "'"llu:LlI} wdl with a d ...·tt:rnlini.,lic lrend Shifting (rends, segmented trends, and infrequent permanent s h ocks Rathef lhan add :lIlothef voice 10 Ihe GIl"Ophony :L:-."ociatcd wilh thc llnit nlol :.nd persistence deh:ne rcvil'wl.'(l al)(l\'c, in thi~ :-.ecl ion I l"(m,idef an :Ihern:.li\·...· (..'o nception o f trc nd. in 1~ a-fl"jl~ • L4 I, It P IS negalIv8 6f1C'1U¢1-1Tla1 IS. below a \1f"O'l CnllCa! value /tIeII _ ,-,ccllfle Ufltt ,oot hypothesis TOOre IS S ,~fIVOIwt{J bierS/Uta 00 fCSlno fot ~I tOOlS WIth PhiIIIp$ Pr!mJtI I~Sl. !he U$I..IIII alfcmal,ya 10 /tie the Dtckey- Fv/Ier lest a mt.t/INatoSlC comC!(/. two 01 mere vanabIes $lJ9/a aGIOI'I"I'7lIOtI SlochaSbC " end v_ores thaI sharea CCIrM10rl SIOCIlaSllC 1T."a WIll also be COIIlIegraled " IS ~ /hal. a"t " Figure 4 Example 01 Shifting and Segmented Trends in a Time Series '" ,., - ~-_/ . '" " M " M 100 ~ 'M 1~ ~ 1~ ~ PerIOd which rcl.lt1\'ely infrcquenlly ()l't:urring economi(: evenL.. or ... hock ... h:lvc important cITl.'t.1.... on Iht: lonWnm hch:lvior of ('"<.'OIlomit' lime ,'>Crit:s, In Ihis case, pcnn:tnent ... hock., on,:ur infrt..-quenlly, hUI when Ihey do occur, they a~ Iypic.:ally largt:, A model of Irl'nd in which pcnnanl'nt :.hocks occur infn..-qllendy has many of the sallle ProlX'rtics :IS tilt.' :-.I:tnd:lru stoch:c.lic lrend ill<KleI dl...·...crilx..'"(\ above: II'K: prt........:rl<:c of a unil root . a rdativdy high mc;lsllre of persi.'\lencc. and a fon..'(:a:-.l V'.lri:tnce that grows linc:lrly wilh limt: '11is m:nd, howt:Vcr, will look like a detenninistic trend that occasionally :.hifts or ('han~l'" slope 'l1,is infrl..'Guent shocks SI(K'h;l:.lk [rend Illay rdk'(.1 [he trend heh:lvior of L'(:onomic lime series, :In<l i[ 1ll:IY (,:af>lure the inlrinsk uncel1:linty PI\,'S('n\ with long-teml foret.";lstir'H better Ih;lI\ either [he simple stochastic tre nd model. in w hich permanent "hod<,.. occur every period, or the detenninistit' trend model. in which the line:lr time trend mayor m:ly not change. Rl.'(·ently, Rappoport and Reichlin (l9B9) and Perron (1989) have :lrglll.."'lh;1I till' l'...idence in • Mucnoi/lltl~"/hlsS«/lO!'IlSdtawrtfrom8aJkeand Fomby (1990) rn.s 1$ flUe .s ilrlO COfI"¥)Clt)(If' IS 4$ IIIfI ~ 01 the pennanen1 Ihe same lot /he two /IlOd(!4$ fa\'or of a Mocha ... tic Ill.'nd i .. over..latcd. In particul:ir, [hey :uguc th:lt :>crk-s ::ouc h :I:. I"C:II GNP :til.' more accur.udy deM:ril'k..'d hy delerministic trend ... thm ocGI ... ion:llly ,hift or change slores. Fi}tuT'l..· 4 prescnt... two example, of c hanging linear time tren<.b : shiftin~ lrend:., in which there are Oll,";I:.ion:11 jumps or chan~cs in the level , and S(;gmcntt."<i trend .... in \\ hkh there are occ:.lsional dl:mgc:. in the s lore of:1 linear timt: trend. In a T'I..--ccnt paper, Tom Fomby and I argue that :.hiflinlo: and M'gmenll.'"d trends, such as thoSt: reprcM!nted in Figure 4, arc entirely cunsiMent with Ihe notion of ,... H)(,'h:I.~lk trends. lU Ollr appro:lch is to COllliider pt.'l'In:lIlent shocks ali (x'curring infr(.'(llrent ly, blrt the time Oil whkh Ihey ()('('ur is ra ndom :md lI npred ictabk: ThllS, trend components would he given hy :1 model si milar to l'quation j excepl lhatlhe shocks (e-, ) do not o(xur eVery reri(xl hllt only oCC'".lsionally and the time al whidl they ocnrr i... random. 'I""~ Appt:ndix hrit:ny descrihes how these shocks or brC-Jks in ITeml might he identified. \'(' hen penn:lnent :.hock .. occur infn:.'GlIcnlly, Ihe (I,::.uiting model of trend i.. observationa lly l.-quivalenl--chat b , indistin~ui~hablc in a given !<O;lIllplt.' -to a line:lr lime trend thai ocGlsion:l lly shifts or change...... Iope.. Funhennore, model:-. in \\ hich infn:."qllent permanent shoc k.. occur have similar Slalbtic;ll propcnie" in large il.1mplc.... , to tht: :.toch;ll'ollc tn:nd nu){Ic!, dc.'>Cri~d in the previolls sc.."'Ction. Thus, ARlr\lA model (;.'stim:Llt:s, Dickey- Fuller leMS. and the mC;lslIres of pcr..istem:e dcscrilx.."'"(1 ahove )'idd Ihe ~:lIn(! re:.uhs for Ihe GIS(' in which there :tre large infrequt:nt permanent shocks, Slid, as the stochastic tre nd l1](){lcl... described in the previous section. II r.loreo\'er. the infrequent permanent shocks 1ll(){ld implies the same degree of llnc.:ertainty :Ibout flllure lon~·run v:llue ... a ... that implil.'(1 hy a sl(x'ha:.tic trend, Tilus, Ihe fOfCC':tst confidence inll'r"'al for :1 ~ hiftinH trend, such as the one depi(1ed in Fifture 4. i:. more like [hat of:l sto(:ha:.lic trend [han thai of:L detcnninistic trend. 11lt: re:t~m i!oo th:1I there h additional unct:rtaimy inhert:nl \\ ith infT'l..'<.Juent , r.lndomly occurrinR pennanell1 ...h(K'b Ih:11 I:' not present in [he dl,tenninbtic Irend ('a,'oC. TfC'Jting ~hiftinR or M.·Rmcntt."ti trend:. like thoM' in FiRUT(' 4 :h determini.sl1c trends :b:.umt::. that Ilojill1her ... hifts or hre:lk:. \\ ill occur, If Ihe trcnd line has chan}tl.-d in the pa!'it, it i!'i qll ite pO~ihk that the tn.'nd will in the flllU!'I..', Fo reC"..Lsts th:a t assume no addit ional brt':aks greatly understate the unc(:'rtainty a'isoci:a",'(1 with Ihc fO~C;ISlS, TIler<: may also be cl'<)flomic Rc"3sonS for con:-idering :-toch:lstic trends in which penn:lnent :-h(x:k:- o{,(:lIr infreqw..'ntly. 'Illere appc:ar to he many examples of rellllively infrl.-quent. hCICrogc1\(.-'O tlS r.mdmn l'''ents Ih:11 h;IVl' :I dramat ic imp:lci on e'conom ic time' scril..'s. For I.'x:llnplc, the' oil price sh(Kks of 1973 a nd 1979 may h:l\'c had an imponant effect o n lon~-nm l'l'onomic perform;IIKe; yet. Ih!.!.'I<:: events do not occur e"ery pcri(xl. Wars, with their los., of life' and their d!.!struction of capit:ll stock, ar!.! a nother exmnpl(:' of infreque'nt. randomly ol'(: lIrri n ~ events that can have imrort;mt effects o n m:u:roeconomic time series. Hebti\'cly infrt.·quent hut m:ljor change'S in po licy regimes. either fisc;d or monetary, may have imponant long-mn !.!ff!.!cts on economic pcrform:lnl'c. '111e founding of the FL"{lcf'J I Reserve SY:-Icm :Ind impon:mt changc, in monetary policy o~r.l t i ng pnX:L'(lurt.'-such as tho:-.t: in 1979 and ag:lin in 19H2-may be examples of IX>licy change:- th:11 h:I\'(' had a l"lCffil;lI\e'nt effect on nominal \·ari;lhlt'S. such :" pricc!'> ;mcl imerest r.lle!'>, if not on re:ll econmnic performance. I! Even tL--chnologil':ll chan~e Ill:!y he due to infn..-:qul'nt tedm()lo~ieal hreakthroughs The unit fOOl or stoc:h..... tie trend in real GNP has often been aHrihutc.."{IIO productivity :-.hock .. Technological hrl.·:l klhro ughs may ~:-ult in infrequent but impon:lOt l'ha ngcs ill prod ul'ti\'ity that overs hadow the smaller increlll!.!lltal c..:hanges in prod ucti"il)' Ihat one miAht as . . ()d~He with a linear ti1l\t: Ir~nd or a random-w:llk st(x:hastic trend. In :-.wn1l\'uy. I have s UAAest~d :10 alte rnative m<xld of tl\.'nd in w hich pennanent shocks OCl'llr infrt..'qtl~ntly . While Ihis model gener.:ltr..-"S !rend l'ompo nents th:1I look simii:tr In a shifting or :-.I.'!-!mc..'ntL"{1 dctennini:-.tic trend. Ihe model implil.'S dl.'grel.'S of pt:r:-.i.'>lcncc :md fOI\.'1..':1....t unct:naint)' char.1\.11.·ri:-lic of:t stoch:l!>til: trend. Funht:nnorc. there arc plau:-ihle cconomll' rLW.l'.(m" for con"iderin~ the po ....,ibility of infl\."'quent pcnnanent !>h(x:k'l c han~,,· ;1~;lin using annual data from 1869 to 1988, Fo r relll GKP. the evidence appears con.<;istenl with a detcrnlinistic trend ; ~vidence of;1 stochastic trend in Ihe annual rC:l 1 GNP d;lI:1 is relatively w/..'3k Indcc:.'(1, I show th:lt ;l detenninistlc trend model lIsing data from 1669 10 1929 would have provided :t reaSon:lhle foree-.J.st of the level of rC'al GNP in 19M. On Ih~ other hand , I :;trgue Ih:llihe GNP defl:llor is chll racte rized by a stochastic trend. but one in which only a few shock... ;Kcount for mOM of the long-tenn v:lri3bility of thc price level ·111e:-.l.' !'> hocks coincide with pcnn:lIlent c h an~e, in th!.! inflation r.ltl.' al Ihe end o f the nineteenth cent ury. in the latc 1960s, and in the early 1980s. The shocks also include three major pe rmanent l'hanges in the pril'e level associated wilb World W:l r I, Ihe Greal Depression, and World War II. Real GNP. Table 1 presenlS Dic key-Ful1c::r and Phillips-Perron t~sts for unit roots a nd lllea:-ures o f persistence for real GNP . Both unit root tesLS reject the lillil rOOl (Moch:lstic trend) hypothesis al the 10-percent confidence le\'el, a nd the Phillip~Pemm test reit'CIs :.1 the 5-pcrcent Ic:vcl While Ihe l'lunul:ativc impulse response fun<:tion from an ARlf-'lA( 2, 1.0) modd is 1,43, Ihe Co(:hr.me ~lfiancc ratio is 0.43. 'Ill is is subsl:lntially less pcr.;i!'>tenl'c than th:.t implil.'(l hy a r.lndom-w:llk stoch:t....tic trend, This r.llher w(..oak evidence in f:.vor of a stochastic trend is in line wit h the results of Cochrane (988) :lnd Delong :Ind Summers Cl9Hl{), who :1150 found little e\'idencc of .. stochastic trclld, lIsing annual data from 1869 until the 1980s Furthermo re, therc is little evidence of large. infrequent pemlanent shocks in the re;11 GNP ,~er i !.!s.l' Wh ile the Great Depression and World \'(fa r 11 h:I\'(' a dr.unalil.: impact on the rcal GNP series. they Glnnot Ix: classified unamhiguous]y as 5H ManIuw. M.ton_ and Willt (19871 lot 811 anaJy$l$ 01 /lie elf6CfS on ... ,erest rates 01 /lie Ioondrng 01 the Fedetal RaserveS)ts11lWll Case study: real GNP and the G~P deflator In thi!> :-.L'Ction, I rc....(:orl'id,,·r the' long-nm propenies of rt:al G~P :lnd the GNP denalor. Econ o m k: Rcvic .... _ .\I:t.y 199 1 " ThtI J\opl!'nch suggests lJIternallV8 malhods lot exarrwvng /1'te ptcscnce 01 shth, or changes in 'rend See Balke and FomIJy (1990) lor • d6ta<lBd BXaIl'WIaIJon 01 boUt file real GNP $CrlC$ and ft'Ie GNP dclta/Of S()f1eS " Ta~l Unit Root Tests and Measures of Persistence for Real GNP, 1869-1988 Urnt (001 fests Augmemed Dickey-fuiJer I stabStIC WIth lour lags -3,27 Ptullips-Perron I statistic WIth m • 4 Measures 01 persistence 57 Coch(ane variance (abo ( V. ' k. 30) CumulatIVe Impulse response lunction from ARIMA(2,1 ,0) model \.43 NOTE : Real GNP data were In Ioganlhms As~mpto\ic CflIK:a1 values IOf both r statistIcs are -3 . t2 at me to' percent SlQnlfi.cance level and -3.1 at the 5·peroent SiQnmeanoe level r,..:n11;II1\:n, ...hOlk... A Ghual ,:-,.unin,lIion of Fi~ut\: -; "UAA"-"'''' ,h,lIlhc.:-.c C\\:.'1l1'" did Ill)! ... uh:-,{,lnli:llly ,Iller Ilx ' IOIlj.t-nm lc\cI of OUlp\ll AI-.(" ,In allin, n:~u.""""'I\ e IIMKlcI wilh :1 dI..11.:nnml .... K tn:nd, 1I"1Il).: IUN <.ttl.1 for IH6l) to 1929, \\()LIld \ !l'kl ,I fOR't.-:'l'>( of ~Il G'\ I' in J9HH Ihat \\()tlkl 1)(1( I'll..' f:lf c,lf I ht' m;lfk C......--c Ftguf\.' -;). \\'Iuk·the k:H'1 ofG"\p in 1968 i... OUI"'KIc: IllI..·l)':;-pen:ent l..'o!1(ldt·lll'\: intl..'f'\:ll ullp!iLxl hy thi... (OI\.'(~I ...I. 1111'> (On..-'(,~I ..t il1lt'I'\'~ll i.. un<k'r.-.t.lltxl some\\ 1\:lt he(~llI"'" il dOl-':-t nCM (1 )lbilicr Ihe :1d<.1ilion'l l UlKl'll ;unlr a ... -.Ql'ialt'{l \\ Ilh l' .... im;ulnj,t Iht' p;I I~lml'II..'r.-. (If IIX' dt'lcrmin l:-.II~· II"I..'I\(I 0\ IT:.,11. Ihe \;,\'idt'I1l'I..' ." l....I11:-. In "ugge:-.I Ihat .1 dt'lt'nnin i ~tic I n..:nd ball ;Kk'qU:IIl' dl:ll':'lClt'ri/": lliorl o f 11\"rld for real GN f' . :llthOll,J.:h tlll.'I't: :tppe:u.... 10 I'll..' ." ll~h t ly m o n..: um:eltainlY ;t~:-.()c:ia'ed will ,ltlrlg-run f()l'I..-'(";I..,ls of Irend 111:111 wilh tl1I..· pure d l'll'rmini,Ii(' Ift'nd model GNP Deflator. T;lhlc 1. l)1'l·"l.'ll\... Oi('k('yFullcr Ie'''' ;In(l llle:l,urc ... o t Ill.:r... i ...I('IlCe for 11ll.' C:--;P dd lilor TI1I..' Dlch') - Fuller ...l.Ili'I;<.· dt';lrly Llib 10 rl'jcl1 ;1 lIlli t root in IIIl' pril'l..' Il'\d -111t' 1ll1..';"'1In.::-. of Ix-r"'i.-.Il.'Jll.'l,: lor I ht.' G .... " (k'n,ltor :.Ire Llrgl': ;n Ell'l, 111l') ,11"1..' '>\:\l·r:.11 time ... brger Ih.m ;.. implied bY;1 r:.lIldol11 \\';IIk. from lilt''>\: "\;III... lk·.. , :1 ,hock to thl' prill' !t-\'d wou ld G I U." " ,I Ix:n1l,II1I..'11I mCl'I..';I-'(" III 11K' pnl'e len:1 Ih:lI 1"'-'];IIi\dy I.., 111;.':trh Ihu.·I..' IUllt'.. the "'"l' 01 IllI..' o n gin:!l ... bo(:k TIul',lhl..' l'\K!t'nl't' Ihalille pnn' it-\I..'l l·onfain... a 26 Figure 5 Real GNP ..• • ", " • , 55 .. GNP SOU RCES OF PRlM ...RY o...r ... &till' and Go":!o" (1 989) U S Depar1menl of Comrnef08 Table 2 Unit Root Tests and Measures of Persistence for GNP Deflator, 1869-1988 UNt root tOSl$ Augmonted Olckey- Fuller I statistIC With four lags - 1.64 Phillips-Perron I statistIC With m . 4 - 1.68 Measures of perSIStellCe Cochrane vanance ratio (V. ' k . 30) 3 .76 Cumulative Impulse response lunclion Irom ARIMA(2.1.0) model 2.26 Measure of long-term variability Var(y,_, - Y,) f /(. /0; . 30 .0092 NOTE- GNP deflator dala were In logarithms ASymplObC crrtlCal va~ IOf bolll l SlaloShC5 are -3 12 al ille IOpercenl 5IOn, Iocance level and -3 41 al the S·parcenl lignrlrcance level .. tl )(. I\;I .. lil' I rl'n tl i .. \L'''~ ..11( 111).: Thl·l"\.' i .. L·\ldL·Il\'L'. hO\\L·\ L·" . ,IMlllI"' ;\ fL·\\ .. hod, .. \.·,pl.lIll 11\0..1 ot t h\.· lo n g run r,...'nlu n\,·!lI \ obtilit} .tnd pl·' ..... I .. IL·nn· in IhL' GK!' cJ .... n alor In p n.'\u lu ", \\01'1.. ( B:ri l.. L• .I n d Fomhy 1?9()). \\ .... IOllnd l h.1I "'IX hr....:I I.. ... in .1 li nea r tim \;' I rt.'nd L""pL" n IUO...1 of I lll· \ol. ltIli l~ in Ihl.' lo ng·run prin' k'n :1 Th t.:"C h re.l l.. ... L'On"""'llC lIld In llefll l.1I1l ·nl cll:lIl ).!l·:' in 11ll' m ll.llio n r~ H L' o r I)K' ).:lIIw l h r: II L' of pril't.::. ,I round 1;';9K. It)(ll-!. :r nd II)S:\ and 10 Ill; lj0 l' p..:nll,llll.'n! dlangL'" 111 IIll' p rK l' !c\ d :r." :'O(:i:I\L'd \\ II h \\ 'o ll d I . Illl' ( ;I'L"II I k prt' ...... U)!l .. Intl I h ...· :lftt.:I"I11.!th 01 \'.: 'u rld \\'.11" II To :r.........·:.:. I hl' 11 \\ 1'1< In;lI1Cl' I If Ih...." .... ... 1101.:1-; .. ji Il' ...·' p lall1in ).: 1110..' IOI\,!.: r'UI1 h.... I1:1\ 101" of Ih ...· (iNP dL·jl;I\(lr. \\ L' :'1I11ply Lk·ll"l ·tld 111l' d ;[l;[ \\ IIII :tPI)f( '1)1;,!tl' dummy \ .1rI:lh k ... h I C.lpHIl\.· 111l' d k'(.h of 11ll' ... hock ... T:.,hk· j PI"""L·!)!:. IIIL·......· n..' .. uh .. 'I1K' dun lill ~ \ ;rn. lhk~ D II)! - . J) I f) iI . .1Ilc.i 1)f 9-16 l':..plllr...· Ih...· p...'nlUnl·nl ... 1"HxJ, ... 111111\.' p nL'L' k·\ d L". rtbL.'(1 h~ \\ orld \\ " 'f 1. Ih l' Gn,.';" 1x,·prL· ...... ion .• lIld \\ orid W .lr II 'Olt' Ih:1t Illl: ......· dUlllrm \:IrI;lhll:" art' "'--<llIl\ ;rkl1l III:' ... hilt in .1 1i1lL":.r tlllll' I f"l..'nc.i T hl: dUTllm y uri.lhk.... 1)7'1,....'<)8. f) ·/I <)(-,.'{ and IJTl983 c.rpllll.... "·.11 Ihl· dk'(.h of;l rl\."fln,II1L·n l ...1)(1\:1.. 10 11lL' gnl\\"Ih roll ...· 0 1 pnn· ... 11"11..' ......· d lllll lll} \.rrlahk .... i1llpl ~ :r dl:lI1gL' in t he ...lop..- of til...' IIIIlL' In.·nd FrV1ll Ih j.., i nIL'f'\ L'nlio n 111(1<.11.'1, wc c:l n l 'o n ...lnKt thl' tfl·nc.i lOl11llCmL' nl l or thL' G:'\'P ddl.llo" Fij.{urL' () plOb till" (iN !' ddlilor a nd t hl.' lI11plil'd trend l 'OlllllC IIll'l1\ /I. .. tn' L~ 1n M'C fro m I'rgun.· (), this ..imp k· 1lll x ld o f tr... nd a p p ...:.rr.-. to l':.tpl ur... th ... lo n ).!-.."n Ix.'h:lvio r o f p ric ...... rc:ro;( lI1:Ihly wdl O n cL' \\l· :'l("l'o\l l1l for t h ...· "'IX :.h{x:k..... rllt ll"h of th l.' pL·f:.",ll·IKl: :md :1 111\0....1 all o f Ih l' 10ng -ll l11 \ :rrr:lh ihl ) III 11ll' (; "J I' ddbto r dis:I Pf)!,.':.lr 'I':lh k· 5 nml: lir,.., lllL·:r .. UI"l..'.... of pl: r... i:.IL'IlC... and :1 lIll'a"un..: of Ihl' lo.,g·t ...-rlll \ ':Iri:lhi lity of lilt.: G'\" P dvl1alor. onc t' Iht.: :.i.-': h l..... : tI,~ h:'I\ L' hL't.:rl :rccollnll:d for Com p:lfing Ill .... :.Ltll .. lil'.. i n T:lh ic j wil h Il1oso.: in T :lh k 2. \\ 0.: :.0.: .... Ih:lI L·:.:tr:.I ...·l ll1g Ih .... :..... hr....:r k .. I"L'(lu L·...·" 11lL' \ 'ari; IlKL' r:llio 1llL':I ... u rl · o f pt:rshl .... l1CL' of Ih ...· (';'1J' d d l:lIo r :lIUI IIIl' IOI1).:-nlll va ri:!b ll iIY. :1'" Il K·: I:.lI .....'d hy \ ;r"( 1 ~.Jo - .I ~ )' k . h r ll1o ro.: Ih:l n 95 \"ealso IaundcVtCJellce 01 a Ofe<Jk", t/l6 pflce level III 1878 andabt&N<lIltne v""1/>f,,relll 19J,f bul lt>eseshtXl<s llle nor ,...,.".ry oIlS tmpOtfalll QUarlMa'~ as thB O/f"Ier shod<s ICJefIfJf-ed here 17 Table 3 A Shlftlng-Segmented Trend Model for the GNP Deflator A. EstilT'lllted Trend fOt" Deflator P, • 2.292 (.018) .0151 + (.001) _033 DT/898 ... .052 DT/968 - .032 DT/983 (.008 ) (.002) (002) ... .407 DI946. 1.026) ... .320 DI917 (. 025) Fit • .996; standard error 01 estimate • .0514; Dulbn-Watson . 1.03. (Figures In parentheses are slandard erTO(s.) Oennhlons 01 dummy variables DT/898 • , - 1897 lor t ~ 1898: 0 otherwise. DT/968 . t - 1967 for t ~ 1968: 0 otherwise. DT/983 . t -1982 for t ~ 1983: 0 otherwise. 01917 . 1 for t ~ D1931 . 1 tor t ~ 1931 ; 0 olhel'Wlse. DI946 . 1 for' ~ 1946; 0 otherwise. 1917; 0 otherwise. B. Properties of Detrended Deflator Measures of persistence Coctv-ane variance ratio (V" k. 30) .11 CumuialJVe impulse response funcbon from AAIMA(2, 1.0) model Measure ollong-Ierm variability Var(r .. , - r,llk, It • 30 6' .00029 NOTE . GNP defIaIordala_• .., ~ms rx.:rn,:nt '1'11 (1 .... tilt: 1( 1Il).: nm Ix.'h:I\·io l' (If pril'l.:... :I.... hy th ...• GN!' d d b to l'. :lpp...\ U..... to Ix' dri\ ...·n prima ri ly hy I llI...·"l' . . i' 1m.::II.. . . 1I:I\·in).: dcll.:l'Ill inni q u;mlll,lI l\ d y how i1ll]lorl:11l1 Ih...·.......· hrC;II..~ .11'1..' for cxpb i nin).: Ih....' lel11g-I""OII I)I.:h,l\ Illr III' Ihl' P'In,' k ·\d. \\ .... 1lli).!hl filld II u:'>4,.·lullo 1....'(;l mlnc" hl'l hl..·r 111\'''1..' .... h<x.'k ... I..'(lrTc .... pond \0 .11l} p:lr1inll.lr I..·t:onolllil· "'·\I..·nb Clearl y. Ihl..· . . hlx·k.... (If 1917, 19.\ 1. ,mel 1916 l-ollludl..· \\ IIh World \'Clr I. Ihe Grl"U 1'k·prt' . . . . . lon. and Ihe.: ,11I1..·fll1.1\ h or World \\'.11' II \X';1I1UlK' delll.llld ;end .1 dr:UlUIIl' IIll U·:I"I..· 11\ dOIll...' ....,Il' 1II01l..'Y . . uppl~ h.ld .... purn:d (".Ip id II1tl.llioll JlI....1 Ixf oi'l' ,lIul dunng l ' ~. P:1I1Ilip;1I10n in \X'orld \X';l r 1lll':I..... url.·d I \Xll l i k· p :lrl (If llu..· \\ :Ir!i lll1..· inn'e.I .......' 111 Illl' prin' lo..·n·1 \\ a~ on·. . ...:1 hy I:l pitl dc.:llallon during Ihl: 19.!O-11 ..'l'On()lll il· I..'tInll~lClion . Ihl..· \\.u- hrouglll ahoul ,I br~..· :lIul pc.:nll:m t:nl lIll'r...·: .....l· in Ihl' pricl' k\d. For l'>lllli Lcr rl·:I't(I!l ..... pril'I..·~ n"""-' dr:lln:nil'ally '1~ .1 rI.., .... uh o r \X 'orld \";lr II. hul thl .... ri .......' \\:1:Plbll'XlIlI.."(l unlll "fl...:r pnn' OUlIf()t.... \\I..'re.: lifl ...,d in 1916 '1110..' d",t:tnll' 111 'lggrq.:.HI..· 1..·(.'O!lOlllil· :It'l i\ ilY ;lnd Ihl..' tlr:I...Iu.. II..·duc.1 10n in Ihl..· nOllli!l;11 1lI0 1lt:y ....llppl} dllfill~ Ihl..· e:lfl} ...1.lgl..· ... nf 1110..' Greal 1k.·pn.· ........ 1C1Il Io..-d II) ,I dr:l lll.llil· n.·t!Ul I IIU1 1111110..' ,1J.,:J.:fl'g.lIl..' pm'"" Io..'\....t \\ hlk- ;( lilllo..' 10..-......... oh\ IOU..... Ihe.: i"X:nlUIlI..'1l1 dl,mgl....... III Ih..· j.!fO\\ Ih r:lIc of prll'l· .... "IIAAI..·.... ll"<.IIO FI..-de,., 1 R~ rvC' R:l.nk o f Dalla... FiQure 6 FIQure 7 GNP Deflator and Estimated Trend Component GNP Deflator loganthms 01 mde. _ 1962 .. 100 Logarilhtns 01 Index. 1982 .. 100 • .. • " • • " , " , ", ", .. " +---~----~---r----~---r--~ SOORCES OF PRIMARY DATA Balke and Gonion (1989) US De!:lanmenl 0' Commerce haH' on:um.:d in IH<)H. 196ft .101I 19X.i ;11M} nunl"idc \\I th l'('()!1I)mic l'\l·nt .., ;\Iudl of the \\(Irld , IncludHl}.: till.: l-nited St.Ul·... l"r'll::nenn'd (k'dimng pric\.· .. dunn~ the LlItl,'r Ih111.l of the Illll\,·h:..:nth t.:\.·ntur) 1100\l'H'r. lJoI.,{';\tL:-o..· much or th ..: "orld \\.1:-' on the ~old .. t.mdar(l. the ~old dl"(.'O\·t'(1l·" 10 "outh Atri{-.1. AIa .. k:1. .lnd Color.ldo dllnn~ the IX'XI.. led to an IIlCrt';I"l' in tll<..' growt h r:.11l· or the 1ll0lWy .. upply }\ ...1 fl·"Uit. prin:,!'> in the I nill'" !'I1:lIl· ... ;... \\dl;1' inman)' ot hl'r t1Juntne:-.. Ix:gan II) ri",' hy till' {'!lel of Ihl' I h·<)O:-.. Th i .. ri:-e in prin: .. conli nlll'(l un;lhated until World \'(' ar I. I ~ TIll' hre:lk idenlifi ...'<1 in I%H coim 'idl'" wil h the i ll{Tl·;I... cd inll:llioll (;;lu"l·d h y till' Victnam W:11' l'Xpalhion FI1l:l lIy. Ihl · .. ho(:1-. III \9X.i ft::flects tht,· .. \II,·(·l·..... fu l dfor1 It\ till' Ft'de l~l( Ik ..t,·I ....I,· \() reduce inl1:ni()!1 in 11ll' 1,':lrly 19X<h SilKe till' " \'okker di'''1Il111lion ~ of tIll' 1.·:l rl} 19HO.. . 1111': i!nih.·d ~t:l[e: ha!'> flot e,\perk-lU'l'(l tIll' high 1Il1l:ilion 1':11.,. .. th:lI \H·rt· nmunon in 11K' 19i (}. '\IOtl' Ih.lt with Iht' Ix, ..."hlt: t.'x(':ep[loll 01 til<.:' hrl·.lk... 111 1l'{i)H :md 19.il. all th.,. otlll'r I1Ulor hrl;'al-.:- in Ihl.· tr.,.nd 1.,.\"1.'1 of pnn'" G in h..: .b'Oc.:i.lli.xl wi th (h'IIl).:<..':- in tht" cOlldu(,t or 1ll00wlal1 IXJlicy, ri"(.';11 policy. or Ix)[h , Ont' might . lr~lIl· Ilut thl' tn:nd model for 1111.' (f,P (kfl.llor 1...1 llunlft' ..t.llioll 0 1' :1 dl'lennin1..11<.' Ifl.·nd Iha l lU~[ lu pp..: n:- 10 ..hlft IIlrl.'e tinw:- "" "" "" "" "" "" " SOURCES Of PRI MARY OAT... Balke and Gordon (1969) US Oepan~1 01 Commefce and (· h.m~e :-Iop'::-' three timl,·.. Indl'Cd , dctremlinJ( the G,P ddbtor. a.. in T.lhll.- .i , i .. al ..o COI1!'iSIt;ot wllh a dclt'rIluni ..tic Irend Ih.lt .. l lIfts or chaog<..·:.. Iupe, To l1l1l"l<.kr the G:'\JP defl;l(or ;1 delennini'~ tic trend , howl'\'l'r. would gn:a[ l} undt'rsl:ue the \ari:mct' a:....odaled w ith any long-t.,.nn forecl!'>1 of [hl' prict' lI.-\l·1. A.. :I w:l y o f iIIu:-.[rattng this poinl . :-uppo'>C \\e 11:ld :I('CC...' 10 d;lI;1 onl}' up unli] 1<)19 O n til<..' Il;l .. i .. of the'\;' d al.l, o ne miAht :Irgue that the G,P ddbtor had :t detennin lsl it: tnmd that hap pt;tl<"'d to <"ha n ~c :.lopc:- tn IH9H and to ~hJft i n 19 17 If. hO\wvl'1'. \\C w.cd [hi .. model to fOl'(.'C:ISI lhe GK [' <leil ator in 1981:1.0111' rorl'<::I:-1 would he far o l r thl' 1I1:l rk ( sec Figure 71 . Not o nly dOl'S our fo rl'casl m i...... th <..· major :- hif! ~ in the price 1(:\'\':"1 dll ring Ihe Grl':lI Oepre:-.sion ;I n(\ ; l rt .... r World \'(' :If It. b ut it 1IIi ....I,· .. thl' ch:mge:-. i n tht· j.tl'Owth r.l[ \: in Ihe !al l' 19(,0.. :10<1 the e:l rl y [9H<1!'> More important . thl' pm.'l· ll-\d i n 19HH i... r.lr out..idc the confidenc<..· 1111<..'1"\,:11 ;t~,)(:i. ll ed \\ 1111 Ih.,. determini .. ti(' [rend forecl:-t Tim:.. Ihe dl,'lcOIuni<;llc trend .Ipproach weatl) unc!t.·r..tat ....:- [he fmc uncenamty ;1,-"oli:Hl.'d \\ Ith pn.:dk1ing 1'1111110.: \ .lllIl·" til till' plKl' Il.'\·d ,,, Of ("OlIrsC . :llmo:.1 :ln~' tffX..' of modd \\ollid h:1\ l.' mi....M.·d Ihc"-C Cpi~Kll.:" ba.'o(.'d on tlal:1 lip to 19.?9, hUllhat i" prl.'ci'.c.:l} Ihl.' POUlt. Thl' lIIKl'rlaint) PI\.'M,'111 III Ihl.: [ung-Il: nn hc.:h:1\ lor of till' G '\'1' dt:flalor j" 1I1l11.:h mort" du r:ll"leri"lil' of ;1 "lodl~"'lil' II\:nd thall a dt'lenllini." lll' trl'nd TIll' rall I hallht:rl' ha\l' hl"l.'n m:l lor "ho('k" 10 Ihl: G'\ I' d ..:il.Hor in thl' p:hl Mlggl,..h th:11 fUlurl' "ho(. k" may hl.' po...:.ihle. lnd(.."cd. if adopll'd in Ihl' l utllrl', a I.l'ro inllal ion rult! would (' h:ln~(' thl.' :-;Io["x: of Ihl.: trl.:lld component of prin'" onn' Illorl.: [n :'UIllI11:1ry. \\ hill.: :lllOlI:1 1 H:al GNP d:ll:l from lH69 to 19HH :lfe, for t ill' Illo:.t p:1I1, l"IlIl:-;i:-;Il.'nt with :I deterlnini:.tic trl.:nd. the lon~- rtl n lx'h:lvior tile GNP dellator OWl' Ih i.... pl'do(1 i:-; Ill'Ul'r dlar:KleriZl.'U by a ." Ux:h:l"'ic trl.:lld . I lo\\,l'\'er, Imly :1 fl'\\ :.hock!oo aC(.·O\lnt for mo:.t of till' lonWlcrm v:lri:lbility of thl.: prKl' k\ d , TIlI.:"l· :.h()(·k" l'oinl'idl.: \\ilh rX'nn:IIH.·nt (' han~I.:." in Ih ...' intl:ilion r:1\l.' al the I.:nd of till.' n inl'll'l'nth l"l'nlury, in Ihl' early :In<l !:II!..' 1970:., :lnd III thl.' l 'ady 19HO:. :1I1d \\ Ilh m :llor I"k:'rm:m('nl c h:mgl.':' in Ihe prit'l' k'\ ..:1 :I" a I'l..'Mllt of \":'orld W;lr I. Ihe Gre:1I n ...:prl.'''"ion, and World \X'ar 11 or Conclusion In tlll~ ,tn idc, I m :1(.k till' (h"ttnl'lion l x'I\\i,.",'n (kK' fll1im"Ii(.' II\.'nd" :Ind "11x.h:t,,lil' tfl.'nd" and hi~hlighIL'(l lhl' impli<';llion" of Ihl''''': :thl'rnaliv...· mOl.kb of lrend for hu ... im'''''-q dl' :m:lly....i:-; :1111.1 fm dl:lr:lcll.:ril.ing fon.x:a.,,1 Ull(·I'I"I;linly. I :<l!~j.(I'''ll'd 11 1:1\ :-lol'li:I-;lic Irend:. wilh illfn.:<jlll.:nl l)l'l'In:lllCnt :-;lio(:k.; :lfL' plau .... ihlc on l'conol1l i(' ground." :lIld :11'i,.· :1 po:-;:.ihiliIY ill Ihl.: dal :1 :1 .... wd1. Imkl.:d. 1110:.1 of Ih\.! ]onA-nm v:l ri:lhilil)' in l lIi,.' .. InIac/ r.tSJIlgdatauplO 1929 lJSlochasbctrendmodelwotn one """', fOOl Of It /"S/ (j,IIcrence modeIoi rh8 della/or y.elds It /arecas/ ~ 10 Illederemw1lSI.oc trendmodel Funher, mote !/'If) lJCluat I)toce /ctIeI" COfIIlCIcnce IfItcrvallor tnI$ model /988 IS far (J(JI$Ide me Thts result S/ICI.Ild not tie SUfI)tIS/flg because the presence 01 ""ecpent sIJOd<s 10 /tIfI growth r.1e 01 pncn 01 a segmented /lend model lor prICes rnpIIcs /hal WI eI/et;t /l'IfJte lIIe I'M1 utilI roots WI me pr.ocelCvel ,. ;t).twq~:HI' pfK"1' k-nd Gill h ...: 1r:ICl'(IIO e"''>l.'llli:lllr "ix 1ll:110J" i,.'\l'nh or hri,.·ak." in :I lill...'ar timt: trend, On\.: i nl ...·f\..·:-;\IIlg rl'~ull hl.'re;.' i" Iht: \'t:I)' dr:1I11:1lic dln'cf\..·IKe III Iht: lonA-Ie;.·nn \:triahllit}' of R':11 Gi'\I' and of Ihe;.· C-":I' dl.:ll;Hor: Ihere i" much IlltJf\.o unl.·...·11:11ntr l"I)I\('l'rning rUl ll re I( mg-rull \':lI ul''' of pr1<'c" Ih:1I\ of OUlplll 111l' :lggn.'g:111.' plil'l ' It,\ d ;llmn.,,1 ('elt:!inl}' i.... l:h ar:Kll'rizl'(l by :1 "It)('ha.'oll( IremJ. ,,0 fort"ca.'oIiIlA pricl.''' in Ihe Ion).: Il'nn I." l'x\I\.'1lld) dillk-ult ,\IIlCh of Ih ... lon~ ll.'rm \'tll:l1llil)' In IIII.' :IGG1't:g:lle pril t: k\d Ill:l}' :IClll:ll1y I'll' policy-indm'l'd . On 1111..' olhl'r hand, IIII.' 1':1(1 Ihal th ...· Irl'nd l 'OI11POllcll1 III re:1I GNP i.... much IllO....: pR'dicl:lhll' Ihan Iht: pricl.: k\'d "llf1,gl.'''['' Ihat long'lenll l.'l'OIlO1l1il' /-trowlh . at !l.';I....1 in Ihl' :IAArt:).\:III.:. 11:'-" 1X:I..'n rl'i:u i\'ciy sIah1c OVl.'r Ihl.' pa:.l IO() }'l·;l r." dl'.... pilc Iht: tllltlll.:rOliS Ch:Ul).\I" in i,.'("(Jil(lmil' ~ln.ll'l t l rl.: and polk)' Appendix Identifying Breaks In a Time Trend In Balke and Fomby (1990) , we essentially used two methods to help identify breaks in the time trend. One method was recursive analysis using the Dickey-Fuller regression. Recursive analysis starts with only a portion of the sample to estimate the model and then adds one observation to the sample ata time, reestimating the model each time . If a shifting or segmented trend is present, then the estimated model will look like a deterministic trend until the break occurs. After that, the Dickey-Fuller test should indicate the presence of a unit root. For a recent examination 01 the use of recursive analysis to search for breaks in a time trend , see Banerjee . Lumsdaine , and Stock (1990). The second method is to look !oroutliers, or evidence of big shocks, in the time series. Here, we used the outlier identification method suggested by Tsay (1988) . If the series is in levels (not lirst diHerences) . then level-shift outliers would be evidence of a shifting trend . If the series is in first diHerences , then levelshift outliers would be evidence of a segmented trend , while temporary outliers (not oHset by other temporary outliers of the opposite sign) would be consistentwilh ashifting trend model. Using this outlier identification procedure and recursive analysis. we identified tentative dates for breaks in the trend. These dates were subsequently verified with intervention analyses. in which the effects of the breaks were captured with dummy variables. References Rllkl;'. f\:athan S . :md Thol\1:I:-. It Fumhy (Ig;X)). -Shiftlnt-t Tr,,-·nd:-.. x'gnll.:nH.:d 'I·r~'mb. ~Ind Infl'l-"'<llI"'llt 1\:rlll:ln4,:nt ~I)()(.·k-..- (A,'ntL'r \'.:'orkint-t l'afX.'f no I}().H. Sollthl.:rn II.kth()(.li ..t Unih'rsit)'. I)(.:p:lnml.:nt ()f F.(.:onomk.. (Ihlb ... , Augu.",). d0111 Walk COllllx)I14,'nt in GNP?" .11111"'1(/1 uJ PoJil iclil/:'WIIfJII/I' % (CX'!olx'r): H'),~-920, CoglC'y, Timothy (11)1)0). "Inlen1alional E\'id.... 1l(~ on Ihe Size of thl.· R:mdolll \'\':,tk in Outpu,: ,101/1lwl oj It,Jiliml J:ixmomy ~ (.lund; ')()1- 18 - - - . and I{ol,...,t J. Gordon (19H91. -'nle I-: ,tim ation of l'l't,.'war GID~" 'btion:1 1 Product: I\ l l;' t h()dolo~y :1I1d New E"idt..'nl.·"'. - .luI/mal (if Pulilicall:'c:lll/fl lII,I' 97 (J:ehru:IIY): ~-9.3 13anerj,,-'C. Anindy:1. Itobin l. l.ull1..;daim:, :tnd James 11 Slo(.'k (1990). "lkcufsi\'\:: :md St:qllt:nri al T ... sts o f llll: Un it Hoot and Trl :nd Brt:ak Ilnx)the:-.I,::-': Thl.·ol)' and [ntl'mational E\'idl'IKt·." N 13E I~ \'(/ork i n}t Papcr St·rk· .... no YdO (Cunh rid1-tl'. Ma:-... .: N:ll iona[ BUl'l'au of Ecunomic Rl'M::lrch . ~(l\l;'lllhcr). ])d.ong. J U I~ldf()rd. and L:l\\ rl.'Ill'I.· I I ~UIl1I1l ... rs ( 1988). -On I IIl' Exi:-.t,,-'nl.·c :lIld Intl'rprl.'t:t1 io n o f :1 'Unit ]{oot' in Il S GN P.- N UEH \'(Iork ing PalX'r Sl'ril.''', no. 27 16 (C:lmhridgl'. I\h...... : N:ll ional IJurl.':l l l (l!' Er.:(lIlomic lk~l'; l rdl. St'pll'nlhcr) D ornbusdl, Rudiger. :1)1d SI:lnll;'}' Fisch ... !' (1990l. .1/rIC/'a'cUI/llmit·s. ~th cd (NI.'\\· ,'()rk : I\kGr.lw- l lill Book Comp:lny) FriL'dl11~1I1. Ol;mtil;ml O l ivil'f J .. ;md Danny Qll:lh Cl9B<)). -Till' D} n:ullit' Effect$ of Aggrl'f,::nl' Demand :Iml Supply Di:-.llIfban(I;':-'. - AIII(''''CII'' Eeer IIUII//(': He/·h·/( · 79 (Scptl;'ml'X:r): 6~~-7.3 Box. Gt..,()f}.:l' E.P" and Gwilym 1\1 J"-'nkms (976). Time S('ri<',~ AJt(l~rsjs, FOrt,(;IWill~ (/ful Comrul. rev cd. (S:m Fr.md.'o(;o : 11okk'n-Day, Inc) C l l11phdl. John Y . :lI1d ;\' Gregol), ,\ I,l nkiw ( 1 9~7). " Arl.' OUI PUI FitIClIl:Hi()I1.. TI':ln...ilOry?QII{//1t'''~I',1flltl'//(/1 oj EI.'C/I/fIlllics 101 (No\'(.'m lx'r ): I'{')":'-HO. - - - , and - - - (1989), " [nt,,-,rn~ t1 i(H1al Evidencl' on til ... P"-'IOSi...t":I1l'C of E~m()l1lic Flllctu:lIions." .luI/mal (!/MoJlellln' J!(:(!Jlllmit:s 2j 11\Iarch): 319-.1 1 Christ iano, l ';I\\·I'I.'l1t·,,-, J . and ,\ I;u1 in Eichen haum ( 19t)O), "l lnit Roo" III Rt..':11 GNP: ])0 WI,; Kno\\, :md Do We Clrl.'?" (.(lI'Ilt1!,ie-RocbeSII!I' COII)<"'("II.'(' St'ries {)II PIIIJ/ic l'uli9' 32: 7-62. Clark. I't''''-''' 1\ . ( I i)H7). "Tht., Cydit'a l Component of U.S El 'onomic Activity," QII((/1('I~I',1ollm{/1 uJ£COJlfJIIII<..S 102 (Non-mlx·r)· 797-H I I Cochr:1l1e. John II ( I<)HH). "Ilow Big I .. thl;' Ran- " I\ Iihon. :ll1d Anna J:l('Oi>-;()I1 Sdlw:tnz ( 19(3). A MOllelMY JJ/~/UI')' uf fbt, l ltiled Slt'Ill'S, J867- 1960( PnI1l.: ...hm : Prinl'I.'t(lO tlnh cr,ity \'Tl''':-' for ;"i:tlion:ll IJllrl.·all of E(.·(>I1omi(.· Ih':"I.':l rdl) Fltlkr . Waynt· A (11)76) , Jllfl'()(III(:l i(lII/fI SWfislicaf Time Selie~ ('\'l'\\ York : John Wik'), :lnd Sons) (iOl'(km. Rol,...n J. ( 11)1)0), .lfaeIlJt...cO/uJlJlic:.... ')tlt 00 <Glt!I1\'it!\\, 111.: S4.:ot:t. FOTl....Ill:1I1 :IIKl COIllP:II1Y) I\i n/-!. Rolx'rI G , C h :lr""~ I 1)1()..... ~ r. .1:11111.':-' I I . Sl o(.'k. :ll1d I\ la rk W. \'\I:1I ..,on ( 19K7). "Slo(.'ha"" til' Tn::ntb :ll1d EnJl10mk Flul'tu:lIion .....· NUER Work in1-t P:lpl.:r St'rks, no 2229 (Cunhrid,ge, l\ l as.~ : N:lIion:tI IhlI'C:lll of EC0I10111il' lkscarch, Apr il) I\onnt.'nd i . Ito).:,,-'r C. and Ph il ip I\lcqUlI\: ( 19?()). " /\ l\l llitilnuntl) Ch;lr.rctt!flZ:llion of 11K' '\'on~t,l t iOI1.l ri t}' o( AAAre~:nc Output: ./0/11'/1(11 (1.1101/(:1'. Git'clil. mid Jjclllki/1.~ 22 (Fehnl:u y): 1""-9.3 .\ !:Inki\\'. N Grl.·1-t(II),.IdTr~r A !\Iinln. :tnd O;l\'id N \'\11.::11 (19H-)' "Th~ Adju:-.tllK'nt III Expen:l + lion, to a Ch:tn1-tl' in ]{q,~illlc: A SllId}, of Ihe Founding of th ... FI.,t!t:r:II n ~ ...... f'\'I.' ,~ tlmericml ECO li o mic 1/('1'1('/1' 77 <Jund. JSH-71 federat Resoe n '", Rank of Dallas Kelson. Ch:u k':o; R.. and Charic:-. I. Plu!t.o;er (1982). RTrendo; :1Ilt! R:moom W.!lk., in j\·I:I(TOI..'<-'Onomic Time Scric.,: Some Evidcocl' and ImphCltk>ru. ... jOllr,/(/1 q/1" Of/(>/llr)' economics 10 (5c'plemIlt:r) ~ 139-62 Perron, Plt.'n\: (1C)H9). 1'he Great Cr:L..h. the Oil. Prn:e Sho(:k. :lnd the L'nil Root HYpolhesi."'Eron0lf1etrll..l1 ';1 C'lo\,cmlkr). 13(}I-l·IOI. Ph lllipe.. PI,.'1er C Ii . :lOd Pierre Perron (1988)......~ LOg for a Unit Root in Timc Scri~ Rl."'gI'e"SSion.lJiol1lt.'flikt,,,S (June) 33S-46. R:lppoport, I>eter, :md Lucrezi:l Reichlin (1989), -$(.'&mcnll,.'(l Trend, :lnd Nun-'t:llionary Time ScriCl'i.~ Ecollomicjollnw/99 (Supplement): 168 T7. Ruddn1:J(h. Glenn D (1990), -Trend:- and Random Walk., in ~ l:1croeconullll<.' Time $cries: A Re cxamin.llinn.· Financc "md Economics DI~L',,()n ~rn.... , no. 139 (\X'a~hlngton, D.C.: Board of Gmcmor. of the FI,.-dcml RCSCf\'c SY.;(I,.'m, I)l\l"On of RCSC:IR:h :md Sulistics. oaoher) ~1 (1987). - Efft."t:h of i\lodel Mis.,pt."I..·lfll.::IlIl)ll on Tot.!> for Cnil Roots in i\ 1.llTt)C.."(l)Jl()mll· Dala.- jOllmul o/Mo11eW1)1 Ecoll{mlll'.~ 20 ( J uly), 73-IOj Schwcn . Gt.-'m).;t.' F.conomk ~icw - Mlr 1991 Simpiro. M.mhl.'w D., :lOd Mark W. Watson (1988). RSourc~' of BlI~lI1l'SS Cycle Fluctu:u ions,- in NBEN MlICfO('COllomlc;s tlmmttl 1988, cd. Sunlcy FI!'>Cher (D.mbridge. Mass .. ~ IIT Press for atic)ll.Il BUf'C".1l! of F.conomic RCSt.'arch), 111- 18 Sirru.. Christopher A., Junes II. Srock, and Mark W. \X'al.-.on (1990). ~ Infcrencr in Unear Time Scn(.'S Mexld.; with Some 1.:01' Roots. ~ Eco"ometnctl sa (January): 11 3-44. SIOCk, Ja nk,,:) H ., and Ma rk W Waoon 0988}. -V:Hi:lblt.' Trends in Economic Time Series: jotlmal 0/Ecollomic Pf!rspeclllJ(,S 2 (Summer): 147-74 . Tsay, RlIey S (19M), ROllllje~, l.xvcJ Shifts. and Variance Changt.'S in Time Scn(.'S.~ jOllnral of Pon'Gusl lIIJ,: 7 (january/ March) l-ZO. Wal.!>On, Mark W 098(}), -Uni\";lri.1tc Ot.1rcnding ~ l ethod, "Ith Stocha.,tic Trl:nc.1s," jOllmai of MQnetary' Ecollomlcs 18 (July): 49-75, w~. Kcnnc...1h 0, (988), -On tilt.' Intt'rprt."tauon of :-.Il"3r R.Jndom·\X';dk Beh;l\'K)f' in GNP.- American Ecollomlc R(!I'ieUl~ (Man:h)~ 202 - 9.
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